WO1999018424A1

WO1999018424A1 - Interferometric method and apparatus

Info

Publication number: WO1999018424A1
Application number: PCT/US1998/019855
Authority: WO
Inventors: Henry Allen Hill
Original assignee: Zygo Corporation
Priority date: 1997-10-02
Filing date: 1998-09-23
Publication date: 1999-04-15
Also published as: WO1999018424A9; JP2001519527A; EP1019703A1; JP3626907B2

Abstract

Interferometric apparatus and method for measuring and monitoring intrinsic optical properties of a gas, especially the reciprocal dispersive power of the gas, so that information about the gas properties can be used in downstream applications, such as interferometric distance measuring instruments, to increase accuracy by correcting for refractive index of the gas and especially environmental and air turbulence effects in the measurement path. The apparatus comprises a concentric measurement cell having an inner chamber containing a vacuum surrounded by an outer occupied by the gas. Wavelength selective mirrors are arranged at each end of the measurement cell and operate in conjunction with plane mirror interferometers to change the phase of orthogonally polarized components of light beams of different wavelength introduced in the measurement cell from opposite ends of the cell. Preferably, the polarized components are frequency-shifted to facilitate the generation of heterodyne and superheterodyne signals which contain information about the intrisinc optical properties of the gas. The heterodyne and superheterodyne signals are electronically analyzed by a general purpose computer programmed for that purpose or from a specially programmed microprocessor.

Description

INTERFEROMETRIC METHOD AND APPARATUS

FIELD OF INVENTION

The present invention generally relates to a method and apparatus for measuring and monitoring the intrinsic optical properties of a gas. More particularly, the invention relates to interferometric measurement of the reciprocal dispersive power of a gas and to optical apparatus which is useful for high accuracy displacement metrology in the presence of an uncontrolled turbulent gas.

Background and Prior Art

Interferometric techniques have broad applicability to a variety of tasks requiring precision measurement.

The precise measurement of length, displacement, geometric features, surface structure, and vibration have been common applications where these techniques have played important roles, which continue to grow and evolve because of the ever increasing demands for greater precision.

However, as with other metrologies, practicalities often intrude to make it difficult to achieve what may be theoretically possible.

One dominant factor which limits the absolute accuracy of interferometric displacement metrology is the uncertainty in the refractive index of the ambient air, see W. T. Estler, "High-Accuracy Displacement Interferometry in Air," Appl . Opt . , 24, pp. 808-815 (1985); C. L. Farrand, V. F. Foster, and . H. Grace, U.S. Pat. No. 4,215,938 issued Aug. 15, 1980; N. Bobroff, "Residual Errors in Laser Interferometry from Air Turbulence and Non-Linearity, " Appl . Opt . 26(13), pp. 2676-2682 (1987) ; and N. Bobroff , "Recent Advances in Displacement Measuring Interferometry, " Measurement Science & Tech . 4(9), pp. 907-926 (1993).

As noted in the aforementioned cited references, interferometric displacement measurements in air are subject to environmental uncertainties, particularly to changes in air pressure, temperature, and humidity; air composition; and to the effects of turbulence in the air. Such factors alter the wavelength of the light used to measure the displacement. Under normal conditions the refractive index of air is approximately 1.0003 with a variation of the order of lxlO^-5 to lxlO^'4. In many applications the refractive index of air must be known with a relative precision of less than 0.1 ppm (parts per million) to 0.003 ppm, these two relative precisions corresponding to a displacement measurement accuracy of 100 nm and 3 nm, respectively, for a one meter interferometric displacement measurement.

One way to detect refractive index fluctuations is to measure changes in pressure and temperature along a measurement path and calculate the effect on refractive index of the path. Mathematical equations for effecting this calculation are disclosed in an article entitled "The Refractivity Of Air" by F. E. Jones, J. Res . NBS 86(1), pp. 27-32 (1981) . An implementation of the technique is described in the cited article by Estler. Unfortunately, this technique provides only approximate values, is cumbersome, and corrects only for slow, global fluctuations in air density.

One prior-art technique of the type described in the preceding paragraph for correcting the environmental uncertainties is based on using individual sensors to measure the barometric pressure, temperature, and humidity, and then using these measurements to correct the measured displacement. The commercially available Automatic Compensator, Model 5510 Opt 010, from Hewlett- Packard uses this technique. This technique has been only partly satisfactory due to the errors in the sensors and due to the errors arising from variations in the composition of the air, e. g. , the percentage C0₂ content and presence of industrial gases, i.e. Freon and solvents are ignored in the technique.

Another type of technique for correcting for the effects of air is based on a measurement of the refractivity of the air. A procedure of this type will hereinafter be referred to as a refractivity technique. One of the more serious limitations encountered with a refractivity technique with regard to use in high precision distance measuring interferometry arises at a fundamental level. The refractivity of a gas is directly proportional to the density of the gas which is dependent in first order on environmental conditions such as temperature and pressure. Thus, to relate the value of a refractivity measured at the site of a refractivity measuring apparatus to a second site, e . g. the measuring path of a distance measuring interferometer, the environmental conditions at the latter site relative to the environmental conditions at the former site must be known with a relative precision of less than 300 ppm to 10 ppm, the required relative precision for the refractive index at the latter site being less than 0.1 ppm to 0.003 ppm in accordance with relative precisions previously cited. This serious limitation in regard to use in high precision distance measuring interferometry will in general be present with all techniques classified as refractivity techniques.

A prior-art refractivity technique for correcting for environmental uncertainties is based on the C. L. Farrand, V. F. Foster, and W. H. Grace U.S. Pat., op . ci t . . This technique incorporates a rigid enclosure, the length of which must be accurately known, independent of environmental conditions and constant in time. The change in optical path length of this enclosure is measured as remotely controlled valves allow the enclosure to be evacuated and refilled with ambient air. The refractivity of the air in the enclosure is proportional to the measured change in optical path length. This technique has been only partly satisfactory due to the fact that the characteristics of the air in the enclosure do not adequately represent those of the air in the measurement path, thusly systematic errors are introduced. It has been found that even with a perforated enclosure, serious systematic differences exist between the characteristics of the air inside of and external to the enclosure in addition to the limitations of the refractivity technique previously cited.

Other prior-art refractivity techniques which incorporate a fixed length optical reference path are found in commonly owned U.S. Pat. No. 4,685,803 issued Aug. 11, 1987 and U.S. Pat. No. 4,733,967 issued March 29, 1988, to G. E. Sommargren. The principal advantages of the inventions disclosed in the two cited Sommargren patents are that the length of the measurement path need not be known with extreme accuracy, small variations in the measurement path length during the measurement are tolerable, and the air around the refractive index cell can truly represent the ambient environment. However, the two cited Sommargren patents measure the refractivity of a gas and therefore encounter the cited limitations of the refractivity technique with regard to use in high precision distance measuring interferometry .

Perhaps the most difficult measurement related to the effects of environmental conditions on the refractive index of air is the measurement of index fluctuations over a measurement path of unknown or variable length, with uncontrolled temperature and pressure. Such circumstances arise frequently in geophysical and meteorological surveying, for which the atmosphere is obviously uncontrolled and the refractive index is changing dramatically because of variations in air density and composition. The problem is described in an article entitled "Effects Of The Atmospheric Phase Fluctuation On Long-Distance Measurement" by H. Matsumoto and K. Tsukahara, Appl . Opt . 23(19), pp. 3388-3394 (1984) and in an article entitled "Optical Path Length Fluctuation In The Atmosphere" by G. N. Gibson, J. Heyman, J. Lugten, . Fitelson, and C. H. Townes, Appl . Opt . 23(23), pp. 4383- 4389 (1984) . Another example situation with respect to uncontrolled atmosphere and changing refractive index is high-precision distance measuring interferometry, such as is employed in micro-lithographic fabrication of integrated circuits. See for example the two cited articles by N. Bobroff. The correction for index fluctuations due to air turbulence is typically on the order of 0.1 ppm in magnitude, and the residual errors due to index fluctuations resulting in part from air turbulence in the corrected measured path length must be with a relative precision less than or of the order of 0.003 ppm in high accuracy displacement interferometry, a relative precision corresponding to a displacement measurement accuracy of 3 nm for a one meter interferometric displacement measurement. This high level of precision involves frequency-stabilized laser sources and high-resolution phase detection.

One direct way to detect index fluctuations over a path is taught in U.S. Patent No. 5,218,426 issued Jun. 8, 1993 to J. L. Hall, P. J. Martin, M. L. Eickhoff, and M. P. Winters and entitled "Highly Accurate In-Situ Determination of the Refractivity of an Ambient

Atmosphere". The system of Hall et. al . includes use of a refractometer exposed to an ambient atmosphere and having light directed thereto to form an optical interference fringe pattern having a dependence upon the refractivity of the ambient atmosphere. The fringe pattern is measured as a function of angle either by sequentially scanning a collimated input beam in angle while detecting the transmitted light, or by imaging (onto a multi-element detector) the angular exit space of the interferometer illuminated with a diverging input beam. The measuring path of the apparatus of Hall et. al . is substantially a combination of two right circular cones whereas the measuring path of a distance measuring interferometer is substantially comprised of a set of right circular cylinders. As a consequence, the apparatus of Hall et. al. is not suited to measuring fluctuations in the optical path length of distance measuring interferometers due to atmospheric turbulence.

Another more direct way to detect index fluctuations over a path is by multiple-wavelength distance measurement. The basic principle may be understood as follows. Interferometers and laser radar measure the optical path length between a reference and an object, most often in open air. The optical path length is the integrated product of the refractive index and the physical path traversed by the measurement beam. In that the refractive index varies with wavelength, but the physical path is independent of wavelength, it is generally possible to separate the physical path length from the contributions of the refractive index, provided that the instrument employs at least two wavelengths. The variation of index with wavelength is known in the art as dispersion, accordingly this technique will be referred to hereinafter as the dispersion technique.

The dispersion technique measures the difference in optical path at two different wavelengths and then uses properties of the refractive index to compute the effects of the refractive index on a path length from the measured difference in optical path at two different wavelengths. The dispersion technique encounters two serious limitations. The more basic limitation arises from the fact that the dispersion technique is by definition a technique which uses properties of the first derivative with respect to wavelength of the refractive index. The second limitation arises from the fact that the properties of the refractive index must be available to the required accuracy.

The first derivative character of the dispersion technique increases the relative precision at which interferometric phase measurements must be made relative to distance measuring interferometers by more than one to two orders of magnitude. The first derivative character of the dispersion technique also increases the relative precision to which properties of the refractive index must be known relative to refractivity techniques by more than one to two orders of magnitude. The information available on the refractive index is not known with sufficient relative precision for certain applications of the refractivity technique and consequently is not known with sufficient relative precision for even fewer applications of the dispersion technique. The dispersion technique for refractive index measurement has a long history, and predates the introduction of the laser. An article entitled "Long-Path Interferometry Through An Uncontrolled Atmosphere" by K. E. Erickson, J^". Opt. Soc . Am . 52(7), pp. 781-787 (1962) describes the basic principles and provides an analysis of the feasibility of the technique for geophysical measurements. Additional theoretical proposals are found in an article entitled "Correction Of Optical Distance Measurements for the Fluctuating Atmospheric Index of Refraction" by P . L. Bender and J. C. Owens, J^". Geo . Res . 70(10), pp. 2461-2462 (1965). Commercial distance-measuring laser radar based on the dispersion technique for index compensation appeared in the 1970' s. An article entitled "Two-Laser Optical Distance-Measuring Instrument That Corrects For The Atmospheric Index Of Refraction" by K. B. Earnshaw and E. N. Hernandez, Appl . Opt . 11(4), pp. 749-754 (1972), discloses an instrument employing microwave-modulated HeNe and HeCd lasers for operation over a 5 to 10 km measurement path. Further details of this instrument are found in an article entitled "Field Tests of a Two-Laser (4416A And 6328A) Optical Distance-Measuring Instrument Correcting for the Atmospheric Index of Refraction" by E. N. Hernandez and K. B. Earnshaw, J. Geo . Res . 77(35), pp. 6994-6998 (1972) . A further example of an application of the dispersion technique is discussed in an article entitled "Distance Corrections for Single- and Dual-Color Lasers by Ray Tracing" by E. Berg and J. A. Carter, J. Geo . Res . 85(B11), pp. 6513-6520 (1980).

Although instrumentation for geophysical measurements typically employs intensity-modulation laser radar, it is understood in the art that optical interference phase detection is more advantageous for shorter distances. In U.S. Patent No. 3,647,302 issued to R. B. Zipin and J. T. Zalusky, Mar. 1972, entitled "Apparatus For And Method Of Obtaining Precision Dimensional Measurements," there is disclosed an interferometric displacement-measuring system employing multiple wavelengths to compensate for variations in ambient conditions such as temperature, pressure, and humidity. The instrument is specifically designed for operation with a movable object, that is, with a variable physical path length. In that the technique of Zipin et al . employs three different wavelengths and assumes knowledge of the wavelength dependent refractive index to correct for changes in environmental conditions along a measurement path, the technique of Zipin et al . is not a dispersion technique. The dispersion technique being described as a technique which uses properties of the first derivative of the refractive index with respect to wavelength, the technique of Zipin et al . may be described as a technique which uses properties of the second derivative of the refractive index with respect to wavelength and accordingly, will hereinafter be referred to a second derivative refractive index technique .

An example of an application of the second derivative refractive index technique in geophysical experiments is found in an article entitled "A Multi-Wavelength Distance- Measuring Instrument For Geophysical Experiments" by L. E. Slater and G. R. Huggett, J^". Geo . Res . 81(35), pp. 6299- 6306 (1976) . The second derivative refractive index technique encounters two serious limitations. The more basic limitation arises from the fact that the second derivative refractive index technique is by definition a technique which uses properties of the second derivative with respect to wavelength of the refractive index. The second limitation arises from the fact that the properties of the refractive index must be available to the required relative precision. The second derivative character of the second derivative refractive index technique increases the relative precision at which interferometric phase measurements must be made relative to dispersion techniques by more than one to two orders of magnitude. The second derivative character of the second derivative refractive index technique also increases the relative precision to which properties of the refractive index must be known relative to dispersion techniques by more than one to two orders of magnitude. The information available on the refractive index is not known with sufficient relative precision for certain applications of the refractivity technique, to fewer applications of the dispersion technique, and consequently to yet an even smaller set of applications of the second derivative refractive index technique.

