Classifications

• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B23/00—Telescopes, e.g. binoculars; Periscopes; Instruments for viewing the inside of hollow bodies; Viewfinders; Optical aiming or sighting devices
  • G02B23/24—Instruments or systems for viewing the inside of hollow bodies, e.g. fibrescopes
  • G02B23/2407—Optical details
  • G02B23/2423—Optical details of the distal end
  • G02B23/243—Objectives for endoscopes
• • G—PHYSICS
  • G02—OPTICS
  • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
  • G02B23/00—Telescopes, e.g. binoculars; Periscopes; Instruments for viewing the inside of hollow bodies; Viewfinders; Optical aiming or sighting devices
  • G02B23/24—Instruments or systems for viewing the inside of hollow bodies, e.g. fibrescopes
  • G02B23/2407—Optical details
  • G02B23/2446—Optical details of the image relay

Definitions

• the present invention relates generally to optical lens systems, and more particularly, to lens systems suitable for endoscopes and the like.
• an image transfer lens which reimages the first image onto the next field lens.
• the pupil and image transfer steps are repeated as often as is needed to obtain a desired tube length, and (4) a focusing lens which presents the final image to a sensor, such as a person's eye, a CCD camera, or a photographic film.
• a sensor such as a person's eye, a CCD camera, or a photographic film.
• One aspect of the present invention is an endoscope having a reduced number of elements compared with conventional endoscopes.
• the elements may advantageously have relatively long radii of curvature which facilitates their mass production.
• the elements are not necessarily of a meniscus shape.
• Some of the exemplary embodiments have an outside entrance pupil location (i.e., the pupil is located between the embodiment and the object to be imaged), so that they are suitable for a tapered probe (e.g., for concealment) or for accommodating a li ⁇ e-of-sight deviating prism on the image side of the pupil location.
• Other embodiments include or may be combined with a field expander, in which the pupil location may be located so as to accommodate a li ⁇ e-of-sight deviating prism.
• many of the embodiments disclosed herein are highly insensitive to tilt and decentration of their components.
• the foregoing advantages are achieved in a lens system characterized by an integrated design in which the locations of the components may not be dictated by the optical functions of the objective and the relays.
• the aberration correction may be advantageously distributed over two or more groups, thereby providing relief to the first group (which conventionally has the highest optical power and is in need of most of the aberration correction) and permitting the radii of curvature of the optical components to be reduced, resulting in a smaller overall power requirement (i.e., the sum of the absolute values of the powers of the optical components is smaller).
• departure from symmetry of the relay system is employed to further the integration.
• a plano-convex lens or a double convex lens can be corrected for astigmatism since such a lens is displaced from the stop location. In this way, optical surfaces of very short radii of curvature may not be needed to correct the astigmatism of the total optical system.
• the spherical aberration of convex-piano lenses used in several of the embodiments herein is greatly reduced and may approach the minimum possible for a single element.
• the chromatic aberrations may be greatly reduced compared to many conventional systems. For example, chromatic aberrations may be reduced by a factor of 2 to 4 without the presence of a chromatic aberration reducing element. Thus, in some embodiments further color correction may not be necessary.
• Other embodiments are disclosed herein which include several transfers and can be basically fully color corrected by the use of a single color correcting element of modest optical power.
• Optical distortion of many kinds can be corrected at more convenient and effective places, resulting in a single integrated system of greatly reduced complexity.
• Additional optics like a close-up lens, a field expander, a field flattening lens, or additional relay groups, may be employed with several of the inventive embodiments disclosed herein.
• Yet another embodiment of the present invention is a color corrected optical endoscope system including an optical system having a plurality of optical elements, comprising an objective element and a first relay system having a first number of curved surfaces, the first relay system including an optical interface having a curvature that provides substantially all of the color correction for the endoscope system, the objective element and the first relay system optically aligned to transfer an image from an input plane of the objective element to an output plane of the endoscope system, wherein the plurality of optical elements are suitable for use with at least a portion of the spectrum extending from the FN to the CN spectral line.
