CN104111120A - Ronchi shearing interferometer based phase extraction method - Google Patents
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Abstract
The invention discloses a Ronchi shearing interferometer based phase extraction method. A Ronchi shearing interferometer structure used in the Ronchi shearing interferometer based phase extraction method comprises a light source, a focusing lens, a scattering optical element, one-dimensional diffraction grating plates, a measured optical system platform, chessboard gratings, a two-dimensional photoelectric sensor and a computer. The one-dimensional diffraction grating plates and the chessboard gratings are arranged on an object plane and an image plane of the measured optical system and the phase is calculated due to collection of 9 interferometric fringe patterns with the shifting interval to be a quarter of pi to eliminate influences to the phase extraction accuracy from multi-level diffraction light in Ronchi shearing interference. The Ronchi shearing interferometer based phase extraction method has the advantages of eliminating the influences of diffraction items in higher levels other than the levels 0, 1 and minus 1, reducing the phase extraction system error in wave aberration detection and improving the wave aberration detection accuracy of the optical system.
Description
Technical Field
The invention relates to a shearing interferometer, in particular to a phase extraction method based on a Langchi shearing interferometer.
Background
The Langqi shearing interference is shearing interference which adopts an extended light source to modulate the spatial coherence of a light field, and has the advantages of no need of an independent ideal reference wave surface, easy realization of common-path interference, no spatial optical path error, high detection precision, high sensitivity and the like. The Langchi shearing interference introduces a phase shift interference technology, a stable phase difference is introduced between a shearing wave surface and a 0-level wave surface by transversely moving a grating, a plurality of interference patterns are obtained by changing the phase shift amount, the phase distribution to be detected is calculated, and the wave aberration of the optical system to be detected is solved. In order to obtain the original wavefront, phase extraction is required to be performed on the interferogram, the phase extraction is an important step of interferometry, and the phase extraction precision directly influences the final detection precision. The commonly used phase extraction method of interferograms includes two types, namely a frequency domain method and a time domain method. The frequency domain method mainly adopts a Fourier transform method, and the time domain method mainly adopts a phase shift interference technology. The Langchi shearing interferometer adopts the phase-shifting interference technology to extract the phase, the phase-shifting interference technology is simple in calculation, high in speed and high in precision, but the error factors influencing the measurement precision are more: on one hand, the air comes from external environments, such as air cleanliness, experiment platform vibration, air disturbance and the like; on the other hand, the optical system is from the inside of the interferometer, such as calibration error and nonlinear error of a piezoelectric crystal of the phase shifter, processing error of the optical system, residual error after installation and adjustment, nonlinear error of a photoelectric sensor and the like. For the langqi shearing interferometer, when the shearing rate is small, the shearing grating interferes with the order 0 except the order ± 1 to obtain the required interference fringes, and the diffraction term of higher order interferes with the light of the order 0 to seriously affect the accuracy of phase extraction. The requirements of the Langchi shearing interferometer on the phase shifter are not high, the grating displacement is in the order of hundreds of nm, so that the phase shift error is small, and under the condition of ensuring a good measurement environment, the mutual influence of grating multi-level diffraction light can be regarded as a main error source of the Langchi shearing interferometer, so that the elimination of the multi-level diffraction error is the premise that the Langchi shearing interferometer is applied to the wave aberration detection of a high-precision optical system.
Joseph Braat et al propose an Improved Langqi shearing interferometer using an extended light source (prior art [1], Joseph Braat, Augusts J.E.Janssen, "Improved Ronchi test with extended source", Journal of Optical Society of America A Vol.16, No.1,1999, pp: 131-. The interferometer extracts the phase by adopting the interference of + 1-order and-1-order diffraction light, but does not consider the influence of higher diffraction order, thereby introducing certain system error and further reducing the measurement precision of displacement; and the method is only suitable for an optical system with a small numerical aperture, and a large amount of measurement errors can be introduced in the detection process of the optical system with a large numerical aperture.
