Abstract:
An endoscope whose magnification may be continuously varied from zero to a microscopic magnification of 40× or more while providing full correction for aberrations at widely different magnifications. The objective comprises a positive lens group in a microscope objective configuration, and a front group which typically includes a negative lens generally near the focal plane of the positive lens group. To achieve high magnification, the objective is moved away from the transfer optics, and placed in contact with the object to be viewed. In such a configuration, the positive lens group functions as a microscope objective while the negative lens group&#39;s contribution to the aberrations is small. At low magnification, the negative lens group cooperates with the positive lens group to provide a wide angle lens. Pupil stabilization is achieved by placing the physical stop so that when the endoscope is used in the microscope mode, the physical stop between the positive and negative lens groups is ineffective or marginally effective. This permits the maximum numerical aperture consistent with the physical diameter of the positive lens group. However, the physical stop between the positive and negative lens groups comes into play when the object plane moves away from the negative lens group. The field lens located at the image plane receives the marginal chief ray at a nearly constant small angle over the entire range of magnification. This allows image transfer to be achieved with conventional means such as alternating field and relay lenses.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This is a continuation-in-part of application Ser. No. 457,337, filed Jan. 12, 1983, now U.S. Pat. No. 4,664,486, issued May 12, 1987, which is itself a continuation of application Ser. No. 133,732, filed Mar. 25, 1980, now abandoned. 
    
    
     FIELD OF THE INVENTION AND RELATED APPLICATIONS 
     The present invention relates generally to endoscopes, and more specifically to variable magnification endoscopes. 
     BACKGROUND OF THE INVENTION 
     An endoscope is an optical instrument for viewing and examining the interior of various body cavities, such as the lung, bladder, abdominal cavity or knee joint. Access to the interior body region may be via a natural body conduit or, in the case of body cavities not so accessible, by a small surgical incision. Broadly, the endoscope comprises a long thin tube, the distal (leading) end of which is inserted into the patient. An eyepiece is mounted to the proximal end of the tube, and within the tube are housed an image-forming objective at the distal end, fiber optic or discrete transfer optical elements for transmitting the optical image formed by the objective to the eyepiece outside the body for viewing by the examining physician, and fiber optic elements for transmitting light from outside the patient to the interior regions under examination for illumination thereof. The illumination fiber optics typically occupy an annular region surrounding the objective and transfer optical elements. When discrete transfer optics are used rather than fiber optics, the transfer optics typically include a front field lens which defines the image plane for all magnification conditions, and alternating relay and field lenses. The endoscope may be rigid or flexible, depending on its intended use. 
     The realm of endoscopic procedures includes, in addition to examination, the excision and removal of tissue. For example, it is a common technique to remove polyps and tumors by such techniques, thus avoiding open surgery. This is accomplished by providing blades or hot wires at the end of the endoscope for excision, and appropriate conduits for withdrawal of the excised tissue. 
     It often happens that endoscopic exploration is performed in conjunction with a biopsy. In such a procedure, the surgeon explores the interior of the body cavity, and upon noticing a suspicious looking region having a tumor, excises a small piece of tissue which is withdrawn for the biopsy. The biopsy is a procedure involving sectioning and microscopic examination in a pathology lab. The result of the biopsy is typically made available within a day or two, and if the results indicate a malignancy, the patient submits to surgery for removal of the tumor, or undergoes other appropriate treatment. 
     It is immediately apparent that while the use of the endoscope eliminates open surgery for the performing of the biopsy, and further can even avoid open surgery for removal of the tumor, the present procedure involving an intermediate pathological examination requires that the patient be subjected to two surgical procedures, each of which may have to be accompanied by a general anesthetic. Furthermore, the biopsy results may cause the surgeon to wish to perform further biopsy procedures. 