A detailed example of a system employing a dispersion technique with the basic limitations previously cited is described by Y. Zhu, H. Matsumoto, and T. O'ishi in an article entitled "Long-Arm Two-Color Interferometer For Measuring The Change Of Air Refractive Index," SPIE, 1319, Optics in complex systems, pp. 538-539 (1990). The system of Zhu et al . employs a 1064 nm wavelength YAG laser and an 632 nm HeNe laser together with quadrature phase detection. Substantially the same instrument is described in Japanese in an earlier article by Zhu et al . entitled "Measurement Of Atmospheric Phase And Intensity Turbulence For Long-Path Distance Interferometer," Proc. 3^rd meeting on lightwave sensing technology, Appl . Phys . Soc . of Jpn . 39 (1989) .

A recent attempt at high-precision interferometry for microlithography using a dispersion technique is represented by U.S. Patent No. 4,948,254 issued to A. Ishida, Aug. 1990. A similar device is described by Ishida in an article entitled "Two Wavelength Displacement-Measuring Interferometer Using Second- Harmonic Light To Eliminate Air-Turbulence- Induced Errors," Jpn . J. Appl . Phys . 28(3), pp. L473-475 (1989). In the article, a displacement-measuring interferometer is disclosed which reduces errors caused by fluctuations in the refractive index by means of two-wavelength dispersion detection. An Ar⁺ laser source provides both wavelengths simultaneously by means of a frequency-doubling crystal known in the art as BBO. The use of a BBO doubling crystal results in two wavelengths that are fundamentally phase-locked, thus greatly improving the stability and accuracy of the dispersion measurement. In addition to the basic limitations of the dispersion technique previously cited, the phase detection and signal processing means are not suitable for dynamic measurements, in which the motion of the object results in rapid variations in phase that are difficult to detect accurately.

In U.S. Patent No. 5,404,222 entitled "Interferometric Measuring System With Air Turbulence

Compensation," issued to S. A. Lis, Apr. 1995, there is disclosed a two-wavelength interferometer employing the dispersion technique for detecting and compensating index fluctuations. A similar device is described by Lis in an article entitled "An Air Turbulence Compensated

Interferometer For IC Manufacturing," SPIE 2440 (1995). Improvement on U. S. Patent No. 5,404,222 by S . A. Lis is disclosed in U. S. Patent No. 5,537,209 issued Jul . 1996. The principle innovation of this system with respect to that taught by Ishida in Jpn . J. Appl . Phys . ( op . ci t . ) is the addition of a second BBO doubling crystal to improve the precision of the phase detection means. The additional BBO crystal makes it possible to optically interfere two beams having wavelengths that are exactly a factor of two different. The resultant interference signal has a phase that is directly dependent on the dispersion but is substantially independent of stage motion. However, the cited patents of Lis are all based on the dispersion technique and therefore have the basic limitations of the dispersion technique previously cited. The relative precision of any dispersion technique depends directly on the accuracy to which both the dispersion and the reciprocal dispersive power of the gas in the measurement path is known, the reciprocal dispersive power being defined as the ratio of the refractivity of a gas measured at a first wavelength to the dispersion of the refractivity of the gas between a second and third wavelengths. The first wavelength is preferably the same wavelength as used in an associated distance measuring interferometer. The second or third wavelengths used in the measurement of the dispersion may be the same as the first wavelength used in the measurement of the refractivity. The reciprocal dispersive power is used to compute the refractivity of a gas in the measuring path of for example a distance measuring interferometer from measured values of the dispersion of the gas in the measuring path of the distance measuring interferometer.

The reciprocal dispersive power depends on the three wavelengths for which a specific reciprocal dispersive power is defined as well as on the composition of the gas. The principle advantage of the dispersion technique is that the reciprocal dispersive power is independent of environmental conditions such as temperature and pressure for environmental conditions normally encountered in high- precision distance-measuring interferometers. However, in many situations the composition of the gas may be unknown, the gas composition may vary in time in an unknown way, and the dispersion of the refractivity and/or the refractivity of the gas constituents is not available or not known to the accuracy required for a given application. Either lack of the knowledge of the gas composition or of the reciprocal dispersive power to the necessary relative precision can pose serious limitations on the utility of the dispersion technique.

With respect to the latter point regarding availability of refractivities and corresponding reciprocal dispersive powers, consider the accuracy to which the reciprocal dispersive power is known for the example of water vapor. The widely used equations for the refractivity of water vapor found in the work of B. Edlen entitled "The Refractive Index of Air," Metrologia 2(2), pp. 71-80 (1966) or the improved results reported by K. P. Birch and M. J. Downs, Appl . Opt . 28(5), pp. 825-826 (1989) may be used to compute the reciprocal dispersive power for water vapor. The Birch and Downs findings have been verified by J. Beers and T. Doiron, Metrologia 29, pp. 315-316 (1992) . The relative precision to which the reciprocal dispersive power can be computed using either of these two cited sources for the refractivity of water vapor is of the order of 0.1%, the first, second, and third wavelengths used in the computing the reciprocal dispersive power being in the visible part of the spectrum, the first and second wavelengths being equal, and the second and third wavelengths being in the ratio of 2:1, respectively. The situation respect to C0₂ is only better by approximately a factor of 3. It is evident from the examples given in the preceding paragraph that current knowledge of the refractivity of water vapor and C0₂ are not accurate enough to make absolute length measurements using dispersion interferometry in ambient air to the relative precision of approximately 0.003 ppm. They may also not be known accurate enough for atmospheric turbulence compensation for the more turbulent environments. The situation with respect to contaminant gases vis-a -vis respective reciprocal dispersive powers may present an even more serious problem in the use of dispersion interferometry [ cf . N. Bobroff, Meas . Sci . Technol . 4, pp. 907-926, (1993) ] .

It is clear from the foregoing, that the prior art does not provide a practical, high-speed, high-precision method and corresponding means for measuring and compensating the refractive index including fluctuations in the refractive index of a gas. The limitations in the prior art arise principally from the following, unresolved technical difficulties: (1) the refractivity technique does not measure for example the refractivity of a gas in a measurement path of a distance measuring interferometer directly and as a consequence, requires detailed high precision knowledge of the environmental conditions at two separated sites; (2) the dispersion technique does not measure the refractivity of a gas in a measurement path of a distance measuring interferometer directly and as a consequence requires knowledge of the constituents of the gas in the measurement path and knowledge of the reciprocal dispersive powers of the gas constituents; (3) the gas composition may not be known with sufficient accuracy for the dispersion technique in either a turbulent or a non turbulent gas; (4) the composition of a gas may be changing significantly on relative short time scales; (5) the data age of composition determinations may be too long; and (6) the refractivity and reciprocal dispersive powers of the gas constituents may not be known with sufficient accuracy.

Consequently, while prior-art techniques for measuring the refractive index of a gas are useful for some applications, none known to the applicant provide the technical performance in a commercially viable form for applications requiring the determination of the reciprocal dispersive power of a gas with the high accuracy required in dispersion interferometry for compensation of air in distance measuring interferometry. Accordingly, it is an object of the invention to provide a method and apparatus for measuring and monitoring intrinsic optical properties of a gas, particularly its reciprocal dispersive power.

It is another object of the invention to provide a method and apparatus for measuring and monitoring a reciprocal dispersive power of a gas wherein the method and apparatus does not require measurement and monitoring of environmental conditions such as temperature and pressure . It is another object of the invention to provide a method and apparatus for measuring and monitoring a reciprocal dispersive power of a gas wherein the method and apparatus does not require knowledge of the gas composition.

It is another object of the invention to provide a method and apparatus for measuring and monitoring a reciprocal dispersive power of a gas wherein the method and apparatus is operative over a wide temporal frequency range with respect to changes in gas composition.

It is another object of the invention to provide a method and apparatus for measuring and monitoring a reciprocal dispersive power of a gas wherein the method and apparatus does not require knowledge of the refractivities and of the dispersions of the refractivities for constituents of the gas. It is another object of the invention to provide a method and apparatus for measuring and monitoring a reciprocal dispersive power of a gas wherein the method and apparatus may use but does not require the use of two or more optical beams of differing wavelengths which are phase locked.

It is another object of the invention to provide a method and apparatus for measuring and monitoring a reciprocal dispersive power of a gas wherein the lengths of measuring paths in an interferometric measurement and monitoring of a reciprocal dispersive power are substantially not used in a computation of the reciprocal dispersive power of the gas.

It is another object of the invention to provide a method and apparatus for measuring and monitoring a reciprocal dispersive power of a gas wherein the frequencies of the optical beams used in an interferometric measurement and monitoring of a reciprocal dispersive power are substantially not used in a computation of the reciprocal dispersive power of the gas. Other objects of the invention will, in part, be obvious and will, in part, appear hereinafter. The invention accordingly comprises methods and apparatus possessing the construction, steps, combination of elements, and arrangement of parts exemplified in the detailed description to follow when read in connection with the drawings.

SUMMARY OF THE INVENTION

The present invention generally relates to apparatus and methods by which information about intrinsic optical properties of gases can be measured and monitored for use in electro-optical metrology and other applications. More specifically, the invention operates to provide measurements of relative dispersion and reciprocal dispersive power, the relative dispersion and the reciprocal dispersive power being substantially independent of environmental conditions such as gas temperature and pressure. In making these measurements, the gas may be turbulent, the gas composition may not be known, the gas composition may be variable in time, and knowledge of refractivities and dispersions of the refractivities for constituents of the gas is not required. The information generated by the inventive apparatus is particularly suitable for use in interferometric distance measuring instruments (DMI) to compensate for errors related to refractive index in the measurement leg and especially to refractive index changes in the measurement leg brought about by environmental effects and turbulence induced by rapid stage slew rates. Several embodiments of the invention have been made and these fall broadly into two categories which address the need for more or less precision in final measurements. While the various embodiments share common features, they differ in some details to achieve individual goals. In general, the inventive apparatus comprises interferometer means having a reference leg and a measurement leg. Each of the constituent legs has a predetermined physical path length with the reference leg configured and arranged to be occupied by a predetermined medium, preferably a vacuum, and the measurement leg configured and arranged to be occupied by the gas whose intrinsic optical properties are to be measured and monitored. In preferred form, the interferometer means comprises a concentric cell having a closed inner chamber that serves as the reference leg and an outer chamber, surrounding the inner chamber, that serves as the measurement leg. The inner chamber is substantially evacuated to provide the vacuum, and the outer chamber is opened to the ambient surroundings which, in a typical interferometric DMI application, is air. The concentric cell is preferably in form a right circular cylinder with end sections capped with wavelength selective mirrors fixed normal to the cell's longitudinal axis.

Means for generating at least two light beams having different wavelengths are included. In preferred embodiments, a source generates a set of light beams, the set of light beams being comprised of at least two light beams, each beam of the set of light beams having a different wavelength, the wavelengths of the beams of the set of light beams having an approximate harmonic relationship to each other. The approximate harmonic relationship is known and expressed as a sequence of ratios, each ratio being comprised of a ratio of low order non zero integers, e . g. 1/2, to a relative precision of an order of magnitude less than the dispersive power of the gas, the dispersive power of the gas being the inverse of the reciprocal dispersive power, times the relative precision required for the measurement of the reciprocal dispersive power.

A set of frequency-shifted light beams is generated from the set of light beams by introducing a frequency difference between two orthogonally polarized components of each beam of the set of light beams such that no two beams of the set of frequency-shifted light beams have the same frequency difference. In a number of the embodiments the ratios of the wavelengths are expressible as a sequence of low order non zero integers to a relative precision, the relative precision of the approximate harmonic relationship, of an order of magnitude less than the dispersive power of the gas times the relative precision required for the measurement of the reciprocal dispersive power of the gas. In other embodiments, where the relative precision of the approximate harmonic relationship is inappropriate to the desired relative precision, means are provided for monitoring the relative precision of the approximate harmonic relationship and either providing feedback to control the relative precision of the approximate harmonic relationship, information to correct subsequent calculations influenced by undesirable departures of the relative precision of the approximate harmonic relationship from the desired relative precision, or some combination of both. At least a portion of each of the frequency shifted light beams are introduced into the interferometer means by suitable optical means so that each light beam portion travels through the predetermined medium and the gas along predetermined paths of substantially the same physical path length. Afterwards, the light beam portions emerge from the interferometer means as exit beams containing information about the optical path length through the predetermined medium (preferably a vacuum) in the reference leg and about the optical path length through the gas in the measurement leg. In preferred form, the optical means for introducing the light beam portions into the interferometer means is configured and arranged to introduce one of the light beam portions corresponding to one wavelength through one of the wavelength selective end mirrors of the concentric cell and another of the light beam portions corresponding to another of the wavelengths through the other wavelength selective mirror of the end sections of the concentric cell. In one of the embodiments three sets of light beam portions are generated, one at one wavelength being introduced into one end of the concentric cell and two at another wavelength into the other end of the concentric cell.

In yet another embodiment, the optical means are configured to cause certain of the light beam portions to undergo multiple passes as they travel through the concentric cell . Combining means are provided for receiving the exit beams to produce mixed optical signals which contain information corresponding to the phase differences between the exit beams of each light beam portion from the reference and measurement legs. The mixed optical signals are then sensed by a photodetector which operates to generate electrical interference signals that contain information corresponding to the refractivities of the gas at the different beam wavelengths. The electrical interference signals are then analyzed by electronic means that operate to determine the select intrinsic optical properties of the gas. The electronic means can be in the form of a microprocessor or a general purpose computer suitably programmed in well-known ways to perform the needed calculations. The electronic means is configured to determine the relative refractivities at different beam wavelengths where the relative refractivities are of the form:

^~x.

where i and j are integers corresponding to wavelengths and different from one another. From this information, the reciprocal dispersive power, T , of the gas can be determined.

In preferred form, the electrical interference signals comprise heterodyne signals containing phase information corresponding to the refractivities of the gas and the apparatus further comprises means for adding the heterodyne signals to generate at least one superheterodyne signal containing phase information corresponding to the dispersion of the refractivities of the gas. Means are also included for resolving phase ambiguities of the heterodyne and superheterodyne signals. Depending on the details of the optical paths experienced by the light beam portions as they travel through the interferometer means of the various embodiments, additional or different electronics are provided which, in one embodiment, requires the production of modified heterodyne signals prior to final data processing.