• Another embodiment of the present invention is a color corrected optical endoscope including a plurality of optical elements, comprising an objective and a relay system, the relay system having at least one optical interface providing color correction for the endoscope, the objective providing substantially no color correction, the objective and the relay system aligned along a common optical axis, and the plurality of optical elements being suitable for use with at least a portion of the spectrum extending from the FN to the CN spectral line.
• Still another embodiment of the present invention is a color corrected endoscopic imaging system including a plurality of optical elements, comprising an objective for imaging an object onto a focal plane and at least one relay that is optically aligned with the objective along a common optical axis, the relay including curved surfaces, at least one curved interface providing color correction for the endoscopic imaging system, wherein the number of the curved surfaces in the relay is not greater than 5.
• Yet another embodiment of the present invention is a color corrected imaging system for use with an endoscope and including a plurality of optical elements, comprising an objective having an optical axis and at least one relay aligned with the objective along the optical axis, the objective having not more than 3 curved surfaces, at least one of the optical elements providing color correction for the imaging system.
• Another embodiment of the present invention is a color corrected endoscope including a plurality of optical elements, the endoscope comprising an objective system and at least three relay systems optically aligned with the objective system, wherein the objective system and three of the at least three relay systems together include not more than 13 curved surfaces.
• Another embodiment of the present invention is a color corrected endoscope including a plurality of optical elements, the endoscope comprising an objective system and at least two relay systems including optical elements, the at least two relay systems optically aligned with the objective system, wherein the objective system and two of the at least two relay systems together include not more than 10 curved surfaces, the optical elements suitable for use with at least a portion of the spectrum extending from the FN to the CN spectral line, and at least one of the optical elements providing color correction to the endoscope.
• Another embodiment of the present invention is a color corrected endoscope, including a plurality of lens elements, comprising an objective and at least one relay, wherein one of the at least one relay includes not more than 3 lens elements, the objective and the at least one relay aligned to transfer an image from an input plane of the objective to an output plane of the endoscope, at least one of the lens elements providing color correction to the endoscope.
• Another embodiment of the present invention is a color corrected endoscopic system including a plurality of optical elements, comprising an objective group and at least two relay groups aligned with the objective group along an optical axis, one of the relay groups including no optical elements of negative optical power, and another of the relay groups providing color correction to the endoscopic system.
• Another embodiment of the present invention is a color corrected endoscopic system including a plurality of optical elements, comprising an objective and at least one relay group aligned with the objective along an optical axis, the objective and the at least one relay group together including not more than 2 elements of negative optical power, at least one of the plurality of optical elements providing color correction for the endoscopic system.
• Another embodiment of the present invention is a color corrected optical endoscope including a plurality of optical elements, comprising means for forming a first image of an object and means for relaying the first image and forming a second image, wherein the relaying means includes means for correcting chromatic aberrations, whereas the means for forming a first image includes substantially no means for correcting chromatic aberrations, the means for forming a first image and the relaying means being aligned along a common optical axis, the plurality of optical elements being suitable for use with at least a portion of the spectrum extending from the FN to the CN spectral line.
• Another embodiment of the present invention is an optical system including a plurality of optical elements, comprising an objective a color-correcting relay providing substantially all color correction for the system using at least one curved interface providing color correction and a non-color correcting relay, wherein the non-color correcting relay, the objective, and the color-correcting relay are aligned along a common optical axis and optically aligned to transfer an image from an input plane of the objective to an output plane of the optical system, in which each of the plurality of optical elements is uniformly refractive and suitable for use with at least a portion of the spectrum extending from the FN to the CN spectral line.