Yugong Zhu et al propose a phase extraction algorithm for two-dimensional grating phase-shifting interferometers (prior art [2], Yugong Zhu, Satoru date, Ayako Sugaya, et al, "" Method for designing phase-calculating calculations for two-dimensional phase shifting interferometry "", Applied Optics,2011,50(18): p.2815-2822). The two-dimensional grating interferometer adopts an object plane grating as an extended light source, the period of the object plane grating is the product of the period of an image plane grating and the imaging magnification of a measured optical system, the object plane grating and the image plane grating are both orthogonal gratings, the algorithm only adopts interference of 0-level light and +/-1 level to extract the phase, and the influence of +/-3-level and +/-5-level diffraction terms of the unwanted grating is eliminated through phase shift. However, in the method, the orthogonal grating is used as an object plane grating, the modulation result of the spatial coherence of the optical field is complex, and a plurality of diffraction terms except for an x axis and a y axis appear, so that a large number of noise terms are introduced, and the detection accuracy is seriously influenced.
Matthieu Visser et al propose an extended light source interferometer for EUV lithography objective wave aberration detection (prior art [3], Matthieu Visser, Martijn K. Dekker, Petra Hegeman, et al, "extended interference optics for at-wavelength test of EUV-optics", engineering Liphographical technologies Iii, Pts 1 and 2,1999.3676: p.253-263). The interferometer adopts a one-dimensional Langqi grating as an object plane grating and an image plane grating, and can reduce the influence on phase extraction caused by interference of + -3-order and 0-order diffracted light by adopting a 5-step phase shift method, but is difficult to eliminate interference of other higher-order diffraction terms and 0-order diffraction terms.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a phase extraction method based on a Langchi shearing interferometer. The method eliminates the influence of the image surface grating multi-order diffraction light on the phase extraction precision in the detection process of the Langchi shearing interferometer, and improves the wave aberration detection accuracy of the detected optical system.
The technical solution of the invention is as follows:
a phase extraction method based on a Langqi shearing interferometer adopts a detection device which is the Langqi shearing interferometer, and the structure of the Langqi shearing interferometer comprises the following steps: the focusing lens, the scattering optical element, the one-dimensional diffraction grating plate, the measured optical system platform, the chessboard grating and the two-dimensional photoelectric sensor are arranged in sequence along the direction of the light beam output by the light source; the one-dimensional diffraction grating plate is arranged on the object plane grating displacement table, the chessboard grating is arranged on the image space grating displacement table, and the two-dimensional photoelectric sensor is connected with a computer;
the scattering optical element is an optical element which enables the illumination light beam to uniformly illuminate in the numerical aperture of the optical system to be detected, such as ground glass and a micro-lens array;
the period P of the one-dimensional diffraction grating plateoAnd the two object plane one-dimensional diffraction gratings with the duty ratio of 50 percent are respectively a first grating with grating lines along the y direction and a second grating with grating lines along the x direction.
The first grating and the second grating are phase gratings or amplitude gratings.
