Abstract:
According to one aspect of the invention there is provided a panoramic imaging arrangement comprising a first and second transparent component both rotationally symmetric about an axis of revolution. The first transparent component has an upper surface and a lower surface. The lower surface includes a reflective portion and a refractive portion both about the axis of revolution. The refractive portion extends radially from the axis of revolution to the start of the reflective portion. The second transparent component is attached to the first transparent component at a refractive interface that extends into the upper surface. The second transparent component includes a distal reflective surface. Light from a portion of a surrounding panoramic scene is refracted by a portion of the upper surface, is reflected by the reflective portion of the lower surface through the refractive interface to the distal reflective surface. Once reflected from the distal reflective surface, the light again passes through the refractive interface and exits the first transparent component through the refractive portion of the lower surface.

Description:
This application is a continuation-in-part from copending U.S. patent application Ser. No. 09/837,750 filed on Apr. 17, 2001. This application also claims priority to provisional application No. 60/360,138 filed on Feb. 26, 2002 with attorney docket number P011XP having the title Panoramic Imaging Arrangement and with the same inventors. This application also claims priority to provisional application No.60/360,748 filed on Mar. 1, 2002 with attorney docket number P011XP2 having the title Panoramic Imaging Arrangement and with the same inventors. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to a panoramic imaging arrangement of the kind capable of capturing, focusing, correcting aberrations and otherwise manipulating colored light received from a part of or all of a 360° surrounding panoramic scene. 
     2. Discussion of Related Art 
     Paroramic imaging arrangements have become popular in recent years for purposes of viewing 360° surrounding panoramic scenes. Older generations of panoramic imaging arrangements generally consisted of revolving periscope-like constructions having relatively complex mechanisms for revolving them. More recently, stationary panoramic imaging arrangements have been developed. A stationary panoramic imaging arrangement generally has one or more lenses, each having a vertical axis of revolution, which are used to refract or reflect light received from a 360° surrounding panoramic scene. The lenses alter the direction of the light, after which the light passes through a series of lenses which are located vertically one above the other and which further manipulate the light by, for example, focusing the light or altering the intensity of the light. 
     The task of receiving light in a sideways direction and altering the direction of the light so that the light then proceeds in a vertical direction is a difficult one. Altering the direction of light to such a degree, especially when coming from a 360° surrounding scene, often leads to aberrations in the resulting light. These aberrations may include astigmatism of the light, defects in color of the light, a loss of image plane flatness, and other defects, some of which are subsequently discussed in more detail. 
     Relatively complex lenses and lens arrangements have been developed in order to overcome these aberrations and produce an acceptable image. These lens arrangements usually include a large number of lenses and oftentimes have lenses with surfaces that are aspherical (see for example U.S. Pat. No. 5,473,474 issued to Powell). Aspherical lenses are difficult to manufacture and therefore are less practical to manufacture than for example spherical lenses. 
     Because of the astigmatism induced by steep surfaces, well corrected prior art panoramic optical systems (those that have angles substantially above and below the horizon) have some lenses/mirrors that are considerably larger than the image size. Thus, these optical systems are large and have a maximum clear aperture (largest required lens/mirror diameter) of more than 10× the image diameter. 
     In addition, lenses that include voids (air spaces) can be more difficult to manufacture than solid lenses because of the difficulty in aligning the parts of the lens system. 
     It would be advantageous to have a panoramic imaging arrangement that is solid, is color corrected, has a maximum clear aperture (largest required lens/mirror diameter) of less than 8× the image diameter, and has an increased aperture (of the order of F4.6 as compared to F20). 
     SUMMARY OF THE INVENTION 
     According to one aspect of the invention there is provided a panoramic imaging arrangement comprising a first and second transparent component both rotationally symmetric about an axis of revolution. The first transparent component has an upper surface and a lower surface. The lower surface includes a reflective portion and a refractive portion both about the axis of revolution. The refractive portion extends radially from the axis of revolution to the start of the reflective portion. The second transparent component is attached to the first transparent component at a refractive interface that extends into the upper surface. The second transparent component includes a distal reflective surface. 
