Abstract:
A zoom projection lens for use with pixelized panels is provided. The projection lens has a negative/positive (retrofocus) form, with the positive lens unit (U 2 ) having two positive subunits (U 2   S1 , U 2   S2 ). The image (screen) side subunit (U 2   S1 ) serves as focus corrector for the lens, i.e., after zooming, this subunit is moved to adjust the focus of the lens. Compared to moving the negative unit (U 1 ), this approach achieves better aberration correction and involves moving less mass through smaller distances.

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a continuation-in-part of pending U.S. application Ser. No. 09/304,693, filed May 4, 1999, and entitled “Projection Lenses Having Reduced Lateral Color for Use with Pixelized Panels,” the content of which in its entirety is incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to projection lenses and, in particular, to zoom projection lenses which can be used, inter alia, to form an image of an object composed of pixels, e.g., an LCD, a reflective LCD, a DMD, or the like. 
     DEFINITIONS 
     As used in this specification, the following terms shall have the following meanings: 
     (1) Telecentric 
     Telecentric lenses are lenses which have at least one pupil at infinity. In terms of principal rays, having a pupil at infinity means that the principal rays are parallel to the optical axis (a) in object space, if the entrance pupil is at infinity, or (b) in image space, if the exit pupil is at infinity. Since light can propagate through a lens in either direction, the pupil at infinity can serve as either an entrance or an exit pupil depending upon the lens&#39; orientation with respect to the object and the image. Accordingly, the term “telecentric pupil” will be used herein to describe the lens&#39; pupil at infinity, whether that pupil is functioning as an entrance or an exit pupil. 
     In practical applications, the telecentric pupil need not actually be at infinity since a lens having an entrance or exit pupil at a sufficiently large distance from the lens&#39; optical surfaces will in essence operate as a telecentric system. The principal rays for such a lens will be substantially parallel to the optical axis and thus the lens will in general be functionally equivalent to a lens for which the theoretical (Gaussian) location of the pupil is at infinity. 
     Accordingly, as used herein, the terms “telecentric” and “telecentric lens” are intended to include lenses which have at least one pupil at a long distance from the lens&#39; elements, and the term “telecentric pupil” is used to describe such a pupil at a long distance from the lens&#39; elements. For the projection lenses of the invention, the telecentric pupil distance will in general be at least about 10 times the lens&#39; focal length. 
     (2) Pseudo-Aperture Stop 
     The term “pseudo-aperture stop” is used herein in the same manner as it is used in commonly-assigned U.S. Pat. No. 5,313,330 to Ellis Betensky, the contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     Projection lens systems (also referred to herein as “projection systems”) are used to form an image of an object on a viewing screen. Such systems can be of the front projection or rear projection type, depending on whether the viewer and the object are on the same side of the screen (front projection) or on opposite sides of the screen (rear projection). 
     The basic structure of such a system is shown in FIG. 2, where  10  is a light source (e.g., a tungsten-halogen lamp),  12  is illumination optics which forms an image of the light source (hereinafter referred to as the “output” of the illumination system),  14  is the object which is to be projected (e.g., an LCD matrix of on and off pixels), and  13  is a projection lens, composed of multiple lens elements, which forms an enlarged image of object  14  on viewing screen  16 . The system can also include a field lens unit, e.g., a Fresnel lens, in the vicinity of the pixelized panel to appropriately locate the exit pupil of the illumination system. 
     For front projection systems, the viewer will be on the left side of screen  16  in FIG. 2, while for rear projection systems, the viewer will be on the right side of the screen. For rear projection systems which are to be housed in a single cabinet, a mirror is often used to fold the optical path and thus reduce the system&#39;s overall size. 
     Projection lens systems in which the object is a pixelized panel are used in a variety of applications. Such systems preferably employ a single projection lens which forms an image of, for example, a single panel having red, green, and blue pixels. In some cases, e.g., large image rear projection systems, multiple panels and multiple projection lenses are used, with each panel/projection lens combination producing a portion of the overall image. In either case, projection lenses used with such systems generally need to have a relatively long back focal length to accommodate the prisms, beam splitters, color wheels, etc. normally used with pixelized panels. 
     A particularly important application of projection lens systems employing pixelized panels is in the area of microdisplays, e.g., front projection systems which are used to display data and rear projection systems which are used as computer monitors. Recent breakthroughs in manufacturing technology has led to a rise in popularity of microdisplays employing digital light valve devices such as DMDs, reflective LCDs, and the like. 
     Projection displays based on these devices offer advantages of small size and light weight. As a result, a whole new class of ultra portable lightweight projectors operating in front-projection mode and employing digital light valves has appeared on the market. Lightweight compact rear-projection systems can also be achieved through the use of these devices. 
     To display images having a high information content, these devices must have a large number of pixels. Since the devices themselves are small, the individual pixels are small, a typical pixel size ranging from 17μ for DMD displays to approximately 8μ or even less for reflective LCDs. This means that the projection lenses used in these systems must have a very high level of correction of aberrations. Of particular importance is the correction of chromatic aberrations and distortion. 
     A high level of chromatic aberration correction is important because color aberrations can be easily seen in the image of a pixelized panel as a smudging of a pixel or, in extreme cases, the complete dropping of a pixel from the image. These problems are typically most severe at the edges of the field. 
     All of the aberrations of the system need to be addressed, with lateral color, chromatic variation of coma, astigmatism, and distortion typically being most challenging. Lateral color, i.e., the variation of magnification with color, is particularly troublesome since it manifests itself as a decrease in contrast, especially at the edges of the field. In extreme cases, a rainbow effect in the region of the full field can be seen. 
     In projection systems employing cathode ray tubes (CRTs) a small amount of (residual) lateral color can be compensated for electronically by, for example, reducing the size of the image produced on the face of the red CRT relative to that produced on the blue CRT. With a pixelized panel, however, such an accommodation cannot be performed because the image is digitized and thus a smooth adjustment in size across the full field of view is not possible. A higher level of lateral color correction, including correction of secondary lateral color, is thus needed from the projection lens. 
     The use of a pixelized panel to display data leads to stringent requirements regarding the correction of distortion. This is so because good image quality is required even at the extreme points of the field of view of the lens when viewing data. As will be evident, an undistorted image of a displayed number or letter is just as important at the edge of the field as it is at the center. Moreover, projection lenses are often used with offset panels. In such a case, the distortion at the viewing screen does not vary symmetrically about a horizontal line through the center of the screen but can increase monotonically from, for example, the bottom to the top of the screen. This effect makes even a small amount of distortion readily visible to the viewer. 
     Low distortion and a high level of color correction are particularly important when an enlarged image of a WINDOWS type computer interface is projected onto a viewing screen. Such interfaces with their parallel lines, bordered command and dialog boxes, and complex coloration, are in essence test patterns for distortion and color. Users readily perceive and object to even minor levels of distortion or color aberration in the images of such interfaces. 
     The above-mentioned microdisplays typically require that the light beam from the illumination system has a near-normal angle of incidence upon the display. In terms of the projection lens, this translates into a requirement that the lens has a telecentric entrance pupil, i.e., the projection lens must be telecentric in the direction of its short imaging conjugate where the object (pixelized panel) is located. This makes the lens asymmetric about the stop which makes the correction of lateral color more difficult. 
     In addition to the foregoing, for rear projection systems, there is an ever increasing demand for smaller cabinet sizes (smaller footprints). In terms of the projection lens, this translates into a requirement that the lens has a wide field of view in the direction of the image (screen). This requirement makes it even more difficult to correct the lateral color of the lens. Similarly, the requirement for a relatively long back focal length also makes it more difficult to correct lateral color. 
     The ability of a projection lens to operate efficiently over a range of focal lengths is desirable since it allows the projection system to be used with screens of different sizes and halls of different dimensions without the need to change any of the components of the system. The challenge, of course, is to maintain a high level of aberration correction throughout the operative range of focal lengths without unduly complicating the lens design. 
     SUMMARY OF THE INVENTION 
     In view of the foregoing, there exists a need in the art for projection lenses for use with pixelized panels which have some and preferably all of the following properties: 
     (1) a high level of lateral color correction, including correction of secondary lateral color; 
     (2) low distortion; 
     (3) a large field of view in the direction of the image; 
     (4) a telecentric entrance pupil; 
     (5) a relatively long back focal length; and 
     (6) the ability to zoom between a maximum effective focal length and a minimum effective focal length. 
     The above-referenced U.S. application Ser. No. 09/304,693 (the &#39;693 application) discusses in detail various approaches for achieving properties (1) to (5) above. The present application is addressed to a particular approach for achieving property (6). The invention of the present application can be used with pixelized panel projection lenses designed in accordance with the &#39;693 application or with lenses designed in other ways. 
     To achieve property (6), the invention provides a projection lens for forming an image of an object, said lens having a zoom range between a minimum effective focal length f min  and a maximum effective focal length f max , said lens consisting in order from its image end (long conjugate or screen end) to its object end (short conjugate or pixelized panel end) of: 
     (A) a first lens unit U 1  having a negative power; 
     (B) a second lens unit U 2  having a positive power, said second lens unit being separated from the first lens unit by a first axial space which is varied during zooming (Space 1 in the Tables 1-3); and 
     (C) an optional field lens unit; 
     wherein: 
     the second lens unit consists in order from its image end to its object end of: 
     (i) a first lens subunit U 2   S1  having a positive power (the focus corrector); 
     (ii) a second lens subunit U 2   S2  having a positive power, said second lens subunit being separated from the first lens subunit by a second axial space which is varied during focusing (Space 2 in the Tables 1-3), said second axial space being varied through movement of the first lens subunit. 
     Preferably, the first lens subunit has less lens elements than the second lens subunit. Most preferably, the first lens subunit is a singlet. Also, the first lens subunit preferably has less optical power than the second lens subunit. 
     The projection lenses of the invention can be designed using the location of the output of the illumination system as a pseudo-aperture stop/entrance pupil of the projection lens (see the above-referenced Betensky patent). In this way, efficient coupling is achieved between the light output of the illumination system and the projection lens. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic side view of a representative projection lens constructed in accordance with the invention. 
     FIG. 2 is a schematic diagram showing an overall projection lens system in which the projection lenses of the present invention can be used. 
    