The period P of the object plane one-dimensional diffraction gratingoWith the period P of the image surface chessboard gratingiThe following relationship is satisfied,
Po＝Pi·M
wherein M is the imaging magnification of the optical system to be detected;
the numerical aperture of the optical system to be detected is NA, and the imaging magnification is M: 1;
the chessboard grating has a chessboard layout, light transmission units andthe shading units are squares with the same size, 4 shading units are arranged around each light-transmitting unit, and 4 light-transmitting units are arranged around each shading unit; the period P of the chessboard gratingiEqual to the diagonal length of the square; the diagonal directions of the chessboard grating light transmitting unit and the shading unit are parallel to the directions of an x axis and a y axis; period PiThe size of the optical fiber is determined by the wavelength lambda of the light source, the numerical aperture NA of the measured optical system and the shearing rate s,
the object plane grating displacement platform is a three-dimensional displacement platform which respectively moves the first grating and the second grating into an object space optical path of the optical system to be measured;
the image surface grating displacement platform is a three-dimensional displacement platform which moves the checkerboard grating into an image space light path of the optical system to be detected and drives the image surface checkerboard grating to move step by step along the x direction and the y direction;
the two-dimensional photoelectric sensor is a camera, a CCD (charge coupled device), a CMOS (complementary metal oxide semiconductor) image sensor or a two-dimensional photoelectric detector array, and a detection surface of the two-dimensional photoelectric sensor receives shearing interference fringes generated by the image surface chessboard grating;
the computer is used for controlling the wave aberration detection process, storing the measurement data and processing and analyzing the interference pattern;
the phase extraction method for eliminating the multi-stage diffraction errors of the Langqi shearing interferometer is characterized by comprising the following steps of:
1) placing an optical system to be measured on the optical system platform to be measured, adjusting a Langchi shearing interferometer to enable the light source to be located on the object plane of the optical system to be measured, selecting an image plane chessboard grating with the period equal to the product of the wavelength lambda of the light source divided by twice the numerical aperture NA of the optical system to be measured and the shearing rate s, and then selecting a one-dimensional diffraction grating plate with the period which is the product of the magnification times the period of the image plane grating at the working distance of the optical system to be measured; the one-dimensional diffraction grating plate is arranged on the object plane grating displacement platform and is adjusted to the object plane of the measured optical system, the object plane grating displacement platform is moved, and the first grating on the one-dimensional diffraction grating plate is moved into the object space view field position of the measured optical system; the chessboard grating is arranged on the image surface grating displacement platform and is adjusted to the image surface of the optical system to be measured, the image surface grating displacement platform is moved, and the chessboard grating is moved into an image space light path of the optical system to be measured;
2) adjusting an object plane grating displacement platform and an image plane grating displacement platform to align the first grating and the checkerboard grating, and adjusting the position of a two-dimensional photoelectric sensor to obtain an interference pattern with clear fringes on a detection surface;
3) moving the chessboard grating along the x direction by the image surface grating displacement table for 9 times, moving for 1/8 grating periods each time, and acquiring a shearing interference pattern I by the two-dimensional photoelectric sensor after each movementxkWherein k is 1,2,3, 9; according to the 9 interference fringe patterns, the phase is calculated according to the following formula:
wherein,representing gradient information of the measured wave front in the x direction as the phase of the measured wave front in the x direction;
4) moving the object plane grating displacement platform, moving a second grating on the one-dimensional diffraction grating plate into the position of an object space view field of the measured optical system, readjusting the object plane grating displacement platform and the image plane grating displacement platform, and aligning the second grating and the chessboard grating;
5) the image surface grating displacement table moves along the y directionThe chessboard grating is moved for 9 times, the grating period is 1/8 grating periods each time, and the two-dimensional photoelectric sensor collects a shearing interference pattern I after each movementykWherein k is 1,2,3, 9; according to the 9 interference fringe patterns, the phase is calculated according to the following formula:
wherein,representing gradient information of the measured wave front in the y direction as the phase of the measured wave front in the y direction;
6) unwrapping the phase extraction result to respectively obtain differential wavefront delta W in the x direction and the y directionxAnd Δ WyShear interference wavefront reconstruction is performed to obtain the wavefront of the measured optical system (see prior art 4, Harbers, G., P.J.Kunst, and G.W.R.Leibbrandt, Analysis of shear imaging interferograms by use of Zernike polymonals, applied Optics,1996.35(31): p.6162-6172).
Compared with the prior art, the invention has the following advantages:
1. compared with the prior art [1], the method considers the influence of higher diffraction orders, improves the measurement precision of the wave aberration of the optical system, and can realize the precise measurement of the wave aberration of the large-numerical-aperture optical system.
2. Compared with the prior art [2], the invention adopts the object plane one-dimensional Langqi grating to modulate the spatial coherence of the optical field, does not have the problem that other noise terms are overlapped with interference fringes of 0 level and +/-1 level, and has less error terms and high precision.
3. Compared with the prior art [3], the invention can better eliminate higher-order diffraction terms except 0 order and +/-1 order, and can better eliminate the influence on the phase extraction precision caused by the interference of multi-order diffraction light in the Langchi shearing interference.