     Light from a portion of a surrounding panoramic scene is refracted by a portion of the upper surface, is reflected by the reflective portion of the lower surface through the refractive interface to the distal reflective surface. Once reflected from the distal reflective surface, the light again passes through the refractive interface and exits the first transparent component through the refractive portion of the lower surface. 
     Another aspect of the invention is a partial panoramic imaging arrangement that includes a first transparent component about an axis of revolution. The first transparent component has an upper surface and a lower surface. The lower surface includes a first reflective portion and a refractive portion both of these portions about the axis of revolution. The refractive portion is radially inward from said first reflective portion. Light from a greater than 90° surrounding partial panoramic scene, is refracted by a portion of said upper surface. The partial panoramic imaging arrangement also includes a second transparent component attached to the first transparent component at a refractive interface. The refractive interface, also about the axis of revolution and extending into the upper surface. The second transparent component also includes a distal reflective surface. 
     The foregoing and many other aspects of the present invention will no doubt become obvious to those of ordinary skill in the art after having read the following detailed description of the preferred embodiments that are illustrated in the various drawing figures. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a sectioned side view of a panoramic imaging arrangement, according to an embodiment of the invention, in a plane of a vertical axis of revolution thereof, and 
     FIG. 2 is a sectioned side view of a color corrected panoramic imaging arrangement using glass components, according to an embodiment of the invention, in a plan of a vertical axis of revolution thereof; and 
     FIG. 3 is a sectioned side view of a color corrected panoramic imaging arrangement using a selection of glass and plastic components, according to an embodiment of the invention, in a plan of a vertical axis of revolution thereof. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1 of the accompanying drawings illustrates a panoramic imaging arrangement  10 , according to an embodiment of the invention, in a plane of a vertical axis of revolution  12  thereof. The panoramic imaging arrangement  10  includes a lens block  14 , a mirror  16 , and a system of lenses  18 . 
     The lens block  14  includes a transparent component  20  having a first, upper, convex surface  22  symmetrically about the axis of revolution  12  and a second, lower, concave surface  24  also symmetrically about the axis of revolution  12 . A reflective material  26  is formed on the lower, concave surface  24 . A hole  28  is formed vertically through the transparent component  20 . 
     The upper, convex surface  22  of the transparent component  20  is spherical and has a radius of about 21.310 mm. An extension of the upper, convex surface  22  intersects the axis of revolution  12  and a first location  32 . 
     The lower, concave surface  24  of the transparent component  20  is spherical and has a radius of about 40.200 mm. Extensions of the upper, convex surface  22  and of the lower, concave surface  24  intersect one another due to the larger radius of the lower, convex surface  24  with respect to the radius of the upper, convex surface  22 . An extension of the lower, concave surface  24  intersects the axis of revolution  12  and a second location  36  which is located about 9 mm below the first location  32  where the extension of the upper, convex surface  22  intersects the axis of revolution  12 . 
     By forming the reflective material  26  on the lower, concave surface  24 , the reflective material  26  provides a convex reflective surface  38  against the lower, concave surface  24  and conforming in shape thereto. 
     An upper portion of the hole  28  is formed by an opening defining a third, internal surface  40  of the transparent component  20  The internal surface  40  is located symmetrically about the axis of revolution  12 . The internal surface  40  is spherical and has a concave profile with a radius of about 7.650 mm. An extension of the internal surface  40  intersects the axis of revolution  12  at a third location  44  which is located about 0.5 mm above the second location  36  where the extension of the lower, concave surface  24  (and therefore also of the reflective surface  38 ) intersects the axis of revolution  12 . 
     The mirror  16  is secured to the transparent component  20  at a location over the hole  28 . The mirror  16  has a concave reflective area  46  that is spherical and is located symmetrically about the axis of revolution  12 . The reflective area  46  has a radius of about 87.750 mm and intersects to the axis of revolution  12  at a fourth location  48  which is located about 8.115 mm above the third location  44  where an extension of the internal surface  40  intersects the axis of revolution  12 . 