    
     The foregoing drawings, which are incorporated in and constitute part of the specification, illustrate the preferred embodiments of the invention, and together with the description, serve to explain the principles of the invention. It is to be understood, of course, that both the drawings and the description are explanatory only and are not restrictive of the invention. 
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The projection lenses of the present invention are of the retrofocus or the inverted telephoto type and consist of two lens units, i.e., a negative unit (U 1 ) on the long conjugate side and a positive unit (U 2 ) on the short conjugate side, which are typically separated by an aperture stop or a pseudo-aperture stop. 
     The use of this overall lens form to produce an image of a pixelized panel has various advantages. Thus, telecentricity is readily achieved by locating the lens&#39; aperture stop or pseudo-aperture stop in the front focal plane of the second positive unit. Additional advantages are a long back focal length and the ability to handle a wide field of view. Both of these characteristics are particularly useful in rear projection systems, where the lens must have a wide field of view to achieve the smallest possible overall package size, and where there is a need to accommodate beam splitting prisms between the lens and the pixelized panel. These prisms may include polarizing beam splitters, as well as color splitting prisms. 
     The lenses of the invention achieve a high level of distortion correction by using one or more aspherical surfaces in the first lens unit. Some residual distortion, as well as spherical aberration of the lens&#39; entrance pupil, is corrected through the use of one or more aspherical surfaces in the second lens unit. The spherical aberration of the entrance pupil should be minimized to achieve telecentricity for any arbitrary point in the object plane of the lens. Preferably, the aspherical surfaces are formed on plastic lens elements. 
     The most critical aberration that must be corrected is the lens&#39; lateral color. Various preferred approaches for correcting this aberration are disclosed in the &#39;693 application. As noted above, although preferred, these approaches need not be used in the practice of the present invention. 
     Zooming of the projection lenses of the invention is achieved by moving the first and second lens units relative to one another. Typically, the units are coupled together mechanically so that both units move together relative to the pixelized panel (see Space 3 in Tables 1-3), and at the same time, the units move relative to one another (see Space 1 in Tables 1-3). 
     In accordance with the prior art, after such zooming, the focus of the lens would be adjusted by moving the first lens unit, i.e., by a further (second) adjustment of Space 1 in Tables 1-3. In accordance with the present invention, the first lens subunit of the second lens unit is moved for this purpose rather than the first lens unit, i.e., Space 2 in Tables 1-3 is adjusted rather than Space 1. 
     This approach has a number of advantages. First, the first lens subunit typically has less lens elements, has a smaller diameter (smaller maximum clear aperture), and a shorter length than the first lens unit. Having less elements and a smaller diameter means that the first lens subunit has less mass than the first unit. Accordingly, it is easier to move this lens subunit using, for example, a motorized drive than to move the first lens unit. 
     Moreover, it was surprisingly found that it was easier to correct the aberrations of the system when focusing was done using the first lens subunit rather than the first lens unit. In part, this is believed to be due to the fact that smaller motions of the first lens subunit are needed to correct focus than would be needed if the first unit were moved. This is an important advantage of the invention since, as discussed above, aberration correction is critical in projection lenses used with pixelized panels. 
     Conventional mechanisms known in the art, e.g., cam mechanisms and motorized drives, can be used to move the lens and/or its component parts during focusing and zooming. 
     Without intending to limit it in any manner, the present invention will be more fully described by the following examples. 
     EXAMPLES 
     FIG.  1  and Tables 1-3 illustrate representative projection lenses constructed in accordance with the invention. The prescription of Table 1 is preferred. 
     HOYA designations are used for the various glasses employed in the lens systems. Equivalent glasses made by other manufacturers (e.g., OHARA or SCHOTT) can be used in the practice of the invention. Industry acceptable materials are used for the plastic elements. 
     The aspheric coefficients set forth in the tables are for use in the following equation:        z   =         cy   2       1   +       [     1   -       (     1   +   k     )          c   2          y   2         ]       1   /   2           +     Dy   4     +     Ey   6     +     Fy   8     +     Gy   10     +     Hy   12     +     Iy   14                              
     where z is the surface sag at a distance y from the optical axis of the system, c is the curvature of the lens at the optical axis, and k is a conic constant, which is zero except where indicated in the prescriptions of Tables 1-3. 
     The designation “a” associated with various surfaces in the tables represents an aspherical surface, i.e., a surface for which at least one of D, E, F, G, H, or I in the above equation is not zero; and the designation “c” indicates a surface for which k in the above equation is not zero. The various planar structures located on the short conjugate side of U 2  in the figure and tables represent components which are used with or are a part of the pixelized panel. They do not constitute part of the projection lens. All dimensions given in the tables are in millimeters. 
     The prescription tables are constructed on the assumption that light travels from left to right in the figures. In actual practice, the viewing screen will be on the left and the pixelized panel will be on the right, and light will travel from right to left. In particular, the references in the prescription tables to objects/images and entrance/exit pupils are reversed from that used in the rest of the specification. The pixelized panel is shown in FIG. 1 by the designation “PP” and the equivalent physical aperture stop is shown by the designation “AS”. 
     The zoom projection lenses of the examples were designed using the pseudo-aperture stop/entrance pupil technique of Betensky, U.S. Pat. No. 5,313,330. In accordance with this approach, the illumination system is used to define the entrance pupil for the projection lens, with the entrance pupil being located at a constant position relative to the pixelized panel for all lens focal lengths and conjugates. The location of this pupil is determined by the substantially parallel light (substantially telecentric light) which passes through the pixelized panel from the illumination system. In the examples, the pseudo-aperture stop/entrance pupil is surface  24 . The image of this surface by the second lens unit places the equivalent physical aperture stop (AS) between the first and second lens units as illustrated in FIG.  1 . 
     The zoom lens of Table 1 has the following properties at its short focal length position: 
     maximum half field of view—32.7°; 
     maximum distortion—1.00%; 
     lateral color at 0.7 field—11.4 microns; 
     lateral color at 1.0 field—17.5 microns; 
     pixel size—28 microns; and 
     BFL/f 0 —1.5; 
     where lateral color values were determined from the chromatic blur in the image focal plane for wavelengths in the range from 460 nanometers to 620 nanometers, pixel size is pixel width, BFL is back focal length, and f 0  is effective focal length of the lens. The lenses of Tables 2 and 3 have similar properties. 
     In general, the zoom projection lenses of the invention will have some and preferably all of the following properties: 
     (i) the lens has a half field of view in the direction of the image of at least 20° and preferably at least 25°; 
     (ii) the lateral color blur of the lens at its full field for wavelengths in the range from 460 nanometers to 620 nanometers is less than a pixel and preferably less than three-quarters of a pixel (note that the level of lateral color correction can be determined at the object plane or the image plane, a magnified pixel being used when the determination is performed at the image plane); 
     (iii) the distortion of the lens is less than 1.5 percent and preferably less than or equal to 1.0 percent; and 
     (iv) the ratio of the lens&#39;s back focal length (BFL) to its focal length is greater than 0.7, preferably greater than 1.0, and most preferably greater than or equal to 1.5; 
     where these properties are evaluated at the zoom lens&#39; short focal length position. 
     Although specific embodiments of the invention have been described and illustrated, it is to be understood that a variety of modifications which do not depart from the scope and spirit of the invention will be evident to persons of ordinary skill in the art from the foregoing disclosure. 
     