• Another embodiment of the present invention is a method of imaging an object, comprising forming a first image of the object with a non-color correcting objective system providing at least a first and a second relay system, aligning the objective system and the first and second relay systems along a common optical axis, receiving the first image from the objective system with the first relay system to form a second image, transferring the second image from the first relay system using the second relay system to form a third image of the object and correcting chromatic aberrations with one of the relay systems by using at least one optical interface, wherein the objective system and the plurality of relay systems are suitable for use with at least a portion of the spectrum extending from the FN to the CN spectral line.
• Another embodiment of the present invention is a method of imaging an object, comprising providing an objective for forming a first image of the object, providing at least three relay systems optically aligned with the objective system, wherein the objective and the relay systems together include not more than 13 curved surfaces, the objective and the relay systems being suitable for use with at least a portion of the spectrum extending from the FN to the CN spectral line, receiving the first image with one of the relay systems, forming an output image with another of the relay systems, in which the output image can be received by a viewer and providing color correction to the output image with at least one curved interface.
• Another embodiment of the present invention is a method of designing an integrated aberration corrected endoscope, comprising providing a plurality of optical groups, wherein the groups are aligned along a common optical axis and each of the groups produces a respective image at a respective focal plane, the groups including an objective and at least one relay and providing a first one of the groups with more aberration correction than the first group requires to be aberration corrected, and providing a second one of the groups with less aberration correction than the second group requires to be aberration corrected, wherein the aberration correction of the first group compensates for lack of aberration correction in the second group to produce an aberration corrected endoscope.
• Another embodiment of the present invention is an integrated aberration corrected endoscope, comprising a first optical group, the first group having more aberration correction than the first group requires to be aberration corrected and at least a second optical group, the second group having less aberration correction than the second group requires to be aberration corrected, in which the aberration correction of the first group compensates for lack of aberration correction in the second group to produce the integrated aberration corrected endoscope, wherein the groups are aligned along a common optical axis and each of the groups produces a respective image at a respective focal plane, the groups including an objective and at least one relay.
• Another embodiment of the present invention is an optical system for transferring an image from a first plane to a second plane via an intermediate plane, comprising an objective comprising at least one optical element disposed between the first plane and the intermediate plane for forming a relatively uncorrected image at the intermediate plane and a relay comprising at least one optical element disposed between the intermediate plane and the second plane for forming a relatively more corrected image at the second plane.
• Figure 1 is an optical schematic view of an endoscope constructed in accordance with a conventional layout in which each component has a single function in the system.
• Figure 2 is an optical schematic view of a first embodiment of the present invention in which the entrance pupil is located outside the first group by a relatively small distance.
• Figure 3 is an optical schematic view of a second embodiment of the present invention in which full advantage of the power reduction and aberration reduction is taken by locating the entrance pupil outside the first group by a large distance.
• Figure 4 is an optical schematic view of a third embodiment of the present invention which incorporates a rod- shaped element.
• Figure 5 is an optical schematic view of a fourth embodiment of the present invention which is made of all glass elements and which incorporates a single negative element that provides chromatic aberration correction for the illustrated system.
• Figure 6 is an optical schematic view of a fifth embodiment of the present invention which is a simple glass and plastic system that basically fully corrects for chromatic aberrations.
• Figure 7 is an optical schematic view of a sixth embodiment of the present invention in which the three basic groups have been augmented with an element near the focal plane of the first group.
• Figure 8 is an optical schematic view of a seventh embodiment of the present invention in which a fourth group (IV) of low optical power has been added near the focal plane of the first group (F), the fourth group containing a single negative element for correcting the chromatic aberrations.
• Figure 9 is an optical schematic view of an eighth embodiment of the present invention which incorporates a meniscus shaped element.
• Figure 10 is an optical schematic view of a ninth embodiment of the present invention which incorporates a second image relay and basically fully corrects for chromatic aberrations with a single element of negative optical power.
• Figure 11 is an optical schematic view of a tenth embodiment of the present invention which incorporates a third image relay while still basically fully correcting for chromatic aberrations using only one element of negative optical power.