     The system of lenses includes a first, upper lens  50  located within a lower portion of the hole  28 , a second, intermediate lens  52  located below the upper lens  50 , and a third, lower lens  54  located below the intermediate lens  52 . The upper lens  50  has a convex upper surface  56  with a radius of about 18.000 mm and a lower surface with a radius of about 20.475 mm. The intermediate lens  52  has an upper, convex surface  60  with a radius of about 6.060 mm and a lower, concave surface  62  with a radius of about 4.700 mm. The lower lens  54  has an upper, concave surface  64  with a radius of about 10.550 mm and a lower, convex surface  66  with a radius of about 5.325 mm. Other features of the upper, intermediate and lower lenses  50 ,  52  and  54  are not discussed further in detail herein as these features would be evident to one of ordinary skill in the art. 
     In use, the light from a 360° surrounding panoramic scene enters the transparent component  20  through the upper, convex surface  22 . Light is received from the surrounding panoramic scene for an unbroken included angle  72 , in a vertical plane of the axis of revolution  12 , extending from an angle  74  which is located about 30° below the horizon to an angle 76 which is located about 30° above the horizon. By extending the upper, convex lens  22  or altering its shape, the angle  76  below the horizon may be increased. When the light enters the transparent component  20 , the light is refracted slightly downwardly by the upper, convex surface  22 , thus reducing the angle of the light with respect to vertical. The light then passes through the transparent component  20  and is then reflected upwardly by the reflective surface  38 . Due to be convex shape of the reflective surface  38 , the angle of the light with respect to vertical is further reduced after reflection from the reflective surface  38 . The light then passes through the transparent component  20  and exits the transparent component through the internal surface  40  Due to the concave shape of the internal surface  40 , the light is refracted slightly upwardly when exiting the transparent component  20  through the internal surface  40 , thus further reducing the angle of the light with respect to vertical. 
     After leaving the transparent component, the light passes upwardly through the hole  28  and is reflected downwardly by the reflective area  46  of the mirror  16 . The light then passes downwardly through the hole  28  and is refracted respectively by the upper lens  50 , the intermediate lens  52 , and the lower lens  54 . The light, after leaving the lower lens  54 , is focused by creating a flat image on a flat focal plane  78 . 
     It can be seen from the previous description that a simple, compact arrangement is provided which is capable of capturing a view of a 360° surrounding panoramic scene. In particular, the panoramic imaging arrangement  10  includes only five components namely the lens block  14 , the mirror  16  and the upper, intermediate and lower lenses  50 ,  52  and  54 . Moreover, all the surfaces of the panoramic imaging arrangement  10  which manipulate light are spherical or substantially spherical so as to be easily manufacturable. 
     A final image is created which is corrected for image flatness and astigmatism. It could be noted that no particular surface or surfaces correct for image flatness and astigmatism, but rather that the sizes, positioning and orientations of all the surfaces cooperate to produce a final image which is corrected for image flatness and astigmatism. It has been found that the panoramic imaging arrangement  10  is particularly suitable for creating a monochromatic image of the surrounding panoramic scene. One of ordinary skill in the art would appreciate that the panoramic imaging arrangement  10  may be modified or may be complemented by additional lenses that would make it more suitable for capturing color images of a surrounding panoramic scene. 
     FIG. 2 illustrates a first color corrected panoramic imaging arrangement  200 , according to one embodiment of the invention, presented around a vertical axis of revolution  201 . In this embodiment, the first color corrected panoramic imaging arrangement  200  includes a first transparent component  203  (a catadioptric lens), a second transparent component  205  (also a catadioptric lens), a third transparent component  206  (a simple lens), a fourth transparent component  207  (also a simple lens), a system of lenses  208 , an image sensor  209 , and a cover plate  211 . The image sensor  209  and the cover plate  211  can be part of an integrated circuit that, in one preferred embodiment, has an imaging area of about ⅔ of an inch. One embodiment of the first color corrected panoramic imaging arrangement  200  is specified by Table 1. All the optical surfaces of the first transparent component  203 , the second transparent component  205 , the third transparent component  206 , and the fourth transparent component  207  are substantially spherical. In this embodiment, the transparent components are glass. 
     One skilled in the art will understand that the references to vertical, upper and lower are for simplicity in writing the description and that the lens can be used in any orientation. 