While the inventive method disclosed may be carried out using the preferred apparatus described, it will be evident that it may also be practiced using other well- known apparatus. In addition, it is shown that apparatus may be employed which uses homodyne signals.

BRIEF DESCRIPTION OF THE DRAWINGS

The structure and operation of the invention, together with other objects and advantages thereof, may best be understood by reading the detailed description in conjunction with the drawings wherein the invention's parts have an assigned reference numeral that is used to identify them in all of the drawings in which they appear and wherein:

FIGS, la-lf taken together illustrate, in diagrammatic form, the presently preferred first embodiment of the present invention with FIG. la showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 69, plane mirror interferometer group 70, measurement cell 90, detectors 85, 86, and 286 and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 85, 86, and 286, electronic processor 108, and computer 109;

FIG. lb illustrates plane mirror interferometer 69;

FIG. lc illustrates plane mirror interferometer group 70;

FIG. Id illustrates measurement cell 90 furnishing the external mirrors for plane mirror interferometer 69;

FIG. le illustrates measurement cell 90 furnishing the external mirrors for plane mirror interferometer group 70;

FIG. If is a drawing showing a block diagram of the processing electronics 108;

FIG. 2a-2b taken together illustrate, in diagrammatic form, the presently preferred variant of the first embodiment of the present invention with FIG. 2a showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 69, plane mirror interferometer 170, measurement cell 90, detectors 85 and 186 and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 85 and 186, electronic processor 1108, and computer 109;

FIG. 2b illustrates plane mirror interferometer 170;

FIGS. 3a-3d taken together illustrate, in diagrammatic form, the presently preferred second embodiment of the present invention with FIG. 3a showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 269, plane mirror interferometer 270, measurement cell 90, and detectors 85 and 86; and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 85 and 86, electronic processor 208, and computer 109;

FIG. 3b illustrates plane mirror interferometer 269; FIG. 3c illustrates plane mirror interferometer 270; FIG. 3d is a drawing showing a block diagram of the processing electronics 208;

FIGS. 4a-4d taken together illustrate, in diagrammatic form, the presently preferred third embodiment of the present invention with FIG. 4a showing optical paths between indicated elements source 1, modulator 3, source 2, modulator 4, plane mirror interferometer 369, plane mirror interferometer 270, measurement cell 90, and detectors 485 and 86 and the paths of electrical signals between indicated elements driver 5, modulator 3, driver 6, modulator 4, detectors 485 and 86, electronic processor 408, and computer 109;

FIG. 4b illustrates plane mirror interferometer 369 for the case of light beam 11 entering plane mirror interferometer 369; FIG. 4c illustrates plane mirror interferometer 369 for the case of light beam 445 exiting plane mirror interferometer 369;

FIG. 4d is a drawing showing a block diagram of the processing electronics 408; FIGS. 5a-5d taken together illustrate, in diagrammatic form, the presently preferred fourth embodiment of the present invention with FIG. 5a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the first preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/% , a number of elements of the apparatus for determination of the ratio K/χ performing analogous operations as apparatus for determination of reciprocal dispersive power of the first preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio

FIG. 5b illustrates measurement cell 90b furnishing the external mirrors for plane mirror interferometer 69b; FIG. 5c illustrates measurement cell 90b furnishing the external mirrors for plane mirror interferometer group 70b;

FIG. 5d is a drawing showing a block diagram of the processing electronics 108b; FIGS. 6a-6b taken together illustrate, in diagrammatic form, the variant of the presently preferred fourth embodiment of the present invention with FIG. 6a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the variant of the first preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/χ , a number of elements of the apparatus for determination of the ratio K/χ performing analogous operations as apparatus for determination of reciprocal dispersive power of the variant of the first preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio K/χ ;

FIG. 6b is a drawing showing a block diagram of the processing electronics 1108b; FIGS. 7a-7b taken together illustrate, in diagrammatic form, the presently preferred fifth embodiment of the present invention with FIG. 7a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the second preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/χ , a number of elements of the apparatus for determination of the ratio K/χ performing analogous operations as apparatus for determination of reciprocal dispersive power of the second preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio κ/χ ;

FIG. 7b is a drawing showing a block diagram of the processing electronics 208b;

FIGS. 8a- 8b taken together illustrate, in diagrammatic form, the presently preferred sixth embodiment of the present invention with FIG. 8a showing optical paths and electronic paths of apparatus for determination of reciprocal dispersive power comprised in part of the same apparatus as for the third preferred embodiment and optical paths and electronic paths of apparatus for determination of the ratio K/χ , a number of elements of the apparatus for determination of the ratio K/χ performing analogous operations as apparatus for determination of reciprocal dispersive power of the third preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio K/χ ;

FIG. 8b is a drawing showing a block diagram of the processing electronics 408b; and

Fig. 9 is a high-level flowchart depicting various steps carried out in practicing a method in accordance with the invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to apparatus and methods by which intrinsic optical properties of a gas, especially its reciprocal dispersive power, may be quickly measured and used in subsequent downstream or contemporaneous applications as, for example, in an interferometric distance measuring instrument to enhance accuracy by compensating for index of refraction changes that take place proximate to or during the measuring period because of changing environmental conditions or air turbulence induced in the measurement leg by rapid stage slew rates.

A number of different embodiments of the apparatus of the invention are shown and described. While they differ in some details, the disclosed embodiments otherwise share many common elements and naturally fall into two broad categories depending on the degree of control demanded of their light sources. As will be seen, the disclosed embodiments within each broad category also differ in the details of how their interferometric optical paths are implemented and/or how certain information signals are handled electronically. The first broad group of embodiments to be described comprise three and a variant of the first embodiment. This group is intended for applications where the stability of the adopted light sources is sufficient and the wavelengths of the light beams generated by the adopted light sources are harmonically related to a relative precision sufficient to meet the required precision imposed on the output data by the final end use application. The second group of embodiments also comprise three and one variant, and these are particularly suitable for use where it is necessary to monitor the stability of the light sources and measure the wavelengths of the light beams generated by the adopted light sources to meet performance requirements on accuracy. For both groups, apparatus is disclosed for dealing with phase ambiguities that may arise in analyzing homodyne, heterodyne, and/or superheterodyne signals, and methods are disclosed for implementing the steps of the invention.

Reference is now made to FIGS, la-lf which depict in diagrammatic form one preferred embodiment of the apparatus of the present invention for measuring intrinsic optical properties of a gas, particularly its reciprocal dispersive power. While the apparatus has application for a wide range of radiation sources, the following description is taken by way of example with respect to an optical measuring system. Referring to FIG. la and in accordance with the preferred method of the first preferred embodiment of the present invention, a light beam 7 emitted from source 1 passes through a modulator 3 becoming light beam 9. Modulator 3 is excited by a driver 5. Source 1 is preferably a laser or like source of coherent radiation, preferably polarized, and having a wavelength λ₁. Modulator 3 may for example be an acousto- optical device or a combination of acousto-optical devices with additional optics for selectively modulating polarization components of beam 7. Modulator 3 preferably shifts the oscillation frequency of one linearly polarized component of beam 7 an amount f with respect to an orthogonally linearly polarized component, the directions of polarizations of the components denoted herein as x and y . In the following description of the first preferred embodiment, it will be assumed that the x polarization component of beam 9 has an oscillation frequency shifted an amount f with respect to the y polarization component of beam 9 without departing from the spirit or scope of the present invention.

In a next step, a light beam 8 emitted from a source

2 passes through a modulator 4 becoming light beam 10. Modulator 4 is excited by a driver 6, similar to modulator

3 and driver 5, respectively. Source 2, similar to source 1, is preferably a laser or like source of polarized, coherent radiation, but preferably at a different wavelength, λ₂ , having a known approximate harmonic relationship with respect to λ_x , i . e .

Pι^₂ = PιK • ^• Pi 'Pi =1,2,3,..., p_λ ≠ p₂ . (1)

The x polarized component of beam 10 has an oscillation frequency shifted an amount f₂ with respect to the y polarized component of beam 10. In addition, the directions of the frequency shifts of the x components of beams 9 and 10 are the same.

It will be appreciated by those skilled in the art that beams 9 and 10 may be provided alternatively by a single laser source emitting more than one wavelength, or by a single laser source combined with optical frequency doubling means, or any equivalent source configuration capable of generating light beams of two or more wavelengths. It will also be appreciated by those skilled in the art that one or both of the frequency shifts f_x and f₂ may be the result of Zeeman splitting or like phenomena characteristic of the laser sources themselves.

In a next step, beam 9 is subsequently reflected by mirror 53 becoming beam 11. A portion of beam 10 is reflected by a beam splitter 54A, preferably a non polarizing type, as beam 12, and a second portion of beam 10 is transmitted by beam splitter 54A and subsequently reflected by mirror 54B becoming beam 212. Beam 11 is incident on differential plane mirror interferometer 69 and beams 12 and 212 are incident on differential plane mirror interferometer group 70 comprised of two differential plane mirror interferometers. Differential plane mirror interferometer 69 and differential plane mirror interferometer group 70 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift φ₁ between the x and y components of beam 11, a phase shift φ₂ between the x and y components of beam 12, and a phase shift φ₃ between the x and y components of beam 212. Measurement cell 90 is conveniently formed as a set of nested, concentric chambers in the form of a right circular cylinder, the inner chamber of which is evacuated to a vacuum and the outer occupied by the gas whose intrinsic optical properties are to be monitored.

A differential plane mirror interferometer measures the optical path changes between two external plane mirrors. In addition, it is insensitive to thermal and mechanical disturbances that may occur in the interferometer beamsplitting cube and associated optical components. Differential plane mirror interferometer 69 as shown in FIG. lb has eight exit/return beams 17, 25, 33, 41, 117, 125, 133, and 141. Beams 17, 25, 33, and 41 originating from one frequency component of beam 11, the first frequency component, comprise beams for one measurement leg and beams 117, 125, 133, and 141 originating from a second frequency component of beam 11 comprise beams for a second measurement leg. Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIG. lb by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIG. lb by dotted lines .

One differential plane mirror interferometer of differential plane mirror interferometer group 70 has four exit/return beams 18, 26, 118, and 126. Beams 18 and 26 originating from one frequency component, a first frequency component of beam 12 comprise beams for one measurement leg and beams 118 and 126 originating from a second frequency component of beam 12 comprise beams for a second measurement leg. Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. lc by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. lc by dotted lines. A second differential plane mirror interferometer of differential plane mirror interferometer group 70 has four exit/return beams 218, 226, 318, and 326. Beams 218 and 226 originating from one frequency component, a first frequency component, of beam 212 comprise beams for one measurement leg and beams 318 and 326 originating from a second frequency component of beam 212 comprise beams for a second measurement leg. Beams for which the first frequency component of beam 212 is the sole progenitor are indicated in FIG. lc by lines comprised of alternating dots and dashes and beams for which the second frequency component of beam 212 is the sole progenitor are indicated in FIG. lc by lines comprised of alternating dot pairs and dashes .

Beams 17, 25, 33, 41, 117, 125, 133, and 141 are incident on measurement cell 90, illustrated in FIG. Id, which results in beams 43 and 143. Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIG. Id by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIG. Id by dotted lines. Beams 43 and 143 contain information at wavelength λ₁ about the optical path length through the gas whose reciprocal dispersive power is to be determined and about the optical path length through a vacuum, respectively. Likewise, beams 18, 26, 118, and 126 are incident on measurement cell 90, illustrated in FIG. le, which results in beams 28 and 128. Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. le by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. le by dotted lines. Similarly, beams 218, 226, 318, and 326 are incident on measurement cell 90, as shown in FIG. le, which results in beams 228 and 328. Beams for which the first frequency component of beam 212 is the sole progenitor are indicated in FIG. le by lines comprised of alternating dots and dashes and beams for which the second frequency component of beam 212 is the sole progenitor are indicated in FIG. le by lines comprised of alternating dot pairs and dashes. Beams 28 and 228 contain information at wavelength λ₂ about optical path lengths through the gas whose reciprocal dispersive power is to be determined and beams 128 and 328 contain information at wavelength λ₂ about optical path lengths through a vacuum.

Beam 43 is reflected by mirror 63B, a portion of which is reflected by beamsplitter 63A, preferably a non polarizing type, to become one component of beam 45. A portion of beam 143 is transmitted by beam splitter 63A to become a second component of beam 45. Beam 45 is a mixed beam, the first and second components of beam 45 having the same linear polarizations. Beam 45 exits the differential plane mirror interferometer 69.

Beam 28 is reflected by mirror 58B, a portion of which is reflected by beamsplitter 58A, preferably a non polarizing beamsplitter, to become a first component of beam 30. A portion of beam 128 is transmitted by beamsplitter 58A to become a second component of beam 30. Beam 30 is a mixed beam, the first and second components of beam 30 having the same linear polarizations.

Beam 228 is reflected by mirror 58D, a portion of which is reflected by beam splitter 58C, preferably a non polarizing beamsplitter, to become a first component of beam 230. A portion of beam 328 is transmitted by beamsplitter 58C to become a second component of beam 230. Beam 230 is a mixed beam, the first and second components of beam 230 having the same linear polarizations. Beams 30 and 230 exit differential plane mirror interferometer group 70.

The magnitude of phase shifts φ , φ₂ , and φ₃ are related to the round-trip physical length Z_ of path of measurement path 97 or reference path 98 shown in FIGS. Id and le according to the formulae

>=Pι ι=Pι

Ψi = ∑ Φι,_ = ∑ [ i («ι« ^{" 1}) + ζi ] , i=l i=l

;=1 ϊ=l

'=Pι '=Pι

<P3 = Σ <P3,f = Σ l^Li^k2 («2ι ^" 1) + ζ3 ] < i=p₂ +l i=P₂ ⁺¹

for the case of p₁ = 2p₂ where the angular wavenumbers k are given by

k_j = 2π/λ_j , j^' = l and 2, (3)

n are the indices of refraction of gas in path i of measurement path 97 corresponding to wavenumber k , and the index of refraction in the reference path 98 has been set to 1. The phase offsets ζ₍ comprise all contributions to the phase shifts ψ_e that are not related to the measurement path 97 or reference path 98. To those skilled in the art, the generalization to the case when p₁ ≠ 2p₂ is a straight forward procedure. It is noteworthy that the coefficients p and p₂ are preferably identical to the like-denoted coefficients p and p used to define the approximate harmonic relationship in Eq. (1) . In FIGS, lb and lc, differential plane mirror interferometer 69 and differential plane mirror interferometer group 70, along with measurement cell 90, are configured so that i =4 and p₂ = 2 so as to illustrate in the simplest manner the function of the apparatus of the first preferred embodiment.

