Abstract:
A catadioptric projection optical system includes a first optical system, for receiving light from an object, a second optical system, for forming an image of the object on an image plane, and a third optical system disposed optically between the first optical system and the second optical system. The first, second and third optical systems have a common straight optical axis. The image of the object is projected onto the image plane through a plurality of real intermediate image formations, and a pupil plane of the catadioptric projection optical system is free of a void area.

Description:
This application is a divisional application of U.S. patent application Ser. No. 11/268,640, filed Nov. 8, 2005 now U.S. Pat. No. 7,092,168, which is a divisional of U.S. patent application Ser. No. 10/992,853, filed Nov. 22, 2004, and issued as U.S. Pat. No. 6,995,918 on Feb. 7, 2006, which is a divisional of U.S. patent application Ser. No. 09/784,021, filed Feb. 16, 2001 now U.S. Pat. No. 7,075,726. 

   FIELD OF THE INVENTION AND RELATED ART 
   This invention relates to a projection optical system and a projection exposure apparatus for projecting a pattern of a mask onto a substrate through the projection optical system. More particularly, the invention concerns a catadioptric projection optical system having a reflection mirror, for printing, by projection exposure, a reticle pattern on a semiconductor wafer. 
   The density of an integrated circuit increases more and more, and the specification and performance required for a projection (exposure) optical system become much stricter. Generally, in order to obtain a higher resolving power, the exposure wavelength is shortened and/or the numerical aperture (NA) of a projection optical system is enlarged. 
   However, as the exposure wavelength reaches a region of 193 nm (ArF excimer laser light) or 157 nm (F 2  excimer laser light), usable lens materials are limited to quartz and fluorite. This is mainly because of decreases of the light transmission factor. For example, in a projection optical system such as disclosed in Japanese Laid-Open Patent Application, Laid-Open No. 79345/1998, wherein it comprises all dioptric lenses of a large number and wherein all lenses have a large glass material thickness, the exposure amount on a wafer becomes low and it causes a decrease of the throughput. Also, due to thermal absorption by the lenses, there occur problems (thermal aberration) such as changes of aberration or shift of the focal point position. When the exposure wavelength is 193 nm, quartz and fluorite can be used as a projection optical system. However, because the difference in dispersion between them is not large, correction of chromatic aberration is difficult to accomplish. In order to correct the chromatic aberration of a projection optical system completely, it is necessary to use a few achromatic lenses having a small curvature radius at its achromatic surface. This leads to an increase of the total glass material thickness of the optical system, which then raises the above-described problems of thermal aberration and transmission factor. Further, currently, it is very difficult to produce a projection optical system by use of fluorite, having a sufficient property to assure its design performance. It is further difficult to produce one having a large diameter. This makes it very difficult to accomplish color correction, and results in an increase of the cost. As for the exposure wavelength of 157 nm, only fluorite is the usable lens material. The chromatic aberration cannot be corrected only with a single lens material. Anyway, it is very difficult to provide a projection optical system only by use of dioptric systems. 
   In consideration of these inconveniences, many proposals have been made to introduce a reflecting system, having a mirror, into an optical system to thereby avoid the problems of transmission factor and color correction. For example, Japanese Laid-Open Patent Applications, Laid-Open Nos. 211332/1997 and 90602/1998 show a catoptric projection optical system which is constituted only by use of reflecting systems. Further, U.S. Pat. No. 5,650,877 and Japanese Laid-Open Patent Applications, Laid-Open Nos. 210415/1987, 258414/1987, 163319/1988, 66510/1990, 282527/1991, 234722/1992, 188298/1993, 230287/1994, and 304705/1996 show a catadioptric projection optical system having a combination of catoptric and dioptric systems. 
   When a projection optical system which includes a catoptric system to meet the shortening of the exposure wavelength and the enlargement of NA (numerical aperture) is produced, the structure should of course be one that enables correction of chromatic aberration. In addition, idealistically, the structure should be simple and sufficient to enable that an imaging region of a sufficient size is defined upon an image plane, that the number of optical elements, such as mirrors or lenses is small, that the mirror incidence angle and reflection angle are not large, and that a sufficient image-side working distance is assured. 
   If an imaging region width of sufficient size is attainable on the image plane, in the case of a scan type projection exposure apparatus, it is advantageous with respect to the throughput, such that the exposure variation can be suppressed. If the number of optical elements is small, the process load in the production of optical elements such as mirrors and lenses can be reduced. Also, since the total glass material thickness can be made smaller, the loss of light quantity can be reduced. Further, the increase of the footprint of the apparatus can be suppressed, and the loss of light quantity due to the film can also be decreased. Particularly, this is very advantageous because, when the exposure wavelength is 157 nm (F 2  excimer laser light), the loss of light quantity at the mirror reflection film cannot be disregarded. When the mirror incidence angle and the reflection angle are not large, the influence of a change in light quantity due to the angular characteristic of the reflection film can be suppressed. If a sufficient image-side working distance can be maintained, it is advantageous with respect to structuring an auto focusing system or a wafer stage conveyance system in the apparatus. If the structure is simple, complexity of a mechanical barrel, for example, can be avoided, and it provides an advantage to the manufacture. 
   Here, the conventional examples are considered with respect to the above-described points. 
   In the projection optical system shown in U.S. Pat. No. 5,650,877, a Mangin mirror and a refracting member are disposed in an optical system to print an image of a reticle on a wafer. This optical system has inconveniences that, in every picture angle used, there occurs light interception (void) at the central portion of a pupil and that the exposure region cannot be made large. If the exposure region is to be enlarged, it disadvantageously causes widening of the light interception at the central portion of the pupil. Further, the refractive surface of the Mangin mirror defines a beam splitting surface such that the light quantity decreases to a half each time the light passes this surface. The light quantity will be decreased to about 10% upon the image plane (wafer surface). 
   In the projection optical systems shown in Japanese Laid-Open Patent Applications, Laid-Open Nos. 211332/1997 and 90602/1998, the basic structure comprises a reflection system only. However, with respect to aberration (Petzval sum) and mirror disposition, it is difficult to keep a sufficient imaging region width on the image plane. Also, since, in this structure, a concave mirror adjacent to the image plane and having a large power mainly has an imaging function, enlargement of the NA is difficult to accomplish. Since a convex mirror is placed just before the concave mirror, a sufficient image-side working distance cannot be maintained. 
   In the projection optical systems shown in Japanese Laid-Open Patent Applications, Laid-Open Nos. 210415/1987 and 258414/1987, a Cassegrain type or Schwarzschild type mirror system is used. An opening is formed at the central portion of the mirror, by which a void is defined in the pupil such that only the peripheral portion of the pupil contributes to the imaging. However, the presence of a void in the pupil will have an influence on the imaging performance. If the pupil void is to be made smaller, the power of the mirror must be large. This causes enlargement of the incidence and reflection angles of the mirror. Further, an enlarged NA (numerical aperture) will cause a large increase of the mirror diameter. 
   In the projection optical systems shown in Japanese Laid-Open Patent Applications, Laid-Open Nos. 163319/1988, 188298/1993 and 230287/1994, the structure is complicated due to deflection and bend of the optical path. Since most of the power of optical groups for imaging an intermediate image, as a final image, is sustained by a concave mirror, it is structurally difficult to enlarge the NA. The magnification of the lens system, which is disposed between the concave mirror and the image plane, is at a reduction ratio, and also it has a positive sign. Because of this, a sufficient image-side working distance cannot be kept. Further, in order that the object plane and the image plane are placed opposed, it is necessary to use two flat mirrors only for the sake of deflection of the optical path, without any contribution to aberration correction. As the exposure wavelength is shortened to 157 nm, this is undesirable also with respect to the loss of light quantity. Further, it is structurally difficult to hold the imaging region width because of the necessity of light path division. Since the optical system has to be large, there is a disadvantage with respect to the footprint. 
   In the projection optical systems shown in Japanese Laid-Open Patent Applications, Laid-Open Nos. 66510/1990 and 282527/1991, the optical path is divided by a beam splitter, and this makes the barrel structure complicated. It needs a beam splitter of a large diameter and, if this is of a prism type, the loss of light quantity is large because of its thickness. For a larger NA, a larger diameter is necessary, and thus the loss of light quantity becomes larger. If the beam splitter is of a flat plate type, there will occur astigmatism and coma even in regard to axial light rays. Further, there may occur aberrations due to a change in characteristic at the light dividing surface or production of asymmetric aberration resulting from thermal absorption. It is, therefore, difficult to manufacture the beam splitter very accurately. 
   In the projection optical systems shown in Japanese Laid-Open Patent Applications, Laid-Open Nos. 234722/1992 and 304705/1996, many of the above-described inconveniences may be removed. However, each time the optical path is deflected, the light path from a concave mirror is divided. This requires eccentric optical handling and it makes the structure and assembling very complicated. 
   SUMMARY OF THE INVENTION 
   It is accordingly an object of the present invention to provide a projection optical system of simple structure and easy assembling wherein an optical system such as disclosed in Japanese Laid-Open Patent Applications, Laid-Open Nos. 234722/1992 and 304705/1996, described above, is improved. It is another object of the present invention to provide a projection exposure apparatus and/or a device manufacturing method using the same. 
   In accordance with the present invention, a projection optical system, a projection exposure apparatus and a device manufacturing method having features as stated in Items (1)-(37) below are provided. 
   (1) A projection optical system for projecting an image of an object onto an image plane, comprising: a first imaging optical system for forming an image of the object; a second imaging optical system for re-imaging the image upon the image plane; wherein said first and second imaging optical systems are disposed in an order from the object side and are disposed along a common straight optical axis, wherein said first imaging optical system includes a first mirror for reflecting and collecting abaxial light from the object, wherein one of said first and second imaging optical systems includes a second mirror for reflecting light from said first mirror to the image plane side, and wherein, with said second mirror, the abaxial light is caused to pass an outside of an effective diameter of said first mirror. 
   (2) A projection optical system according to Item (1) wherein said first imaging optical system has a magnification β which satisfies a relation |β|≧1. 
   (3) A projection optical system according to Item (1) or (2) wherein said first imaging optical system includes at least one lens. 
   (4) A projection optical system according to Item (3) wherein said lens has a positive refracting power. 
   (5) A projection optical system according to any one of Items (1) to (4) wherein said second imaging optical system includes at least one lens. 
   (6) A projection optical system according to Item (5) wherein said lens has a positive refracting power. 
   (7) A projection optical system according to any one of Items (1) to (6), further comprising a lens group disposed between said first and second mirrors. 
   (8) A projection optical system according to Item (7) wherein said lens group has a negative refracting power and wherein said lens group is disposed between said first mirror and a refractive lens of said first imaging optical system, having a positive refracting power. 
   (9) A projection optical system according to Item (1), further comprising a field optical system disposed between said first and second imaging optical systems, for projecting a pupil of said first imaging optical system onto said second imaging optical system, wherein said first imaging optical system comprises a first mirror group of positive refracting power, including at least said first mirror, and a second mirror group including said second mirror, wherein light from said first mirror group as reflected by said second mirror group is caused to pass an outside of an effective diameter of said first mirror group. 
   (10) A projection optical system according to Item (9) wherein said second imaging optical system is constituted by lenses only and it has a positive refracting power. 
   (11) A projection optical system according to Item (9) or (10) wherein said second imaging optical system has a magnification BG 2  which satisfies a relation −0.5&lt;BG 2 &lt;−0.05. 
   (12) A projection optical system according to any one of Items (9) to (11), wherein said first imaging optical system has a magnification BG 1  which satisfies a relation −40.0&lt;BG 1 &lt;−0.5. 
   (13) A projection optical system according any one of Items (9) to (12), wherein said field optical system is constituted by lenses. 
   (14) A projection optical system according to any one of Items (9) to (12), wherein said field optical system comprises a first field mirror and a second field mirror group including a second field mirror, wherein abaxial light passed through the outside of the effective diameter of said first mirror group is reflected by said first field mirror and said second field mirror, in this order, and after that, the light passes a region adjacent to the optical axis of said first field mirror and enters said second imaging optical system. 
   (15) A projection optical system according to Item (14) wherein said first field mirror comprises a concave mirror and wherein said second field mirror comprises a convex mirror. 
   (16) A projection optical system according to Item (14) wherein said first field mirror comprises a concave mirror and wherein said second field mirror comprises a concave mirror. 
   (17) A projection optical system according to any one of Items (9) to (16), wherein relations P 1 &lt;0 and Pf+P 2 &gt;0 are satisfied where P 1 , Pf and P 2  are Petzval sums of said first imaging optical system, said field optical system and said second imaging optical system, respectively. 
   (18) A projection optical system according to any one of Items (9) to (17), wherein a relation 0.6&lt;e/LM 1 &lt;2.5 is satisfied where LM 1  is a paraxial distance between the object and said first mirror, and e is a distance from the object to a pupil conjugate point defined by an optical element positioned at the object side of said first mirror. 
   (19) A projection optical system according to any one of Items (9) to (18), wherein the distance LM 1  satisfies a relation 0.5&lt;OIL/(LM 1 +2×LM 2 )&lt;20 where LM 2  is a paraxial distance between said first and second mirrors, and OIL is a paraxial distance along the optical path, from the object to the image defined by said first imaging optical system. 
   (20) A projection optical system according to any one of Items (9) to (19), wherein the distances LM 1  and LM 2  satisfy a relation 0.2&lt;LM 2 /LM 1 &lt;0.95. 
   (21) A projection optical system according to any one of Items (9) to (20), wherein the distance LM 1  satisfies a relation 0.15&lt;LM 1 /L&lt;0.55 where L is a distance from an object plane to an image plane in said projection optical system. 
   (22) A projection optical system according to any one of Items (9) to (21), wherein said first mirror group has a magnification BGM 1  which satisfies a relation −2.0&lt;1/BGM 1 &lt;0.4. 
   (23) A projection optical system according to any one of Items (9) to (22), wherein said first imaging optical system has a lens group of positive refracting power, disposed closest to the object side. 
   (24) A projection optical system according to any one of Items (9) to (23), wherein said first mirror group includes a lens of negative refracting power and said first mirror. 
   (25) A projection optical system according to any one of Items (9) to (24), wherein said second mirror group includes said second mirror and a lens. 