• Figures 12A-12C provide an optical schematic view of an eleventh embodiment of the present invention which includes three image relays, with the color correction basically being performed by a single element in the first optical relay.
• Figure 12D is an enlarged view of the objective of Figure 12A.
• Figures 13A-13C provide an optical schematic view of a twelfth embodiment of the present invention which includes three image relays, with the color correction basically being performed by a single element in the second optical relay.
• Figure 13D is an enlarged view of the objective of Figure 13A.
• Figures 14A-14C provide an optical schematic view of a thirteenth embodiment of the present invention which includes three image relays, with the color correction basically being performed by a single element in the third optical relay.
• Figure 14D is an enlarged view of the objective of Figure 14A.
• Figures 15A-15C provide an optical schematic view of a fourteenth embodiment of the present invention which includes three image relays but has only nine optical elements with optical power.
• Figure 15D is an enlarged view of the objective of Figure 15A.
• Figures 16A-16C provide an optical schematic view of a fifteenth embodiment of the present invention which includes three image relays that comprise plastic elements.
• Figure 16D is an enlarged view of the objective of Figure 16A.
• Figures 17A-17C provide an optical schematic view of a sixteenth embodiment of the present invention which includes three image relays that comprise glass molded elements.
• Figure 17D is an enlarged view of the objective of Figure 17A.
• Figures 18A-18C provide an optical schematic view of a seventeenth embodiment of the present invention which includes three image relays, in which plano-plano interfaces divide the image relays into segments so that the endoscope is less susceptible to breakage when bent.
• Figure 18D is an enlarged view of the objective of Figure 18A.
• Embodiments 1-11 corresponding to Figures 2-12 described below, are standardized such that the objective and the first relay have a length of about 100 millimeters, and most have a nominal magnification of unity. In this way, the performance of Embodiments 1-11 can be conveniently compared.
• Embodiments with other magnifications, fields of view, numerical apertures, and with additional relays are presented in order to show that the general concept of the invention is effective over a wide range of applications.
• the embodiments described herein (1-18) use conventional, non- GRIN (gradient refractive index) lens elements, and thus each lens has a uniform refractive index, though other lens types may be used as well.
• GRIN gradient refractive index
• the object and image planes are indicated by an 'Obj' and 'lm,' respectively.
• Intermediate focal planes and pupil planes are indicated at various points in the optical train by an 'F' and a 'P in ,', respectively.
• Optical system features of the object plane ("surface 0" in Figures 1-18), the first pupil plane (or stop, corresponding to "surface 1" in Figures 1-11 and “surface 4" in Figures 12-18), lens surfaces, and the final image plane are numbered sequentially. Note that in Figures 1-11, the entrance pupil P ent and the stop are coincident, though in other embodiments, they may be displaced from one another. The propagation of marginal and chief rays is indicated throughout the figures with hashed lines.
• Tables 1-18 present the construction parameters of the embodiments illustrated in Figures 1-18.
• Table 1 refers to the system shown in Figure 1
• Table 2 to the system of Figure 2, and so on for the other tables and figures.
• the first column indicates the surface number (“SURF”) shown in the figures
• the second column indicates the radius of curvature
• RD axial separations
• TH axial separations
• TH optical component materials
• DIAMETER diameters of the respective components, object, pupil, or image.
• CC conic constant
• Figure 1 is an optical schematic of an endoscope system which is constructed in accordance with the classical, conventional, concept of separation of the various functions.
• Group I is an objective which contains the entrance pupil plane (P ent ), while Group II represents a field lens which is located at the focal plane of the objective (F).
• Group III represents a transfer lens which transfers the image formed by the objective onto a subsequent focal plane (here, the image plane, Im). All groups are located at pupil planes or focal planes. It is apparent from Figure 1, as well as from the radii of curvature data of Table 20, that the distribution of optical power is very uneven.