       
         
               
               
               
               
               
               
               
             
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
             
             
               
                 Surf. 
                   
                   
                   
                   
                 Clear Aperture 
                   
               
               
                 No. 
                 Type 
                 Radius 
                 Thickness 
                 Glass 
                 Diameter 
               
               
                   
               
               
                 1 
                 a 
                 316.4987 
                 9.00000 
                 ACRYLIC 
                 106.50 
                   
               
               
                 2 
                 ac 
                 48.5107 
                 79.22000 
                   
                 83.70 
               
               
                 3 
                   
                 −68.2336 
                 4.10000 
                 FCD1 
                 53.00 
               
               
                 4 
                   
                 290.7899 
                 7.00000 
                 TAF3 
                 53.00 
               
               
                 5 
                   
                 −157.0756 
                 Space 1 
                   
                 52.00 
               
               
                 6 
                   
                 154.9494 
                 8.14000 
                 FD60 
                 54.20 
               
               
                 7 
                   
                 758.2655 
                 Space 2 
                   
                 55.40 
               
               
                 8 
                   
                 −1067.2049 
                 8.92000 
                 FCD1 
                 65.80 
               
               
                 9 
                   
                 −119.5453 
                 13.48000 
                   
                 67.20 
               
               
                 10 
                   
                 −78.2658 
                 6.00000 
                 FD5 
                 68.80 
               
               
                 11 
                   
                 158.5274 
                 13.50000 
                 FCD1 
                 77.70 
               
               
                 12 
                   
                 −158.5274 
                 0.10000 
                   
                 79.90 
               
               
                 13 
                   
                 139.1541 
                 16.70000 
                 FCD1 
                 88.00 
               
               
                 14 
                   
                 −176.7399 
                 35.55000 
                   
                 88.60 
               
               
                 15 
                   
                 112.2150 
                 19.30000 
                 FCD1 
                 89.00 
               
               
                 16 
                   
                 −157.8763 
                 0.90000 
                   
                 88.00 
               
               
                 17 
                   
                 −217.6579 
                 8.00000 
                 FEL6 
                 85.70 
               
               
                 18 
                   
                 217.6579 
                 8.72000 
                   
                 80.50 
               
               
                 19 
                 a 
                 −1204.7930 
                 9.00000 
                 ACRYLIC 
                 79.90 
               
               
                 20 
                   
                 −266.7334 
                 Space 3 
                   
                 79.70 
               
               
                 21 
                   
                 ∞ 
                 17.00000 
                   
                 80.00 
               
               
                 22 
                   
                 ∞ 
                 55.00000 
                 BSC7 
                 80.00 
               
               
                 23 
                   
                 ∞ 
                 32580.94922 
                   
                 70.00 
               
               
                 24 
                   
                 Aper. stop 
                 −32580.94922 
                   
                 12029.19 
               
               
                 25 
                   
                 ∞ 
                 0.00000 
                   
                 70.00 
               
               
                 26 
                   
                 ∞ 
                 2.50000 
                 BSC7 
                 70.00 
               
               
                 27 
                   
                 ∞ 
                 Image distance 
                   
                 70.00 
               
               
                   
               
             
          
           
               
                 Symbol Description 
               
               
                 a - Polynomial asphere 
               
               
                 c - Conic section 
               
             
          
           
               
                 Even Polynomial Aspheres and Conic Constants 
                   
               
             
          
           
               
                 Surf. 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 No. 
                 k 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 1 
                   
                 −3.7810E − 08 
                  3.8833E − 11 
                  4.3571E − 15 
                 −1.0785E − 18 
                 −3.9211E − 22 
                  6.9576E − 26 
                   
               
               
                 2 
                 −1.2000E + 00 
                  4.3607E − 07 
                  1.0988E − 10 
                 −3.6564E − 14 
                  2.5559E − 17 
                  1.2829E − 20 
                 −7.5081E − 24 
               
               
                 19 
                   
                 −7.7096E − 07 
                 −5.1172E − 11 
                 −2.0446E − 14 
                  1.5579E − 17 
                 −2.9214E − 21 
                 −7.1999E − 25 
               
               
                   
               
             
          
           
               
                 Variable Spaces 
                   
               
             
          
           
               
                 Zoom/Focus 
                 Space 1 
                 Space 2 
                 Space 3 
                 Focal 
                 Image 
                   