   (26) A projection optical system according to any one of Items (9) to (25), wherein the abaxial light from the object passes a lens of said second mirror group before it is incident on said first mirror group. 
   (27) A projection optical system according to any one of Items (9) to (26), wherein a positive lens, included by said field optical system, is disposed just after the image plane side of said first mirror group of said first imaging optical system. 
   (28) A projection optical system according to any one of Items (14) to (16), wherein a relation 0.45&lt;LFM 1 /LFM 2 &lt;0.8 is satisfied where LFM 1  is a distance between said second field mirror and said first field mirror, and LFM 2  is a distance between said second field mirror and the image plane. 
   (29) A projection optical system according to any one of Items (14) to (16), wherein said second field mirror group includes said second field mirror and a lens. 
   (30) A projection optical system according to any one of Items (14) to (16), (28) and (29), wherein a positive lens, included by said field optical system, is disposed between said first mirror of said first imaging optical system and said second field mirror of said field optical system, wherein light reflected by said second mirror of said first imaging optical system passes said positive lens and then is reflected by said first field mirror. 
   (31) A projection optical system according to any one of Items (1) to (30), wherein said projection optical system is telecentric with respect to each of the object side and the image plane side. 
   (32) A projection optical system according to any one of Items (1) to (31), wherein said projection optical system has a magnification of a reduction ratio. 
   (33) A projection optical system according to any one of Items (1) to (32), further comprising a field stop disposed at the position of the image defined by said first imaging optical system, for changing at least one of a size and a shape of an imaging region upon the image plane. 
   (34) A projection optical system according to any one of Items (1) to (33), further comprising a stop disposed inside said second imaging optical system. 
   (35) A projection exposure apparatus for projecting a pattern of a mask onto a substrate through a projection optical system as recited in any one of Items (1) to (34). 
   (36) A projection exposure apparatus according to Item (35) wherein laser light from one of an ArF excimer laser and an F 2  laser is used for the projection exposure. 
   (37) A device manufacturing method, comprising the steps of: printing a device pattern on a wafer by exposure, using a projection exposure apparatus as recited in Item (35) or (36); and developing the exposed wafer. 
   These and other objects, features and advantages of the present invention will become more apparent upon a consideration of the following description of the preferred embodiments of the present invention taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a schematic view of an example of the structure of a projection optical system according to an embodiment of the present invention. 
       FIG. 2  is a schematic view of an example of the structure of a projection optical system according to a first embodiment of the present invention, wherein a refractive lens group R is disposed in a group L 2 . 
       FIG. 3  is a schematic view of a basic structure of a projection optical system according to a second embodiment of the present invention. 
       FIG. 4  is a sectional view of a lens structure in Example 1 of the present invention. 
       FIG. 5  is a sectional view of a lens structure in Example 2 of the present invention. 
       FIG. 6  is a sectional view of a lens structure in Example 3 of the present invention. 
       FIG. 7  is a sectional view of a lens structure in Example 4 of the present invention. 
       FIG. 8  illustrates aberrations in Example 1 of the present invention. 
       FIG. 9  illustrates aberrations in Example 2 of the present invention. 
       FIG. 10  illustrates aberrations in Example 3 of the present invention. 
       FIG. 11  illustrates aberrations in Example 4 of the present invention. 
       FIG. 12  is a schematic view of a light path in a case, in Example 5 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 13  is a schematic view of a light path in a case, in Example 6 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 14  is a schematic view of a light path in a case, in Example 7 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 15  is a schematic view of a light path in a case, in Example 8 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 16  is a schematic view of a light path in a case, in Example 9 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 17  is a schematic view of a light path in a case, in Example 10 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 18  is a schematic view of a light path in a case, in Example 11 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 19  is a schematic view of a light path in a case, in Example 12 of the present invention, wherein a field optical system is constituted by lens systems. 
       FIG. 20  is a schematic view of a light path in a case, in Example 13 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 21  is a schematic view of a light path in a case, in Example 14 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 22  is a schematic view of a light path in a case, in Example 15 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 23  is a schematic view of a light path in a case, in Example 16 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 24  is a schematic view of a light path in a case, in Example 17 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 25  is a schematic view of a light path in a case, in Example 18 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 26  is a schematic view of a light path in a case, in Example 19 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 27  is a schematic view of a light path in a case, in Example 20 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 28  is a schematic view of a light path in a case, in Example 21 of the present invention, wherein a field optical system includes two mirrors. 
       FIG. 29  illustrates aberrations in Example 5 of the present invention. 
       FIG. 30  illustrates aberrations in Example 6 of the present invention. 
       FIG. 31  illustrates aberrations in Example 7 of the present invention. 
       FIG. 32  illustrates aberrations in Example 8 of the present invention. 
       FIG. 33  illustrates aberrations in Example 9 of the present invention. 
       FIG. 34  illustrates aberrations in Example 10 of the present invention. 
       FIG. 35  illustrates aberrations in Example 11 of the present invention. 
       FIG. 36  illustrates aberrations in Example 12 of the present invention. 
       FIG. 37  illustrates aberrations in Example 13 of the present invention. 
       FIG. 38  illustrates aberrations in Example 14 of the present invention. 
       FIG. 39  illustrates aberrations in Example 15 of the present invention. 
       FIG. 40  illustrates aberrations in Example 16 of the present invention. 
       FIG. 41  illustrates aberrations in Example 17 of the present invention. 
       FIG. 42  illustrates aberrations in Example 18 of the present invention. 
       FIG. 43  illustrates aberrations in Example 19 of the present invention. 
       FIG. 44  illustrates aberrations in Example 20 of the present invention. 
       FIG. 45  illustrates aberrations in Example 21 of the present invention. 
       FIG. 46  illustrates numerical parameters in Examples 1-12 of the present invention. 
       FIG. 47  illustrates numerical parameters in Examples 13-21 of the present invention. 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   In accordance with an embodiment of the present invention, a catadioptric projection optical system, such as shown in  FIG. 1 , is provided (First Embodiment). Denoted at  101  is a reticle which is illuminated with an illumination system, not shown. Denoted at  102  is a wafer, and denoted at  103  is an optical axis of an optical system in the first embodiment. Here, the optical system comprises at least first and second imaging optical systems G 1  and G 2 , in an order from the object side. The reticle  101  and the wafer  102  are held by movable stages (not shown), respectively. 
   The first imaging optical system G 1  comprises, in an order from the object side, at least a first mirror M 1 , having a refracting element L 1 , and a second mirror M 2 . Light from the reticle  101  is imaged by the first imaging optical system G 1 , whereby an intermediate image Io is formed. Here, abaxial light from the reticle  101  passes an outside of the effective diameter of the first mirror M 1 . The intermediate image Io as imaged by the first imaging optical system G 1  is then imaged on the wafer  102  by the second imaging optical system G 2 , comprising a refracting element, at a predetermined magnification. In the structure described above, the optical system of the first embodiment has one optical axis  103 , and it accomplishes a multiple-number imaging optical system wherein abaxial light without light interception of a pupil is imaged. 
   The first imaging optical system G 1  comprises, at least, one or more refracting lenses and two mirrors. The refractive lens group L 1  mainly functions to keep the telecentricity at the object side and contributes to correction of distortion aberration. Also, it serves so that light is incident on the first mirror M 1  without excessive expansion. 
   The second mirror M 2  is disposed opposed to the first mirror M 1  and the optical axis  103 , and it functions to deflect the light from the first mirror M 1  toward the positive direction and also to direct the light toward the outside of the effective diameter of the first mirror M 1 . Here, the direction from the reticle  101  toward the wafer  102  is taken as a positive direction. With the structure described above, light can be directed to the second imaging optical system without a void in a pupil and without bend of the optical axis. 
   The refractive lens group L 1  should desirably have a positive refracting power. With the positive refracting power, the incidence height on the first mirror M 1  can be kept moderate and also the incidence angle on the first mirror M 1  with respect to the optical axis can be made large such that separation of light by the second mirror M 2  is made easy. The first mirror M 1  should desirably be a concave mirror. 
   In the optical system of the first embodiment, the pupil of the first imaging optical system G 1  is present before or after the first mirror M 1 . In the portion adjacent there, the width of light at each picture angle in the first imaging optical system G 1  becomes large. Additionally, dispersion of light due to the difference in picture angle becomes small. Thus, the first mirror M 1  as it has a positive power, i.e., as being provided by a concave mirror, is effective to converge lights, of each picture angle, from the refractive lens group L 1 , such that separation of light after the second mirror M 2  is made easier. Also, a curvature of field is produced in an “over” direction, thereby to cancel an “under” curvature of field in the second imaging optical system G 2 . 
   The second mirror M 2  plays a role of returning the light from the first mirror M 1  toward the positive direction along the optical axis  103 . Here, the second mirror M 2  may be a concave mirror or a flat mirror, or a convex mirror. It should have a required shape based on the difference in power arrangement. It is to be noted that, in the first imaging optical system G 1 , for cancellation of the curvature of field of the second imaging optical system G 2  as well as other aberrations, the second mirror M 2  may be a concave mirror. This is preferable since the refracting power of the first mirror M 1  is shared by it. 
   The second imaging optical system G 2  has a function for imaging the intermediate image Io, being imaged by the first imaging optical system G 1 , upon the wafer  102 . The second imaging optical system G 2  operates to cancel aberrations such as curvature of field in the “over” direction, for example, as produced by the first imaging optical system G 1 . The second imaging optical system G 2  comprises a refractive lens system. By constituting a final imaging optical system with use of a refractive lens system, an optical system having a large numerical aperture can be accomplished easily. 
   The second imaging optical system has a reduction magnification, and this prevents an excessive increase of the width of light at the first imaging optical system G 1  as well as it facilitates separation of light by the first and second mirrors M 1  and M 2 . There is an aperture stop inside the second imaging optical system G 2 . 
   The refractive lens group R may be disposed in the group L 2 , including two mirrors, that is, the first and second mirrors M 1  and M 2 . 
     FIG. 2  is a schematic view of an example wherein a refractive lens group R is disposed in the structure of  FIG. 1 . Here, the same reference numerals as those of  FIG. 1  are assigned to members having corresponding functions. 
   When the refractive lens group R is disposed between the refractive lens group L 1  and the first mirror M 1 , the structure is called a reciprocal optical system. Namely, into this refractive lens group R, the light refracted by the refractive lens group L 1  enters and, additionally, the light reflected by the second mirror M 2  passes therethrough. When this refractive lens group R is used, the refracting power thereof should desirably be negative. If the refracting power of the refractive lens group R is negative, the Petzval sum, which the first mirror M 1  bears, is shared. Also, it contributes to correction of chromatic aberration in the whole system. Thus, if the refractive lens group R is provided, it should desirably have a negative refracting power. Further, simultaneously, it contributes to correction of coma aberration and spherical aberration of the whole system. 
   As described hereinbefore, mainly for correction of axial chromatic aberration, or the like, the refractive lens group R should preferably be disposed about the first mirror M 1 . However, it may be disposed adjacent to the second mirror R. Namely, it may be disposed at a position for transmitting the reflection light from the first mirror M 1  and the reflection light from the second mirror. Further, the refractive lens group R may be disposed at any place within the range of the group L 2 , including two mirrors. Also, lens elements of any number may be used. 
   The projection optical system in this embodiment, particularly when it is provided by a double-imaging optical system, has a positive magnification. 
   In the first embodiment, with the structure such as described above, a catadioptric optical system having constituent elements of a smaller number, having a high resolving power, having an assured wide exposure region, and being easy for assembling and adjustment, can be accomplished without light interception at the central portion of a pupil. 
   In accordance with another embodiment of the present invention, a catadioptric projection optical system such as shown in  FIG. 3 , for example, is provided (Second Embodiment). In this embodiment, the region of the object plane from which the light reaches the image plane and which is attributable to the imaging is a semi-arcuate zone (ring-like field) outside the optical axis, and there is no void at the central portion of the light upon the pupil plane. The projection optical system comprises, in an order along the optical path from the object side, a first imaging system GR 1  having a function for forming an intermediate image of the object, a field optical system Grf for projecting a pupil of the first imaging system GR 1  onto a pupil of a second imaging system Gr 2 , and the second imaging system Gr 2  is disposed just before the image plane and operates to form a final image. The first imaging system GR 1  includes two mirror groups, i.e., a first mirror group Gm 1  including a first mirror M 1  and having a positive refracting power, and a second mirror group GM 2  including a second mirror M 2 . The second mirror group GM 2  is disposed physically at the object side of the first mirror group GM 1 , and the first mirror M 1  is a concave mirror having its concave surface facing to the object side. The light from the object side is reflected by the first and second mirrors M 1  and M 2 , in this order, inside the first imaging system Gr 1 . After this, the light goes through the outside of the effective diameter of the first mirror group GM 1  toward the image side, and it passes through the field optical system Grf and the second imaging system Gr 2 . Thus, the whole system of the projection optical system is defined along a straight optical axis  103 . The object plane and the image plane are opposed to each other, at the opposite ends of the optical axis  103 . The magnification of the projection optical system is a reduction ratio. 
     FIG. 3  is a schematic view of a basic structure of the second embodiment, and  FIGS. 12-45  show Examples 5-21, respectively, to which the second embodiment is applied, to be described later. In all examples, the first imaging system Gr 1  has two mirrors, and the second imaging system Gr 2  comprises refractive lens systems only.  FIGS. 12-19  show cases wherein the field optical system Grf is provided by lens systems, and  FIGS. 20-28  show cases wherein the field optical system Grf has two mirrors. 
   Generally, when a mirror is used, the optical system functions as follows.
         (a) No chromatic aberration occurs at the mirror.       