• the value of the sum of the absolute values of the curvatures which is a measure of difficulty of fabrication, is 1.62/mm (see column 5 of Table 20) for this prior art embodiment, which is uncorrected for chromatic aberrations. If this embodiment were corrected for chromatic aberrations, the sum of the absolute values of the curvatures would more than double. This would be disadvantageous, since, in general, the greater the sum of the absolute values of the curvatures, the higher the manufacturing costs.
• the pertinent performance data are listed in Table 20, and the construction parameters are listed in Table 1.
• Figure 2 illustrates one embodiment of the present invention, which is an endoscope using a very small number of components.
• This design shows that by allowing the locations of the pupils and the intermediate image to depart modestly from their classical positions (cf. Figure 1), the sum of the absolute values of the curvatures (SC) can be reduced to 1.15
• a cone-shaped tip can be included in many applications, such as those which do not have a line-of-sight deviating prism. Such a tip may be advantageously used as a probe to reduce any disturbances to the object being examined or to reduce the exposure of the embodiment itself.
• the pertinent performance data are listed in Table 20, and the construction parameters are listed in Table 2.
• Figure 3 is an optical schematic of another embodiment of the present invention.
• This endoscope also uses few components and is simple in construction, but is nevertheless highly corrected for aberrations, including chromatic aberrations, with the maximum axial chromatic (wavefront) aberration being only 0.21 waves (see column 23 of Table 20).
• the axial chromatic aberration is more than a factor four smaller than in the classical layout (0.90 waves, cf. Fig. 1 and Table' 20) and is within the diffraction limit.
• this example shows the advantage of a redistribution of power, which in this example is related to the attendant shift of pupil (Pin t ).
• Embodiment 3 departs even further from the classical layout than does Embodiment 2, the SC is only 0.55, and the peak-to-valley wavefront aberration has been reduced to 0.21 waves (see Table 20).
• Figure 4 is an optical schematic of an endoscope which consists of two components.
• the second and third groups II, III are cemented to a rod-shaped element, so that there are only four glass/air surfaces.
• aberrations are at the diffraction limit.
• the peak-to-valley wavefront aberration is only 0.27 waves
• the maximum axial chromatic aberration is only 0.31 waves, as indicated in Table 20.
• This example shows that rod-shaped elements can be beneficially employed in the present invention.
• the advantage of using a rod-shaped element is that the optical distance from the object to the image plane is increased without increasing the diameter of the optical system.
• FIG. 5 is an optical schematic of an endoscope which is constructed entirely of glass elements, none of which is meniscus-shaped.
• plastic lenses may be used in addition to or in place of the glass elements, as illustrated in other exemplary embodiments.
• the curvatures are shallow and spherical, with all but one of the surfaces having radii of curvature greater than 8 mm.
• the first group I easily provides the needed space for a line-of-sight deviation prism (which includes surfaces 2 and 3) between the entrance pupil P Elrt and the first group (I), even though the field of view is relatively large (70 degrees).
• FIG. 6 is an optical schematic of an endoscope which is constructed partly of glass and partly of plastic, demonstrating how lenses of different materials can be combined in a single endoscope.
• N.A. numerical aperture
• the distortion is well corrected, with the maximum image distortion being only -3% (see Table 20).
• the object has been set at infinite distance to show that the basic design is not affected by a change in magnification as is generally the case with endoscopes.
• the color correction is basically provided by surface 6.
• Figure 7 is an endoscope to which an additional group of optical power (IV) has been added, resulting in a modestly improved monochromatic performance.
• the added element IV is positioned close to the image plane (F) of the objective where element IV is most effective.
• the relatively weak power of element IV shows that most of the burden of the optical functions, as well as the aberration corrections, are performed by the groups I, II, and III, which are displaced from the image planes and pupil planes. This example shows that an additional element near an image plane or a pupil plane can be used with the present invention.