     The first transparent component  203  has an upper refractive convex surface  213 , a lower reflective convex surface  215 , and a refractive interface  217  each symmetrically rotated about the vertical axis of revolution  201 . The lower reflective convex surface  215  has the same curvature as, and extends inward to a lower refractive convex surface  219 . One skilled in the art will understand that the lower portion of the first transparent component  203  can be formed to have a lower curvature, and that the outer portion of the lower curved surface can support a reflective material placed on the curved surface leaving a refractive portion of the lower surface symmetric around the vertical axis of revolution  201  through which light can pass. 
     The second transparent component  205  fits within the depression formed by the refractive interface  217  of the first transparent component  203  and can be glued thereto. 
     The second transparent component  205  has an upper reflective surface  221  distal from the refractive interface  217  that depending on the embodiment can be concave, flat or convex. 
     The second transparent component  205  has a significantly lower index of refraction than the first transparent component  203 . By using the second transparent component  205  to support the upper reflective surface  221  instead of requiring a separate mirror to be mounted on the lens block (such as mirror  16 ), the manufacturing process for making the first color corrected panoramic imaging arrangement  200  is simplified over the process used to make the panoramic imaging arrangement  10 . 
     The third transparent component  206  can be glued to the first transparent component  203  at the lower refractive convex surface  219  while the fourth transparent component  207  can be glued to the third transparent component  206 . Subsequently described embodiments eliminate the third transparent component  206 . 
     The system of lenses  208  can be supported using an optical tube. 
     The described implementation of the first color corrected panoramic imaging arrangement  200  is designed to be placed on an image sensor device such an integrated circuit package having the cover plate  211  made from BK7 glass and where the image sensor  209  is about ⅔ of an inch. Light from a surrounding panorama can be focused as an annular image (or partial annular image) on the image sensor  209 . One skilled in the art would understand from the previous description and Tables 1-4 how to modify the arrangement for other integrated circuits, and for use with digital still or video cameras. Further, although one preferred embodiment described herein is for a miniature lens, the design can be significantly enlarged. Table 2 provides parameters for a second preferred embodiment that is designed for the image sensor  209  being about ½ inch. 
     In operation, light  223  enters the first color corrected panoramic imaging arrangement  200  from the surrounding panorama at the upper refractive convex surface  213  of the first transparent component  203  where it is refracted and directed to the lower reflective convex surface  215 . The light  223  is reflected towards the refractive interface  217  where it is refracted as it enters the second transparent component  205 . Once in the second transparent component  205 , the light  223  is reflected by the upper reflective surface  221  back towards the first transparent component  203  again being refracted at the refractive interface  217  (but this surface is now treated as a refractive concave surface). The light  223  then exits the first transparent component  203  at the lower refractive convex surface  219 , passes through the third transparent component  206 , the fourth transparent component  207 , the system of lenses  208  and the cover plate  211  and is captured by the image sensor  209 . 
     This embodiment of the first color corrected panoramic imaging arrangement  200  has a field-of-view  225  of approximately 80° (from 20° below the horizon line to 60° above the horizon line). 
     Another embodiment of the first color corrected panoramic imaging arrangement  200  is parameterized in Table 2. This embodiment is designed to be used where the image sensor  209  size is about ½ inch. 
     FIG. 3 illustrates a second color corrected panoramic imaging arrangement  300  presented around a vertical axis of revolution  301  where the transparent components are a mixture of glass and plastic components. In this embodiment, the second color corrected panoramic imaging arrangement  300  includes a first transparent component  303  (a catadioptric lens), a second transparent component  305  (also a catadioptric lens), a third transparent component  307  (also a simple lens), a system of lenses  308 , an image sensor  309 , and a cover plate  311 . The image sensor  309  and the cover plate  311  can be part of an integrated circuit that, in one preferred embodiment, has an imaging area of about ½ of an inch. One embodiment of the second color corrected panoramic imaging arrangement  300  is specified by Table 3. All the optical surfaces of the first transparent component  303 , the second transparent component  305 , and the third transparent component  307  are substantially spherical. The system of lenses  308  includes a lens  312 . In one preferred embodiment, the second transparent component  305  and the lens  312  are acrylic instead of class. In addition, the third transparent component  307  is polystyrene instead of glass. As in the previously described embodiment, the second transparent component  305  includes an upper reflective surface  321  that is slightly convex. 