   With this feature, when a concave lens and a concave mirror are combined to provide a Mangin mirror, even by a positive power, excessive dichromatism can be produced.
         (b) The relation between the power of the mirror and the Petzval sum is opposite to that of an ordinary refractive lens.       

   With this feature, since a concave mirror, for example, has a negative value of Petzval sum while it has a positive power, the power load of a negative lens in the optical system for correction of Petzval sum can be reduced.
         (c) Light rays are reflected.       

   Because of this, the optical system has to be complicated to place the object and image planes opposed to each other. For example, there occurs a void in the pupil, ring field, and bend of the optical path. 
   In this embodiment, to accomplish the above-described purposes, the functions of a mirror such as described above are effectively reflected to the optical system. As shown in  FIG. 3 , the structure is simple and the projection optical system is disposed along a straight optical axis  103 , although it uses a first imaging system, a field optical system, a second imaging system and a mirror, as shown in  FIG. 3 . This provides significant advantages. Since there is no necessity of bending the optical path, the barrel structure can be made simple like that of a conventional refractive lens system. As regards the self-weight deformation of an optical element, since the gravity direction and the optical axis direction are registered with each other, there does not occur asymmetrical deformation. Thus, an asymmetrical aberration does not occur easily. Current equipment for the manufactures, such as peripheral equipment for assembling and adjustments, as well as instruments for measurement, for example, can be used. This is very advantageous with respect to the cost. Further, since the footprint of the apparatus is substantially the same as that of a conventional refractive lens system, the area to be occupied is unchanged. This feature is accomplished by the arrangement that, while an optical system concept (ring field system) in which only paraxial light contributes to the imaging, is set, the function (c) described above is used twice in the first imaging system Gr 1 , and double reflections are accomplished with the use of two mirrors, and that the light from the object side is directed through the outside of the effective diameter of the first mirror group GM 1  to the image side. The light thereafter passes through the field optical system Grf and the second imaging system Gr 2 , and it reaches the image plane. Thus, an optical system having a single optical axis is accomplished. 
   The second imaging system Gr 2  is provided by a refractive lens system, and it has a positive refracting power. With this structure, enlargement of the NA can be met and, additionally, the image side working distance can be assured easily. If the second imaging system Gr 2  has a concave mirror, as described with reference to the conventional examples, it becomes difficult to enlarge the NA and to keep the image side working distance. The field optical system Grf may be provided by refractive lens systems, as shown at (A) in  FIG. 3 . Alternatively, it may comprise two mirrors, such as shown at (B) in  FIG. 3 . As will be described later in relation to the examples, depending on the power arrangement, the positive lens FL 1  may be omitted. In the case of (B) in  FIG. 3 , the field optical system Grf includes a first field mirror FM 1 , comprising a concave mirror, and a second field mirror FM 2 , comprising a convex mirror. The second field mirror may be provided by a concave mirror. 
   As regards the color correction, the achromatic state of the first imaging system Gr 1  may be made “over achromatism” on the basis of the function (a) described above, when the first mirror group GM 1  is constituted by a lens LN 1  of negative refracting power as well as the first mirror M 1 , which is a concave mirror. Thus, even though a single glass material is used for the lens, correction of chromatic aberration can be attained. This is very advantageous, particularly for use of an ArF excimer laser or an F 2  excimer laser. 
   As regards reduction in the number of optical elements or reduction in size and weight, since this embodiment concerns a ring field system using abaxial light only, the mirror diameter can be made smaller than that of an optical system of a Cassegrain type or Schwarzschild type. Further, the number of mirrors is small in this embodiment, as at least two. 
   In the first imaging system Gr 1 , due to the function (b) described above, the first mirror group GM 1  of the first imaging system Gr 1  provides a large negative Petzval sum. Thus, the field optical system Grf and the second imaging system Gr 2  can be provided, without using many negative refracting power lenses for correction of the Petzval sum as in the conventional refractive lens system. As a result, the number of lenses can be reduced. Further, where the second mirror group GM 2  of the first imaging system Gr 1  is provided by a lens LP 1  and a mirror M 2 , the power sharing of the lens LP 1  and the second mirror M 2  can be changed, while keeping the total power of the second mirror group GM 2  unchanged. Thus, the Petzval sum can be controlled as desired. The degree of freedom for aberration correction increases, and it contributes to reduction of the number of optical elements. This is also the case with the second field mirror FM 2  shown at (B) in  FIG. 3  and, by combining the second field mirror FM 2  and the lens LF into a second field mirror group, the degree of freedom for the Petzval sum correction increases, which contributes to reduction in the number of optical elements. There arises a necessity that the positive refracting power of the second imaging system Gr 2  should be made large so as to cancel the large negative Petzval sum of the first imaging system Gr 1 . Since the principal light ray height emitted from the first imaging system Gr 1  passes the outside of the first mirror group GM 1 , it is incident on the field optical system Grf at a high position. Thus, the angle of the principal light ray entering the second imaging system Gr 2  from the field optical system Grf becomes larger. As a result, in order to maintain the image-side telecentricity, there arises a necessity that the positive refracting power of the second imaging system Gr 2  should be larger. Since the positive refracting power of the second imaging system Gr 2  can be enlarged without contradiction to these two necessities, the effective diameter of the second imaging system Gr 2  becomes smaller. Thus, the reduction in size and weight is accomplished. 
   As regards the incidence angle and reflection angle of light on the mirror, because this embodiment concerns a ring field system, the incidence angle and the reflection angle of the light on the mirror can be made smaller than that in an optical system of a Cassegrain type or Schwarzschild type. Further, in the first imaging system Gr 1 , the first mirror M 1  is disposed adjacent to a point optically conjugate with a pupil, and the light reflected by the second mirror M 2  passes about the outside of the effective diameter of the first mirror group GM 1 . Since the light is not reflected at a high position away from the optical axis of the mirror, the incidence angle and the reflection angle of the light on the first and second mirrors M 1  and M 2  do not become extraordinarily large. In a case where the field optical system Grf has a structure as shown at (B) in  FIG. 3 , the spacing between the first and second field mirrors FM 1  and FM 2  is kept large as much as possible. Also, the width of the light is narrow. Therefore, the incidence angle and the reflection angle do not become extraordinarily large. 
   As regards the width of the imaging region on the image plane, the mirror should be disposed so as to keep the effective light as much as possible. When the field optical system Grf comprises only a refractive lens system ( FIG. 3 , (A)) or it includes a mirror ( FIG. 3 , (B)), in the first imaging system Gr 1 , the object height may be made high within the tolerable range of aberration correction. Thus, this is not an obstacle. In the field optical system Grf having a field mirror ( FIG. 3 , (B)), since the width of light is narrow, it is easy to avoid an eclipse of the effective light flux. Therefore, a sufficient imaging region width can be attained. 
   In the first imaging system Gr 1 , a positive lens group G 1  may be disposed just after the object plane. This is effective for the correction of distortion aberration, for example, and to maintain its object-side telecentricity satisfactorily. Therefore, in order to reduce any warp of the object plane (reticle) or image plane (wafer) or to decrease a change in magnification due to defocus, it is desirable to provide an optical system being telecentric both in the object side and the image side, by using the positive lens group G 1  and the second imaging system Gr 2 . In the present invention, as shown in  FIG. 3 , the second mirror M 2  should have a half disk-like shape, for separation of light. The positive lens group G 1  may have either a half disk-like shape, or it may have a disk-like shape for easiness of lens manufacture and lens holding. Further, the second mirror M 2  may be formed at the surface portion below the optical axis. For the same reason, the lens LP 1  having a half disk-like shape, may have a disk-like shape. On that occasion, the light passes the lens LP 1  three times. Similarly, the second mirror M 2  may be formed at the lower surface portion of the lens LP 1 . Also, the first mirror M 1  may be formed as a back-surface mirror of the lens LN 1 . The mirrors used in the present invention may be back-surface mirrors, with respect to the aberration correction. 
   As shown at (A) and (B) of  FIG. 3 , the field optical system includes a positive lens FL 1  disposed at the back, on the image plane side, of the first mirror group GM 1  of the first imaging system Gr 1 . This structure suppresses enlargement of the diameter. While it is necessary to form the first face of the positive lens FL 1  to have a discontinuous shape such as dual curvature, for example, the first mirror M 1  may be formed at the central portion of the positive lens FL 1 . Further, a field stop may be disposed at the position of an intermediate image of the first imaging system, to define a variable imaging region on the image plane. This is effective to make the illumination system (not shown) very simple. 
   In the second embodiment, the optical system should preferably satisfy the following conditions. 
   When the magnification of the second imaging system Gr 2  is BG 2 , the following relation should be satisfied:
 