               
               
                 Pos. 
                 T(5) 
                 T(7) 
                 T(20) 
                 Shift 
                 Distance 
               
               
                   
               
               
                 1 
                 78.612 
                 26.342 
                 19.043 
                 −0.064 
                 0.408 
               
               
                 2 
                 40.873 
                 26.342 
                 30.135 
                 −0.088 
                 0.401 
               
               
                 3 
                 7.086 
                 26.342 
                 44.452 
                 −0.089 
                 0.394 
               
               
                 4 
                 78.612 
                 27.165 
                 18.223 
                 −0.083 
                 0.406 
               
               
                 5 
                 7.086 
                 27.457 
                 43.334 
                 −0.052 
                 0.390 
               
               
                 6 
                 78.612 
                 25.832 
                 19.554 
                 −0.074 
                 0.408 
               
               
                 7 
                 7.086 
                 25.415 
                 45.379 
                 −0.106 
                 0.399 
               
               
                   
               
             
          
           
               
                 POS 1 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1500.0 
                 f/ 2.81 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11789. 
               
             
          
           
               
                   
                 EFL: 51.3345 
                 FVD: 446.536 
                 ENP: 68.0696 
               
               
                   
                 IMD: 0.408490 
                 BRL: 446.127 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2265.24 
                 OVL: 2711.77 
               
               
                   
                   
               
             
          
           
               
                 POS 2 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1400.0 
                 f/ 2.81 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11791. 
               
             
          
           
               
                   
                 EFL: 61.1831 
                 FVD: 419.881 
                 ENP: 59.1300 
               
               
                   
                 IMD: 0.400794 
                 BRL: 419.480 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2721.80 
                 OVL: 3141.68 
               
               
                   
                   
               
             
          
           
               
                 POS 3 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1400.0 
                 f/ 2.81 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11784. 
               
             
          
           
               
                   
                 EFL: 73.8712 
                 FVD: 400.404 
                 ENP: 47.6042 
               
               
                   
                 IMD: 0.394117 
                 BRL: 400.010 
                 EXP: 32579.3 
               
               
                   
                 OBD: −3310.01 
                 OVL: 3710.42 
               
               
                   
                   
               
             
          
           
               
                 POS 4 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −4800.0 
                 f/ 2.81 MAG: 
                 −0.0064 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11788. 
               
             
          
           
               
                   
                 EFL: 51.3519 
                 FVD: 446.536 
                 ENP: 68.1940 
               
               
                   
                 IMD: 0.405961 
                 BRL: 446.130 
                 EXP: 32579.3 
               
               
                   
                 OBD: −7955.46 
                 OVL: 8401.99 
               
               
                   
                   
               
             
          
           
               
                 POS 5 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −4640.0 
                 f/ 2.81 MAG: 
                 −0.0066 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11780. 
               
             
          
           
               
                   
                 EFL: 73.7874 
                 FVD: 400.398 
                 ENP: 47.9533 
               
               
                   
                 IMD: 0.390076 
                 BRL: 400.008 
                 EXP: 32579.3 
               
               
                   
                 OBD: −11131.8 
                 OVL: 11532.2 
               
               
                   
                   
               
             
          
           
               
                 POS 6 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −960.00 
                 f/ 2.81 MAG: 
                 −0.0321 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11790. 
               
             
          
           
               
                   
                 EFL: 51.3237 
                 FVD: 446.536 
                 ENP: 67.9925 
               
               
                   
                 IMD: 0.408276 
                 BRL: 446.127 
                 EXP: 32579.3 
               
               
                   
                 OBD: −1530.80 
                 OVL: 1977.33 
               
               
                   
                   
               
             
          
           
               
                 POS 7 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −890.00 
                 f/ 2.81 MAG: 
                 −0.0346 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11788. 
               
             
          
           
               
                   
                 EFL: 73.9411 
                 FVD: 400.409 
                 ENP: 47.3132 
               
               
                   
                 IMD: 0.399310 
                 BRL: 400.010 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2089.54 
                 OVL: 2489.95 
               
               
                   
                   
               
             
          
           
               
                 First−Order Data 
               
             
          
           
               
                 Zoom/Focus Position 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 f/number 
                 2.81 
                 2.81 
                 2.81 
                 2.81 
                 2.81 
                 2.81 
                 2.81 
               
               
                 Magnification 
                 −0.0220 
                 −0.0220 
                 −0.0220 
                 −0.0064 
                 −0.0066 
                 −0.0321 
                 −0.0346 
               
               
                 Object Height 
                 −1500.0 
                 −1400.0 
                 −1400.0 
                 −4800.0 
                 −4640.0 
                 −960.00 
                 −890.00 
               
               
                 Object Distance 
                 −2265.2 
                 −2721.8 
                 −3310.0 
                 −7955.5 
                 −11132. 
                 −1530.8 
                 −2089.5 
               
               
                 Effective Focal Length 
                 51.335 
                 61.183 
                 73.871 
                 51.352 
                 73.787 
                 51.324 
                 73.941 
               
               
                 Image Distance 
                 0.40849 
                 0.40079 
                 0.39412 
                 0.40596 
                 0.39008 
                 0.40828 
                 0.39931 
               
               
                 Overall Length 
                 2711.8 
                 3141.7 
                 3710.4 
                 8402.0 
                 11532. 
                 1977.3 
                 2490.0 
               
               
                 Forward Vertex Distance 
                 446.54 
                 419.88 
                 400.40 
                 446.54 
                 400.40 
                 446.54 
                 400.41 
               
               
                 Barrel Length 
                 446.13 
                 419.48 
                 400.01 
                 446.13 
                 400.01 
                 446.13 
                 400.01 
               
               
                 Stop Surface Number 
                 24 
                 24 
                 24 
                 24 
                 24 
                 24 
                 24 
               
               
                 Distance to Stop 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 Stop Diameter 
                 −11789.348 
                 −11791.152 
                 −11784.277 
                 −11787.995 
                 −11780.033 
                 −11790.147 
                 −11787.969 
               
               
                 Entrance Pupil Distance 
                 68.070 
                 59.130 
                 47.604 
                 68.194 
                 47.953 
                 67.993 
                 47.313 
               
               
                 Exit Pupil Distance 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
               
               
                   
               
             
          
           
               
                 First Order Properties of Elements 
                   
               
             
          
           
               
                 Element 
                 Surface 
                   
                   
                   
                   
               
               
                 Number 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.84925E − 02 
                 −117.75 
                   
               
               
                 2 
                 3 
                 4 
                 −0.90534E − 02 
                 −110.46 
               
               
                 3 
                 4 
                 5 
                  0.78703E − 02 
                 127.06 
               
               
                 4 
                 6 
                 7 
                  0.41980E − 02 
                 238.21 
               
               
                 5 
                 8 
                 9 
                  0.37141E − 02 
                 269.25 
               
               
                 6 
                 10 
                 11 
                 −0.13065E − 01 
                 −76.539 
               
               
                 7 
                 11 
                 12 
                  0.61994E − 02 
                 161.31 
               
               
                 8 
                 13 
                 14 
                  0.62897E − 02 
                 158.99 
               
               
                 9 
                 15 
                 16 
                  0.74185E − 02 
                 134.80 
               
               
                 10 
                 17 
                 18 
                 −0.49410E − 02 
                 −202.39 
               
               
                 11 
                 19 
                 20 
                  0.14407E − 02 
                 694.10 
               
               
                   