     This embodiment of the second color corrected panoramic imaging arrangement  300  has a field-of-view  325  of approximately 80° (from 20° below the horizon line to 60° above the horizon line). 
     This embodiment is also less complex as one of the lenses in the embodiment illustrated in FIG. 2 has been replaced by an air-spaced singlet. This can also be done with the embodiment shown in FIG. 2 with compensating changes to the other components. 
     The second color corrected panoramic imaging arrangement  300  is less difficult to manufacture because some of the lenses can be made using well known plastic molding techniques. In addition, the use of plastic molding techniques simplifies the alignment of the lenses in the optical tube. 
     The second color corrected panoramic imaging arrangement  300  operates in essentially the same manner as the first color corrected panoramic imaging arrangement  200  where the air-spaced singlet replaces the third transparent component  206 . One skilled in the art would understand the operation of the arrangement after reading the operational description previously provided in view of the provided figures. 
     Yet another embodiment of the invention is described by Table 4. This embodiment has the same fundamental arrangement of components as the second color corrected panoramic imaging arrangement  300 , except that the first transparent component  303  is now made of polystyrene instead of glass. In addition, the upper reflective surface  321  is concave instead of convex. The other components are adjusted as indicated in Table 4. In addition, this embodiment has a field-of-view  325  of approximately 86° (from 20° below the horizon line to and 66° above the horizon line). 
     This arrangement of two reflections in combination with various refracting surfaces lends itself to miniaturization. This is important for certain applications such as helmet mounting and covert security systems. Depending on the chosen vertical field of view, numerical aperture, required degree of correction, manufacturing cost goals, choice of materials, etc., the maximum clear aperture (largest required lens/mirror diameter) of this type of system can be as small as about 2× the image diameter containing the chosen vertical field of view. In the preferred embodiments herein, this ratio ranges from about 2× to 6× the image diameter. 
     One skilled in the art will understand that many different materials and configurations can be used to practice the invention extending from all glass components to all plastic components and with a wide variety of sizes of the lens and image sensors. 
     One skilled in the art will understand that some embodiments of the invention are small enough to be used with a visual and/or video conferencing device that can be placed in the middle of a conference table much like existing audio conferencing devices. A visual conferencing device is one that is similar to a video conferencing device, but need not transmit video signals (such as would be received by a television) and instead transmits a stream of frames that can be displayed by a computer. In addition, some embodiments of the invention are small enough to be placed on a moving object such as a vehicle or a person&#39;s helmet. In addition, embodiments of the invention can be used as unobtrusive surveillance sensors that can be placed so as to capture images of people from a normal point-of-view (as compared to the point-of-view of a surveillance camera mounted in a ceiling). These embodiments can be physically and unobtrusively placed on cash registers, shop shelves or other locations. 
     Other embodiments of the invention can be used with a video camera (either digital or analog) and/or a still digital or film camera. Further, some embodiments of the invention can be used with video or visual surveillance systems. 
     One skilled in the art will understand that embodiments of the invention can be used to capture light from a greater than 90° surrounding partial panoramic scene including a 360° surrounding panoramic scene. 
     From the foregoing, it will be appreciated that embodiments of the invention have (without limitation) the following advantages over the invention of FIG.  1 : 
     1) It is simpler to make because the upper mirror is not positioned over a void. 
     2) It is color corrected. 
     3) It has an increased aperture. 
     4) The maximum clear aperture (largest required lens/mirror diameter) of this type of system can be as small as about 2× the image diameter containing the chosen vertical field of view. 
     While certain exemplary embodiments have been described and shown in the accompanying drawings, it is to be understood that such embodiments are merely illustrative and not restrictive of the current invention, and that this invention is not restricted to the specific constructions and arrangements shown and described, since modifications may occur to those ordinarily skilled in the art. 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 SRF 
                 RADIUS 
                 THICKNESS 
                 GLASS 
                 Note 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  2 
                 15.390623 
                 2.358848 
                 O_S-LAH58 
                   