−0.5 &lt;BG 2&lt;−0.05  (1)
 
   When the magnification of the first imaging system Gr 1  is BG 1 , the following relation should be satisfied:
 
−40.0 &lt;BG 1&lt;−0.5  (2)
 
   When the Petzval sums of the first imaging system Gr 1 , of the field optical system Grf and of the second imaging system are P 1 , Pf and P 2 , respectively, the following relations are satisfied:
 
P1&lt;0
 
 Pf+P 2&gt;0  (3)
 
   When the paraxial distance between the object and the first mirror is LM 1 , and the distance from the object to a pupil conjugate point defined by an optical element, which is at the object side of the first mirror, is e, these distances satisfy the following relation:
 
0.6&lt; e/LM 1&lt;2.5  (4)
 
   When the paraxial distance between the first and second mirrors is LM 2 , and the paraxial distance from the object plane to the intermediate image by the first imaging system OIL, the distance LM 1  described above satisfies the following relation:
 
0.5&lt;OIL/( LM 1+2× LM 2)&lt;20  (5)
 
   The distances LM 1  and LM 2  satisfy the following relation:
 
0.2&lt; LM 2/ LM 1&lt;0.95  (6)
 
   When the distance from the object plane to the image plane with respect to the projection optical system is L, the distance LM 1  described above satisfies the following relation:
 
0.15&lt; LM 1/ L&lt; 0.55  (7)
 
   When the magnification of the first mirror group is BGM 1 , the following relation is satisfied:
 
−2.0&lt;1/ BGM 1&lt;0.4  (8)
 
   The condition (1) defines the magnification of the second imaging system Gr 2  in a proper range, so as to obtain a good imaging performance and to assure the back focus (image side working distance), while meeting enlargement of the NA. By keeping a negative value throughout the whole range, the back focus is assured easily. 
   Here, if the lower limit is exceeded, the power of the second imaging system Gr 2  becomes small, such that the diameter of the second imaging system becomes large, or the virtual object height with respect to the second imaging system Gr 2  becomes low. As a result, the powers of the groups constituting the field optical system Grf become larger, causing difficulties in correction of distortion aberration or curvature of field. Alternatively, the magnification of the first imaging system Gr 1  becomes too small, such that there may occur interference of the reflection light from the second mirror M 2  with the first mirror group GM 1 . This makes the power arrangement difficult. On the other hand, if the upper limit is exceeded, the power of the second imaging system Gr 2  increases, and it makes the correction of aberration difficult to accomplish. Further, the diameter of the field optical system Grf disadvantageously increases. 
   The condition (2) defines the magnification of the first imaging system Gr 1  so that, while keeping an appropriate power of the first imaging system Gr 1 , the reflection light from the second mirror M 2  efficiently passes without interference with the first mirror group GM 1 . If the lower limit is exceeded, the width of light becomes large at the outside of the first mirror group GM 1 , to cause an enlargement of the field optical system Grf or an increase of the power of the second imaging system Gr 2 . This makes the aberration correction difficult to accomplish. 
   If the upper limit is exceeded, the power of the first imaging system Gr 1  increases to cause difficulties in aberration correction. Alternatively, there may occur an inconvenience that the reflection light from the second mirror M 2  interferes with the first mirror group GM 1 . Here, the lower limit of the condition (2) may preferably be equal to −5.0. 
   The condition (3) relates to the Petzval sum which determines the field curvature of the optical system as a whole. The Petzval sum of the whole system may preferably be equal to about zero. However, in this embodiment, due to the presence of the first mirror group GM 1 , the Petzval sum of the first imaging system Gr 1  has a large negative value. In order to cancel this, the total of the Petzval sum of the field optical system Grf and that of the second imaging system Gr 2  has a large positive value. If this condition is not satisfied, for correction of the Petzval sum, the number of lenses becomes larger, or the correction of curvature of field becomes difficult to accomplish. 
   The condition (4) concerns the positional relation of the pupil conjugate point of the first imaging system and the first mirror M 1 . Taking into account a decrease of curvature of field or higher order distortion aberration and a decrease of the mirror incidence angle such as described above, it is desirable to take the positional relation substantially registered. If the lower limit is exceeded, the heights as the principal rays from each object height are reflected by the first mirror M 1  differ from each other. This causes increases of higher order distortion aberration and the curvature of field. Also, since the diameter of the first mirror group GM 1  becomes larger, there occurs an inconvenience of interference of the reflection light from the second mirror M 2  with the first mirror group GM 1 . If the upper limit is exceeded, similarly the heights as the principal rays from each object height are reflected by the first mirror M 1  differ from each other, and it causes increases of higher order distortion aberration as well as the curvature of field. Also, since the angle of the reflection light from the second mirror M 2  with respect to the optical axis becomes larger, the power sharing of the field optical system Grf becomes large, which makes it difficult to accomplish the aberration correction. 
   Condition (5) concerns the positional relation of the intermediate image by the first imaging system Gr 1  and the first mirror M 1 . Under the condition, the reflection light from the second mirror M 2  efficiently passes toward the image side without interference with the first mirror group GM 1 . As shown in  FIG. 3 , it is preferable that an intermediate image is formed substantially outside the first mirror M 1 . Thus, if this range is exceeded, the width of light outside the first mirror M 1  becomes large, and the diameter of the field optical system Grf becomes large. This causes an increase of aberration. Particularly, if the lower limit is exceeded, the magnification of the first imaging system Gr 1  becomes too small, and there may occur an inconvenience of interference of the reflection light from the second mirror M 2  with the first mirror group GM 1 . Further, the powers of the first and second mirrors M 1  and M 2  become too large, and the amount of aberration production undesirably increases. If the upper limit is exceeded, to the contrary, the magnification of the first imaging system Gr 1  becomes too large. As a result, an excessive space is produced outside the first mirror M 1 , or the magnification has to be reduced by means of the second imaging system Gr 2 . Thus, the power balance of the optical system as a whole is undesirably destroyed. The upper limit of the condition (5) may preferably be equal to 3.0. 
   Condition (6) defines a proper position of the second mirror M 2  with respect to the first mirror M 1 . If the lower limit is exceeded, it causes an inconvenience that the light directed from the object plane to the first mirror M 1  is eclipsed by the second mirror M 2 . If the upper limit is exceeded, the second mirror M 2  and the object plane come close to each other, and the space at the object side becomes small. 
   Condition (7) defines a proper position of the first mirror M 1  with respect to the total length of the optical system. If this range is exceeded, the power balance of the optical system as a whole is undesirably destroyed. Particularly, if the lower limit is exceeded, the power of the first imaging system Gr 1  increases. If the upper limit is exceeded, the power of the second imaging system increases. The balance of Petzval sum or aberration cancelling relation is undesirably destroyed. 
   Condition (8) defines the magnification of the first mirror group GM 1  in the first imaging system Gr 1 . If this range is exceeded, the power of the first mirror group GM 1  goes beyond a proper range. The power of the second mirror group GM 2  for causing the reflection light from the second mirror M 2  to pass through the outside of the first mirror group GM 1 , is restricted. This results in higher order aberration or curvature of field. The light may interfere with the first mirror group GM 1 . Further, the power balance with the second imaging system Gr 2  is influenced, to cause the aberration correction more difficult. Particularly, if the lower limit is exceeded, the magnification of the first imaging system Gr 1  becomes larger toward the enlargement side, so that the power of the second imaging system Gr 2  becomes larger. Any way, the aberration correction is difficult to accomplish. The upper limit of the condition (8) may preferably be equal to −0.2. 
   Particularly, in an embodiment such as shown at (B) in  FIG. 3 , the field optical system Grf comprises a first field mirror FM 1  being a concave mirror having a concave surface facing to the object side, and a second field mirror group GFM 2  including a second field mirror FM 2 . The first field mirror FM 1  is physically disposed at the image plane side of the second field mirror group GFM 2 . The second imaging system Gr 2  is constituted by refractive lenses only, and it has a positive refracting power. Light from the object is reflected in the first imaging system Gr 1  by the first and second mirrors M 1  and M 2 , in this order, and after this, the light passes the outside of an effective diameter of the first mirror group GM 1  to the image side. Then, the light is reflected in the field optical system, by the first and second field mirrors FM 1  and FM 2  in this order. Thereafter, the light goes about the optical axis center of the first field mirror FM 1  to the image plane side, and finally it passes the second imaging system Gr 2 . Thus, the projection optical system as a whole is provided along a straight line of optical axis  103 . The object plane and the image plane are opposed to each other, at the opposite ends of the optical axis  103 . The magnification of the projection optical system as a whole is at a reduction ratio. 
   Important features of an embodiment such as shown at (B) in  FIG. 3  reside in that, in the first imaging system Gr 1 , the above-described function (c) is used twice such that the reflection is performed twice by using two mirrors of the first and second mirrors M 1  and M 2 , and that the light from the object is directed through the outside of the effective diameter of the first mirror group GM 1  to the image plane side. Also, even in the field optical system Grf, the above-described function (c) is used twice, and the reflection is made twice by using two mirrors of first and second field mirrors FM 1  and FM 2 , so that the light is directed to the image plane side through the optical axis central portion of the first field mirror FM 1 . 
   The optical system of this embodiment preferably satisfies the following conditions. 
   When the magnification of the first imaging system Gr 1  is BG 1 , the following relation should be satisfied:
 
−40.0 &lt;BG 1&lt;−0.9  (9)
 
   When the distance between the object plane and the first mirror M 1  is LM 1 , and the distance of a pupil conjugate point defined by an optical element, which is at the object side of the first mirror M 1 , is e, these distances satisfy the following relation:
 
0.8&lt; e/LM 1&lt;1.5  (10)
 
   The distance LM 1 , the distance LM 2  between the first and second mirrors M 1  and M 2 , and the paraxial distance OIL from the object plane to the intermediate image by the first imaging system Gr 1  satisfy the following relation:
 
0.6&lt;OIL/( LM 1+2× LM 2)&lt;20  (11)
 
   The distance LM 1  and the conjugate length L of the projection optical system as a whole satisfy the following relation:
 
0.25&lt; LM 1/ L&lt; 0.55  (12)
 
   When the magnification of the first mirror group GM 1  is BGM 1 , the following relation is satisfied:
 
−1.2&lt;1/ BGM 1&lt;0.4  (13)
 
   The distance LFM 1  between the first and second field mirrors FM 1  and FM 2 , and the distance LFM 2  between the second field mirror FM 2  and the image plane, satisfy the following relation:
 
0.45&lt; LFM 1/ LFM 2&lt;0.8  (14)
 