     This difficulty could be overcome if an endoscope capable of viewing microscopically as well as telescopically could be used. With such an instrument, the examining physician could scan the interior region, and upon noticing a suspicious region, directly view in situ the single cells to make a pathological determination during the course of a single endoscopic procedure. Variable magnification endoscopes are known. A typical technique for achieving this result is shown in U.S. Pat. Nos. 3,608,998 and 4,076,018 and provides variable magnification elements near or in the eyepiece of the endoscope. Such an arrangement has the clear disadvantage that the resolution of the instrument is fixed once the front lens group (objective) is fixed. Thus, at the microscopic setting, the increased magnification is likely not to be accompanied by correspondingly increased resolution. A further difficulty with providing a variable magnification endoscope that allows true microscopic as well as telescopic examination arises from the great difficulty in correcting a lens for more than one set of conditions, unless a zoom lens having elements movable with respect to one another is used. While it is conceptually easy to visualize such a zoom lens at the distal end of the endoscope, such a solution is highly impractical due to the fact that zoom lens designs dictate a complex mechanical configuration and many lens elements. Since endoscope lens elements typically have a diameter in the neighborhood of two to three millimeters, a zoom lens is clearly impractical in the context of an endoscope. 
     U.S. Pat. No. 3,941,121 discloses an endoscope having an objective, the elements of which are fixed relative to one another, that is relatively movable with respect to a fiber optics transfer system. However, at the high magnification necessary for microscopy, the objective disclosed therein is incapable of producing the necessary image resolution. More specifically, it is impossible to obtain a sufficient numerical aperture at the level of correction necessary for performing pathological microscopy. 
     A further difficulty arises in the interaction between the objective and the transfer system. The use of a fiber optics transfer system tends to be accompanied by a loss in resolution. While this situation can be improved somewhat through the use of exotic techniques such as vibrating the input end of the fiber bundle or introducing aberrations which are subsequently corrected, maximum resolution is still likely to be achieved through the use of discrete lenses alternating field and relay lenses). However, when discrete transfer optics are used, the problem of pupil coupling is aggravated. In particular, pupil coupling is critical in order to provide evenness of illumination, but where the objective moves relative to the transfer optics, the exit pupil location varies so much with large magnification changes that the image transfer to the eyepiece suffers unacceptable vignetting. 
     U.S. Pat. No. 4,111,529 discloses an endoscope objective for use in wide angle viewing, but the objective does not possess sufficient resolution to render it suitable for microscopic viewing. Moreover, the numerical aperture is insufficient due to the stop positioning disclosed. 
     Therefore, while variable magnification endoscopes are known, and microscopic endoscopes are known, there is presented the need for an endoscope that provides a continuous variation of magnification over a wide range while providing suitable corrections and pupil coupling under such widely varying conditions. 
     SUMMARY OF THE INVENTION 
     The present invention provides an endoscope whose magnification may be continuously varied from zero to a microscopic magnification of 40× or more at the objective while providing full correction for aberrations at widely different magnifications. 
     The above results are achieved by moving the objective only with respect to the transfer optics. The objective comprises a positive lens group in a microscope objective configuration, and a front group which typically includes a negative lens group (which may comprise a single element) and a physical stop in front of the positive lens group (between the positive and negative lens groups), the stop being located generally near the focal plane of the positive lens group. 
     For microscopic examination at high magnification, the objective is moved away from the transfer optics, and placed in contact with the object to be viewed. In such a configuration, the outer surface of the negative lens group functions as an object plane locator, while the positive lens group functions as a microscope objective. For telescopic viewing at low magnification, the objective is moved toward the transfer optics. In such a configuration, the negative lens group cooperates with the positive lens group to provide a wide angle lens, with the negative lens group acting as a field expander. 
     The overall power of the objective is provided essentially by the positive lens group. The negative group contributes little to the overall power, and contributes little to the aberrations in the microscope mode. However, the negative group may have substantial negative power, generally comparable in magnitude to the positive power. This negative power may be chosen to correct the field curvature. If P(obj), P(pos), and P(neg) are the overall power of the objective and the respective powers of the positive and negative groups, the ratio P(pos)/P(obj) preferably lies between 0.8 and 1.4 and the ratio (P(neg)/P(obj) preferably lies between -1.2 and -0.4. 