               
               
                  3 
                 — 
                 4.056893 
                 O_S-LAH58 
                 dummy surface 
               
               
                  4 
                 13.481452 
                 −4.056893 
                 REFLECT 
               
               
                  5 
                 −6.072127 
                 −5.822116 
                 O_S-FPL53 
               
               
                  6 
                 309.080513 
                 5.822116 
                 REFLECT 
               
               
                  7 
                 −6.072127 
                 4.056893 
                 O S-LAH58 
               
               
                  8 
                 13.481452 
                 — 
                 AIR 
               
               
                  9 
                 13.481452 
                 0.500000 
                 O S-FPL51 
               
               
                 10 
                 5.621376 
                 1.267815 
                 O S-TIH11 
               
               
                 11 
                 −7.693857 
                 0.043000 
                 AIR 
               
               
                 12 
                 1.964969 
                 1.000000 
                 O_S-YGH51 
               
               
                 13 
                 −3.523882 
                 0.390000 
                 O_S-NPH1 
               
               
                 14 
                 2.625178 
                 0.113989 
                 AIR 
               
               
                 AST 
                 — 
                 1.760425 
                 AIR 
                 Aperture Radius 
               
               
                   
                   
                   
                   
                 0.628 
               
               
                 16 
                 −0.986432 
                 1.067350 
                 O_S-FPL51 
               
               
                 17 
                 −1.741826 
                 1.524088 
                 AIR 
               
               
                 18 
                 — 
                 1.000000 
                 BK7 
               
               
                 19 
                 — 
                 0.500000 
                 AIR 
               
               
                 20 
                 — 
                 — 
                 AIR 
                 *⅔″ CCD 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 SRF 
                 RADIUS 
                 THICKNESS 
                 GLASS 
                 NOTE 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  2 
                 18.200000 
                 2.300000 
                 O_S-LAH58 
                   
               
               
                  3 
                 — 
                 4.100000 
                 O_S-LAH58 
                 dummy surface 
               
               
                  4 
                 13.029000 
                 −4.100000 
                 REFLECT 
               
               
                  5 
                 −5.000000 
                 −4.280000 
                 O_S-FPL53 
               
               
                  6 
                 421.000000 
                 4.280000 
                 REFLECT 
               
               
                  7 
                 −5.000000 
                 4.100000 
                 O_S-LAH58 
               
               
                  8 
                 13.029000 
                 — 
                 AIR 
               
               
                  9 
                 13.029000 
                 0.360000 
                 O_S-FPL51 
               
               
                 10 
                 4.480000 
                 1.760000 
                 O_S-TIH11 
               
               
                 11 
                 −6.900000 
                 0.160000 
                 AIR 
               
               
                 12 
                 1.621941 
                 0.740000 
                 O_S-YGH51 
               
               
                 13 
                 −3.160000 
                 0.440000 
                 O_S-NPH1 
               
               
                 14 
                 2.131000 
                 0.071000 
                 AIR 
               
               
                 AST 
                 — 
                 1.350000 
                 AIR 
                 Aperture radius 
               
               
                   
                   
                   