Drawings
FIG. 1 is a schematic diagram of a Langchi shearing interferometer apparatus used in the present invention;
FIG. 2 is a schematic diagram of an object plane one-dimensional diffraction grating;
fig. 3(a) is a schematic diagram of the image plane checkerboard grating, and fig. 3(b) is a diffraction intensity distribution diagram of the image plane checkerboard grating.
Fig. 4(a) is a diagram of diffraction orders that can interfere after modulating the spatial coherence of the light field, and fig. 4(b) is a diagram of shearing interference.
Detailed Description
In order to make the contents, implementation processes and advantages of the present invention clearer, the following description of the present invention is made with reference to the following examples and accompanying drawings, but the scope of the present invention should not be limited by the examples.
A schematic diagram 1 of a langqi shearing interferometer apparatus used in the present invention is shown. As can be seen from the figure, the detection device adopted by the invention is a Langchi shearing interferometer, and the structure of the Langchi shearing interferometer comprises: the focusing lens 2, the scattering optical element 3, the one-dimensional diffraction grating plate 4, the measured optical system platform, the chessboard grating 7 and the two-dimensional photoelectric sensor 9 are arranged in sequence along the direction of the light beam output by the light source 1; the one-dimensional diffraction grating 4 is arranged on an object plane grating displacement table 5, the chessboard grating 7 is arranged on an image space grating displacement table 8, and the two-dimensional photoelectric sensor 9 is connected with a computer 10;
the scattering optical element 3 is an optical element which enables the illumination light beam to be uniformly illuminated in the numerical aperture of the optical system 6 to be detected, such as ground glass, a micro lens array and the like;
the one-dimensional diffraction grating 4 (see FIG. 2) has a period PoAnd two object plane one-dimensional diffraction gratings with duty ratio of 50%, respectivelyA first grating 401 with grating lines in the y-direction and a second grating 402 with grating lines in the x-direction.
The first grating 401 and the second grating 402 are phase gratings or amplitude gratings.
The period P of the object plane one-dimensional diffraction gratingoWith the period P of said image surface chessboard grating 7iThe following relationship is satisfied,
Po＝Pi·M
wherein M is the imaging magnification of the optical system 6 under test.
The numerical aperture of the optical system 6 to be detected is NA, and the imaging magnification is M: 1;
the chessboard grating 7 is in a chessboard layout, the light transmitting units and the shading units are squares with the same size, 4 shading units are arranged around each light transmitting unit, and 4 light transmitting units are arranged around each shading unit. For an amplitude-type checkerboard grating, the transmission function is
Wherein, PiIs the period of the grating in the x and y directions, and N is the number of grating periods.
The diffraction intensity function of the chessboard grating 7 in the far field is
I(ξ,η)＝I0·|[sinc(ξ,η)]{1+exp[-j2π(ξ,η)]}×comb(2ξ,2η)*sinc(2Nξ,2Nη)|2
Wherein I (xi, eta) is a far field diffraction light intensity function, I0The intensity of 0 th order diffracted light. In the ideal case, the checkerboard grating has only 0 and odd diffraction orders, and the light energy is mainly concentrated on the 0 and odd diffraction ordersOn the order of ± 1, each odd diffraction order interferes with the 0 order in the far field. Under the action of the chessboard grating, the measured wave surface generates a shear wave surface forming an angle of 45 degrees with the x-axis direction in an overlapping area, and the period of the equivalent grating in the shear direction is equal to the side length of each unit structure square of the chessboard gratingAnd (4) doubling.
The checkerboard grating 701 is placed in a state that the diagonal directions of the light transmitting unit and the light shielding unit are parallel to the x-axis direction and the y-axis direction (see fig. 3(a)), and is a lambertian grating when viewed along the x-direction and the y-direction, and the duty ratio is 50%.
Example (b):
in the Langchi shearing interferometer, the wavelength of the output light of the light source 1 is 193nm, the numerical aperture of the measured optical system 6 is 0.75, the imaging magnification is 4 x, the shearing ratio is set to be 1/30, the period Pi of the chessboard grating 702 is selected to be 3.86 μm, and the period P of the object plane one-dimensional diffraction grating is selected to be PoIt was 15.44 μm.