In a next step as shown in FIG. la, beams 45, 30, and 230 impinge upon photodetectors 85, 86, and 286, respectively, resulting in three interference signals, heterodyne signals s₁ , s₂ , and s₂ , respectively, preferably by photoelectric detection. The signal s_λ corresponds to wavelength λ₁ and signals s₂ and s₃ correspond to the wavelength λ₂. The signals s_e have the form

s₍ = A_e cos[a_e(ή] , £ = 1, 2, and 3, (4)

where the time-dependent arguments α_;(t) are given by

α₂(t) = 2π ₂t + φ₂ , ( 5 ) α₃ (t) = 2π/₂t + φ₃

Heterodyne signals s₁ , s₂ , and s₃ are transmitted as electronic signals 103, 104, and 304, respectively, to electronic processor 108 for analysis.

Referring now to FIG. If, electronic processor 108 preferably comprises electronic processor 1081 for electronically adding the heterodyne signals s₂ and s₃ together to create a superheterodyne signal S , the first superheterodyne signal, having the mathematical form

The first superheterodyne signal S₁ may be rewritten as

5Ϊ = sin(2π/₂t + θ₁)sinΦ₁ ( 7 )

where

The first superheterodyne signal S_λ is therefore comprised of a carrier signal , A₂ + A₃ = cosΦ_x cos(2π ₂t + θ₁) ( 10 )

of frequency f₂ with amplitude [(A₂ +

modulated by an envelope signal of zero frequency plus what can be a negligible secondary term.

The second term on the right hand side of Eq. (7) is a term that enters as a second order term in [A₂ -

and

Φ₁. The amplitude factor A₂ -

is made small by the design of the electronic processor 1081 and the respective detectors 86 and 286. Further, the phase Φ₁ is in general quite small, differential plane mirror interferometer group 70 being comprised of two differential plane mirror interferometers with associated measurement and reference paths substantially the same. Combining Eqs. (2) and (9), the phase Φ_λ can be written as

Note from Eq. (11) that Φ_x is not sensitive to either displacements or tilts of either reflecting surfaces 95 or 96, a feature of differential plane mirror interferometers; not sensitive to changes in the mean temperature or pressure or to gradients in temperature or pressure of the gas in measuring path 97, a consequence of the paths in 90 associated with s₂ and of the paths in 90 associated with s₃ having center lines that are collinear in differential plane mirror interferometers; and not sensitive to composition of the gas in measuring path 97 The primary contributions to phase Φ_τ will be second order derivatives with respect to spatial coordinates of temperature and pressure of the gas and through air turbulence in measuring path 97. The magnitudes of the latter two contributions will generally be quite small, i.e. «1 rad., for applications such as high precision distance measuring interferometry .

Referring to FIG. If, electronic processor 108 further comprises electronic processor 1083 for electronically adding together the heterodyne signal s and the carrier signal C_x from 1081 to create a second level superheterodyne signal S₂ , the second superheterodyne signal, having the mathematical form

^2 ^{_ S}l ⁺ : i2 )

The second superheterodyne signal S₂ may be rewritten as

A. + A,

+ ^{2 ' "3 l} cos(2π ₂t + θ₁)(cosΦ₁ - l)

2

A₂ - A₃ sin(2π/₂t + θ₁)sinΦ₁ where

C₂ = cos(2πvt+ θ₂) (14)

M₂ = cos(2πEt+ Φ₂) (15)

and

Φ₂=(φ₁-θ₁)/2 = i

The second superheterodyne signal S₂ is therefore comprised of a carrier signal C₂ of frequency v modulated by an envelope signal M₂ of frequency F and what can be a series of negligible secondary terms by proper adjustment of amplitude coefficients A_τ , A₂ , and A₃ , by keeping Φ_x close to zero as described above, and by use of the proper phase in the extraction of the M₂C₂ term.

Referring once again to FIG. If, electronic 108 preferably comprises processor 1085 to separate envelope signal M₂ from carrier signal C₂ , using rectification and filtering, signal squaring, or any of the like techniques for extracting an amplitude modulation and demodulating a carrier. Electronic processor 108 further comprises a processor 1086 to determine the modulation phase Φ₂ using time-based phase detection or the like. Electronic processor 108 additionally comprises processors 1082 to determine the phase shift φ₁ .

The reciprocal dispersive power T of the gas defined as

r "ι(λι)^~l

(20) "₂(^λ ₂)-«ι(^λι)

can be expressed by the formula

where L_G and L_v are the average physical lengths of measurement path 97 and reference path 98, respectively,

Z₂ = (2_jPlζ₁ -_jp₂ζ₂ -_jp₃ζ₃)/4 . ( 25 ) The quantities K and χ introduced in Eq. (21) will be referred to as the vacuum superheterodyne wavenumber and the vacuum carrier wavenumber, respectively. This terminology will be supported by phase equations subsequently developed in regard to the fourth, fifth, and sixth preferred embodiments and variant thereof of the present invention.

The approximate harmonic ratio can be expressed in terms of K and χ from Eqs. (22) and (23) with the result

λ^ p₂ ] l + (K/χ)

26) Pj _.ι-( /χ)

When operating under the condition

the ratio of the modulation phase Φ₂ and carrier phase θ₂ has a value

(Φ₂/θ₂)≤-[l/(2r)] . (28)

Therefore, for the case where the approximate harmonic relationship (λ₂/λ_x) is expressible as the ratio of low order non zero integers, e . g. 1/2, to a relative precision of an order of magnitude less than the dispersive power of the gas, 1/r, times the relative precision ε desired for the measurement of the reciprocal dispersive power T , Eq. (21) reduces to the more simple form [(<Pi- i)-(A^;- v)x] : 29 ) (- ₂+^₂)

Note that only the difference of the lengths L_G and L_v , ( _G-Z_V), enter as a factor in a correction term in the computation of T . The quantity (E_G - Z_V) can be made less than the magnitude of the wavelengths λ_x and λ₂ as a consequence of the design of and use of differential plane mirror interferometers and the design of the measuring cells. Thus the quantities L_G and J_v need not be explicitly measured for the computation of T but only the difference (Z,_G - E_V) is required to a precision relative to

L_G of the order of ε^-l). Also note the vacuum carrier wavenumber χ enters into the computation of T only as a factor in the correction term (Z_G-Z,_v)χ, a correction term wherein (E_G - _v)χ «: as a result of L_G and E_v being substantially equal. Thus the relative precision required for quantity χ in the computation of T is of the order of ε(n₁ - l)Z_G /{L_G - L_v) , a quantity which generally is substantially larger than the relative precision obtained for T .

Eq. (29) is the equation used in the first preferred embodiment to compute the reciprocal dispersive power T . The condition on the wavelengths λ_λ and λ₂ which leads to Eq. (29) from Eq. (21) expressed as an equation is

Eq. (30) is the basis for the conclusion that sources 1 and 2 need not be phase locked for the first preferred embodiment. Eq. (30) is actually a weak condition when viewed in terms of a phase- locked requirement for sources 1 and 2. Consider for an example a desired precision of ε≤3xl0^~6 for the reciprocal dispersive power, corresponding to a relative distance measuring precision of approximately lxlO^-9 in a distance measuring interferometer, (/^ -l) = 3 x 10^"4 , and (n₂ -«₁) ≤ lxlO^-5. For the example, the condition expressed by Eq. (30) written in terms of source frequencies v^_^ and v₂ instead of wavelengths λ₁ and λ₂ , respectively, is

For source wavelengths in the visible part of the spectrum and for low order integers for p and p₂ , Eq. (31) translates into a condition

The result expressed in Eq. (32) is clearly a significantly less restrictive condition on the frequencies of sources 1 and 2 than a phase- locked condition.

In a next step, electronic processing means 108 transmits to the computer 109 φ₁ and Φ₂ as electronic signal 105 in either digital or analog format for the computation of T according to Eq. (29) .

The computation of T using Eq. (29) requires resolution of the phase redundancy in φ₁ and Φ₂. In the first preferred embodiment, the equivalent wavelengths comprising φ₁ and Φ₂ are significantly larger than either of the wavelengths λ_λ and λ₂ and as a consequence, produces a significant simplification in a procedure implemented for resolution of phase redundancy in φ₁ and Φ₂. The equivalent wavelengths λ_φ and λ_Φ for φ₁ and Φ₂ , respectively, are

>. -__-LΪ_ (33)

^{Φl "}(» -l)

λ, ^λΦ, - : 34 )

(«2-"l)

For the example of λ₁=0.633μm, (n_λ -l) ≤ 3 x 10⁴ , and

(n₂ - n^) = lxl0^~5 , the equivalent wavelengths given by Eqs (33) and (34) are

λ_φ = 60 mm ( 36 ;

Any one of several procedures may be easily employed to resolve the phase redundancy in φ₁ and Φ₂ , given their equivalent wavelengths as expressed by Eqs. (35) and (36). One procedure which may be employed to resolve the phase redundancy in φ₁ and Φ₂ is based on the use of a series of measurement cells where the physical lengths for the measuring and reference paths of the series of measurement cells form a geometric progression. The smallest or first physical length in the series will be approximately λ /pA divided by the relative precision that the initial value of φ_τ is known. The physical length of the second measurement cell in the series will be approximately the length of the first measurement cell divided by the relative precision that φ_x is measured using the first measurement cell. This is a geometric progression procedure, the resulting physical lengths forming a geometric progression, which is continued until the length of the measurement cell used to measure T would be exceeded if the number of measurement cells in the series were incremented by one. A typical physical length for the first measurement cell in the series is of the order of 0.5 mm, a typical physical length for the second measurement cell in the series is of the order of 50 mm, and a typical physical length for a third measurement cell in the series if required is of the order of 5000 mm.

A second procedure is based upon the use of a source (not shown in FIGS, la-lf) of a series of known wavelengths and measuring φ₁ and Φ₂ for these wavelengths . The number of known wavelengths required for the resolution of the phase redundancy is generally comprised of a small set as a direct consequence of the relatively large equivalent wavelengths as expressed by Eqs. (35) and (36) .

Another procedure to resolve the phase redundancy in φ_l and Φ₂ would be to observe the changes in φ₁ and Φ₂ as the reference path 98 is changed from gas as present in the measuring path 97 to an evacuated state (the vacuum pump and requisite gas handling system are not shown in FIGS, la-lf) to resolve the phase redundancy in φ₁ and Φ₂. The problems normally encountered in measuring absolute values for refractivity and dispersion of refractivity based in part on changing the gas pressure from a non zero value to a vacuum are not present in the first preferred embodiment because of the relatively large equivalent wavelengths as expressed by Eqs. (35) and (36) . A second reciprocal dispersive power, T₂ , may also be defined for the gas where

However, T₂ can be obtained directly from F since

r, = r + 1 (38)

Therefore, the description of first preferred embodiment with regard to T₂ is substantially the same as the description of first preferred embodiment with regard to r.

The intrinsic property of a gas represented by T may be obtained and subsequently used down stream in another form such as the ratio (n₁ - l)/(n₂ - 1) . The ratio

(n₁ - 1)/(«₂ - 1) can be written in terms of measured quantities by the formula

("..-i) _ f(Pι-/>ι^ζι)-fe- r)χ ι+( /χ) ι-(κ/χ) (39;

("2 - ¹) \ (ψ₂ -p₂ - (^LG - Lv)ι ι-( /χ) .1 + ( /*).

The ratio (n₁ - l)/(«₂ - 1) can also be expressed in terms of T or r and T₂ by the equations

As a consequence of Eq. (40) , the description of the first preferred embodiment with regard to the ratio (n₁ - l)/(n₂ - l) is substantially the same as the description of first preferred embodiment with regard to T and T₂.

FIG. lb depicts in schematic form one embodiment of the differential plane mirror interferometer 69 shown in FIG. la. It operates in the following way: Beam 11 is incident on beamsplitter 55A, preferably a polarizing beamsplitter, with a portion of beam 11 being transmitted as beam 13. A second portion of beam 11 is reflected by beam splitter 55A, subsequently reflected by mirror 55B, and then transmitted by half -wave phase retardation plate 79 as beam 113, the half-wave phase retardation plate 79 rotating the plane of polarization of the reflected portion of beam 11 by 90°. Beams 13 and 113 have the same polarizations but still have different frequencies. Beam 13 and beams for which beam 13 is the sole progenitor are indicated in FIGS, lb and Id by dashed lines and beam 113 and beams for which beam 113 is the sole progenitor are indicated in FIGS, lb and Id by dotted lines. The function of beamsplitter 55A and mirror 55B is to spatially separate the two frequency components of beam 11 using conventional polarization techniques.

Beams 13 and 113 enter polarizing beam splitter 71, which has a polarizing coating 73, and are transmitted as beams 15 and 115, respectively. Beams 15 and 115 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 17 and 117, respectively. Beams 17 and 117 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 15 and 115. These beams are reflected by polarizing coating 73 to become beams 19 and 119, respectively. Beams 19 and 119 are reflected by retroreflector 75 to become beams 21 and 121, respectively. Beams 21 and 121 are reflected by polarizing coating 73 to become beams 23 and 123, respectively. Beams 23 and 123 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 25 and 125, respectively. Beams 25 and 125 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams the same as the original incident beams 15 and 115. These beams are transmitted by polarizing coating 73 to become beams 27 and 127, respectively. Beam 27 is reflected by mirrors 57A and 57B and beam 127 is reflected by mirrors 59C and 59D to become beams 29 and 129, respectively.

Beams 29 and 129 enter polarizing beam splitter 71 and are transmitted by polarizing beam splitter 71 with polarizing coating 73 as beams 31 and 131, respectively. Beams 31 and 131 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 33 and 133, respectively. Beams 33 and 133 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 31 and 131. These beams are reflected by polarizing coating 73 to become beams 35 and 135, respectively. Beams 35 and 135 are reflected by retroreflector 75 to become beams 37 and 137, respectively. Beams 37 and 137 are reflected by polarizing coating 73 to become beams 39 and 139, respectively. Beams 39 and 139 pass through quarter-wave phase retardation plate 77 and are converted into circularly polarized beams 41 and 141, respectively. Beams 41 and 141 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 77, and are converted back into linearly polarized beams the same as the original incident beams 15 and 115. These beams are transmitted by polarizing coating 73 to become beams 43 and 143, respectively. Beams 43 and 143 contain information at wavelength λ_x about the optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about the optical path lengths through a vacuum, respectively.