• Figure 8 is a highly corrected endoscope using plastic elements with a relatively high N.A. of 0.025. Only one of the elements, element IV, is preferably positioned close to an image or pupil plane but is again of low optical power. Although four optical elements are used, the SC is still only 1.06 and the maximum axial chromatic aberration is only 0.31 waves.
• the color correction is basically provided by surface 8.
• Figure 9 is an endoscope similar to the one shown in Figure 8.
• the magnification has been increased to 2X, showing that the design remains very similar to the 1X and OX designs, as is generally the case with endoscopes.
• a meniscus element has been employed to show that despite the fact that the present invention can be used with nonmeniscus elements, their employment is by no means excluded.
• the fourth group (IV, the meniscus element) is of negative power, again showing that the fourth element is a nonessential addition to the other three groups of the invention.
• the color correction is basically provided by surface 9.
• Figure 10 is an endoscope in which a second relay (designated as group IV) is used.
• This embodiment has a very large field of view of 80 degrees and a relatively high N.A. of 0.025. Despite these large values, a deviation prism (which includes surfaces 2 and 3) can be readily accommodated between the objective (I) and the entrance pupil (P ent ), as shown in
• Figure 10 The total system is still very well corrected at surface 10 by a single color correcting element of low power, which basically provides full correction of the chromatic aberrations, e.g., the maximum axial chromatic aberration is only 0.35 waves (see Table 20).
• the first three groups (I, II, III) are together fully correctable, the addition of classical relays to those first three groups is not excluded.
• Figure 11 shows an endoscope having three image relays that is still very well corrected, with a maximum axial chromatic aberration of only 0.04 waves (see Table 20).
• the chromatic aberrations are basically fully corrected at surface 10 with a single element of negative optical power, though additional elements may be used. In other embodiments, additional color correcting elements may be required.
• the optical power of the color correcting element even though it provides basically the full color correction, approaches a value comparable to those of the other components.
• surfaces 9 and 10 have radii of curvature of 50 mm and 4.5 mm, respectively.
• the elements are of glass, and no aspheric surfaces are employed.
• Figures 12-18 corresponding to Tables 12-18, show exemplary embodiments of the present invention in which a field expander (corresponding to surfaces 1-2 in each of Figures 12-18) has been included in or with the objective (corresponding to surfaces 1-6 in each of Figures 12-18).
• the field expander permits a large field of view (110 degrees) to be imaged and may also correct for the field curvature (with the Petzvalsu being correspondingly smaller).
• Embodiments 12-18 include a 3 relay system, with the lengths indicated in Tables 12-18 corresponding to a system that can be used in medical applications.
• a single color correcting element basically provides all the color correction.
• Figures 12A-D illustrate an embodiment which has only 9 lens elements, 12 curved surfaces, and a sum of the absolute values of the curvatures of the optical elements equal to 3.65/mm (see Table 20). These values represent a significant improvement as compared with conventional systems, which may contain 30-35 optical elements and have a correspondingly higher sum of the absolute values of the curvatures. As indicated in Table 20 and as discussed below, these design advantages are also reflected in Embodiments 13-18.
• the first relay extends between "surface
• the second relay extends between surfaces 16 and 19, and in Figure 12C, the third relay extends between surfaces 21 and 24.
• the color correction in Embodiment 12 is performed by the first transfer or relay, and in particular, at surface 11.
• the optical performance of the system is quite good, with the peak-to- valley wavefront aberration and the maximum axial chromatic aberration being 0.34 and 0.22 waves, respectively.
• the embodiment of Figures 13A-D is similar to that of Embodiment 12; however, the second relay rather than the first relay is now the color correcting relay, with basically all of the color correction in the system being performed at optical surface 18.
• the color correction is performed in the second half of the color correcting relay, in contrast with the embodiment of Figures 12A-D, in which the color correction is performed in the first half of the color correcting relay.