     Although the wide range of operating conditions makes a normal computer solution for an optimum set of optical parameters ill-conditioned, the present design allows a convergent solution as follows. The positive lens group is initially designed as a high power microscope objective whose parameters are chosen so that the aberrations are substantially full corrected. This is done without reference to the front group. The parameters for the negative lens group and the stop are then chosen to optimize the objective as a wide angle lens. The field aberrations of the objective in the wide angle mode are typically most sensitive to the stop location and size. The stop parameters (as well as those of the negative lens group), once established, may have a deleterious effect on the performance in the microscope mode. The positive group is then re-optimized as a microscope objective, leaving the parameters of the negative group and the stop fixed, but taking them into account in the overall optimization. This sequence may then be repeated to provide full correction for two widely different magnifications. At intermediate magnifications, the objective is surprisingly well corrected. 
     According to a further aspect of the present invention, pupil stabilization is achieved by placing the physical stop so that when the endoscope is used in the microscope mode, the physical stop between the positive and negative lens groups is ineffective or marginally effective. This permits the maximum numerical aperture consistent with the physical diameter of the positive lens group. Regardless of whether the pupil is at the stop or the positive group, at high magnification, the chief ray is nearly parallel to the optic axis since the distance between the objective and the image plane is large relative to the diameter of the lens. However, the physical stop between the positive and negative lens groups comes into play when the object plane moves away from the negative lens group. The location of the stop is chosen to be near the focal plane of the positive lens group, thus providing a substantially parallel chief ray for conditions of lower magnification. Thus, the field lens located at the image plane receives the marginal chief ray at a nearly constant small angle over the entire range of magnification. This allows image transfer to be achieved with conventional means such as alternating field and relay lenses. 
     For a further understanding of the nature and advantages of the present invention, reference should be made to the remaining portions of this specification and to the attached drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1A is a simplified sectioned oblique view of a variable magnification endoscope according to the present invention, with the endoscope in a position for wide angle viewing at low magnification; 
     FIG. 1B is a similar view of the endoscope in a position for microscopic viewing at large magnification; 
     FIG. 2A is an optical schematic of the endoscope objective; 
     FIG. 2B shows a modified front element; 
     FIGS. 3A and 3B are ray diagrams showing image formation and pupil definition in the microscope mode; 
     FIGS. 4A and 4B are ray diagrams showing image formation and pupil definition in the wide angle mode; 
     FIG. 5 is a ray diagram illustrating the role of the intermediate physical stop in the wide angle mode; 
     FIG. 6 is a ray diagram showing image formation and pupil definition at an intermediate magnification setting; 
     FIG. 7A shows plots of lateral aberration as a function of relative height in the pupil for three wavelengths; 
     FIG. 7B shows similar plots with the power of the front element removed; and 
     FIG. 8 is an optical schematic of an alternate embodiment of the objective. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1A is a simplified, sectioned, oblique view of an endoscope 10 according to the present invention. Endoscope 10 is an elongate instrument characterized by a distal end 12 for insertion into a patient&#39;s internal body region and a proximal end 15 that remains outside the patient. Transverse dimensions are greatly exaggerated for clarity; it should be understood that endoscope 10 typically has a length of about 250 millimeters and an outer diameter of about 5 millimeters. 
     The mechanical construction of the endoscope is defined primarily by three coaxial thin-walled tubes 17, 20, and 22, of decreasing diameters, with outer tube 17 defining the outermost diameter of the endoscope. Outer tube 17 and middle tube 20 and relative to one another and sized to define therebetween an annular region within which is located a fiber optics lighting bundle 25 having an input end 27 near proximal end 15 and an output end 30 generally at distal end 12. As will be described below, at least a portion 31 of bundle 25 may be angled to terminate so that the fibers therein are directed toward the central axis. Inner tube 22 is movable relative to tubes 17 and 20, and is sized to slide smoothly within the bore of middle tube 20. This relative sliding movement provides variable magnification as will be described in detail below. In order to provide a seal between the interior of tube 20 and the outside atmosphere, appropriate sealing means such as an O-ring seal 32, is provided. A groove 33 in inner tube 22 and a ball plunger 34 provide a positioning detent to facilitate relative positioning. 