               
             
          
           
               
                 First−Order Properties of Doublets 
                   
               
             
          
           
               
                   
                 Element 
                 Surface 
                   
                   
                   
                   
               
               
                   
                 Numbers 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
                   
               
             
          
           
               
                   
                 2 
                 3 
                 3 
                 5 
                 −0.84544E − 03 
                 −1182.8 
                   
               
               
                   
                 6 
                 7 
                 10 
                 12 
                 −0.63038E − 02 
                 −158.64 
               
               
                   
                   
               
             
          
           
               
                 First Order Properties of Groups 
                   
               
             
          
           
               
                 Group 
                 Surface 
                   
                   
                   
                   
               
               
                 Number 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 5 
                 −0.95858E − 02 
                 −104.32 
                   
               
               
                 2 
                 6 
                 7 
                  0.41980E − 02 
                 238.21 
               
               
                 3 
                 8 
                 20 
                  0.75751E − 02 
                 132.01 
               
               
                   
               
             
          
           
               
                 First Order Properties of the Lens 
                   
               
             
          
           
               
                 Zoom/Focus Position 
                   
                   
                   
               
               
                 Number 
                 Power 
                 f′ 
               
               
                   
               
               
                 1 
                 0.19480E − 01 
                 51.335 
               
               
                 2 
                 0.16344E − 01 
                 61.183 
               
               
                 3 
                 0.13537E − 01 
                 73.871 
               
               
                 4 
                 0.19473E − 01 
                 51.352 
               
               
                 5 
                 0.13552E − 01 
                 73.787 
               
               
                 6 
                 0.19484E − 01 
                 51.324 
               
               
                 7 
                 0.13524E − 01 
                 73.941 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                 Surf. 
                   
                   
                   
                   
                 Clear Aperture 
                   
               
               
                 No. 
                 Type 
                 Radius 
                 Thickness 
                 Glass 
                 Diameter 
               
               
                   
               
               
                 1 
                 a 
                 256.2114 
                 9.00000 
                 ACRYLIC 
                 104.16 
                   
               
               
                 2 
                 ac 
                 46.6427 
                 71.04216 
                   
                 81.05 
               
               
                 3 
                   
                 −68.5819 
                 4.10000 
                 FCD1 
                 54.77 
               
               
                 4 
                   
                 230.5086 
                 8.00000 
                 TAF3 
                 54.54 
               
               
                 5 
                   
                 −172.4161 
                 Space 1 
                   
                 54.45 
               
               
                 6 
                   
                 170.1619 
                 8.14000 
                 FD60 
                 50.53 
               
               
                 7 
                   
                 985.0964 
                 Space 2 
                   
                 51.90 
               
               
                 8 
                   
                 −1806.9340 
                 12.90000 
                 FCD1 
                 63.83 
               
               
                 9 
                   
                 −119.5506 
                 12.76572 
                   
                 66.37 
               
               
                 10 
                   
                 −78.5134 
                 6.00000 
                 FD5 
                 68.04 
               
               
                 11 
                   
                 182.0865 
                 13.50000 
                 FCD1 
                 76.59 
               
               
                 12 
                   
                 −155.7738 
                 0.10000 
                   
                 79.19 
               
               
                 13 
                   
                 143.0293 
                 16.40000 
                 FCD1 
                 86.91 
               
               
                 14 
                   
                 −185.9051 
                 33.71327 
                   
                 87.70 
               
               
                 15 
                   
                 121.7684 
                 19.33261 
                 FCD1 
                 89.21 
               
               
                 16 
                   
                 −165.2038 
                 1.22690 
                   
                 88.11 
               
               
                 17 
                   
                 −274.4370 
                 9.00000 
                 FEL6 
                 85.52 
               
               
                 18 
                   
                 232.5454 
                 8.00000 
                   
                 80.76 
               
               
                 19 
                 a 
                 −1162.4850 
                 11.00000 
                 ACRYLIC 
                 80.29 
               
               
                 20 
                   
                 −250.2591 
                 Space 3 
                   
                 80.19 
               
               
                 21 
                   
                 ∞ 
                 17.00000 
                   
                 75.54 
               
               
                 22 
                   
                 ∞ 
                 55.00000 
                 BSC7 
                 72.41 
               
               
                 23 
                   
                 ∞ 
                 32580.94922 
                   
                 65.76 
               
               
                 24 
                   
                 Aper. stop 
                 −32580.94922 
                   
                 12022.52 
               
               
                 25 
                   
                 ∞ 
                 0.00000 
                   
                 65.76 
               
               
                 26 
                   
                 ∞ 
                 2.50000 
                 BSC7 
                 65.76 
               
               
                 27 
                   
                 ∞ 
                 Image distance 
                   
                 65.46 
               
               
                   
               
             
          
           
               
                 Symbol Description 
               
               
                 a - Polynomial asphere 
               
               
                 c - Conic section 
               
             
          
           
               
                 Even Polynomial Aspheres and Conic Constants 
                   
               
             
          
           
               
                 Surf. 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 No. 
                 k 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 1 
                   
                  7.6142E − 08 
                  2.1400E − 11 
                  3.5721E − 15 
                 −1.8127E − 19 
                 −2.7585E − 22 
                  4.2049E − 26 
                   
               
               
                 2 
                 −1.2000E + 00 
                  6.9750E − 07 
                  1.5171E − 10 
                 −3.5735E − 14 
                  2.2817E − 17 
                  1.1872E − 20 
                 −4.3252E − 24 
               
               
                 19 
                   
                 −7.1999E − 07 
                 −2.8786E − 11 
                 −2.5403E − 14 
                  1.0105E − 17 
                  9.9122E − 22 
                 −1.2757E − 24 
               
               
                   
               
             
          
           
               
                 Variable Spaces 
                   
               
             
          
           
               
                 Zoom/Focus 
                 Space 1 
                 Space 2 
                 Space 3 
                 Focal 
                 Image 
                   
               
               
                 Pos. 
                 T(5) 
                 T(7) 
                 T(20) 
                 Shift 
                 Distance 
               
               
                   
               
               
                 1 
                 78.798 
                 27.949 
                 20.652 
                 −0.048 
                 0.399 
               
               
                 2 
                 41.563 
                 27.949 
                 32.019 
                 −0.060 
                 0.400 
               
               
                 3 
                 9.348 
                 27.949 
                 46.123 
                 −0.054 
                 0.400 
               
               
                 4 
                 78.798 
                 28.761 
                 19.841 
                 −0.058 
                 0.402 
               
               
                 5 
                 9.348 
                 29.097 
                 44.975 
                 −0.033 
                 0.399 
               
               
                 6 
                 78.798 
                 27.436 
                 21.164 
                 −0.052 
                 0.398 
               
               
                 7 
                 9.348 
                 27.006 
                 47.066 
                 −0.071 
                 0.400 
               
               
                   
               
             
          
           
               
                 POS 1 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1500.0 
                 f/ 2.81 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11785. 
               
             
          
           
               
                   
                 EFL: 51.1386 
                 FVD: 446.519 
                 ENP: 67.4777 
               
               
                   
                 IMD: 0.399020 
                 BRL: 446.120 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2256.93 
                 OVL: 2703.44 
               
               
                   
                   
               
             
          
           
               
                 POS 2 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1400.0 
                 f/ 2.81 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11532. 
               