The object plane grating displacement platform 5 is a three-dimensional displacement platform which respectively moves the first grating 401 and the second grating 402 into an object space optical path of the measured optical system 6;
the image surface grating displacement table 8 is a three-dimensional displacement table which moves the checkerboard grating 701 into an image side light path of the optical system 6 to be detected and drives the checkerboard grating 701 to move in a 1/8 grating period stepping mode along the x direction and the y direction;
the two-dimensional photoelectric sensor 9 is a camera, a CCD, a CMOS image sensor, or a two-dimensional photoelectric detector array, and receives the shearing interference fringes generated by the image surface chessboard grating 701 on the detection surface;
the computer 10 is used for controlling the wave aberration detection process, storing the measurement data, and processing and analyzing the interferogram.
The phase extraction method for eliminating the multi-stage diffraction errors of the Langqi shearing interferometer is characterized by comprising the following steps of:
1) placing an optical system 6 to be measured on the optical system platform to be measured, adjusting an Langqi shearing interferometer to enable the light source 1 to be positioned on the object plane of the optical system 6 to be measured, selecting an image plane chessboard grating 7 with the period equal to the product of the wavelength lambda of the light source 1 divided by twice the numerical aperture NA of the optical system 6 to be measured and the shear rate s, and selecting a one-dimensional diffraction grating 4 with the period equal to the product of the magnification factor at the working distance of the optical system 6 to be measured and the period of the image plane grating 7; the one-dimensional diffraction grating 4 is arranged on the object plane grating displacement platform 5 and is adjusted to the object plane of the measured optical system 6, the object plane grating displacement platform 5 is moved, and the first grating 401 on the one-dimensional diffraction grating 4 is moved into the object space view field position of the measured optical system 6; the chessboard grating 7 is arranged on the image surface grating displacement platform 8 and is adjusted to the image surface of the measured optical system 6, the image surface grating displacement platform 8 is moved, and the chessboard grating 7 is moved into the image side light path of the measured optical system 6;
2) adjusting an object plane grating displacement platform 5 and an image plane grating displacement platform 8 to align the first grating 401 and the checkerboard grating 701, and adjusting the position of a two-dimensional photoelectric sensor 9 to obtain a clear fringe interference pattern on a detection plane;
3) the image surface grating displacement table 8 moves the chessboard grating 701 along the x direction for 9 times, the grating period is 1/8 times of movement, and the two-dimensional photoelectric sensor 9 collects a shearing interference image I after each time of movementxkWherein k is 1,2,3, 9; according to the 9 interference fringe patterns, the phase is calculated according to the following formula:
wherein,representing the gradient information of the measured wave front in the x direction for the phase of the measured wave front in the x direction；
4) Moving the object plane grating displacement table 5, moving the second grating 402 on the one-dimensional diffraction grating 4 into the object space view field position of the measured optical system 6, readjusting the object plane grating displacement table 5 and the image plane grating displacement platform 8, and aligning the second grating 402 and the checkerboard grating 701;
5) the image surface grating displacement table 8 moves the chessboard grating 701 along the y direction for 9 times, the grating period is 1/8 grating periods each time, and the two-dimensional photoelectric sensor 9 collects a shearing interference image I after each movementykWherein k is 1,2,3, 9; according to the 9 interference fringe patterns, the phase is calculated according to the following formula:
wherein,representing gradient information of the measured wave front in the y direction as the phase of the measured wave front in the y direction;
6) unwrapping the phase extraction result to respectively obtain differential wavefront delta W in the x direction and the y directionxAnd Δ WyAnd performing shearing interference wavefront reconstruction to obtain the wavefront of the measured optical system 6.