Beam 43 is reflected by mirror 63B, and then a portion reflected by beam splitter 63A, preferably a non polarizing type, as a first component of beam 45. Beam 143 is incident on beamsplitter 63A with a portion of beam 143 being transmitted as a second component of beam 45, the first and second components of beam 45 having the same linear polarizations but still having different frequencies . FIG. lc depicts in schematic form one embodiment of differential plane mirror interferometer group 70 shown in FIG. la. It operates in the following way: Beam 12 is incident on beamsplitter 56A, preferably a polarizing beamsplitter, with a portion of beam 12 being transmitted as beam 14. A second portion of beam 12 is reflected by beam splitter 56A, subsequently reflected by mirror 56B, and then transmitted by half-wave phase retardation plate 80 as beam 114, the half-wave phase retardation plate 80 rotating the plane of polarization of the reflected portion of beam 12 by 90°. Beams 14 and 114 have the same polarizations but still have different frequencies. Beam 14 and beams for which beam 14 is the sole progenitor are indicated in FIGS, lc and le by dashed lines and beam 114 and beams for which beam 114 is the sole progenitor are indicated in FIGS, lc and le by dotted lines. The function, in part, of beamsplitter 56A and mirror 56B is to spatially separate the two frequency components of beam 12 using conventional polarization techniques.

Beams 14 and 114 enter polarizing beam splitter 72, which has a polarizing coating 74, and are transmitted as beams 16 and 116, respectively. Beams 16 and 116 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 18 and 118, respectively. Beams 18 and 118 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 16 and 116. These beams are reflected by polarizing coating 74 to become beams 20 and 120, respectively. Beams 20 and 120 are reflected by retroreflector 76 to become beams 22 and 122, respectively. Beams 22 and 122 are reflected by polarizing coating 74 to become beams 24 and 124, respectively. Beams 24 and 124 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 26 and 126, respectively. Beams 26 and 126 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams the same as the original incident beams 16 and 116. These beams are transmitted by polarizing coating 74 to become beams 28 and 128, respectively. Beams 28 and 128 contain information at wavelength λ₂ about the optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about the optical path lengths through a vacuum, respectively. Beam 28 is reflected by mirror 58B, and then a portion reflected by beam splitter 58A, preferably a non polarizing type, as a first component of beam 30. Beam 128 is incident on beamsplitter 58A with a portion of beam 128 being transmitted as a second component of beam 30, the first and second components of beam 30 having the same linear polarizations but still having different frequencies .

Beam 212 is incident on beamsplitter 56A with a portion of beam 212 being transmitted as beam 214. A second portion of beam 212 is reflected by beam splitter 56A, subsequently reflected by mirror 56B, and then transmitted by half-wave phase retardation plate 80 as beam 314, the half-wave phase retardation plate 80 rotating the plane of polarization of the reflected portion of beam 212 by 90°. Beams 214 and 314 have the same polarizations but still have different frequencies. Beam 214 and beams for which beam 214 is the sole progenitor are indicated in FIGS, lc and le by lines comprised of alternating dots and dashes and beam 314 and beams for which beam 314 is the sole progenitor are indicated in FIGS, lc and le by lines comprised of alternating dot pairs and dashes. The function, in part, of beamsplitter 56A and mirror 56B is to spatially separate the two frequency components of beam 212 using conventional polarization techniques.

Beams 214 and 314 enter polarizing beam splitter 72, which has a polarizing coating 74, and are transmitted as beams 216 and 316, respectively. Beams 216 and 316 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 218 and 318, respectively. Beams 218 and 318 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams that are orthogonally polarized to the original incident beams 216 and 316. These beams are reflected by polarizing coating 74 to become beams 220 and 320, respectively. Beams 220 and 320 are reflected by retroreflector 76 to become beams 222 and 322, respectively. Beams 222 and 322 are reflected by polarizing coating 74 to become beams 224 and 324, respectively. Beams 224 and 324 pass through quarter-wave phase retardation plate 78 and are converted into circularly polarized beams 226 and 326, respectively. Beams 226 and 326 are reflected back on themselves by mirrors within measurement cell 90, pass back through quarter-wave retardation plate 78, and are converted back into linearly polarized beams the same as the original incident beams 216 and 316. These beams are transmitted by polarizing coating 74 to become beams 228 and 328, respectively. Beams 228 and 328 contain information at wavelength λ₂ about the optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about the optical path lengths through a vacuum, respectively. Beam 228 is reflected by mirror 58D, and then a portion reflected by beam splitter 58C, preferably a non polarizing type, as a first component of beam 230. Beam 328 is incident on beamsplitter 58C with a portion of beam 328 being transmitted as a second component of beam 230, the first and second components of beam 230 having the same linear polarizations but still having different frequencies .

FIGS. 2a-2b depict in schematic form a variant of the first preferred embodiment of the present invention for measuring the reciprocal dispersive power or other intrinsic optical properties of a gas. The description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the variant of the first preferred embodiment is the same as the description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment .

As illustrated in FIG. 2a, beam 9 is reflected by mirror 53 becoming beam 11. Beam 11 is incident on differential plane mirror interferometer 69. A portion of beam 10 is reflected by a beam splitter 54A, preferably a non polarizing type, as beam 12, and a portion of beam 10 is transmitted by beam splitter 54A and subsequently reflected by mirror 54B becoming beam 212. Beams 12 and 212 are incident on differential plane mirror interferometer group 170 comprised of two differential plane mirror interferometers. Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. 2b by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. 2b by dotted lines.

Beams for which the first frequency component of beam 212 is the sole progenitor are indicated in FIG. 2b by lines comprised of alternating dots and dashes and beams for which the second frequency component of beam 212 is the sole progenitor are indicated in FIG. 2b by lines comprised of alternating dot pairs and dashes. Differential plane mirror interferometer 69 and differential plane mirror interferometer group 170 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift φ_x between the x and y components of beam 11 and a phase shift (φ₂+φ₃)/2 between the x and y components of beam

10.

Differential plane mirror interferometer 69 is the same as differential plane mirror interferometer 69 of the first preferred embodiment. The paths of the optical beams in differential plane mirror interferometer group 170 are the same as the paths of the optical beams in differential plane mirror interferometer group 70 of the first preferred embodiment up through and including the generation of beams 28, 228, 128, and 328 as illustrated in FIG. 2b. In the variant of the first preferred embodiment, beams 28, 228, 128, and 328 are combined optically to generate beam 32. Beam 32 is a mixed beam detected by detector 186, beam 32 being comprised of two components having the same polarizations but different frequencies. The heterodyne signal generated in detector 186, preferably by photoelectric detection, from the mixed beam 32 is transmitted to electronic processor 1108 as electronic signal 1104. Beam 32 is generated from beams 28, 228, 128, and 328 by the following steps. Beam 28 is reflected by mirror 60B, a portion subsequently reflected by mirror 60A, preferably a 50/50 non polarizing beam splitter, to form one part of beam 30A. A portion of beam 228 is transmitted by beam splitter 60A to form a second part of beam 30A, the first and second parts of beam having the same polarization and the same frequencies. To the extent that the amplitudes of beams 28 and 228 are the same, to the extent that beam splitter 60A is a 50/50 beam splitter, and to the extent that the optical paths lengths for beams 28 and 228 are the same, substantially all of the beams 28 and 228 will be present in beam 30A because of constructive interference.

Beam 128 is reflected by mirror 60D, a portion subsequently reflected by mirror 60C, preferably a 50/50 non polarizing beam splitter, to form one part of beam 130A. A portion of beam 328 is transmitted by beam splitter 60C to form a second part of beam 130A, the first and second parts of beam 130A having the same polarizations and the same frequencies. To the extent that the amplitudes of beams 128 and 328 are the same, to the extent that beam splitter 60C is a 50/50 beam splitter, and to the extent that the optical paths lengths for beams 128 and 328 are the same, substantially all of the beams 128 and 328 will be present in beam 130A because of constructive interference. Beams 30A and 130A also have the same polarizations but different frequencies. Beam 30A and 130A contain information at wavelength λ₂ about optical path lengths through the gas and about optical path lengths through a vacuum, respectively. In a next step, beam 30A is reflected by mirror 62B and then a portion of beam 30A reflected by beamsplitter 62A, preferably a non polarizing beamsplitter, to become a first component of beam 32. A portion of beam 130A is transmitted by beamsplitter 62A to become a second component of beam 32. Beam 32 is a mixed beam, the first and second components of beam 32 having the same polarizations but different frequencies. In a next step as shown in FIG. 2a, beam 32 impinges upon photodetector 186 resulting in two interference signals, heterodyne signals s₂ and s₃ , preferably by photoelectric detection. The signals s₂ and s₃ correspond to the wavelength λ₂ and are added in photodetector 186 to form superheterodyne signal S₁ , the same as the signal S_λ generated in electronic processor 1081 of the first preferred embodiment. Processor 1108 and 108 differ only by 1081. The remainder of the description of the variant of the first embodiment is the same as the description for corresponding aspects of the first embodiment.

Reference is now made to FIGS. 3a-3d which depict in diagrammatic form the second preferred embodiment of the present invention for measuring the reciprocal dispersive power or other intrinsic optical properties of a gas. The description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the second embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment of the present invention.

As illustrated in FIG. 3a, beam 9 is reflected by mirror 53 becoming beam 11 and beam 10 is reflected by mirror 54 becoming beam 12. Beam 11 is incident on differential plane mirror interferometer 269 and beam 12 is incident on differential plane mirror interferometer 270. Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIG. 3b by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIG. 3b by dotted lines. Beams for which the first frequency component of beam 12 is the sole progenitor are indicated in FIG. 3c by dashed lines and beams for which the second frequency component of beam 12 is the sole progenitor are indicated in FIG. 3c by dotted lines. Differential plane mirror interferometers 269 and 270 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift φ₁ between the x and y components of beam 11 and a phase shift φ₂ between the x and y components of beam 12. Differential plane mirror interferometer 269 has four exit/return beams 17, 25, 117, and 125 as shown in FIG. 3b. Beams 17 and 25 originating from one frequency component of beam 11 comprise one measurement leg and beams 117 and 125 originating from a second frequency component of beam 11 comprise a second measurement leg. Differential plane mirror interferometer 270 has four exit/return beams 18, 26, 118, and 126 as shown in FIG. 3c. Beams 18 and 26 originating from one frequency component of beam 12 comprise one measurement leg and beams 118 and 126 originating from a second frequency component of beam 12 comprise a second measurement leg.

Beams 17, 25, 117, and 125 are incident on measurement cell 90, the same as described in detail in FIG. Id which results in beams 27 and 127. Beams 27 and 127 contain information at wavelength λ₁ about the optical path length through the gas whose reciprocal dispersive power r is to be determined and about the optical path lengths through a vacuum, respectively. Beams 18, 26, 118, and 126 are incident on measurement cell 90, the same as described in detail in FIG. le which results in beams

28 and 128. Beam 28 and 128 contain information at wavelength λ₂ about optical path lengths through the gas and about optical path lengths through a vacuum, respectively.

The magnitude of phase shifts φ₁ and φ₂ are related to the round-trip physical length Z. of path i of measurement path 97 or reference path 98 shown in FIGS. Id and le according to the formulae

where the illustration in FIGS. 3b and 3c is for p = A so as to illustrate in the simplest manner the function of the invention in the second preferred embodiment.

Beam 27 is reflected by mirror 63B and then a portion reflected by beamsplitter 63A, preferably a non polarizing beamsplitter, to become a first component of phase shifted beam 29A. A portion of beam 127 is transmitted by beamsplitter 63A to become a second component of phase- shifted beam 29A. Phase shifted beam 29A is a mixed beam, the first and second components of beam 29A having the same polarizations but different frequencies.

Beam 28 is reflected by mirror 58B and then a portion reflected by beamsplitter 58A, preferably a non polarizing beamsplitter, to become a first component of phase-shifted beam 30. A portion of beam 128 is transmitted by beamsplitter 58A to become a second component of phase- shifted beam 30. Phase shifted beam 30 is a mixed beam, the first and second components of beam 30 having the same polarizations but different frequencies.

In a next step as shown in FIG. 3a, phase-shifted beams 29A and 30 impinge upon photodetectors 185 and 86, respectively, resulting in two interference signals, heterodyne signals s_λ and s₂ , respectively, preferably by photoelectric detection. The signal 5^, ₁ corresponds to wavelength λ_x and signal s₂ corresponds to the wavelength λ₂. The signals s₍ have the form expressed by Eq. (4) with time-dependent arguments .₍(t) given by Eq. (5) .

Heterodyne signals s₁ and s₂ are transmitted to electronic processor 208 for analysis as electronic signals 203 and 104, respectively, in either digital or analog format.

Referring now to FIG. 3d, electronic processing means 208 preferably comprises means 281 for electronically multiplying time-dependent arguments α_x(t) and ₂(t) of heterodyne signals s_λ and s₂ , respectively, by coefficients p_λ and p₂ , respectively, so as to create two modified heterodyne signals 7_X and ?₂ having the form

The multiplication may be achieved by any one of the conventional frequency multiplying techniques commonly known in the art, such as signal squaring followed by electronic filtering. It will be understood by those skilled in the art that such electronic multiplying techniques may introduce offsets and modifications in signal strength that may be neglected in the present, simplified description of the analysis technique of the present invention. It is noteworthy that the coefficients p_l and p₂ are preferably identical to the like-denoted coefficients p_τ and p₂ used to define the approximate harmonic relationship in Eq. (1) .