             
          
           
               
                   
                 EFL: 61.0036 
                 FVD: 420.651 
                 ENP: 58.7259 
               
               
                   
                 IMD: 0.399612 
                 BRL: 420.252 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2714.05 
                 OVL: 3134.70 
               
               
                   
                   
               
             
          
           
               
                 POS 3 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1400.0 
                 f/ 2.81 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11282. 
               
             
          
           
               
                   
                 EFL: 73.2246 
                 FVD: 402.540 
                 ENP: 47.8756 
               
               
                   
                 IMD: 0.399977 
                 BRL: 402.140 
                 EXP: 32579.3 
               
               
                   
                 OBD: −3280.35 
                 OVL: 3682.89 
               
               
                   
                   
               
             
          
           
               
                 POS 4 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −4800.0 
                 f/ 2.81 MAG: 
                 −0.0064 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11784. 
               
             
          
           
               
                   
                 EFL: 51.1401 
                 FVD: 446.523 
                 ENP: 67.6082 
               
               
                   
                 IMD: 0.401728 
                 BRL: 446.121 
                 EXP: 32579.3 
               
               
                   
                 OBD: −7922.95 
                 OVL: 8369.47 
               
               
                   
                   
               
             
          
           
               
                 POS 5 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −4640.0 
                 f/ 2.81 MAG: 
                 −0.0066 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11279. 
               
             
          
           
               
                   
                 EFL: 73.0988 
                 FVD: 402.538 
                 ENP: 48.2536 
               
               
                   
                 IMD: 0.398550 
                 BRL: 402.140 
                 EXP: 32579.3 
               
               
                   
                 OBD: −11027.2 
                 OVL: 11429.7 
               
               
                   
                   
               
             
          
           
               
                 POS 6 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −960.00 
                 f/ 2.81 MAG: 
                 −0.0321 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11786. 
               
             
          
           
               
                   
                 EFL: 51.1377 
                 FVD: 446.518 
                 ENP: 67.3953 
               
               
                   
                 IMD: 0.398357 
                 BRL: 446.119 
                 EXP: 32579.3 
               
               
                   
                 OBD: −1525.60 
                 OVL: 1972.12 
               
               
                   
                   
               
             
          
           
               
                 POS 7 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −890.00 
                 f/ 2.93 MAG: 
                 −0.0346 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11285. 
               
             
          
           
               
                   
                 EFL: 73.3284 
                 FVD: 402.541 
                 ENP: 47.5641 
               
               
                   
                 IMD: 0.400345 
                 BRL: 402.140 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2071.59 
                 OVL: 2474.13 
               
               
                   
                   
               
             
          
           
               
                 First−Order Data 
               
             
          
           
               
                 Zoom/Focus Position 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 f/number 
                 2.81 
                 2.87 
                 2.93 
                 2.81 
                 2.93 
                 2.81 
                 2.93 
               
               
                 Magnification 
                 −0.0220 
                 −0.0220 
                 −0.0220 
                 −0.0064 
                 −0.0066 
                 −0.0321 
                 −0.0346 
               
               
                 Object Height 
                 −1500.0 
                 −1400.0 
                 −1400.0 
                 −4800.0 
                 −4640.0 
                 −960.00 
                 −890.00 
               
               
                 Object Distance 
                 −2256.9 
                 −2714.1 
                 −3280.4 
                 −7923.0 
                 −11027. 
                 −1525.6 
                 −2071.6 
               
               
                 Effective Focal Length 
                 51.139 
                 61.004 
                 73.225 
                 51.140 
                 73.099 
                 51.138 
                 73.328 
               
               
                 Image Distance 
                 0.39902 
                 0.39961 
                 0.39998 
                 0.40173 
                 0.39855 
                 0.39836 
                 0.40034 
               
               
                 Overall Length 
                 2703.4 
                 3134.7 
                 3682.9 
                 8369.5 
                 11430. 
                 1972.1 
                 2474.1 
               
               
                 Forward Vertex Distance 
                 446.52 
                 420.65 
                 402.54 
                 446.52 
                 402.54 
                 446.52 
                 402.54 
               
               
                 Barrel Length 
                 446.12 
                 420.25 
                 402.14 
                 446.12 
                 402.14 
                 446.12 
                 402.14 
               
               
                 Stop Surface Number 
                 24 
                 24 
                 24 
                 24 
                 24 
                 24 
                 24 
               
               
                 Distance to Stop 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 Stop Diameter 
                 −11785.247 
                 −11532.072 
                 −11282.355 
                 −11783.909 
                 −11278.769 
                 −11786.057 
                 −11285.433 
               
               
                 Entrance Pupil Distance 
                 67.478 
                 58.726 
                 47.876 
                 67.608 
                 48.254 
                 67.395 
                 47.564 
               
               
                 Exit Pupil Distance 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
               
               
                   
               
             
          
           
               
                 First Order Properties of Elements 
                   
               
             
          
           
               
                 Element 
                 Surface 
                   
                   
                   
                   
               
               
                 Number 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.85362E − 02 
                 −117.15 
                   
               
               
                 2 
                 3 
                 4 
                 −0.94733E − 02 
                 −105.56 
               
               
                 3 
                 4 
                 5 
                  0.81220E − 02 
                 123.12 
               
               
                 4 
                 6 
                 7 
                  0.39684E − 02 
                 251.99 
               
               
                 5 
                 8 
                 9 
                  0.39034E − 02 
                 256.19 
               
               
                 6 
                 10 
                 11 
                 −0.12467E − 01 
                 −80.209 
               
               
                 7 
                 11 
                 12 
                  0.58583E − 02 
                 170.70 
               
               
                 8 
                 13 
                 14 
                  0.60639E − 02 
                 164.91 
               
               
                 9 
                 15 
                 16 
                  0.69513E − 02 
                 143.86 
               
               
                 10 
                 17 
                 18 
                 −0.42708E − 02 
                 −234.15 
               
               
                 11 
                 19 
                 20 
                  0.15545E − 02 
                 643.31 
               
               
                   
               
             
          
           
               
                 First−Order Properties of Doublets 
                   
               
             
          
           
               
                   
                 Element 
                 Surface 
                   
                   
                   
                   
               
               
                   
                 Numbers 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
                   
               
             
          
           
               
                   
                 2 
                 3 
                 3 
                 5 
                 −0.99328E − 03 
                 −1006.8 
                   
               
               
                   
                 6 
                 7 
                 10 
                 12 
                 −0.60688E − 02 
                 −164.78 
               
               
                   
                   
               
             
          
           
               
                 First Order Properties of Groups 
                   
               
             
          
           
               
                 Group 
                 Surface 
                   
                   
                   
                   
               
               
                 Number 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 5 
                 −0.98030E − 02 
                 −102.01 
                   
               
               
                 2 
                 6 
                 7 
                  0.39684E − 02 
                 251.99 
               
               
                 3 
                 8 
                 20 
                  0.78383E − 02 
                 127.58 
               
               
                   
               
             
          
           
               
                 First Order Properties of the Lens 
                   
               
             
          
           
               
                 Zoom/Focus Position 
                   
                   
                   
               
               
                 Number 
                 Power 
                 f′ 
               
               
                   
               
               
                 1 
                 0.19555E − 01 
                 51.139 
               
               
                 2 
                 0.16392E − 01 
                 61.004 
               
               
                 3 
                 0.13657E − 01 
                 73.225 
               
               
                 4 
                 0.19554E − 01 
                 51.140 
               
               
                 5 
                 0.13680E − 01 
                 73.099 
               
               
                 6 
                 0.19555E − 01 
                 51.138 
               
               
                 7 
                 0.13637E − 01 
                 73.328 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
               
               
             
               
             
               
               
             
               
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
               
             
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
             
               
               
             
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                 Surf. 
                   