The specific theory for eliminating the multi-order diffraction error of the Langqi shearing interferometer by the phase extraction method is discussed as follows:
according to the Langqi shearing interferometer principle, when the modulation of the spatial coherence by the one-dimensional diffraction grating of the object plane is not considered, the chessboard grating 701 is adopted, and the light intensity on the detection plane is
Wherein, a0As background light intensity, aijIs the contrast of interference fringes of the ith order diffracted by the grating in the x-axis direction and the jth order diffracted by the grating in the y-axis direction,is the phase difference corresponding to the two diffraction orders; i is the 0 th, m or m 'th diffraction order in the x-axis direction, j is the 0 th, n or n' th diffraction order in the y-axis direction, and k, k ', l' are all non-zero integers.
According to the 'Van Seattle-Zernike theorem', the spatial coherence of the light field is equal to the Fourier transform of the light source intensity distribution, so that the spatial coherence is modulated by the one-dimensional diffraction grating of the object plane, and when the one-dimensional diffraction grating of the object plane is the first grating 401 with the grating lines along the y direction and the duty ratio of 50%, the spatial coherence in the x direction is the corresponding value of the Fourier transform of the first grating 401; while the light field in the y-direction is still incoherent, so that no interference occurs in the y-direction (see fig. 4), the expression for the light intensity is rewritten to
Wherein, a0As background light intensity, am0Is the contrast of the interference fringes of the m-th order diffracted by the grating in the x direction and 0 th order,is the phase difference between the m-th diffraction order and 0-th diffraction order of the grating in the x direction. Wherein the phase differences are respectively
Wherein W (x, y) is a wavefront function, λ is a wavelength, and S is a shear volume. The expression for the intensity of light is rewritten as when phase shift is considered
Where δ is the phase shift amount of the 1 st order diffraction caused by each step of the movement of the checkerboard grating 701 in the shearing direction in the phase-shift interference, then m δ represents the phase shift amount of the m-th order diffraction when the grating is moved in the shearing direction,is the phase difference between the m-th diffraction order in the x-direction and 0-th diffraction order. Because the intensity of the diffraction light above the 5 th order diffracted by the chessboard grating is less than 1% of the light of the 0 th order, the measurement result is basically not influenced, and therefore, the influence of the diffraction light above the 5 th order can be ignored. The expression for the light intensity can be written as
Wherein, k is 1,2,3, N, which represents the phase shift of the k step, and N is the total phase shift step number;is the phase difference between the m-th diffraction order in the x direction and 0, where m is ± 1, ± 3, ± 5; deltakIs the amount of phase shift.
In order to suppress the influence of grating multi-order diffracted light on the phase extraction precision, the phase shift interval is collectedThe interferogram of (i.e. each step phase shift amount is respectively)Where j is 0,1,2.. 8. The light intensity of each step is
From equations (6) to (14), it is possible to obtain:
since it is satisfied at a small shearing amount when the phase shift is not considered
(16)
And coefficient a1And a-1Equal to the spatial coherence of the optical field, and has a for the Langqi shearing interferometer1＝a-1The phase of the measured optical system 6 along the x direction
In order to recover the two-dimensional original wavefront of the measured optical system 6, the one-dimensional diffraction grating of the object plane is switched to the second grating 402 with the grating lines along the x direction, and the phase of the measured optical system 6 along the y direction is obtained in the same wayAndrepresenting gradient information of the measured wavefront in the x-direction and the y-direction, respectively. Unwrapping the phase extraction result to obtain the x direction and the y direction respectivelyA differential wave front Δ W of directionxAnd Δ WyAnd performing shearing interference wavefront reconstruction to obtain the wavefront of the measured optical system 6.
The invention is applied to the Langchi shearing interferometer to detect the wave aberration of the measured optical system, can effectively eliminate the influence of grating multi-level diffraction light interference on the phase extraction precision, and improves the wave aberration detection accuracy of the measured optical system.
It will be appreciated by those skilled in the art that the above embodiments are illustrative only and not intended to be limiting, and that changes and modifications may be made to the above embodiments without departing from the true spirit and scope of the invention, which is defined by the appended claims.