Referring again to FIG. 3d, electronic processing means 108A preferably comprises means 108b for electronically adding two modified heterodyne signals and ^"s₂ together to create a superheterodyne signal S₂ having the mathematical form

£,=^+5₂ (43)

which may be rewritten as

S₂=2M₂C₂ (44;

where

C₂ =cos(2πvt + θ₂) (45;

M₂=cos(2πFt + φ \ , (46;

and

v = i(_Λ/_{1 +}p₂/₂) (47)

&₂=ι{Pι<?ι+P₂<P₂) (⁴⁸> F = ^₂ {p₁f₁ - P₂f₂) (49 )

Superheterodyne signal S₂ is therefore a carrier signal C₂ of frequency v modulated by an envelope signal M₂ of frequency F . Those skilled in the art will appreciate that when modified heterodyne signals 7 and s₂ are of different amplitude, the resulting mathematical expression is more complicated, but nonetheless may be described in terms of a carrier signal modulated by an envelope signal. For simplicity in the present disclosure, it is assumed that modified heterodyne signals 7₁ and 7₂ have the same amplitude. The remaining description of the second embodiment of the present invention is the same as the description given for corresponding steps of the first embodiment of the present invention.

It will be appreciated by those skilled in the art that alternative data processing may be considered for the second preferred embodiment without departing from the spirit and scope of the present invention. For example, it may prove useful to multiply modified heterodyne signals J_λ and 7₂ together, rather than adding them as was proposed above, resulting in the expression:

S_2H = ϊ₁ ^'s₂ . (51) Alternative signal S_2M may be generated by selecting the appropriate term in the binomial expansion of (s^ +.s₂) through the use of phase sensitive detection. Alternative signal S_2M would then be comprised of the sum, rather than the product, of two signals having frequencies F and v. Such a processing technique would prove advantageous for example if it were found useful to replace detectors 185 and 86 in FIG. 3a with a single detector.

Reference is now made to FIGS. 4a-4d which depict in diagrammatic form the third preferred embodiment of the present invention for measuring the reciprocal dispersive power or other intrinsic optical properties of a gas. The description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the third embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment of the present invention.

As illustrated in FIG. 4a, beam 9 is reflected by mirror 53 becoming beam 11 and beam 10 is reflected by mirror 54 becoming beam 12. Beam 11 is incident on differential plane mirror interferometer 369 and beam 12 is incident on differential plane mirror interferometer 270. Beams for which the first frequency component of beam 11 is the sole progenitor are indicated in FIGS. 4b and 4c by dashed lines and beams for which the second frequency component of beam 11 is the sole progenitor are indicated in FIGS. 4b and 4c by dotted lines. Differential plane mirror interferometers 269 and 270 with external mirrors furnished by measurement cell 90 comprise interferometric means for introducing a phase shift φ₁ between the x and y components of beam 11 and a phase shift φ₂ between the x and y components of beam 12.

Differential plane mirror interferometer 369 has eight exit/return beams, four exit/return beams 417, 425, 517, and 525 as shown in FIG. 4b and four exit/return beams 433, 441, 533, and 541 as shown in FIG. 4c. Beams 417, 425, 433, and 441 originating from one frequency component of beam 11 comprise one measurement leg and beams 517, 525, 533, and 541 originating from a second frequency component of beam 11 comprise a second measurement leg. Beams 417, 425, 433, 441, 517, 525, 533, and 541 are incident on measurement cell 90, as described in detail in FIGS. 4b and 4c, which results in beams 443 and 543. Beam 443 and 543 contain information at wavelength λ about optical path lengths through the gas whose reciprocal dispersive power T is to be determined and about optical path lengths through a vacuum, respectively.

Differential plane mirror interferometer 270 has four exit/return beams 18, 26, 118, and 126 the same as for the second preferred embodiment as shown in FIG. 3c. Beams 18 and 26 originating from one frequency component of beam 12 comprise one measurement leg and beams 118 and 126 originating from a second frequency component of beam 12 comprise a second measurement leg. Beams 18, 26, 118, and 126 are incident on measurement cell 90, which results in beams 28 and 128. Beam 28 and 128 contain information at wavelength λ₂ about optical path lengths through the gas and about optical path lengths through a vacuum, respectively. The magnitude of phase shifts ψ₁ and φ₂ are related to the round-trip physical length Z, of path i of measurement path 97 or reference path 98 shown in FIGS. Id and le according to the formulae

where the illustration in FIGS. 4b, 4c, and 4d is for p₁ - 8 and p₂ = A so as to illustrate in the simplest manner the function of the invention in the third preferred embodiment. It is noteworthy that the coefficients p_x and p₂ are preferably identical to the like-denoted coefficients p₁ and p₂ used to define the approximate harmonic relationship in Eq. (1) . Beam 443 is transmitted by half-wave phase retardation plate 179C and Faraday rotator 179A, reflected by beam splitter 61A, transmitted by beam splitter 61B, and then reflected by mirror 63 to become a first component of phase shifted beam 445. Half-wave phase retardation plate 179C and Faraday rotator 179A each rotate the polarization of beam 443 by 45° so that the first component of phase shifted beam 445 is orthogonally polarized to the polarization of beam 443. Beam splitter 61A is preferably a polarizing beam splitter and beam splitter 61B is preferably a non polarizing beam splitter. Beam 543 is transmitted by half-wave phase retardation plate 179D and Faraday rotator 179B, reflected by beam splitter 61C, reflected by mirror 61D, reflected by beam splitter 61B, and then reflected by mirror 63 to become a second component of phase shifted beam 445. Half-wave phase retardation plate 179D and Faraday rotator 179B each rotate the polarization of beam 543 by 45° so that the second component of phase shifted beam 445 is orthogonally polarized to the polarization of beam 543. Beam splitter 61C is preferably a polarizing beam splitter. Phase shifted beam 445 is a mixed beam, the first and second components of phase shifted beam 445 having the same polarizations but different frequencies.

Beam 28 is reflected by mirror 58B and then a portion reflected by beamsplitter 58A, preferably a non polarizing beamsplitter, to become a first component of phase-shifted beam 30. A portion of beam 128 is transmitted by beamsplitter 58A to become a second component of phase- shifted beam 30. Phase shifted beam 30 is a mixed beam, the first and second components of phase shifted beam 30 having the same polarizations but different frequencies. In a next step as shown in FIG. 4a, phase-shifted beams 445 and 30 impinge upon photodetectors 485 and 86, respectively, resulting in two interference signals, heterodyne signals ^ and s₂ , respectively, preferably by photoelectric detection. The signal s_λ corresponds to wavelength λ and signal s₂ corresponds to the wavelength λ₂ . The signals s₍ have the form expressed by Eq. (4) with time-dependent arguments a_e(t) given by Eq. (5) . Heterodyne signals s₁ and s₂ are transmitted to electronic processor 408 for analysis as electronic signals 403 and 104, respectively, in either digital or analog format. Referring again to FIG. 4d, electronic processing means 408 preferably comprises means 1084 for electronically adding the two heterodyne signals s₁ and s₂ together to create a superheterodyne signal S₂ having the mathematical form

S₂ = s₁ + s₂ (53;

which may be rewritten as

S₂=2 ₂C₂ (54)

where

C₂ =cos(2πvt + θ₂) , (55)

M₂ =cos(2πEt + Φ₂) , (56)

and

= (f₁+f₂) > (57)

θ₂ = (φ₁+φ₂) , (58)

Superheterodyne signal S₂ is therefore a carrier signal C₂ of frequency v modulated by an envelope signal M₂ of frequency F. Those skilled in the art will appreciate that when heterodyne signals s₁ and s₂ are of different amplitude, the resulting mathematical expression is more complicated, but nonetheless may be described in terms of a carrier signal modulated by an envelope signal. For simplicity in the present disclosure, it is assumed that heterodyne signals s₁ and s₂ have the same amplitude. The operation of differential plane mirror interferometer 369 is the same as the operation described for differential plane mirror interferometer 69 except for the means used to separate the two frequency components of input beam 11 and the means used to create the mixed output beam 445. Referring to FIG. 4b, a portion of beam 11 is reflected by beam splitter 55A, preferably a polarizing beam splitter, reflected by mirror 55B, transmitted by half-wave phase-retardation plate 79, transmitted by beam splitter 61C, preferably a polarizing beam splitter, transmitted by Faraday rotator 179B, and transmitted by half-wave phase-retardation plate 179D to become beam 513. The Faraday rotator 179B and the half- wave phase-retardation plate 179D rotate the plane of polarization of transmitted beams by ±45° and +45°, respectively, producing no net rotation of the plane of polarization of transmitted beams. A portion of beam 11 is transmitted by beam splitter 55A, transmitted by beam splitter 61A, preferably a polarizing beamsplitter, transmitted by Faraday rotator 179A, and transmitted by half-wave phase-retardation plate 179C to become beam 413. The Faraday rotator 179A and the half-wave phase- retardation plate 179C rotate the plane of polarization of transmitted beams by ±45° and +45°, respectively, producing no net rotation of the plane of polarization of transmitted beams. Half-wave phase-retardation plate 79 rotates the plane of polarization of transmitted beam by 90° so that beams 413 and 513 have the same polarizations but have different frequencies. The purpose of the Faraday rotators 179A and 179B and the half-wave phase- retardation plates 179C and 179D is to have substantially no effect on the properties of beams 413 and 513 but to rotate the polarizations of beams 443 and 543 by 90° as previously described so as to achieve an efficient spatial separation of beams 443 and 543 from the path of beam 11. The remaining description of the third embodiment is the same as the description given for corresponding steps of the first embodiment of the present invention.

The second three preferred embodiments of the present invention and variant thereof, the preferred fourth preferred embodiment, the variant of the fourth preferred embodiment, the fifth preferred embodiment, and the sixth preferred embodiment of the present invention illustrated in FIGS. 5a-5d, 6a-6b, 7a-7b, and 8a-8b, respectively, are all embodiments to measure a reciprocal dispersive power when the condition set fourth in Eq. (30) for the first three preferred embodiments and variant thereof, the preferred first preferred embodiment, the variant of the first preferred embodiment, the second preferred embodiment, and the third preferred embodiment of the present invention, is not satisfied, i.e.

Under the condition set fourth in Eq. (61), the approximate harmonic ratio, preferably the ratio (K/χ) , must be either known or measured in accordance with Eq.

(21) for the first three preferred embodiments and variant thereof in addition to already described quantities in order to achieve the required accuracy in the determination of a refractive-dispersion constant. Each of the first three preferred embodiments and variant thereof can be converted from an apparatus and method for measuring a reciprocal dispersive power T to an apparatus and method for measuring the ratio (K/χ) by changing the measurement cell of a given embodiment so that the measuring path through the gas has substantially zero physical length, a property demonstrated in the following descriptions. Accordingly, each of the second three preferred embodiments and variant thereof are comprised of an unmodified and a modified apparatus and method from one of the first three preferred embodiments and variant thereof, the modified apparatus and method being comprised of the unmodified apparatus and method with a modified measurement cell.

Reference is now made to FIGS. 5a-5d which depict in diagrammatic form the fourth preferred embodiment of the present invention. The description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the fourth preferred embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the first preferred embodiment of the present invention except that the condition on wavelengths λ_λ and λ₂ expressed by Eq. (30) is replaced by the condition set fourth in Eq. (61) . Because of the requirement in the fourth preferred embodiment to measure the ratio (K/χ) , the fourth preferred embodiment is comprised in part of the same apparatus and method as for the first preferred embodiment and of additional means for determination of the ratio {K/χ) ■ The additional means for determination of the ratio (K/χ) is the same as the apparatus and method of the first preferred embodiment except for the measurement cell. Consequently, a number of elements of the apparatus shown in FIGS. 5a-5d for determination of the ratio (K/χ) perform analogous operations as apparatus for determination of reciprocal dispersive power T of the third preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio

(κ/x) • The measurement cell 90b of the fourth preferred embodiment is shown in FIGS. 5b and 5c. The description of measurement cell 90b is the same as that for measurement cell 90 except with respect to the coatings on surfaces 95b and 96b. Referring to FIG. 5b, surface 95b is coated so as to reflect with high efficiency beams 17b, 25b, 33b, and 41b and to transmit with high efficiency beams 117b, 125b, 133b, and 141b. Referring to FIG. 5c, surface 96b is coated so as to reflect with high efficiency beams 18b, 26b, 218b, and 226b and to transmit with high efficiency beams 118b, 126b, 318b, and 326b. The differences in the measurement cells 90b and 90 lead to modifications of Eqs. (2) such that the magnitude of phase shifts φ_lb , φ_2b , and φ_3b are related to the round-trip physical length Z, of path i of reference path

98 and to measuring paths of zero lengths as shown in FIGS. 5b and 5c according to the formulae

In a subsequent series of steps, a first superheterodyne signal S_lb and a second superheterodyne signal S_2b are generated by electronic processors 1081b, 1083b, and 1084b, electronic processors 1081b, 1083b, and 1084b performing analogous operations on heterodyne signals s_lb , s_2h , and s_3b of the fourth preferred embodiment the same as electronic processors 1081, 1083, and 1084 perform on heterodyne signals s₁ , s₂ , and s₃ of the first preferred embodiment. The second superheterodyne signal S_2b is comprised of a carrier signal C_2b of frequency v modulated by an envelope signal M_2b of frequency F where

C_2b = cos(2πvt + θ_2b) , (63) _2b=cos(2πEt + Φ_2b) (64)

and

θ 2b = (φib+θⁱb)/ Φ lb (66)

^= -/₂)/² (67)

The quantities K and χ are related to the carrier phase θ_2b and the modulation phase Φ_2b according to the formulae

x = (^θ _2b-^ξ _2b)A (70)

where

^z ₂b = (²/>iCib -/>₂ζ_2b -_JP₃ζ₃b)/⁴ (71)

ξ_2b ={2_{P ι} + p₂ζ_2b +p₃ζ_3b)/4 (72) Eqs. (69) and (70) show that within a multiplicative factor (l/Z) and phase offset terms, χ and K are equal to the carrier phase θ_2b and the modulation phase Φ_2b , respectively, which is the basis for referring in the description of the first preferred embodiment to K and χ as the vacuum superheterodyne wavenumber and the vacuum carrier wavenumber, respectively.

The ratio (K/χ) can be expressed by the formula

K_ (φ_2b - z_2b) (73)

X (θ_2b -ξ_2b)

using Eqs. (68) and (69) . Therefore the ratio (K/χ) is obtained by substantially dividing Φ_2b by θ_2b without the requirement of an accurate measurement of Z to the same precision as required for (K/χ) . The phase redundancy of θ_2b as well as Φ_2b can be determined as part of the same procedure used to remove the phase redundancy of φ₁ and Φ₂ in the unmodified apparatus and method of the first preferred embodiment incorporated as part of the fourth preferred embodiment. Although the respective wave length associated with θ_2b is of the order of λ and λ₂ , the procedure to determine the phase redundancy θ_2b and Φ_2b will generally not introduce additional complexity beyond that present in the procedure used to remove the phase redundancy of φ_x and Φ₂ when λ₁ , λ₂ , and Z are known with relative precisions of < (f^-l). The reciprocal dispersive power T is subsequently obtained using Eq. (21) . The remainder of the description of the fourth preferred embodiment is the same as that given for corresponding aspects of the first preferred embodiment .