   Conditions (9) to (13) are similar to those described hereinbefore. Condition (14) defines the positional relation of the first and second field mirrors FM 1  and FM 2 . If the lower limit is exceeded, the space between the first and second field mirrors FM 1  and FM 2  becomes narrower, and the powers of the mirrors become larger. Thus, the aberration at the mirror surface disadvantageously increases. If the upper limit is exceeded, the lens space for constituting the second imaging system Gr 2  becomes narrower, and the aberration disadvantageously increases due to an increase of the power of each lens. 
   In the second embodiment of the present invention as described above, the optical system comprises a first imaging system, a field optical system and a second imaging system. Two mirrors of the first imaging system are used to perform reflection twice, to direct light to the image plane side. By this, the structure becomes very simple, wherein the optical axis extends along a single straight line. Further, when predetermined conditions such as positional relations of the mirrors, and magnification sharing of each imaging system and each mirror group, are satisfied, a sufficient imaging region width is attainable. Thus, a catadioptric projection optical system, which is small in size and light in weight, which has optical elements of a reduced number, which has incidence angles and reflection angles on the mirrors not being very large, and which has a sufficient image side working distance, is accomplished. 
   A specific example of the present invention will now be described. Examples 1-4 are those based on the first embodiment described above, and examples 5-21 are those based on the second embodiment. 
   EXAMPLE 1 
     FIG. 4  shows a specific lens structure of Example 1. The projection magnification was 1:4, and the design base wavelength was 157 nm. The glass material was fluorite. 
   The projection optical system comprises, in an order from the object side, a refractive lens group L 1  having a positive refracting power, a refractive lens group R which is a reciprocal optical system wherein both the incidence light and reflection light of a first mirror M 1  (to be placed later) transmit therethrough, a concave mirror (first mirror) M 1 , a concave mirror (second mirror) M 2 , a field lens group F, and a second imaging optical system G 2 . 
   In this embodiment, the image side numerical aperture was NA=0.6, the reduction magnification was 1:4, and the object-to-image distance (from the first object plane to the second object plane) was L=about 1170 mm. The design base wavelength was 157 nm. In the range of the image height of about 11.25-19.75 mm, the aberration was corrected. An abaxial exposure region of arcuate shape, having at least a size of about 26 mm in the lengthwise direction and 8 mm in the width was assured. 
     FIG. 8  shows longitudinal and transverse aberrations of this example, and structural specifications of a numerical example are shown in Table 1. The aberrations in the drawing concern the base wavelength 157 nm±2 pm. 
   The refractive lens group L 1  comprises, in an order from the object side, an aspherical positive lens having a biconvex shape, and an aspherical positive lens of approximately flat-convex shape having a convex surface facing to the object side. With the refractive lens group L 1 , the telecentricity and the balance of distortion aberration are held satisfactorily and, additionally, the light is refracted toward the first mirror M 1  and the reciprocal optical system R. 
   The refractive lens group R (reciprocal optical system) comprises an aspherical negative lens of a meniscus shape, having a concave surface facing to the object side. With this negative lens, mainly, the curvature of field and axial chromatic aberration are corrected. Also, with the aspherical surface, mainly, the spherical aberration and coma aberration, for example, are corrected. 
   The first mirror M 1  comprises an aspherical surface concave mirror having a concave surface facing to the object side. It has a positive refracting power and functions to produce a curvature of field in the positive direction to cancel the negative curvature of field of the second imaging optical system which comprises a refractive lens. The second mirror M 2  comprises a concave mirror having a concave surface facing to the image side, and it serves to direct the abaxial light on the first object  101  to the outside of the effective diameter of the first mirror M 1 . An intermediate image is formed adjacent to the outside of the effective diameter of the first mirror M 1 . In this example, the first imaging optical system is an enlarging system, and separation between the reflection light from the first mirror M 1  and the reflection light from the second mirror M 2  is accomplished easily. 
   In this example, a single aspherical lens of biconvex shape is disposed, as a field lens group F, adjacent to the intermediate image. 
   The second imaging optical system G 2  comprises, in an order from the object side, an aspherical positive lens of a meniscus shape having a concave surface facing to the object side, an aperture stop, an aspherical positive lens of approximately flat-convex shape having a convex surface facing to the image side, an aspherical positive lens having a convex surface facing to the object side, an aspherical lens having a concave surface facing to the image side, an aspherical lens having a convex surface facing to the image side, and an aspherical positive lens having a convex surface facing to the object side. The second imaging optical system G 2  provides a reduction system for imaging the light from the field lens group F onto the second object surface  102 . Because the light is incident on the aperture stop with a certain angle, the effective diameter of the refractive lens about the aperture stop can be suppressed to be small. With this arrangement, various aberrations, such as axial chromatic aberration and spherical aberration, can be reduced and, additionally, they can be cancelled with various aberrations produced in the first imaging optical system. Thus, satisfactory aberration correction is accomplished in the whole system. 
   In this example, the second mirror M 2  is a spherical mirror, and all the remaining elements have an aspherical surface. However, the refractive lenses of the first and second imaging optical systems G 1  and G 2  and the first mirror M 1  may not be defined by an aspherical surface. A spherical lens or spherical mirror may be used therefor. However, use of an aspherical surface can correct the aberrations better. 
   EXAMPLE 2 
     FIG. 5  shows a specific lens structure of Example 2. The projection magnification was 1:4, and the design base wavelength was 157 nm. The glass material was fluorite. 
   The projection optical system comprises, in an order from the object side, a refractive lens group L 1  having a positive refracting power, a refractive lens group R which is a reciprocal optical system wherein both the incidence light and reflection light of a first mirror M 1  (to be placed later) transmit therethrough, a concave mirror (first mirror) M 1 , a flat mirror (second mirror) M 2 , a field lens group F, and a second imaging optical system G 2 . 
   In this embodiment, the image side numerical aperture was NA=0.60, the reduction magnification was 1:4, and the object-to-image distance (from the first object plane to the second object plane) was L=about 1205 mm. In the range of the image height of about 10-16.25 mm, the aberration was corrected. An abaxial exposure region of arcuate shape, having at least a size of about 26 mm in the lengthwise direction and 4 mm in the width was assured. 
     FIG. 9  shows longitudinal and transverse aberrations of this example, and structural specifications of a numerical example are shown in Table 2. The aberrations in the drawing concern the base wavelength and a wavelength ±2 pm. 
   The refractive lens group L 1  comprises, in an order from the object side, a single aspherical positive lens having a biconvex shape. The group Le including two mirrors comprises a refractive lens group R (reciprocal optical system) and first and second mirrors M 1  and M 2 . 
   The refractive lens group R (reciprocal optical system) comprises an aspherical negative lens having a concave surface facing to the object side. The first mirror M 1  comprises an aspherical surface concave mirror having a concave surface facing to the object side. The second mirror M 2  is a flat mirror. 
   A field lens group F is disposed adjacent to an intermediate image as formed by the first imaging optical system. The field lens group F comprises, in an order from the object side, an aspherical positive lens of biconvex shape, and an aspherical positive lens of meniscus shape having a concave surface facing to the image side. 
   The second imaging optical system G 2  comprises, in an order from the object side, an aspherical negative lens of meniscus shape having a concave surface facing to the image side, an aperture stop, an aspherical positive lens of biconvex shape, a spherical positive lens of meniscus shape having a convex surface facing to the object side, an aspherical positive lens having a convex surface facing to the image side, an aspherical positive lens having a convex surface facing to the image side, and an aspherical positive lens of approximately flat-convex shape having a convex surface facing to the object side. In this example, the second imaging optical system G 2  includes a strong negative lens. 
   EXAMPLE 3 
     FIG. 6  shows a specific lens structure of Example 3. The projection magnification was 1:4, and the design base wavelength was 157 nm. The glass material was fluorite. 
   In this embodiment, the image Side numerical aperture was NA=0.68, the reduction magnification was 1:4, and the object-to-image distance (from the first object plane to the second object plane) was L=about 1185 mm. In the range of the image height of about 11.25-20.25 mm, the aberration was corrected. An abaxial exposure region of arcuate shape, having at least a size of about 26 mm in the lengthwise direction and 8 mm in the width was assured. 
     FIG. 10  shows longitudinal and transverse aberrations of this example, and structural specifications of a numerical example are shown in Table 3. The aberrations in the drawing concern the base wavelength 157 mn ±2 pm. 
   The refractive lens group L 1  comprises, in an order from the object side, an aspherical positive lens of meniscus shape having a concave surface facing to the object side, and an aspherical positive lens of biconvex shape. The refractive lens group R (reciprocal optical system) comprises an aspherical negative lens of meniscus shape, having a concave surface facing to the object side. 
   The first mirror M 1  comprises an aspherical surface concave mirror having a concave surface facing to the object side. It has a positive refracting power and functions to produce a curvature of field in the positive direction to cancel the negative curvature of field of the second imaging optical system, which comprises a refractive lens. The second mirror M 2  comprises an aspherical surface concave mirror having a concave surface facing to the image side, and it serves to direct the abaxial light on the first object  101  to the outside of the effective diameter of the first mirror M 1 . An intermediate image is formed adjacent to the outside of the effective diameter of the first mirror M 1 . In this example, a field lens group F is disposed adjacent to the intermediate image. This field lens group F comprises, in an order from the object side, an aspherical positive lens of a meniscus shape having a convex surface facing to the image side, and an aspherical positive lens of a biconvex shape. 
   The second imaging optical system G 2  comprises, in an order from the object side, an aspherical positive lens of a meniscus shape having a convex surface facing to the object side, an aperture stop, an aspherical positive lens of approximately flat-convex shape having a convex surface facing to the image side, an aspherical positive lens having a convex surface facing to the object side, an aspherical lens having a concave surface facing to the image side, an aspherical lens having a convex surface facing the to the image side, and an aspherical positive lens having a convex surface facing to the object side. The second imaging optical system G 2  provides a reduction system for imaging the light from the field lens group F onto the second object surface  102 . Because the light is incident on the aperture stop with a certain angle, the effective diameter of the refractive lens about the aperture stop can be suppressed to be small. With this arrangement, various aberrations such as axial chromatic aberration and spherical aberration can be reduced and, additionally, they can be cancelled with various aberrations produced in the first imaging optical system. Thus, satisfactory aberration correction is accomplished in the whole system. 
   EXAMPLE 4 
     FIG. 7  shows a specific lens structure of Example 4. The projection magnification was 1:5, and the design base wavelength was 157 nm (wavelength of an F 2  excimer laser). The glass material was fluorite. 
   In this embodiment, the image side numerical aperture was NA=0.60, and the object-to-image distance (from the first object plane to the second object plane) was L=about 1411 mm. In the range of the image height of about 9-15 mm, the aberration was corrected. An abaxial exposure region of an arcuate shape, having at least a size of about 20.8 mm in the lengthwise direction and 5 mm in the widths, was assured. 
     FIG. 11  shows longitudinal and transverse aberrations of this example, and structural specifications of a numerical example are shown in Table 4. 
   The projection optical system comprises, in an order from the object side, a refractive lens group L 1  having a positive refracting power, a concave mirror (first mirror) M 1 , a concave mirror (second mirror) M 2 , and a second imaging optical system G 2 . In this example, there is no refractive lens group R or field lens group F, inside the group L 2  having two mirrors. 
   The refractive lens group L 1  comprises, in an order from the object side, an aspherical positive lens having a convex surface facing to the image side, and an aspherical positive lens of biconvex shape. 
   The first mirror M 1  comprises an aspherical surface concave mirror having a concave surface facing to the object side. The second mirror M 2  comprises an aspherical surface concave mirror having a concave surface facing to the image side, and it serves to direct the abaxial light on the first object  101  to the outside of the effective diameter of the first mirror M 1 . An intermediate image is formed adjacent to the outside of the effective diameter of the first mirror M 1 . In this example, the first imaging optical system G 1  constitutes a reduction system. 
   The second imaging optical system G 2  comprises, in an order from the object side, an aspherical positive lens of biconvex shape, an aperture stop, two aspherical positive lenses of meniscus shape having a concave surface facing to the image side, and an aspherical positive lens having a convex surface facing to the object side. The second imaging optical system G 2  provides a reduction system for imaging the light from the second mirror M 2  upon the second object surface  102 . 
   In the four examples described above, except Example 2, the first mirror M 1  is defined by an aspherical surface. Further, except Examples 1 and 2, all the refractive lenses are aspherical lenses. However, a spherical lens may be used in combination. 
   As regards the aspherical lenses, although the surface opposite to the aspherical surface is spherical, it may be flat or spherical. Further, the first mirror or the second mirror may be provided by an aspherical surface having no refracting power. 
   In Examples 1-4 described above, the exposure region has an arcuate shape. However, as long as it is inside the aberration-corrected range, any other shape, such as a rectangular shape, may be used. Further, while the group L 2  having two mirrors is shown as including the refractive lens group R, the refractive lens group R and the mirrors may be integrated (Mangin mirror structure). Alternatively, the refractive lens group R and the second mirror M 2  may be integrated into a Mangin mirror structure. 
   In the examples described above, while there is aspherical surface data in which the conical constant k is taken as zero, the design may be made while using the conical constant as a variable. 
   The exposure light source used an F 2  laser of a wavelength 157 nm. However, a KrF excimer laser (wavelength 248 nm) or an ArF excimer laser (wavelength 193 nm), for example, may be used. Particularly, the invention is effective when the wavelength is shortened and usable optical materials are limited, and the number of optical elements should be reduced. Thus, the present invention is effective for an optical system to be used with a wavelength not longer than 250 nm. 
   In these examples, fluorite was used as the glass material for the wavelength of 157 nm from the F 2  excimer laser. However, any other glass material such as fluorine-doped quartz, for example, may be used. When a KrF or an ArF light source is used, fluorite and quartz may be used in combination, or only one of them may be used. 
   EXAMPLE 5 
     FIG. 12  is an optical path view of Example 5 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:6. The lens conjugate distance L was 1005 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 8.64 mm to 14.40 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and nine lenses. 
   In this example, denoted at r 1 -r 2  are components of a first imaging system Gr 1 , and it comprises a first mirror M 1  (concave surface) and a second mirror M 2  (concave surface). Denoted at r 3 -r 8  are components of a field optical system Grf, and it comprises two positive lenses, including a positive lens FL 1  disposed at the image side of the first mirror M 1 , and one negative lens. Denoted at r 9 -r 21  are components of a second imaging system Gr 2 , and it comprises a stop r 11 , four positive lenses and two negative lenses. 
   In this example, the magnification of the first imaging system Gr 1  is at the most reduction rate and, therefore, a value close to the upper limit of condition (2) is taken. 