                   
                 .475 
               
               
                 16 
                 −0.804501 
                 0.480000 
                 O_S-FPL51 
               
               
                 17 
                 −1.264000 
                 1.087453 
                 AIR 
               
               
                 18 
                 — 
                 1.000000 
                 BK7 
               
               
                 19 
                 — 
                 0.500000 
                 AIR 
               
               
                 20 
                 — 
                 — 
                 AIR 
                 ½″ CCD 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                 SRF 
                 RADIUS 
                 THICKNESS 
                 CLASS 
                 NOTE 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  2 
                 19.374750 
                 2.266620 
                 O_S-LAH58 
                   
               
               
                  3 
                 — 
                 4.912728 
                 O_S-LAH58 
                 dummy surface 
               
               
                  4 
                 12.808952 
                 −4.912728 
                 REFLECT 
               
               
                  5 
                 −4.358388 
                 −3.580382 
                 ACRYL 
               
               
                  6 
                 299.451974 
                 3.580382 
                 REFLECT 
               
               
                  7 
                 −4.358388 
                 4.912728 
                 O_S-LAH58 
               
               
                  8 
                 12.808952 
                 0.430101 
                 AIR 
               
               
                  9 
                 4.195110 
                 0.750000 
                 STYRE 
               
               
                 10 
                 −7.113288 
                 0.441961 
                 AIR 
               
               
                 11 
                 1.557779 
                 0.730000 
                 O_S-LAM60 
               
               
                 12 
                 −2.669135 
                 0.280000 
                 O_S-TIH6 
               
               
                 13 
                 2.298896 
                 0.075351 
                 AIR 
               
               
                 AST 
                 — 
                 1.314989 
                 AIR 
                 Aperture radius 
               
               
                   
                   
                   
                   
                 0.487 
               
               
                 15 
                 −0.780919 
                 0.652154 
                 ACRYL 
               
               
                 16 
                 −1.414348 
                 0.951240 
                 AIR 
               
               
                 17 
                 — 
                 1.000000 
                 BK7 
               
               
                 18 
                 — 
                 0.500000 
                 AIR 
               
               
                 19 
                 — 
                 — 
                 AIR 
               
               
                 20 
                 — 
                 — 
                 AIR 
                 ½″ CCD 
               
               
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
               
                   
               
               
                 SRF 
                 RADIUS 
                 THICKNESS 
                 GLASS 
                 NOTE 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                  2 
                 16.088826 
                 2.266620 
                 STYRE 
                   
               
               
                  3 
                 — 
                 4.912728 
                 STYRE 
                 dummy surface 
               
               
                  4 
                 13.817131 
                 −4.912728 
                 REFLECT 
               
               
                  5 
                 −4.358388 
                 −3.580382 
                 ACRYL 
               
               
                  6 
                 −19.606938 
                 3.580382 
                 REFLECT 
               
               
                  7 
                 −4.358388 
                 4.912728 
                 STYRE 
               
               
                  8 
                 13.817131 
                 0.629899 
                 AIR 
               
               
                  9 
                 5.115189 
                 0.750000 
                 STYRE 
               
               
                 10 
                 −7.710574 
                 0.100000 
                 AIR 
               
               
                 11 
                 1.434568 
                 0.734555 
                 O_S-LAM60 
               
               
                 12 
                 −3.101590 
                 0.280000 
                 O_S-TIH6 
               
               
                 13 
                 1.991805 
                 0.075351 
                 AIR 
               
               
                 AST 
                 — 
                 1.314989 
                 AIR 
                 Aperture Radius 
               
               
                   
                   
                   
                   
                 0.487 
               
               
                 15 
                 −0.722183 
                 1.295103 
                 ACRYL 
               
               
                 16 
                 −1.841323 
                 0.213029 
                 AIR 
               
               
                 17 
                 — 
                 1.000000 
                 BK7 
               
               
                 18 
                 — 
                 0.500000 
                 AIR 
               
               
                 19 
                 — 
                 — 
                 AIR 
               
               
                 20 
                 — 
                 — 
                 AIR 
                 ½″ CCD