                   
                   
                   
                 Clear Aperture 
                   
               
               
                 No. 
                 Type 
                 Radius 
                 Thickness 
                 Glass 
                 Diameter 
               
               
                   
               
               
                 1 
                 a 
                 302.1309 
                 9.00000 
                 ACRYLIC 
                 104.09 
                   
               
               
                 2 
                 ac 
                 47.4329 
                 78.37469 
                   
                 81.77 
               
               
                 3 
                   
                 −70.3606 
                 4.10000 
                 FCD1 
                 52.72 
               
               
                 4 
                   
                 272.0798 
                 7.00000 
                 TAF3 
                 52.85 
               
               
                 5 
                   
                 −161.8160 
                 Space 1 
                   
                 52.77 
               
               
                 6 
                   
                 156.5210 
                 8.14000 
                 FD60 
                 54.31 
               
               
                 7 
                   
                 730.4220 
                 Space 2 
                   
                 55.33 
               
               
                 8 
                   
                 −1473.8400 
                 9.00000 
                 FCD1 
                 66.20 
               
               
                 9 
                   
                 −119.4897 
                 13.46569 
                   
                 67.52 
               
               
                 10 
                   
                 −78.2719 
                 6.00000 
                 FD5 
                 69.04 
               
               
                 11 
                   
                 162.3287 
                 13.50000 
                 FCD1 
                 77.92 
               
               
                 12 
                   
                 −162.3287 
                 0.10000 
                   
                 80.18 
               
               
                 13 
                   
                 137.3497 
                 17.00000 
                 FCD1 
                 88.34 
               
               
                 14 
                   
                 −175.1294 
                 35.71132 
                   
                 89.01 
               
               
                 15 
                   
                 114.2469 
                 19.00000 
                 FCD1 
                 88.81 
               
               
                 16 
                   
                 −160.1066 
                 0.78711 
                   
                 87.72 
               
               
                 17 
                   
                 −221.1460 
                 8.00000 
                 FEL6 
                 85.59 
               
               
                 18 
                   
                 221.1460 
                 8.62819 
                   
                 80.38 
               
               
                 19 
                 a 
                 −1075.3290 
                 9.00000 
                 ACRYLIC 
                 79.76 
               
               
                 20 
                   
                 −260.9656 
                 Space 3 
                   
                 79.58 
               
               
                 21 
                   
                 ∞ 
                 17.00000 
                   
                 75.55 
               
               
                 22 
                   
                 ∞ 
                 55.00000 
                 BSC7 
                 72.42 
               
               
                 23 
                   
                 ∞ 
                 32580.94922 
                   
                 65.78 
               
               
                 24 
                   
                 Aper. stop 
                 −32580.94922 
                   
                 12031.11 
               
               
                 25 
                   
                 ∞ 
                 0.00000 
                   
                 65.78 
               
               
                 26 
                   
                 ∞ 
                 2.50000 
                 BSC7 
                 65.78 
               
               
                 27 
                   
                 ∞ 
                 Image distance 
                   
                 65.48 
               
               
                   
               
             
          
           
               
                 Symbol Description 
               
               
                 a - Polynomial asphere 
               
               
                 c - Conic section 
               
             
          
           
               
                 Even Polynomial Aspheres and Conic Constants 
                   
               
             
          
           
               
                 Surf. 
                   
                   
                   
                   
                   
                   
                   
                   
               
               
                 No. 
                 k 
                 D 
                 E 
                 F 
                 G 
                 H 
                 I 
               
               
                   
               
               
                 1 
                   
                 −8.2781E − 08 
                  4.5513E − 11 
                  6.6948E − 15 
                 −9.6646E − 19 
                 −7.5403E − 22 
                  1.1147E − 25 
                   
               
               
                 2 
                 −1.2000E + 00 
                  4.5209E − 07 
                  7.3282E − 11 
                 −1.1459E − 14 
                  3.5740E − 17 
                  1.0182E − 20 
                 −9.0498E − 24 
               
               
                 19 
                   
                 −7.8117E − 07 
                 −3.8380E − 11 
                 −2.2648E − 14 
                  8.6573E − 18 
                  1.8343E − 21 
                 −1.6207E − 24 
               
               
                   
               
             
          
           
               
                 Variable Spaces 
                   
               
             
          
           
               
                 Zoom/Focus 
                 Space 1 
                 Space 2 
                 Space 3 
                 Focal 
                 Image 
                   
               
               
                 Pos. 
                 T(5) 
                 T(7) 
                 T(20) 
                 Shift 
                 Distance 
               
               
                   
               
               
                 1 
                 78.865 
                 27.019 
                 18.928 
                 −0.059 
                 0.398 
               
               
                 2 
                 40.861 
                 27.019 
                 29.970 
                 −0.071 
                 0.399 
               
               
                 3 
                 12.269 
                 27.019 
                 41.546 
                 −0.075 
                 0.400 
               
               
                 4 
                 78.865 
                 27.840 
                 18.111 
                 −0.071 
                 0.403 
               
               
                 5 
                 12.269 
                 28.109 
                 40.454 
                 −0.053 
                 0.399 
               
               
                 6 
                 78.865 
                 26.507 
                 19.440 
                 −0.065 
                 0.398 
               
               
                 7 
                 12.269 
                 26.116 
                 42.449 
                 −0.086 
                 0.400 
               
               
                   
               
             
          
           
               
                 POS 1 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1500.0 
                 f/ 2.81 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11788. 
               
             
          
           
               
                   
                 EFL: 51.1920 
                 FVD: 446.517 
                 ENP: 67.4879 
               
               
                   
                 IMD: 0.398173 
                 BRL: 446.119 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2259.34 
                 OVL: 2705.86 
               
               
                   
                   
               
             
          
           
               
                 POS 2 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1400.0 
                 f/ 2.87 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11534. 
               
             
          
           
               
                   
                 EFL: 60.9989 
                 FVD: 419.557 
                 ENP: 58.5814 
               
               
                   
                 IMD: 0.399452 
                 BRL: 419.157 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2713.98 
                 OVL: 3133.54 
               
               
                   
                   
               
             
          
           
               
                 POS 3 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −1400.0 
                 f/ 2.93 MAG: 
                 −0.0220 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11285. 
               
             
          
           
               
                   
                 EFL: 71.2712 
                 FVD: 402.541 
                 ENP: 49.2460 
               
               
                   
                 IMD: 0.400403 
                 BRL: 402.140 
                 EXP: 32579.3 
               
               
                   
                 OBD: −3190.20 
                 OVL: 3592.74 
               
               
                   
                   
               
             
          
           
               
                 POS 4 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −4800.0 
                 f/ 2.81 MAG: 
                 −0.0064 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11787. 
               