   Structural specifications of numerical examples are shown in Table 5. In this example, an image side working distance of 30 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 224.7 mm. While the largest diameter of the optical system as a whole is 227 mm at the field optical system, the largest diameter of the second imaging system is as small as 125 mm, regardless of that the NA is 0.6.  FIG. 29  shows aberrations, and from this, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 6 
     FIG. 13  is an optical path view of Example 6 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnifications β was 1:5. The lens conjugate distance L was 956 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 7.2 mm to 14.40 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and ten lenses. 
   In this example, denoted at r 1 -r 4  are components of a first imaging system Gr 1 , and it comprises a positive lens (group G 1 ) at r 1  and r 2 , a first mirror M 1  (concave surface) and a second mirror M 2  (concave surface). Denoted at r 5 -r 10  are components of a field optical system Grf, and it comprises two positive lenses, including a positive lens FL 1  disposed at the image side of the first mirror M 1 , and one negative lens. Denoted at r 11 -r 23  are components of a second imaging system Gr 2 , and it comprises a stop r 13 , four positive lenses and two negative lenses. 
   In this example, the magnification of the first imaging system Gr 1  is at a smaller rate and, therefore, a value close to the lower limit of condition (8) is taken. Further, based on this, the intermediate image at a paraxial portion of the first imaging system Gr 1  is formed at a position after the light is reflected by the first mirror M 1  and before it is incident on the second mirror M 2 . Therefore, a value close to the lower limit of condition (5) is taken. 
   Structural specifications of numerical examples are shown in Table 6. In this example, an image side working distance of 31 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 232.1 mm. While the largest diameter of the optical system as a whole is 196 mm at the field optical system, the largest diameter of the second imaging system is as small as 143 mm, regardless of that the NA is 0.6.  FIG. 30  shows aberrations, and from this, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 7 
     FIG. 14  is an optical path view of Example 5 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 1199 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 8.4 mm to 14.0 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and nine lenses. 
   In this example, denoted at r 1 -r 4  are components of a first imaging system Gr 1 , and it comprises a positive lens (group G 1 ) at r 1  and r 2 , a first mirror M 1  (concave surface) and a second mirror M 2  (concave surface). Denoted at r 5 -r 12  are components of a field optical system Grf, and it comprises three positive lenses, including a positive lens FL 1  disposed at the image side of the first mirror M 1 , and one negative lens. Denoted at r 13 -r 21  are components of a second imaging system Gr 2 , and it comprises a stop r 13  and four positive lenses. 
   In this example, since the position of a pupil conjugate point of the first imaging system Gr 1  is largely remote, in the positive direction, from the position of the first mirror M 1 , a value close to the upper limit of condition (4) is taken. Further, since the distance from the object plane to the first mirror M 1  is short as compared with the whole optical length, a value close to the lower limit of condition (7) is taken. 
   Structural specifications of numerical examples are shown in Table 7. In this example, an image side working distance of 31 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 333.8 mm. While the largest diameter of the optical system as a whole is 250 mm at the field optical system, the largest diameter of the second imaging system is as small as 143 mm, regardless the NA is 0.6.  FIG. 31  shows aberrations, and from this, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 8 
     FIG. 15  is an optical path view of Example 8 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 1198 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 8.4 mm to 14.0 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and ten lenses. 
   In this example, denoted at r 1 -r 10  are components of a first imaging system Gr 1 , and it comprises a positive lens (group G 1 ), a first mirror M 1  (concave mirror) and a second mirror (concave mirror) M 2 . The imaging system group G 1  comprises a positive lens at r 1  and r 2 , negative lenses at r 3  and r 4 ; r 6  and r 7 ; and r 9  and r 10   a  of the same type which are physically disposed between the first and second mirrors M 1  and M 2 . Denoted at r 11 -r 18  are components of a field optical system Grf, and it comprises three positive lenses, including a positive lens FL 1  disposed at the image side of the first mirror M 1 , and one negative lens. Denoted at r 19 -r 27  are components of a second imaging system Gr 2 , and it comprises a stop r 19  and four positive lenses. 
   In this example, the negative lenses are provided in the first imaging system Gr 1 , between the first mirror M 1  and the second concave mirror M 2 , so as to avoid the inconvenience of interference of the reflection light from the second mirror with the first mirror M 1  and also to correct distortion aberration, for example. 
   Structural specifications of numerical examples are shown in Table 8. In this example, an image side working distance of 36.1 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 337.6 mm. While the largest diameter of the optical system as a whole is 245 mm at the field optical system, the largest diameter of the second imaging system is as small as 142 mm, regardless of that the NA is 0.6.  FIG. 32  shows aberrations, and from this, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 9 
     FIG. 16  is an optical path view of Example 9 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 1166 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 7.7 mm to 14.0 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and twelve lenses. 
   In this example, denoted at r 1 -r 14  are components of a first imaging system Gr 1 , and it comprises a positive lens (group G 1 ) at r 1  and r 2 , and positive lenses LP 1  at r 3  and r 4 ; r 10  and r 11 ; and r 13  and r 14  of the same type which constitute a second mirror group GM 2  in combination with a second mirror M 2 . Also, it comprises negative lenses LN 1  at r 5  and r 6 ; and r 8  and r 9  of the same type, for constituting a first mirror group GM 1  in combination with a first mirror M 1 . 
   Denoted at r 15 -r 22  are components of a field optical system Grf, and it comprises three positive lenses, including a positive lens FL 1  disposed at the image side of the first mirror M 1 , and one negative lens. Denoted at r 23 -r 33  are components of a second imaging system Gr 2 , and it comprises a stop r 27 , four positive lenses and one negative lens. 
   In this example, the position of the intermediate image formed by the first imaging system Gr 1  is substantially coincident with the position of the first mirror M 1 , and the intermediate image is formed outside the first mirror group GM 1 . Therefore, undesirable interference between the light and the first mirror group GM 1  can be avoided easily. Further, the structure is efficient since enlargement of the diameter of the field optical system can be suppressed. The second mirror group GM 2  is provided by the positive lens LP 1  and the second mirror M 2 , to thereby control the Petzval sum. On the other hand, since the imaging state of the intermediate image is moderate, a field stop may be provided at that position. 
   Structural specifications of numerical examples are shown in Table 9. In this example, an image side working distance of 30.3 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 400.5 mm. While the largest diameter of the optical system as a whole is 213 mm at the field optical system, the largest diameter of the second imaging system is as small as 157 mm, regardless of that the NA is 0.6.  FIG. 33  shows aberrations, and from this, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 10 
     FIG. 17  is an optical path view of Example 10 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 1160 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 7.7 mm to 14.0 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and twelve lenses. 
   In this example, denoted at r 1 -r 14  are components of a first imaging system Gr 1 , and it comprises a positive lens (group G 1 ) at r 1  and r 2 , and positive lenses LP 1  at r 3  and r 4 ; r 10  and r 11 ; and r 13  and r 14  of the same type which constitute a second mirror group GM 2  in combination with a second mirror M 2 . Also, it comprises negative lenses LN 1  at r 5  and r 6 ; and r 8  and r 9  of the same type, for constituting a first mirror group GM 1  in combination with a first mirror M 1 . 
   Denoted at r 15 -r 22  are components of a field optical system Grf, and it comprises three positive lenses, including a positive lens FL 1  disposed at the image side of the first mirror M 1 , and one negative lens. Denoted at r 23 -r 33  are components of a second imaging system Gr 2 , and it comprises a stop r 27 , four positive lenses and one negative lens. 
   In this example, particularly, the first mirror group GM 1  of the first imaging system Gr 1  is provided by the negative lens LN 1  and the first mirror M 1 , and the power of each element is strengthened. By this, the effect of correcting chromatic aberration with respect to the whole optical system is enhanced. Further, the second mirror group GM 2  is provided by the positive lens LP 1  and the second mirror M 2 , to thereby control the Petzval sum. 
   Structural specifications of numerical examples are shown in Table 10. In this example, an image side working distance of 30.0 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 375.9 mm. While the largest diameter of the optical system as a whole is 266 mm at the field optical system, the largest diameter of the second imaging system is as small as 105 mm, regardless of that the NA is 0.6.  FIG. 34  shows aberrations with respect to the base wavelength 157 nm and a wavelength range of 2 pm. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 11 
     FIG. 18  is an optical path view of Example 11 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:4. The lens conjugate distance L was 1430 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 8.19 mm to 13.65 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and twelve lenses. 
   In this example, denoted at r 1 -r 12  are components of a first imaging system Gr 1 , and it comprises a positive lens (group G 1 ) at r 1  and r 2 , and negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type which constitute a first mirror group GM 1  in combination with a first mirror M 1 . Also, it comprises positive lenses LP 1  at r 8  and r 9 ; and r 11  and r 12  of the same type, for constituting a second mirror group GM 2  in combination with a second mirror M 2 . 
   Denoted at r 13 -r 20  are components of a field optical system Grf, and it comprises three positive lenses, including a positive lens FL 1  disposed at the image side of the first mirror M 1 , and one negative lens. Denoted at r 21 -r 31  are components of a second imaging system Gr 2 , and it comprises a stop r 25 , four positive lenses and one negative lens. 
   In this example, like Example 10, due to the structure of the first mirror group GM 1  as described, the effect of correcting chromatic aberration is enhanced. Further, the second mirror group GM 2  is provided by the positive lens LP 1  and the second mirror M 2 , to thereby control the Petzval sum. 
   Structural specifications of numerical examples are shown in Table 11. In this example, an image side working distance of 30.0 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 371.9 mm. While the largest diameter of the optical system as a whole is 328 mm at the field optical system, the largest diameter of the second imaging system is as small as 141 mm, regardless of that the NA is 0.6.  FIG. 35  shows aberrations with respect to the base wavelength 157 nm and a wavelength range of 2 pm. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 12 
     FIG. 19  is an optical path view of Example 12 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:4. The lens conjugate distance L was 1430 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 8.19 mm to 13.65 mm. The optical system was provided by a small number of optical elements, i.e., two mirrors and twelve lenses, like Example 11. 
   In this example, denoted at r 1 -r 12  are components of a first imaging system Gr 1 , and it comprises a positive lens (group G 1 ) at r 1  and r 2 , and negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type which constitute a first mirror group GM 1  in combination with a first mirror M 1 . Also, it comprises positive lenses LP 1  at r 8  and r 9 ; and r 11  and r 12  of the same type, for constituting a second mirror group GM 2  in combination with a second mirror M 2 . In  FIG. 20 , the positive lens group G 1  as well as the positive lens LP 1  are of half disk-like shape. 
   Denoted at r 13 -r 20  are components of a field optical system Grf, and it comprises three positive lenses, including a positive lens FL 1  of a doughnut shape, being hollow at its center, and being disposed outside the first mirror M 1 , and one negative lens. Denoted at r 21 -r 31  are components of a second imaging system Gr 2 , and it comprises a stop r 25 , four positive lenses and one negative lens. 
   In this example, since the pupil conjugate point of the first imaging system Gr 1  is placed closer to the object side, a value close to the lower limit of condition (4) is taken. Further, like Example 10, due to the structure of the first mirror group GM 1  as described, the effect of correcting chromatic aberration is enhanced. Also, the positive lens FL 1  of the field optical system Grf is made into a doughnut shape, and the first mirror group GM 1  of the first imaging system Gr 1  is disposed at the central portion of the doughnut shape. With this structure, the light rays can be refracted at a position closer to the object side and, therefore, the powers of the field optical system Grf and the second imaging system Gr 2  can be made smaller. This is very advantageous with respect to the aberration correction. Further, the second mirror group GM 2  is provided by the positive lens LP 1  and the second mirror M 2 , to thereby control the Petzval sum. 
   Structural specifications of numerical examples are shown in Table 12. In this example, an image side working distance of 30.0 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 377.0 mm. While the largest diameter of the optical system as a whole is 328 mm at the field optical system, the largest diameter of the second imaging system is as small as 144 mm, regardless of that the NA is 0.6.  FIG. 36  shows aberrations with respect to the base wavelength 157 nm and a wavelength range of 2 pm. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 13 
     FIG. 20  is an optical path view of Example 13 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 1100 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 10.24 mm to 13.65 mm. The optical system was provided by an extraordinarily simple structure, i.e., with four mirrors and five lenses. 
   In this example, denoted at r 1 -r 2  are components of a first imaging system Gr 1 , and it comprises a first mirror M 1  (concave surface) and a second mirror M 2  (concave surface), only. Denoted at r 3 -r 4  are components of a field optical system Grf, and it comprises a first field mirror FM 1  (concave surface) and a second field mirror FM 2  (convex surface), only. Denoted at r 5 -r 15  are components of a second imaging system Gr 2 , and it comprises a stop r 5 , four positive lenses and one negative lens. 
   In this example, the first mirror M 1  is positioned relatively at the object side, with respect to the conjugate distance of the whole optical system, and therefore a value close to the lower limit of condition (12) is taken. 
   Structural specifications of numerical examples are shown in Table 22. In this example, an image side working distance of 30.0 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 192.2 mm. While the largest diameter of the optical system as a whole is 388 mm at the field optical system, the largest diameter of the second imaging system is as small as 167 mm, regardless of that the NA is 0.6.  FIG. 37  shows aberrations. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 14 
     FIG. 21  is an optical path view of Example 14 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 1100 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 10.24 mm to 13.65 mm. The optical system was provided by a simple structure, i.e., with four mirrors and six lenses (one lens added to Example 13). 
   In this example, denoted at r 1 -r 2  are components of a first imaging system Gr 1 , and it comprises a first mirror M 1  (concave surface) and a second mirror M 2  (concave surface which is very close to a flat surface), only. Denoted at r 3 -r 8  are components of a field optical system Grf, and it comprises a first field mirror FM 1  (concave surface), a second field mirror FM 2  (convex surface), and negative lenses LF at r 4  and r 5 ; and r 7  and r 8  of the same type. Denoted at r 9 -r 19  are components of a second imaging system Gr 2 , and it comprises a stop r 9 , four positive lenses and one negative lens. 
   In this example, with use of the second field mirror group GFM 2  which is provided by the second field mirror FM 2  (concave) and the negative lens LF, the Petzval sum is also controlled. Further, the magnification of the second imaging system Gr 2  is made small, such that a value close to the upper limit of condition (1) is taken. Since the first imaging system Gr 1  does not include the positive lens group G 1 , the second mirror M 2  is positioned closer to the object side. Therefore, a value close to the upper limit of condition (6) is taken. 
   Structural specifications of numerical examples are shown in Table 14. In this example, an image side working distance of 30 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 156.4 mm. While the largest diameter of the optical system as a whole is 444 mm at the field optical system, the largest diameter of the second imaging system is as small as 144 mm, regardless of that the NA is 0.6.  FIG. 38  shows aberrations. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 15 