Reference is now made to FIGS. 6a- 6b which depict in diagrammatic form a variant of the fourth preferred embodiment of the present invention for measuring the reciprocal dispersive power of a gas. The description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the variant of the fourth embodiment is the same as that for description of the sources of light beams 9 and 10 for the fourth preferred embodiment of the present invention. As a consequence, the ratio (K/χj has to be measured in the variant of the fourth preferred embodiment, the same as in the fourth preferred embodiment, in order to achieve the required accuracy in the determination of a refractive-dispersion constant.

Because of the requirement in the variant of the fourth preferred embodiment to measure the ratio (K/χ) , the variant of the fourth embodiment is comprised in part of the same apparatus and method as for the variant of the first preferred embodiment and of additional means for determination of the ratio (K/χ) . The additional means for determination of the ratio (K/χ) is the same as the apparatus and method of the variant of the first preferred embodiment except for the measurement cell. Consequently, a number of elements of the apparatus shown in FIGS. 6a-6b for determination of the ratio (K/χ) perform analogous operations as apparatus for determination of reciprocal dispersive power T of the variant of the first preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio (K/χj .

The measurement cell 90b of the variant of the fourth preferred embodiment is the same as the measurement cell 90b of the fourth preferred embodiment. Consequently, the remaining description of the variant of the fourth preferred embodiment is the same as the description given for corresponding aspects of the fourth preferred embodiment.

Reference is now made to FIGS. 7a-7b which depict in diagrammatic form the fifth preferred embodiment of the present invention for measuring the reciprocal dispersive power r . The description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the fifth embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the fourth preferred embodiment of the present invention. As a consequence, the ratio (K/χ) has to be measured in the preferred fifth embodiment in order to achieve the required accuracy in the determination of a reciprocal dispersive power T .

Because of the requirement in the fifth preferred embodiment to measure the ratio (K/χ) , the fifth embodiment is comprised in part of the same apparatus and method as for the second preferred embodiment and of additional means for determination of the ratio (K/χ) .

The additional means for determination of the ratio (K/χ) is the same as the apparatus and method of the second preferred embodiment except for the measurement cell. The measurement cell 90b is the same as the measurement cell 90b of the fourth preferred embodiment. Consequently, a number of elements of the apparatus shown in FIGS. 7a-7b for determination of the ratio (K/χ) perform analogous operations as apparatus for determination of reciprocal dispersive power T of the second preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio (K/χ .

The differences in the measurement cells 90b of the fifth preferred embodiment and 90 of the second preferred embodiment lead to modifications of Eqs. (41) such that the magnitude of phase shifts φ_lb and φ_2b are related to the round-trip physical length Z, of path i of reference path 98 and to measuring paths of zero lengths according to the formulae

1 1==11

( 74 ;

In a subsequent series of steps, a superheterodyne signal S_2b is generated by electronic processors 281b and 1084b, electronic processors 281b and 1084b performing analogous operations on heterodyne signals s_lb and s_2b of the fifth preferred embodiment the same as electronic processors 281 and 1084 perform on heterodyne signals s and s₂ of the second preferred embodiment. The superheterodyne signal S_2b is comprised of a carrier signal C_2b of frequency v modulated by an envelope signal M_2b of frequency F where

C ",2_κb = cos 2πvt+ θ 2b (75;

_2b = cos 2πFt + Φ₂, ( 76 )

and

where

The ratio (K/χ) is obtained from Eqs. (81) and (82) as

The reciprocal dispersive power T is subsequently obtained using Eq. (21) . The remainder of the description of the fifth preferred embodiment is the same as that given for corresponding aspects of the second preferred embodiment .

Reference is now made to FIGS. 8a-8b which depict in diagrammatic form the sixth preferred embodiment of the present invention for measuring the reciprocal dispersive power r . The description of the sources of light beams 9 and 10 and of light beams 9 and 10 for the sixth embodiment is the same as that for description of the sources of light beams 9 and 10 and of light beams 9 and 10 given for the fourth preferred embodiment of the present invention. As a consequence, the ratio (K/χj has to be measured in the preferred sixth embodiment in order to achieve the required accuracy in the determination of the reciprocal dispersive power T .

Because of the requirement in the sixth preferred embodiment to measure the ratio (K/χ) , the sixth embodiment is comprised in part of the same apparatus and method as for the third preferred embodiment and of additional means for determination of the ratio (K/χ) .

The additional means for determination of the ratio (K/χ) is the same as the apparatus and method of the third preferred embodiment except for the measurement cell . The measurement cell 90b is the same as the measurement cell 90b of the fourth preferred embodiment. Consequently, a number of elements of the apparatus shown in FIGS. 8a-8b for determination of the ratio (K/χ) perform analogous operations as apparatus for determination of reciprocal dispersive power F of the second preferred embodiment, apart from the suffix "b" when referring to apparatus for determination of the ratio (K/χ) .

The differences in the measurement cell 90b of the sixth preferred embodiment and 90 of the third preferred embodiment lead to modifications of Eqs. (52) such that the magnitude of phase shifts φ_lb and φ_2b are related to the round-trip physical length Z_ of path of reference path 98 and to measuring paths of zero lengths according to the formulae

In a subsequent series of steps, a superheterodyne signal S_2b is generated by electronic processor 1084b, electronic processor 1084b performing analogous operations on heterodyne signals s_lb and ,s_2b of the sixth preferred embodiment the same as electronic processors 1084 perform on heterodyne signals s and s₂ of the third preferred embodiment. The superheterodyne signal S_2b is comprised of a carrier signal C_2b of frequency v modulated by an envelope signal M_2b of frequency F where

C_2b = cos(2πvt + θ_2b) , (87)

M_2b = cos(2πFt + Φ_2b) , (88)

and

where

The ratio (K/χ) is obtained from Eqs . ( 93 ) and ( 94 ) as

The reciprocal dispersive power T is subsequently obtained using Eq. (21) . The remainder of the description of the sixth preferred embodiment is the same as that given for corresponding aspects of the third preferred embodiment .

The illustrations in FIGS, la-le, 2a-2b, 3a-3c, 4a- 4c, 5a-5c, 6a, 7a, and 8a depict six preferred embodiments and two variants thereof of the present invention wherein all of the optical beams for an embodiment are in a single plane. Clearly, modifications using multiple planes can be made to one or more of the six preferred embodiments and two variants thereof without departing from the scope or spirit of the invention.

The six preferred embodiments and two variants thereof of the present invention have measurement cells 90 or 90b wherein the measurement paths for λ_x and λ₂ have the same physical lengths and the reference paths for λ_λ and λ₂ have the same physical lengths. It will be appreciated by those skilled in the art that the measurement paths for λ₁ and λ₂ can have different physical lengths and the reference paths for λ_j^ and λ₂ can have different physical lengths without departing from the scope and spirit of the present invention as defined in the claims. It will be further appreciated by those skilled in the art that the measurement paths for λ₁ and λ₂ can be physically displaced one from the other and the reference paths for λ₁ and λ₂ can be physically displaced one from the other without departing from the scope and spirit of the present invention as defined in the claims. The six preferred embodiments and two variants thereof of the present invention are all configured for use of heterodyne detection. It will be appreciated by those skilled in the art that homodyne detection can be employed in each of the six preferred embodiments and two variants thereof without departing from the scope and spirit of the present invention as defined in the claims. Homodyne receivers would be employed such as disclosed in commonly owned U.S. Pat. No. 5,663,793 entitled "Homodyne Interferometric Receiver and Method" issued Sept. 2, 1997 to P. de Groot . The computation of the reciprocal dispersive power T would be obtained for example in the homodyne version of the first preferred embodiment directly from homodyne phases φ_1H and φ_2H , the homodyne phases φ_1H and φ_2H corresponding to phases φ_x and φ₂ of the first preferred embodiment, and with homodyne versions of Eqs. (39) and (40) . The computation would preferably not involve the generation of a homodyne phase which is an analogue of the superheterodyne phases such as Φ₂.

The second set of preferred embodiments of the present invention and variant thereof measure the ratio {K/χ) and use the measured value of (K/χ) in the computation of the reciprocal dispersive power T . It will be appreciated by those skilled in the art that the measured value of (K/χ) can be used as an error signal in a feedback system such the condition expressed by Eq. (30) is satisfied without departing from the scope and spirit of the present invention as defined in the claims. The measured value of (K/χ) in the feedback system is sent to either source 1 or source 2 and used to control the respective wavelength of either source 1 or source 2, for example by controlling the injection current and/or temperature of a diode laser or the cavity frequency of an external cavity diode laser.

It will be appreciated by those skilled in the art that combinations of the means of the second series of preferred embodiments and variant thereof to measure the ratio (K/χ) and of the means of the first series of preferred embodiments and variant thereof may be used to determine the reciprocal dispersive power T other than the combinations used in the second series of preferred embodiments and variant thereof without departing from the scope or spirit of the invention as defined in the claims.

It will also be appreciated by those skilled in the art that the functions of the measurement cells 90 and 90b of the second set of preferred embodiments and variant thereof can be combined into one measurement cell comprised of only one pair of elements, 91 and 92, without departing from the scope or spirit of the invention as defined in the claims.

It will also be appreciated by those skilled in the art that the differential plane mirror interferometers and the measurement cell may be configured such that the light beams corresponding to two or more differing wavelengths may enter and exit from the same end of the measurement cell in contrast to opposite ends as disclosed in the preferred embodiments and variants thereof without departing from the scope or spirit of the invention as defined in the claims.

Reference is now made to FIG. 9 which is a generalized flowchart depicting via blocks 600-626 various steps for practicing an inventive method for measuring intrinsic optical properties of a gas, particularly its reciprocal dispersive power. While it will be evident that the inventive method depicted in FIG. 9 may be carried out using the inventive apparatus disclosed hereinabove, it will also be apparent to those skilled in the art that it may also be implemented with apparatus other than that disclosed. For example, it will be apparent that one need not use a concentric measurement cell arrangement such as that used in the preferred embodiments, but rather may use more conventional interferometric arrangements so long as the required reference and measurement legs are present. In addition, it will be evident that one may use either a homodyne approach or one in which heterodyning techniques are advantageously employed. As will be further appreciated, many of the steps in FIG. 9 may be carried out via appropriate software run on a general purpose computer or a suitably programmed microprocessor either of which may be used to control other elements of the system as needed. As seen in FIG. 9, one starts in block 600 by providing two or more light beams having different wavelengths which preferably have an approximate harmonic relationship as previously described. In block 602, the light beams are separated into components which in block 604 are preferably altered by either polarization or spatial encoding, or frequency shifting or both.

Otherwise, the light beams may simply be left unaltered and passed through to block 606.

As shown in blocks 622 and 624, the relationship of the wavelengths of the light beams may be monitored and if their wavelengths are not within the limits previously discussed, one can adopt corrective measures to compensate from departures of the relationship of the wavelengths from the desired relationship of the wavelengths. Either the departures can be used to provide feedback to control the wavelengths of the light beam sources or corrections can be established and used in subsequent calculations which are influenced by departures or some combination of both approaches can be implemented.

In parallel or contemporaneously with generating the light beams in block 600, one also provides as indicated in block 626 an interferometer having two legs, one occupied preferably by a vacuum (reference leg) and the other by the gas whose intrinsic optical properties are to be measured. As shown by blocks 606 and 608, the previously generated light beam components are introduced into the interferometer legs so that each component has its phase shifted based on the optical path length it experiences in traveling through the physical length of its assigned leg. Preferably, the physical length for a commonly related pair of components is the same.

After the beams emerge from block 608, they are combined in block 610 to generate a mixed optical signal. These mixed optical signals are then sent to block 612 where by means of photodetection corresponding electrical signals, preferably heterodyne, are generated, and these electrical signals contain information about the relative phases between the light beam components. Preferably the electrical signals are heterodyne signals brought about by previously frequency shifting treatment. In block 614, the electrical signals may be analyzed to extract relative phase information which can then be passed on to blocks 616-620 or, preferably, superheterodyne signals are generated for this purpose. Alternatively, depending on the wavelength relationships between the original beams and the optical paths over which they subsequently traveled, modified heterodyne signals are generated prior to making superheterodyne signals .

In block 616, any phase ambiguities in homodyne, heterodyne, and/or superheterodyne signals are resolved, preferably by means and calculations previously elaborated in connection with describing the preferred apparatus.

In block 618, the intrinsic optical properties including the relative dispersive power are calculated, corrections are applied as previously decided, and output signals are generated for subsequent downstream applications or data format requirements.

Those skilled in the art may make other changes to the inventive apparatus and methods without departing from the scope of the inventive teachings. Therefore, it is intended that the embodiments shown and described be considered as illustrative and not in a limiting sense.

Claims

1. Interferometric apparatus for monitoring select intrinsic optical properties of a gas, said interferometric apparatus comprising: interferometer means; means for generating at least two light beams having different wavelengths; means for introducing at least a portion of each of said light beams into said interferometer means, characterized in that: the interferometer means comprises a reference leg and a measurement leg each of which has predetermined physical path lengths, said reference leg being configured and arranged to be occupied by a predetermined medium and said measurement leg being configured and arranged to be occupied by the gas; the means for introducing are arranged so that each beam portion travels through said predetermined medium and said gas along predetermined paths of substantially the same physical path lengths, said portions of said beams emerging from said interferometer means as exit beams containing information about the respective optical path lengths through said predetermined medium in said reference leg and about the optical path lengths through said gas in said measurement leg; means for combining said exit beams to produce mixed optical signals containing information corresponding to the phase differences between each of said exit beams from corresponding ones of said predetermined paths of said reference and measurement legs; means for detecting said mixed optical signals and generating electrical interference signals containing information corresponding to the refractivities of the gas at said different beam wavelengths; and electronic means for analyzing said interference signals and determining the select intrinsic optical properties of the gas.