             
          
           
               
                   
                 EFL: 51.2062 
                 FVD: 446.525 
                 ENP: 67.6122 
               
               
                   
                 IMD: 0.403203 
                 BRL: 446.122 
                 EXP: 32579.3 
               
               
                   
                 OBD: −7933.27 
                 OVL: 8379.80 
               
               
                   
                   
               
             
          
           
               
                 POS 5 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −4640.0 
                 f/ 2.93 MAG: 
                 −0.0066 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11282. 
               
             
          
           
               
                   
                 EFL: 71.1979 
                 FVD: 402.538 
                 ENP: 49.5662 
               
               
                   
                 IMD: 0.398532 
                 BRL: 402.139 
                 EXP: 32579.3 
               
               
                   
                 OBD: −10737.8 
                 OVL: 11140.4 
               
               
                   
                   
               
             
          
           
               
                 POS 6 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −960.00 
                 f/ 2.81 MAG: 
                 −0.0321 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11789. 
               
             
          
           
               
                   
                 EFL: 51.1831 
                 FVD: 446.517 
                 ENP: 67.4104 
               
               
                   
                 IMD: 0.397928 
                 BRL: 446.119 
                 EXP: 32579.3 
               
               
                   
                 OBD: −1527.00 
                 OVL: 1973.52 
               
               
                   
                   
               
             
          
           
               
                 POS 7 System First Order Properties 
                   
               
             
          
           
               
                   
                 OBJ. HT: −890.00 
                 f/ 2.93 MAG: 
                 −0.0346 
               
             
          
           
               
                   
                 STOP: 0.00 after surface 24. DIA: −11288. 
               
             
          
           
               
                   
                 EFL: 71.3321 
                 FVD: 402.541 
                 ENP: 48.9803 
               
               
                   
                 IMD: 0.400167 
                 BRL: 402.140 
                 EXP: 32579.3 
               
               
                   
                 OBD: −2012.48 
                 OVL: 2415.02 
               
               
                   
                   
               
             
          
           
               
                 First−Order Data 
               
             
          
           
               
                 Zoom/Focus Position 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
               
                 f/number 
                 2.81 
                 2.87 
                 2.93 
                 2.81 
                 2.93 
                 2.81 
                 2.93 
               
               
                 Magnification 
                 −0.0220 
                 −0.0220 
                 −0.0220 
                 −0.0064 
                 −0.0066 
                 −0.0321 
                 −0.0346 
               
               
                 Object Height 
                 −1500.0 
                 −1400.0 
                 −1400.0 
                 −4800.0 
                 −4640.0 
                 −960.00 
                 −890.00 
               
               
                 Object Distance 
                 −2259.3 
                 −2714.1 
                 −3190.2 
                 −7933.3 
                 −10738. 
                 −1527.0 
                 −2012.5 
               
               
                 Effective Focal Length 
                 51.192 
                 60.999 
                 71.271 
                 51.206 
                 71.198 
                 51.183 
                 71.332 
               
               
                 Image Distance 
                 0.39817 
                 0.39945 
                 0.40040 
                 0.40320 
                 0.39853 
                 0.39793 
                 0.40017 
               
               
                 Overall Length 
                 2705.9 
                 3133.5 
                 3592.7 
                 8379.8 
                 11140. 
                 1973.5 
                 2415.0 
               
               
                 Forward Vertex Distance 
                 446.52 
                 419.56 
                 402.54 
                 446.53 
                 402.54 
                 446.52 
                 402.54 
               
               
                 Barrel Length 
                 446.12 
                 419.16 
                 402.14 
                 446.12 
                 402.14 
                 446.12 
                 402.14 
               
               
                 Stop Surface Number 
                 24 
                 24 
                 24 
                 24 
                 24 
                 24 
                 24 
               
               
                 Distance to Stop 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
                 0.00 
               
               
                 Stop Diameter 
                 −11787.868 
                 −11534.243 
                 −11285.378 
                 −11786.588 
                 −11282.079 
                 −11788.625 
                 −11288.220 
               
               
                 Entrance Pupil Distance 
                 67.488 
                 58.581 
                 49.246 
                 67.612 
                 49.566 
                 67.410 
                 48.980 
               
               
                 Exit Pupil Distance 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
                 32579. 
               
               
                   
               
             
          
           
               
                 First Order Properties of Elements 
                   
               
             
          
           
               
                 Element 
                 Surface 
                   
                   
                   
                   
               
               
                 Number 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 2 
                 −0.86732E − 02 
                 −115.30 
                   
               
               
                 2 
                 3 
                 4 
                 −0.89517E − 02 
                 −111.71 
               
               
                 3 
                 4 
                 5 
                  0.79087E − 02 
                 126.44 
               
               
                 4 
                 6 
                 7 
                  0.41052E − 02 
                 243.59 
               
               
                 5 
                 8 
                 9 
                  0.38418E − 02 
                 260.30 
               
               
                 6 
                 10 
                 11 
                 −0.12961E − 01 
                 −77.152 
               
               
                 7 
                 11 
                 12 
                  0.60563E − 02 
                 165.12 
               
               
                 8 
                 13 
                 14 
                  0.63580E − 02 
                 157.28 
               
               
                 9 
                 15 
                 16 
                  0.73039E − 02 
                 136.91 
               
               
                 10 
                 17 
                 18 
                 −0.48626E − 02 
                 −205.65 
               
               
                 11 
                 19 
                 20 
                  0.14382E − 02 
                 695.33 
               
               
                   
               
             
          
           
               
                 First−Order Properties of Doublets 
                   
               
             
          
           
               
                   
                 Element 
                 Surface 
                   
                   
                   
                   
               
               
                   
                 Numbers 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
                   
               
             
          
           
               
                   
                 2 
                 3 
                 3 
                 5 
                 −0.71667E − 03 
                 −1395.3 
                   
               
               
                   
                 6 
                 7 
                 10 
                 12 
                 −0.63590E − 02 
                 −157.26 
               
               
                   
                   
               
             
          
           
               
                 First Order Properties of Groups 
                   
               
             
          
           
               
                 Group 
                 Surface 
                   
                   
                   
                   
               
               
                 Number 
                 Numbers 
                   
                 Power 
                 f′ 
               
               
                   
               
             
          
           
               
                 1 
                 1 
                 5 
                 −0.95572E − 02 
                 −104.63 
                   
               
               
                 2 
                 6 
                 7 
                  0.41052E − 02 
                 243.59 
               
               
                 3 
                 8 
                 20 
                  0.76042E − 02 
                 131.51 
               
               
                   
               
             
          
           
               
                 First Order Properties of the Lens 
                   
               
             
          
           
               
                 Zoom/Focus Position 
                   
                   
                   
               
               
                 Number 
                 Power 
                 f′ 
               
               
                   
               
               
                 1 
                 0.19534E − 01 
                 51.192 
               
               
                 2 
                 0.16394E − 01 
                 60.999 
               
               
                 3 
                 0.14031E − 01 
                 71.271 
               
               
                 4 
                 0.19529E − 01 
                 51.206 
               
               
                 5 
                 0.14045E − 01 
                 71.198 
               
               
                 6 
                 0.19538E − 01 
                 51.183 
               
               
                 7 
                 0.14019E − 01 
                 71.332