     FIG. 22  is an optical path view of Example 15 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:4. The lens conjugate distance L was 1190 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 9.56 mm to 13.65 mm. The optical system was provided by use of four mirrors and eight lenses (two lenses added to Example 13). 
   In this example, denoted at r 1 -r 8  are components of a first imaging system Gr 1 , and it comprises a positive lens (G 1 ) at r 1  and r 2 , negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type, a first mirror M 1  (concave surface) and a second mirror M 2  (convex surface). Denoted at r 9 -r 14  are components of a field optical system Grf, and it comprises a first field mirror FM 1  (concave surface), a second field mirror FM 2  (convex surface), and positive lenses LF at r 10  and r 11 ; and r 13  and r 14  of the same type. Denoted at r 15 -r 25  are components of a second imaging system Gr 2 , and it comprises a stop r 15 , four positive lenses and one negative lens. 
   In this example, the convex lens group G 1  is provided in the first imaging system Gr 1 , by which the optical system is made telecentric on the object side. Also, the first mirror group GM 1  is provided by the negative lens LN 1  and the first mirror M 1 , by which color correction is performed. Further, with use of the second field mirror group GFM 2  which is provided by the second field mirror FM 2  (convex) and the positive lens LF, the Petzval sum is also controlled. Further, since the pupil conjugate point of the first imaging system Gr 1  is closer to the object side, a value close to the lower limit of condition (10) is taken. Also, since the spacing between the second and first field mirrors FM 2  and FM 1  is relatively large, a value close to the upper limit of condition (14) is taken. 
   Structural specifications of numerical examples are shown in Table 15. In this example, an image side working distance of 36 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 203.7 mm. While the largest diameter of the optical system as a whole is 512 mm at the field optical system, the largest diameter of the second imaging system is as small as 146 mm, regardless of that the NA is 0.6.  FIG. 39  shows aberrations with respect to the base wavelength 157 nm and a wavelength range of 4 pm. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 16 
     FIG. 23  is an optical path view of Example 16 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 1190 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 9.56 m to 13.65 mm. The optical system was provided by use of four mirrors and nine lenses (one lens added to Example 15). 
   In this example, denoted at r 1 -r 8  are components of a first imaging system Gr 1 , and it comprises a positive lens (G 1 ) at r 1  and r 2 , negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type, a first mirror M 1  (concave surface) and a second mirror M 2  (convex surface). Denoted at r 9 -r 16  are components of a field optical system Grf, and it comprises a positive lens FL 1 , a first field mirror. FM 1  (concave surface), a second field mirror FM 2  (convex surface), and negative lenses LF at r 12  and r 13 ; and r 15  and r 16  of the same type. Denoted at r 17 -r 27  are components of a second imaging system Gr 2 , and it comprises a stop r 17 , four positive lenses and one negative lens. 
   In this example, the magnification of the first imaging system Gr 1  is slightly enlarged to −3.838× and, in consideration of it, the positive lens FL 1  included in the field optical system Grf is disposed at the back, on the image side, of the first mirror M 1  to thereby suppress the increase of diameter. Further, with use of the first mirror group GM 1  including the negative lens LN 1  and the first mirror M 1 , as well as the second field mirror group GFM 2  which is provided by the second field mirror FM 2  (convex) and the negative lens LF, the Petzval sum is also controlled. 
   Structural specifications of numerical examples are shown in Table 16. In this example, an image side working distance of 36 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 292.8 mm. While the largest diameter of the optical system as a whole is 294 mm at the field optical system, the largest diameter of the second imaging system is as small as 184 mm, regardless of that the NA is 0.6.  FIG. 40  shows aberrations. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 17 
     FIG. 24  is an optical path view of Example 17 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:4. The lens conjugate distance L was 1188 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 9.56 mm to 13.65 mm. The optical system was provided by the use of four mirrors and nine lenses. 
   In this example, denoted at r 1 -r 8  are components of a first imaging system Gr 1 , and it comprises a positive lens (G 1 ) at r 1  and r 2 , negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type, a first mirror M 1  (concave surface) and a second mirror M 2  (convex surface). Denoted at r 9 -r 16  are components of a field optical system Grf, and it comprises a positive lens FL 1 , a first field mirror FM 1  (concave surface), a second field mirror FM 2  (concave surface), and positive lenses LF at r 12  and r 13 ; and r 15  and r 16  of the same type. Denoted at r 17 -r 27  are components of a second imaging system Gr 2 , and it comprises a stop r 17 , four positive lenses and one negative lens. 
   In this example, the second field mirror FM 2  as well as the positive lens LF, at the back thereof, are provided in the field optical system Grf. With this structure, an intermediate image is formed also just after (image side) of the positive lens LF. Thus, in the whole optical system, the imaging is executed three times. Therefore, after the field optical system Grf, the positive power becomes larger and the space is made smaller. Thus, the position of the first mirror M 1  is placed relatively at the image side, and a value close to the upper limit of condition (12) is taken. Further, since the magnification at the first mirror M 1  is made smaller, a value close to the lower limit of condition (13) is taken. As a result, the paraxial intermediate image at the first imaging system Gr 1  is produced after the light which is reflected by the second mirror M 2  and at a position closer to the object side. Thus, a value close to the lower limit of condition (11) is taken. Additionally, with use of the first mirror group GM 1  provided by the negative lens LN 1  and the first mirror M 1 , color correction is made. 
   Structural specifications of numerical examples are shown in Table 17. In this example, an image side working distance of 36 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 303.3 mm. While the largest diameter of the optical system as a whole is 323 mm at the field optical system, the largest diameter of the second imaging system is as small as 125 mm, regardless of that the NA is 0.6.  FIG. 41  shows aberrations, with respect to the base wavelength 157 nm and a wavelength range of 2 pm. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 18 
     FIG. 25  is an optical path view of Example 18 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:4. The lens conjugate distance L was 1190 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 10.0 mm to 20.0 mm. The optical system was provided by use of four mirrors and nine lenses, like Example 16. 
   In this example, denoted at r 1 -r 8  are components of a first imaging system Gr 1 , and it comprises a positive lens (G 1 ) at r 1  and r 2 , negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type, a first mirror M 1  (concave surface) and a second mirror M 2  (convex surface). Denoted at r 9 -r 16  are components of a field optical system Grf, and it comprises a positive lens FL 1 , a first field mirror FM 1  (concave surface), a second field mirror FM 2  (convex surface), and positive lenses LF at r 12  and r 13 ; and r 15  and r 16  of the same type. Denoted at r 17 -r 27  are components of a second imaging system Gr 2 , and it comprises a stop r 17 , four positive lenses and one negative lens. 
   In this example, with use of the first mirror group GM 1  as provided by the negative lens LN 1  and the first mirror M 1 , color correction is accomplished. Further, with use of the second field mirror group GFM 2  which is provided by the second field mirror FM 2  (convex) and the positive lens LF, the Petzval sum is also controlled. 
   Structural specifications of numerical examples are shown in Table 18. In this example, an image side working distance of 37 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 286.8 mm. While the largest diameter of the optical system as a whole is 442 mm at the field optical system, the largest diameter of the second imaging system is as small as 165 mm, regardless of that the NA is 0.6.  FIG. 42  shows aberrations, with respect to the base wavelength 157 nm and a wavelength range of 4 pm. From the drawing, it is seen that the aberrations are corrected satisfactorily. 
   EXAMPLE 19 
     FIG. 26  is an optical path view of Example 18 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:5. The lens conjugate distance L was 934 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 7.7 mm to 14.0 mm. The optical system was provided by use of four mirrors and ten lenses. 
   In this example, denoted at r 1 -r 10  are components of a first imaging system Gr 1 , and it comprises positive lenses (G 1 ) at r 1  and r 2 ; and r 3  and r 4 , negative lenses LN 1  at r 5  and r 6 ; and r 8  and r 9  of the same type, a first mirror M 1  (concave surface) and a second mirror M 2  (concave surface). Denoted at r 11 -r 18  are components of a field optical system Grf, and it comprises a positive lens FL 1 , a first field mirror FM 1  (concave surface), a second field mirror FM 2  (convex surface), and positive lenses LF at r 14  and r 15 ; and r 17  and r 18  of the same type. Denoted at r 19 -r 29  are components of a second imaging system Gr 2 , and it comprises a stop r 19 , four positive lenses and one negative lens. 
   In this example with the use of the first mirror group GM 1  as provided by the negative lens LN 1  and the first mirror M 1 , color correction is accomplished. Further, with the use of the second field mirror group GFM 2 , which is provided by the second field mirror FM 2  (convex) and the positive lens LF, the Petzval sum is also controlled. Since the magnification of the first imaging system Gr 1  is at the most reduction rate, a value close to the upper limit of condition (9) is taken. Since the spacing between the second and first field mirrors FM 2  and FM 1  is relatively small, a value close to the lower limit of condition (14) is taken. 
   Structural specifications of numerical examples are shown in Table 19. In this example, an image side working distance of 33.7 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 264.4 mm. Further, the largest diameter of the whole optical system is very short, as small as 293 mm, and also, the largest diameter of the second imaging system is as small as 130 mm, regardless that the NA is 0.6.  FIG. 43  shows aberrations, with respect to the base wavelength 157 nm and a wavelength range of 2 pm. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   EXAMPLE 20 
     FIG. 27  is an optical path view of Example 20 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:8. The lens conjugate distance L was 1190 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 9.56 mm to 13.65 mm. The optical system was provided by use of four mirrors and nine lenses, like Example 16. 
   In this example, denoted at r 1 -r 8  are components of a first imaging system Gr 1 , and it comprises a positive lens (G 1 ) at r 1  and r 2 , negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type, a first mirror M 1  (concave surface) and a second mirror M 2  (convex surface). Denoted at r 9 -r 16  are components of a field optical system Grf, and it comprises a positive lens FL 1 , a first field mirror FM 1  (concave surface), a second field mirror FM 2  (convex surface), and negative lenses LF at r 12  and r 13 ; and r 15  and r 16  of the same type. Denoted at r 17 -r 27  are components of a second imaging system Gr 2 , and it comprises a stop r 17 , four positive lenses and one negative lens. 
   In this example, since the magnification of the first imaging system Gr 1  is strongly enlarged, a value close to the lower limit of condition (9) is taken. This is because the magnification of the first mirror group GM 1  is positive, and because a value close to the upper limit of condition (13) is taken. As a result, a value close to the upper limit of condition (11) is taken, and the position of the intermediate image produced by the first imaging system Gr 1  is far remote from the first mirror M 1 . Further, since the pupil conjugate point of the first imaging system Gr 1  is at the image plane side with respect to the first mirror M 1 , a value close to the upper limit of condition (10) is taken. Additionally, with the use of the second field mirror group GFM 2 , which is provided by the second field mirror FM 2  (convex) and the negative lens LF, the Petzval sum is also controlled. 
   Structural specifications of numerical examples are shown in Table 20. In this example, an image side working distance of 36 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 315.5 mm. While the largest diameter of the optical system as a whole is 355 mm at the field optical system, the largest diameter of the second imaging system is as small as 177 mm, regardless of that the NA is 0.6.  FIG. 44  shows aberrations. From the drawing, it is seen that the aberrations are corrected satisfactorily. 
   EXAMPLE 21 
     FIG. 28  is an optical path view of Example 21 of the present invention. The design base wavelength was 157 nm of F 2  excimer laser light, the NA was 0.6, and the projection magnification β was 1:10. The lens conjugate distance L was 1190 mm. The optical system had an exposure region (imaging region) upon an image plane, of an arcuate shape, at the image height from 9.56 mm to 13.65 mm. The optical system was provided by the use of four mirrors and nine lenses, like Example 16. 
   In this example, denoted at r 1 -r 8  are components of a first imaging system Gr 1 , and it comprises a positive lens (G 1 ) at r 1  and r 2 , negative lenses LN 1  at r 3  and r 4 ; and r 6  and r 7  of the same type, a first mirror M 1  (concave surface) and a second mirror M 2  (convex surface which is substantially flat). Denoted at r 9 -r 16  are components of a field optical system Grf, and it comprises a positive lens FL 1 , a first field mirror FM 1  (concave surface), a second field mirror FM 2  (convex surface), and negative lenses LF at r 12  and r 13 ; and r 15  and r 16  of the same type. Denoted at r 17 -r 27  are components of a second imaging system Gr 2 , and it comprises a stop r 17 , four positive lenses and one negative lens. 
   In this example, the magnification of the second imaging system Gr 2  has a value close to the lower limit of condition (1). Also, the distance between the second and first mirrors M 2  and M 1  is short, and a value close to the lower limit of condition (6) is taken. Further with the use of the first mirror group GM 1  being provided by the negative lens LN 1  and the first mirror M 1  as well as the second field mirror group GFM 2 , which is provided by the second field mirror FM 2  (convex) and the negative lens LF, the Petzval sum is also controlled. 
   Structural specifications of numerical examples are shown in Table 21. In this example, an image side working distance of 36 mm is assured, and the total glass material length along the optical path is extraordinarily shortened to 301.7 mm. While the largest diameter of the optical system as a whole is 310 mm at the field optical system, the largest diameter of the second imaging system is as small as 180 mm, regardless of that the NA is 0.6.  FIG. 45  shows aberrations. From the drawing, it is seen that aberrations are corrected satisfactorily. 
   In Examples 5-21 described above, aspherical surfaces are used and, among the aspherical surfaces used, there are lens surfaces having a conical constant k set to zero. However, a design may be made while taking the conical constant k as a variable. Further, in these examples, the wavelength of an F 2  excimer laser was used as a design wavelength, and fluorite (n=1.5600) was used as the glass material for it. However, any other glass material such as fluorine-doped quartz, for example, may be used. When a KrF or an ArF light source is used, fluorite and quartz may be used in combination. Alternatively, only one of them may be used and, on that occasion, since the dispersion of glass material is smaller, the correction of chromatic aberration becomes easier. 
   A projection optical system according to these examples may be used as a projection optical system in a scan type projection exposure apparatus for projecting a pattern (device pattern such as a circuit pattern) of a reticle or a mask onto a substrate or a wafer in accordance with a step-and-scan procedure. A wafer is exposed to a device pattern by use of such an exposure apparatus, and then, the exposure wafer is developed. Through subsequent processes, such as etching, devices (semiconductor chips) are produced. 
   Structural specifications of numerical examples according to Examples 1-21 are shown in Tables 1-21 below. 
   In the numerical examples, r i  denotes the curvature radius at the i-th lens surface, in an order from the object side, d i  is the i-th lens thickness or air spacing in an order from the object side, and n i  is the refractive index of the i-th lens glass, in an order from the object side, with respect to the base wavelength=157 nm. 
   Further, the refractive indices of the wavelength +2 μm and −2 μm with respect to the base wavelength, are 1.5599949 and 1.5600051, respectively. 
   The shape of an aspherical surface can be given by the following equation: 
                 X   =       ⁢           H   2       r   i         1   +       (     1   -       (     1   +   k     )     ·       (     H   n     )     2         )       1   2           +     A   ·     H   4       +     B   ·     H   6       +     C   ·     H   8       +     D   ·     H   10       +                     ⁢       E   ·     H   12       +     F   ·     H   14       +     G   ·     H   16       +   …                 
where X is the amount of displacement from the lens vertex along the optical axis direction, H is the distance from the optical axis, r i  is the curvature radius, k is the conical constant, and A, B, . . . and G are aspherical coefficients.
 