2. Apparatus according to claim 1 characterized in that the electronic means is configured to perform at least one of the following: (a) to determine the refractivities of the gas corresponding to each light beam wavelength; (b) to determine the relative refractivities at different beam wavelengths where said relative refractivities are of the form:

1

~x. ^{~ X}

where i and j are integers corresponding to wavelengths and different from one another; (c) to determine the reciprocal dispersive power, T , of the gas; and (d) to provide output signals representative of said select intrinsic optical properties of the gas for subsequent downstream applications.

3. Apparatus according to either of the preceding claims characterized in that said predetermined medium comprises a vacuum.

4. Apparatus according to any one of the preceding claims characterized in that said interferometer means comprises a concentric cell, said concentric cell comprising a closed inner chamber that serves as said reference leg and an outer chamber surrounding said inner chamber that serves as said measurement leg.

5. Apparatus according to claim 4 characterized in that said inner chamber is substantially evacuated so that said predetermined medium is a vacuum and said outer chamber is opened to the ambient surroundings.

6. Apparatus according to claim 4 or 5 characterized in that said concentric cell is in form a right circular cylinder with end sections each of which includes wavelength selective mirrors as part of said interferometer means .

7. Apparatus according to claim 6 characterized in that said means for introducing at least a portion of each of said light beams into said interferometer means is configured and arranged to introduce one of said portions of said light beams corresponding to one wavelength into one of said end sections of said concentric cell and another of said portions of said light beams corresponding to another of said wavelengths into the other one of said end sections of said concentric cell.

8. Apparatus according to any one of the preceding claims characterized in that said means for generating said light beams further includes means for generating orthogonally polarized components of each of said light beams .

9. Apparatus according to any one of the preceding claims characterized by means for separating said light beams into pairs of orthogonally polarized components having a common wavelength.

10 Apparatus according to claim 9 characterized by means for spatially separating the components of said orthogonally polarized pairs of components for subsequent downstream use in said interferometer means .

11. Apparatus according to claim 9 or 10 characterized in that said wavelengths of said light beams have an approximate harmonic relationship to each other, said approximate harmonic relationship being expressed as a sequence of ratios, each ratio being comprised of a ratio of low order non-zero integers.

12. Apparatus according to claim 11 characterized by means for introducing a frequency difference between said orthogonally polarized components of each of said light beams to generate a set of frequency-shifted light beams such that no two beams of said set of frequency-shifted light beams have the same frequency difference.

13. Apparatus according to claim 12 characterized by optical means for dividing each beam of said set of frequency-shifted light beams into one or more beams to provide an expanded set of at least three frequency- shifted light beams from said set of frequency-shifted light beams such that the number of frequency-shifted light beams for each wavelength in said expanded set of frequency-shifted light beams is inversely related in accordance with said approximate harmonic relationship.

14. Apparatus according to claim 13 characterized in that said interferometer means introduces phase shifts between said orthogonally polarized components of each beam of said expanded set of at least three frequency- shifted light beams to produce said exit beams as a set of phase-shifted, frequency-shifted light beams and aligns and directs said beams of said expanded set of at least three frequency-shifted light beams so that the combined measurement and reference paths traversed by each subset of phase-shifted, frequency-shifted light beams are substantially the same where a subset of said phase- shifted, frequency-shifted light beams comprises beams of the phase-shifted, frequency-shifted light beams having the same wavelength, the measurement and reference paths traversed by any two beams of a subset of phase-shifted, frequency-shifted light beams being substantially non- overlapping.

15. Apparatus according to claim 14 characterized in that said means for detecting comprises a photodetector for generating said electrical interference signals as a set of at least three heterodyne signals from the intensities of said set of mixed output beams, said set of at least three heterodyne signals being characterized by oscillations at heterodyne frequencies related to said frequency differences between said orthogonally polarized components of the beams of said expanded set of frequency- shifted light beams, said set of at least three heterodyne signals being further characterized by a set of heterodyne phases, said set of at least three heterodyne signals being comprised of a set of subsets of heterodyne signals, a subset of heterodyne signals being the heterodyne signals generated from a subset of phase-shifted, frequency-shifted light beams.

16. Apparatus according to claim 15 characterized by means for adding said heterodyne signals of each subset of heterodyne signals to produce a set of superheterodyne signals, each superheterodyne signal of said set of superheterodyne signals being comprised of an amplitude- modulated carrier signal having a superheterodyne carrier frequency equal to the average of the heterodyne frequencies of said subset of heterodyne signals added to produce said superheterodyne signal and a superheterodyne carrier phase equal to the average of the heterodyne phases of said subset of heterodyne signals added to produce said superheterodyne signal, said superheterodyne carrier phases being substantially null except for differences due to the refractivity of the gas in the measurement and reference legs of the set of phase- shifted, frequency-shifted light beams.

17. Apparatus according to claim 16 characterized in that said electronic means further includes means for extracting the carrier signals of two of said set of superheterodyne signals and adding the carrier signals to produce a second level superheterodyne signal, said second level superheterodyne signal being comprised of an amplitude-modulated carrier having a superheterodyne modulation frequency comprising the second level superheterodyne modulation frequency equal to half the difference of the superheterodyne carrier frequencies of the superheterodyne signals added to produce the second level superheterodyne signal and a superheterodyne modulation phase comprising the second level superheterodyne modulation phase equal to half the difference of the superheterodyne carrier phases of the superheterodyne signals added to produce the second level superheterodyne signal, the second level superheterodyne modulation phase is substantially null except for differences due to the dispersion of the refractivity of gas in the measurement and reference legs of the set of phase-shifted, frequency-shifted light beams.

18. Apparatus according to claim 17 characterized in that the relative precision of said approximate harmonic relationship expressed as said sequence of ratios is of an order of magnitude less than the dispersive power of the gas times the relative precision required for the measurement of the reciprocal dispersive power of the gas.

19. Apparatus according to any one of claims 11 to 18 characterized by means responsive to said means for monitoring said relative precision of said approximate harmonic relationship for correcting reciprocal dispersive power of the gas as determined by said electronic means for analyzing and determining the reciprocal dispersive power of the gas .

20. Apparatus according to any one of claims 15, 16, 17 and 18 characterized in that said electronic means operates on one of said superheterodyne carrier phases and said second level superheterodyne modulation phase to determine the reciprocal dispersive power of the gas.

21. Apparatus according to any one of claims 11 to 18 characterized in that said interferometer means introduces phase shifts between the orthogonally polarized components of each beam of said set frequency-shifted light beams to produce a set of phase-shifted, frequency- shifted light beams and aligns and directs said beams of said set of frequency-shifted light beams so that said measurement and reference legs traversed by each beam of said set of phase-shifted, frequency-shifted light beams are substantially the same.

22. Apparatus according to any one of claims 11 to 18 and 21 characterized in that said physical path lengths for said measurement leg and said reference leg of any beam of the phase-shifted, frequency-shifted light beams are substantially the same.

23. Apparatus according to claim 22 characterized in that the magnitude of the phase shifts introduced into each beam of said set of frequency-shifted light beams is proportional to the product of a number of passes over said measurement and reference legs, of the physical lengths of the measurement and reference legs, and the differences in refractivity of the gas in said measurement leg and the predetermined medium in said reference leg, the refractivity of the gas in said measurement leg for each beam of phase-shifted, frequency-shifted light beams being different, one with respect to another, the refractivity of the gas being a function of wavelength.

24. Apparatus according to claim 23 characterized in that said combining means is arranged to produce said mixed optical signals as a set of mixed output beams comprised of at least two mixed output beams, each beam of the set of mixed output beams being derived from one, and only one, beam of the set of phase-shifted, frequency- shifted light beams.

25. Apparatus according to claim 24 characterized in that said means for detecting comprises photodetector means for generating said electrical interference signals as a set of heterodyne signals from the intensities of said set of mixed output beams, said set of heterodyne signals being comprised of at least two heterodyne signals and being characterized by oscillations at heterodyne frequencies related to said frequency differences between said orthogonally polarized components of said beams of said set of frequency-shifted light beams, said set of heterodyne signals being further characterized by a set of heterodyne phases, said heterodyne phases being substantially inversely related to said approximate harmonic relationship between said light beam wavelengths except for differences related to the refractivity of the gas in said measurement leg.

26. Apparatus according to claim 25 characterized by means for processing said set of heterodyne signals to generate a set of modified heterodyne signals, said set of modified heterodyne signals being characterized by modified heterodyne frequencies, said modified heterodyne frequencies being harmonically related to said heterodyne frequencies in accordance with said approximate harmonic relationship between said light beam wavelengths and by modified heterodyne phases, said modified heterodyne phases being harmonically related to said heterodyne phases in accordance with said approximate harmonic relationship between the wavelengths, said set of modified heterodyne phases of the set of modified heterodyne signals being substantially equal except for differences due to the refractivity of the gas in said measurement leg and of the predetermined medium in the reference leg of the set of the phase-shifted, frequency-shifted light beams.

27. Apparatus according to claim 26 characterized by electronic means for adding two of said modified heterodyne signals, said pair of modified heterodyne signals, to produce a superheterodyne signal comprised of an amplitude-modulated carrier having a superheterodyne modulation frequency equal to half the difference of said modified heterodyne frequencies of said pair of modified heterodyne signals and a superheterodyne modulation phase equal to half the difference between said modified heterodyne phases of said pair of modified heterodyne signals, said superheterodyne modulation phase being substantially null accept for differences due to the dispersion of the refractivity of gas in the measurement leg and of the predetermined medium in the reference leg of said set of phase-shifted, frequency- shifted light beams.

28. Apparatus according to any one of claims 11 to 27 characterized in that the relative precision of said approximate harmonic relationship expressed as said sequence of ratios is of an order of magnitude less than the dispersive power of the gas times the relative precision required for the measurement of the reciprocal dispersive power of the gas.

29. Apparatus according to any one of claims 21 to 28 characterized in that said interferometer means comprises means for generating multiple passes over said measurement leg and said reference leg for said set of phase-shifted, frequency-shifted light beams, the number of multiple passes for a beam of said set of phase- shifted, frequency-shifted light beams being proportional to the wavelength of the beam of said set of phase- shifted, frequency-shifted light beams, the physical lengths of said measurement leg and said reference leg of any beam of said set of phase-shifted, frequency-shifted light beams being substantially the same.

30. Apparatus according to claim 29 characterized in that the magnitude of the phase shifts introduced into each beam of said set of frequency-shifted light beams is proportional to the product of the number of passes over said measurement and reference legs, of the physical lengths of said measurement and reference legs, and the differences in refractivity of the gas in said measurement leg and said predetermined medium in said reference leg, the refractivity of the gas in said measurement leg for each beam of phase-shifted, frequency-shifted light beams being different, one with respect to another, the refractivity of the gas being a function of wavelength.

31. Apparatus according to claim 30 wherein said means for detecting comprises photodetector means for generating said electrical interference signals as a set of heterodyne signals from the intensities of said set of mixed output beams, said set of heterodyne signals being comprised of at least two heterodyne signals and being characterized by oscillations at heterodyne frequencies related to said frequency differences between said orthogonally polarized components of said beams of said set of frequency-shifted light beams, said set of heterodyne signals being further characterized by a set of heterodyne phases, said heterodyne phases being substantially equal except for differences related to the refractivity of the gas in said measurement leg and the refractivity of the predetermined medium in said reference leg.

32. Apparatus according to claim 31 characterized by electronic means for adding two of said heterodyne signals, said pair of heterodyne signals, to produce a superheterodyne signal comprised of an amplitude-modulated carrier having a superheterodyne modulation frequency equal to half the difference of said heterodyne frequencies of said pair of heterodyne signals and a superheterodyne modulation phase equal to half the difference between said heterodyne phases of said pair of heterodyne signals, said superheterodyne modulation phase being substantially null except for differences due to the dispersion of the refractivity of gas in said measurement leg and of the predetermined medium in said reference leg of the set of phase-shifted, frequency-shifted light beams.

33. Apparatus according to any one of claims 11 to 32 characterized by means for monitoring the relative precision of said approximate harmonic relationship expressed as said sequence of ratios.

34. Apparatus according to claim 33 characterized by means responsive to said means for monitoring said relative precision of said approximate harmonic relationship for providing a feedback signal to control said means for generating said light beams so that said relative precision of said approximate harmonic relationship is of an order of magnitude less than the dispersive power of the gas times the relative precision required for the measurement of the reciprocal dispersive power of the gas.

35. Apparatus according to claim 32 or 33 characterized by means responsive to said means for monitoring said relative precision of said approximate harmonic relationship for correcting said reciprocal dispersive power of the gas in said measurement leg as determined by said electronic means for analyzing and determining said reciprocal dispersive power of the gas in said measurement leg.

36. Apparatus according to any one of the preceding claims characterized in that said electrical interference signals comprise heterodyne signals containing phase information corresponding to the refractivities of the gas and said apparatus further comprises means for adding said heterodyne signals to generate at least one superheterodyne signal containing phase information corresponding to the dispersion of the refractivities of the gas .

37. Apparatus according to claim 36 further including means for resolving phase ambiguities of the said heterodyne and said superheterodyne signals.

38. An interferometric method for monitoring select intrinsic optical properties of a gas, said interferometric method comprising the steps of: providing interferometer means; generating at least two light beams having different wavelengths ; and introducing at least a portion of each of said light beams into said interferometer means, characterized in that : the interferometer means comprises a reference leg and a measurement leg each of which has predetermined physical path lengths, said reference leg being configured and arranged to be occupied by a predetermined medium and said measurement leg being configured and arranged to be occupied by the gas; the introduction of the light beams into the interferometer means is arranged so that each beam portion travels through said predetermined medium and said gas along predetermined paths of substantially the same physical path length, said portions of said beams emerging from said interferometer means as exit beams containing information about the respective optical path lengths through said predetermined medium in said reference leg and about the optical path lengths through said gas in said measurement leg; combining said exit beams to produce mixed optical signals containing information corresponding to the phase differences between each of said exit beams from corresponding ones of predetermined paths of said reference and measurement legs; detecting said mixed optical signals and generating electrical interference signals containing information corresponding to the refractivities of the gas at said different beam wavelengths; and electronically analyzing said interference signals and determining the select intrinsic optical properties of the gas.

39. A method according to claim 66 characterized in that it is carried out using an apparatus according to any one of claims 2 to 37.

40. A method according to claim 66 characterized in that said gas is air.