     An objective lens system 35, to be described in detail below, is rigidly mounted within middle tube 20 at proximal end 12. The remaining optical components are rigidly mounted within inner tube 22 so that they may move relative to objective 35 when inner tube 22 so that they may move relative to objective 35 when inner tube 22 is moved relative to outer tube 17. In particular, the optical elements mounted within inner tube 22 include a transfer system defined by a plurality of field and relay lenses 40 and an eyepiece 45 at the end of inner tube 22 remote from objective 35. Lenses 40 are preferably rod lenses of a type well known in the endoscope art. Alternately, a fiber optics transfer system within inner tube 22 may be used. An eyepiece ring 50 surrounds eyepiece 45 and is rigidly mounted to inner tube 22. The image formed by objective 35 must be located in a plane 52 fixed relative to the transfer optics in order to provide proper eyepiece image formation. Thus, depending on the distance between objective 35 and the object to be viewed, inner tube 22 must be moved in order to properly locate the image formed by objective 35. 
     FIG. 1A shows endoscope 10 with inner tube 22 at a position of closest approach to objective 35. FIG. 1B is a similar view to FIG. 1A except that inner tube 22 is in a position farther removed from objective 35. As will be discussed below, this latter position provides high magnification. Thus, from a physician&#39;s point of view, examination proceeds as follows. Endoscope 10 is inserted into the patient while in the position shown in FIG. 1A. This provides a wide-angle view that permits the physician to scan the interior of the region under examination. When a closer examination of a particular spot is desired, the physician moves distal end 12 closer to the spot and withdraws inner tube 22 by an amount necessary to provide a focused image in eyepiece 45. When microscopic examination is required, the outer (front) surface of objective 35 is brought into proximity with the spot to be examined, and inner tube 22 is withdrawn to the position of FIG. 1B which represents the maximum extension that has any practical usefulness. In the preferred embodiment, microscopic examination occurs with the front surface of objective 35 in actual contact with the spot under examination. 
     FIG. 2A is an optical schematic of objective 35. Objective 35 comprises a front group 58 and a magnifying positive lens group 62. Front group 58 preferably comprises a negative element 60 and an aperture stop 65 located between negative element 60 and positive group 62. Negative element 60 preferably has a convex or planar front surface 60a which is exposed at distal end 12 and is brought into contact with the object to be microscopically examined. Positive lens groups 62 comprises a triplet having elements 70, 72 and 74 with the latter two forming a cemented doublet. All the lens elements are centered on a common optic axis 76. 
     FIG. 2B illustrates an alternate form of front negative element 60, designated 60&#39;, modified to permit illumination of an object contacting the front surface, designated 60a&#39;. To accomplish this, peripheral regions of element 60&#39; are cut away to define a frustoconical peripheral surface 60b&#39;. The ends of the fibers in bundle portion 31 terminate at surface 60b&#39; so that the light emanating from the fiber ends is directed forward toward the central region of surface 60a&#39;. 
     As was described above, microscopic examination occurs with front surface 60a of negative lens 60 contacting the object, thus acting as an object plane locator. The contribution of negative lens 60 contacting the object, thus acting as an object plane locator. The contribution of negative lens 60 to the aberrations is small, thus allowing the parameters of positive lens group 62 to be chosen to provide a substantially fully corrected microscope objective. Once front lens surface 60a is moved away from the object, negative lens 60 acts as a field expander, and its effect on field aberrations is no longer small. Thus, the parameters of negative lens 60 and aperture stop 65 may be chosen to correct the field aberrations of the entire objective at the position of low magnification. 
     The above description regarding the selection of the optical parameters is somewhat of an oversimplification, since the parameters of positive group 62 are affected by the insertion of negative element 60 and aperture stop 65. In particular, when these elements (especially stop 65), are inserted, the performance of positive group 62 as a microscope is typically degraded. However, re-optimization may be achieved, as for example, by adjusting the thicknesses of one or more of the triplet elements to effectively eliminate the effect of aperture stop 65 during microscopic viewing. Once this is done, the front group may be re-adjusted to further optimize the objective for wide angle viewing. This process may be iterated to bring the aberrations to a desired level of correction. Since the effect of the front group on microscopic viewing is small (once the stop effect is minimized or eliminated), the parameters for the front group and the positive group become generally decoupled, and the iterative process is convergent. With objective 35 thus corrected at its two extremes of magnification, it has been found that aberrations at intermediate magnifications are surprisingly small. A further constraint on the location and size of aperture stop 65 is imposed by pupil coupling considerations to be described below. 