• the color correction may be placed in any group of elements.
• the first relay extends between "surface 8" and surface 13.
• the second relay extends between surfaces 15 and 19, and in Figure 13C, the third relay extends between surfaces 21 and 24.
• the optical performance of the system is quite good, with the peak-to-valley wavefront aberration and the maximum axial chromatic aberration being 0.32 and 0.19 waves, respectively.
• Embodiments 12-14 are substantially comparable, with the peak-to-valley wavefront aberration and the maximum axial chromatic aberration in Embodiment 14 being 0.51 and 0.17 waves, respectively.
• the embodiment of Figures 15A-D has just 8 optical elements with optical power. This design, like the other embodiments herein that include three relays, approaches the theoretical limit of 7 curved surfaces needed for a three relay endoscope. This limit is based on the fact that each relay has two or more curved surfaces and the objective has at least one curved surface.
• the maximum values of the peak to valley wavefront aberration and the maximum axial chromatic aberration in Embodiment 15 (0.81 and 0.68 waves, respectively) are higher than in the other field expander embodiments of Figures 12-18, the overall performance is still good, and the Petzvalsum is just 0.04/mm.
• the first relay extends between "surface 8" and surface 13.
• the second relay extends between surfaces 15 and 18, and in Figure 15C, the third relay extends between surfaces 20 and 23.
• the color correction is basically provided by surface 11.
• the components with curved surfaces are advantageously made of plastic, COC, or polystyrene, which makes the components relatively inexpensive.
• the rods with flat surfaces can be made of glass or of plastic, or they-sJan be molded as part of the components with the curved surfaces.
• plastic materials can present special problems, e.g., the refractive index of these materials is relatively low.
• plastic elements are cemented onto the flat faces of glass rods, resulting in an endoscope that is inexpensive but has good performance.
• the peak-to-valley wavefront aberration is 0.41 waves
• the maximum axial chromatic aberration is 0.19 waves.
• the first relay extends between "surface 8" and surface 17.
• the second relay extends between surfaces 19 and 23
• the third relay extends between surfaces 25 and 30.
• the color correction is basically provided by surface 13.
• aspheric surfaces are molded into glass rods, such that the rod and lens form a single piece, thereby reducing the number of optical elements.
• the peak-to-valley wavefront distortion has been reduced to 0.28 waves, which is less than that of Embodiment 16, and the maximum axial chromatic aberration is only 0.28 waves.
• the color correction is basically provided by surface 11.
• the embodiment illustrated in Figures 18A-D is similar to that of Figures 12A-D, except that the longer elements in Figures 12A-D have now been broken up into two shorter segments by introducing a flat-flat interface within each of the longer elements.
• the first optical relay is shown in Figure 18A to extend between "surface” 8 and surface 20.
• the second relay ( Figure 18B) extends between surface 22 and surface 32, and the third relay extends between surface 34 and surface 43.
• the color correction is basically provided by surface 14:
• three groups an objective, a field lens, and a relay lens
• an endoscope in such a way that the sum of the absolute values of the powers of the individual optical elements is greatly reduced.
• the reduction in the optical power reduces the amount of aberrations to be corrected, which considerably reduces the complexity of the optical system, thereby reducing its cost.
• An additional and often valuable feature of some embodiments is that the entrance pupil is located outside the system, thereby facilitating the addition of other optical components such as prisms.
• AD represents the aspheric constant "d” in Equation 1
• AE represents the aspheric constant "e” in Equation 1.
• Equation 1 is the well-known formula for describing an aspheric surface: in which z is in the direction of the optical axis, p is the distance from the optical axis, and c is the surface curvature (1/RD).
• the aspheric constants f and g in the exemplary Embodiments 1-18 are equal to zero.
• SURF 1 ENTRANCE PUPIL PLANE
• SURF 16 IMAGE PLANE
• AD 9.0E-4
• AE 2.0E-5.

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