Claims (1)
1. A phase extraction method based on a Langqi shearing interferometer adopts a detection device which is the Langqi shearing interferometer, and the structure of the Langqi shearing interferometer comprises the following steps: a focusing lens (2), a scattering optical element (3), a one-dimensional diffraction grating plate (4), a measured optical system platform, a chessboard grating (7) and a two-dimensional photoelectric sensor (9) are arranged in sequence along the direction of a light beam output by a light source (1); the one-dimensional diffraction grating plate (4) is arranged on the object plane grating displacement table (5), the chessboard grating (7) is arranged on the image space grating displacement table (8), and the two-dimensional photoelectric sensor (9) is connected with the computer (10); the method is characterized by comprising the following steps:
placing an optical system (6) to be measured on a platform of the optical system to be measured, adjusting a Langqi shearing interferometer to enable the light source (1) to be located on an object plane of the optical system (6) to be measured, selecting an image plane chessboard grating (7) with a period equal to the wavelength lambda of the light source (1) divided by the product of twice the numerical aperture NA of the optical system (6) to be measured and the shear rate s, and selecting a one-dimensional diffraction grating plate (4) with a period which is the product of the magnification times of the working distance of the optical system (6) to be measured and the period of the image plane grating (7); the one-dimensional diffraction grating plate (4) is arranged on the object plane grating displacement table (5) and is adjusted to the object plane of the measured optical system (6), the object plane grating displacement table (5) is moved, and the first grating (401) on the one-dimensional diffraction grating plate (4) is moved into the object space view field position of the measured optical system (6); the chessboard grating (7) is arranged on the image surface grating displacement platform (8) and is adjusted to the image surface of the optical system (6) to be measured, the image surface grating displacement platform (8) is moved, and the chessboard grating (7) is moved into the image side light path of the optical system (6) to be measured;
adjusting an object plane grating displacement platform (5) and an image plane grating displacement platform (8), aligning the first grating (401) and the checkerboard grating (701), and adjusting the position of a two-dimensional photoelectric sensor (9) to obtain a clear fringe interference pattern on a detection plane;
thirdly, the chessboard grating (701) is moved by the image surface grating displacement platform (8) along the x direction for 9 times, the grating period is 1/8 times of movement each time, and the two-dimensional photoelectric sensor (9) collects a shearing interference pattern I after each time of movementxkWherein k is 1,2,3, 9; according to the 9 interference fringe patterns, the phase is calculated according to the following formula:
wherein,representing gradient information of the measured wave front in the x direction as the phase of the measured wave front in the x direction;
moving the object plane grating displacement table (5), moving a second grating (402) on the one-dimensional diffraction grating plate (4) into the position of an object space view field of the measured optical system (6), readjusting the object plane grating displacement table (5) and the image plane grating displacement table (8), and aligning the second grating (402) and the checkerboard grating (701);
fifthly, moving the chessboard grating (701) by the image surface grating displacement platform (8) along the y direction for 9 times, moving the grating for 1/8 grating periods each time, and collecting a shearing interference pattern I by the two-dimensional photoelectric sensor (9) after each movementykWherein k is 1,2,3, 9; according to the 9 interference fringe patterns, the phase is calculated according to the following formula:
wherein,representing gradient information of the measured wave front in the y direction as the phase of the measured wave front in the y direction;
sixthly, unwrapping the phase extraction result to respectively obtain the differential wavefront delta W in the x direction and the y directionxAnd Δ WyAnd performing shearing interference wavefront reconstruction to obtain the wavefront of the detected optical system (6).
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| CN110608677A (en) * | 2019-10-22 | 2019-12-24 | 西安工业大学 | Three-dimensional displacement measurement method based on circular grating radial shearing interferometer |
| CN110608677B (en) * | 2019-10-22 | 2021-04-06 | 西安工业大学 | Three-dimensional displacement measurement method based on circular grating radial shearing interferometer |
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| WO2022083735A1 (en) * | 2020-10-23 | 2022-04-28 | 深圳晶源信息技术有限公司东方晶源微电子科技（北京）有限公司深圳分公司 | Method for calculating ronchi shear interference image in photolithography projection objective |
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