     FIGS. 3A and 3B are ray diagrams showing the formation of an image 77 in image plane 52 for an object 78 located at front surface 60a of negative lens 60. FIG. 3B is a fragmented enlargement of FIG. 3A. In this position, corresponding to FIG. 1B, the physical mounting of positive lens group 62 defines the stop location at a position 79. Given the large distance between image plane 52 and objective 35 in relation to the diameter of inner tube 22, the marginal chief ray, designated 80, is at a small angle (about 1°) with respect to the optic axis. In this position, aperture stop 65 serves no function so that an image of maximum brightness occurs. 
     FIGS. 4A and 4B are ray diagrams showing the formation of an image 82 in image plane 52 for telescopic viewing of an object 85 positioned in an object plane 87 at a substantial distance from front surface 60a. The maximally off-axis bundle is characterized by a chief ray 90 which is incident on the transfer optics at the same small angle as in FIGS. 3A and 3B. This matching of the chief ray angle results from the positioning of stop 65 proximate the focal plane of positive lens group 62. 
     Given the large magnification at which the objective is designed to operate, the focal plane (for infinity) of the positive group is actually located inside negative element 60. However, it is preferred to have the marginal ray in the bundle, rather than the central (chief) ray, emerge parallel to the axis. This means that the marginal ray crosses the axis inside the negative element while chief ray 90 crosses the axis at a point closer to the positive group. This results in better utilization of the lens diameter, and provides a more convenient location to place stop 65. 
     The significance of stop 65 is best illustrated by considering the objective&#39;s performance without the stop. FIG. 5 shows image formation as in FIG. 4B, except for the absence of stop 65. Under these circumstances, the stop location is defined by the positive lens mount, and thus the maximally off axis bundle is characterized by a chief ray 91 which is incident on the transfer optics at a relatively large angle (say about 14°). This leads to unacceptable non-uniformity of illumination over the entire field of view if discrete transfer optical elements are used. 
     FIG. 6 is a ray diagram showing the formation of an image 92 in image plane 52 for viewing of an object 95 in an object plane 97 at an intermediate distance from front surface 60a. For this position of approximate unit magnification, aperture stop 65 remains effective to stabilize the pupil so that the marginal chief ray enters the transfer optics at a small angle. As the magnification is increased, the aperture stop becomes less effective so that it is effective or only marginally effective at the microscopic position described above. 
     for purposes of illustration, optical parameters for two examples are set forth in Appendices 1A and 1B. The geometric parameters include the radii and separation of all the element surfaces; the optical material parameters include the refractive indices and dispersion factors. Dimensions are in millimeters. The dimensions are appropriate for an overall objective diameter of about 2 mm. Naturally, the geometric parameters could be scaled if such were required. 
     For ease of nomenclature, surfaces proceeding back from front surface 60a are designated in numerical order with surface 60a being designated for the present purpose as surface 101. Referring again to FIG. 2A, negative lens element 60 is characterized by front and rear surfaces 101 and 102; aperture stop 65 is located within a plane 103; positive singlet 70 has surfaces 104 and 105; and the doublet (elements 72 and 74) has surfaces 106, 107 (cemented), and 108. The radius of a given surface 10i will be denoted by r i  so that front surface 101 has radius r 1 , while rear-most surface 108 has radius r 8 . Aperture stop has a diameter d 3 . Additionally, the distance between a given pair of adjacent surfaces 10j and 10k will be designated t jk . Moreover, the index of refraction and dispersion factor of the medium between surfaces 10j and 10k will be designated n jk  and df jk . For convenience, the Schott designations for the glasses are also shown. 
     The objective is color corrected for blue (4800 A), green (5461 A) and red (6438 A) light with equal spectral weights. The front focus is located near (slightly behind) front surface 101 to provide 40× magnification for objects at the front surface. This is also seen in FIG. 6 where the ray emerging parallel to the optical axis crosses the axis just inside the negative front element. FIG. 7A shows plots, for the example of Appendix 1A, of lateral aberration against relative height in the pupil at three wavelengths. FIG. 7B shows similar plots, but obtained with the power of front negative element 60 removed. These two sets of plots illustrate two important features of the present invention. First, the objective is extremely well corrected at 40× magnification. Second, the positive group, acting without the negative element&#39;s power, operates as a very well corrected microscope objective in its own right. 
     The embodiment described above includes a three-element positive group. However, the present invention contemplates the use of any positive group in a microscope objective configuration. To illustrate this important point, an additional embodiment will be described. 
     FIG. 8 is an optical schematic of an objective 180 which includes a front group 182 and a positive group 183. Front group 182 includes a negative element 184 and an aperture stop 185. Objective 182 differs from objective 35 of FIG. 2A in that positive group 182 is a Petzval-type microscope objective having four elements 186, 188, 190, and 192, arranged as first and second cemented doublets. 
     Negative lens element 184 has front and rear surfaces 201 and 202; aperture stop 185 is located within a plane 203, the first doublet (elements 186 and 188) has surfaces 204, 205 (cemented), and 206; and the second doublet (elements 190 and 192) has surfaces 207, 208 (cemented), and 209. The optical parameters for two examples are set forth in Appendices 2A and 2B, with the same nomenclature described above. 
     Table I shows the powers of the objectives and their respective positive and negative groups for the examples of Appendices 1A-B and 2A-B. All powers are in diopters. 
     
                       TABLE I______________________________________P(obj)    P(pos)  P(neg)  P(pos)/P(obj)                              P(neg)/P(obj)______________________________________App. IA 483.9     502.6   -440.4  1.04     -0.91App. 1B 486.9     503.0   -376.1  1.03     -0.77App. 2A 476.8     516.4   -481.9  1.08     -1.01App. 2B 475.7     497.8   -270.4  1.05     -0.57______________________________________ 
    
     As described above, the negative group plays its primary role when the objective operates away from the microscope mode. Thus, the overall power of the objective P(obj) is provided essentially by the positive lens group (having power P(pos)), even though the negative lens has substantial negative power (P(neg)). The near equality of P(pos) and P(obj) reflects the fact that the front surface of the negative lens lies at the 40× focal point of the positive group. Thus the negative lens contributes little to the overall power and the ratio P(pos)/P(obj) is generally near 1, preferably lying between 0.8 and 1.4. The negative power is used mainly to correct the field curvature with the ratio P(neg)/P(obj) preferably lying between -1.2 and -0.4. 
     In summary it can be seen that the present invention provides an endoscope objective that is substantially fully corrected for field aberrations over an extremely wide range of magnification. Moreover, the design provides a stabilized pupil location when such is necessary, as when discrete transfer optical elements are used. For an endoscope using fiber optics transfer, the pupil stabilization requirement may be relaxed and parameters varied to provide other advantages such as greater ease of fabrication and the like. 
     While the above provides a full and complete disclosure of the preferred embodiments of the invention, various modifications, alternate constructions, and equivalents may be employed without departing from the true spirit and scope of the invention. For example, the positive group could include more than three or four elements. Additionally, it should be possible to make front element 60 flat on both of its surfaces, relying on aperture stop 65 to optimize the objective as a wide-angle lens. In such a case, aperture stop 65 would typically be defined by a coating on the rear surface of front element 60. Moreover, while a particular physical stop location and size are shown, it should be understood that the aperture stop could in principle be located at other optically equivalent points. Therefore, the above description and illustrations should not be construed as limiting the scope of the invention which is defined by the appended claims. 
     
         ______________________________________ APPENDIX 1A______________________________________r.sub.1 = ∞           LaF 21     n.sub.12 = 1.792266t.sub.12 = 0.250000        df.sub.12 = 0.064r.sub.2 = 1.798864           airt.sub.23 = 0.300000d.sub.3 = 0.600000           airt.sub.34 = 0.759514r.sub.4 = -13.198478           LaSF 31    n.sub.45 = 1.885793t.sub.45 = 1.000000        df.sub.45 = 0.156r.sub.5 = -1.798864           airt.sub.56 = 0.100000r.sub.6 = 8.851848           SF 57      n.sub.67 = 1.855035t.sub.67 = 0.600000        df.sub.67 = 1.033r.sub.7 = 1.798864           PSK 3      n.sub.78 = 1.554398t.sub.78 = 1.000000        df.sub.78 = 0.069r.sub.8 = -3.077912  Effective focal length =                2.0665  Back focal length =                85.5176  Magnification =                -39.969367  Numerical aperture =                0.5______________________________________ 
    
     
         ______________________________________ APPENDIX 1B______________________________________r.sub.1 = ∞           LaF 21     n.sub.12 = 1.792266t.sub.12 = 0.250000        df.sub.12 = 0.064r.sub.2 = 2.106310           airt.sub.23 = 0.300000d.sub.3 = 0.600000           airt.sub.34 = 0.757206r.sub.4 = -12.991887           LaSF 31    n.sub.45 = 1.885793t.sub.45 = 1.000000        df.sub.45 = 0.156r.sub.5 = -1.799147           airt.sub.56 = 0.100000r.sub.6 = 8.753429           SF 57      n.sub.67 = 1.855035t.sub.67 = 0.600000        df.sub.67 = 1.033r.sub.7 = 1.801988           PSK 3      n.sub.78 = 1.554398t.sub.78 = 1.000000        df.sub.78 = 0.069r.sub.8 = -3.080649  Effective focal length =                2.0537  Back focal length =                84.0989  Magnification =                -39.660418  Numerical aperture =                0.5______________________________________ 
    
     
         ______________________________________ APPENDIX 2A______________________________________r.sub.1 = ∞           LaF 21     n.sub.12 = 1.792266t.sub.12 = 0.400000        df.sub.12 = 0.064r.sub.2 = 1.644080           airt.sub.23 = 0.250000d.sub.3 = 0.600000           airt.sub.34 = 0.264474r.sub.4 = 36.942089           SF 6       n.sub.45 = 1.812647t.sub.45 = 0.600000        df.sub.45 = 0.991r.sub.5 = 2.937294           LaF N2     n.sub.56 = 1.747949t.sub.56 = 1.000000        df.sub.56 = 0.181r.sub.6 = -1.636253           airt.sub.67 = 0.561421r.sub.7 = 7.888618           SF 6       n.sub.78 = 1.812647t.sub.78 = 0.400000        df.sub.78 = 0.991r.sub.8 = 1.983490           BaF 3      n.sub.89 = 1.585648t.sub.89 = 0.900000        df.sub.89 = 0.580r.sub.9 =  -3.665581  Effective focal length =                2.0973  Back focal length =                87.8771  Magnification =                -40.634309  Numerical aperture =                0.5______________________________________ 
    
     
         ______________________________________ APPENDIX 2B______________________________________r.sub.1 = ∞           LaF 21     n.sub.12 = 1.792266t.sub.12 = 0.400000        df.sub.12 = 0.064r.sub.2 =2.930140           airt.sub.23 = 0.250000d.sub.3 = 0.600000           airt.sub.34 = 0.346655r.sub.4 = 51.294217           SF 6       n.sub.45 = 1.812647t.sub.45 = 0.400000        df.sub.45 = 0.991r.sub.5 = 2.348542           LaF N2     n.sub.6 = 1.747949t.sub.56 = 1.000000        df.sub.56 = 0.181r.sub.6 = -1.637301           airt.sub.67 = 0.802218r.sub.7 = 7.775985           SF 6       n.sub.78 = 1.812647t.sub.78 = 0.400000        df.sub.78 = 0.991r.sub.8 = 2.013554           BaF 3      n.sub.89 = 1.585648t.sub.89 = 0.900000        df.sub.89 = 0.580r.sub.9 = - 3.673853  Effective focal length =                2.1023  Back focal length =                86.0183  Magnification =                -40.11219  Numerical aperture =                0.5______________________________________