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
               EXAMPLE 1 
             
             
                 
             
           
           
             
               FIRST OBJECT TO FIRST SURFACE DISTANCE: 83.739 mm 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
             
             
                 
             
           
        
         
             
                1 
               989.392 
               18.000 
               1.56000 
                 
             
             
                2 
               −3595.508 
               1.697 
             
             
                3 
               236.000 
               24.359 
               1.56000 
             
             
                4 
               2462.140 
               300.511 
             
             
                5 
               −114.548 
               18.000 
               1.56000 
             
             
                6 
               −946.909 
               7.879 
             
             
                7 
               −185.804 
               −7.879 
                 
               M1 
             
             
                8 
               −946.909 
               −18.000 
               1.56000 
             
             
                9 
               −114.548 
               −286.511 
             
             
               10 
               1428.922 
               324.390 
                 
               M2 
             
             
               11 
               380.000 
               48.405 
               1.56000 
             
             
               12 
               −345.892 
               434.726 
             
             
               13 
               102.426 
               18.000 
               1.56000 
             
             
               14 
               225.926 
               45.944 
             
           
        
         
             
               15 
               0.0 (stop) 
               21.343 
                 
             
           
        
         
             
               16 
               2291.779 
               28.288 
               1.56000 
                 
             
             
               17 
               −232.971 
               1.000 
             
             
               18 
               68.389 
               22.403 
               1.56000 
             
             
               19 
               275.504 
               1.000 
             
             
               20 
               139.927 
               19.297 
               1.56000 
             
             
               21 
               275.224 
               5.771 
             
             
               22 
               −963.793 
               27.452 
               1.56000 
             
             
               23 
               −228.789 
               1.000 
             
             
               24 
               106.934 
               18.000 
               1.56000 
             
             
               25 
               −742.488 
             
             
                 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               0.000000e+000 
               3.268074e−008 
               −6.656739e−012 
               1.084352e−016 
               −1.466501e−020 
             
             
                4 
               0.000000e+000 
               −5.945159e−008 
               9.367805e−012 
               −3.675672e−016 
               1.878106e−020 
             
             
                5 
               0.000000e+000 
               −1.045454e−008 
               9.094085e−013 
               4.644093e−017 
               6.202292e−019 
             
             
                7 
               0.000000e+000 
               −1.020658e−008 
               −2.127267e−013 
               −2.970263e−017 
               1.066496e−019 
             
             
                9 
               0.000000e+000 
               −1.045454e−008 
               9.094085e−013 
               4.644093e−017 
               6.202292e−019 
             
             
               12 
               0.000000e+000 
               1.276943e−008 
               −3.269379e−014 
               −1.148753e−018 
               1.871030e−022 
             
             
               13 
               0.000000e+000 
               −1.177280e−007 
               −9.735382e−012 
               −5.058594e−016 
               −7.794080e−020 
             
             
               16 
               0.000000e+000 
               7.415847e−008 
               −1.533594e−011 
               2.908683e−015 
               −1.312466e−019 
             
             
               18 
               −2.765242e−001 
               −4.548406e−009 
               8.093119e−012 
               −1.772233e−015 
               −2.169524e−018 
             
             
               20 
               −3.452390e+000 
               −1.157411e−007 
               −3.193404e−011 
               −1.695026e−015 
               3.936837e−018 
             
             
               22 
               0.000000e+000 
               1.441342e−007 
               1.875541e−011 
               8.365199e−015 
               −6.884476e−018 
             
             
               24 
               −5.937621e−001 
               −2.497358e−007 
               −8.672718e−011 
               −1.119851e−014 
               −1.058646e−017 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               2.506755e−024 
               −9.840963e−029 
               0.000000e+000 
             
             
                 
                4 
               −1.827522e−024 
               7.013708e−029 
               0.000000e+000 
             
             
                 
                5 
               −1.963400e−022 
               2.716627e−026 
               0.000000e+000 
             
             
                 
                7 
               −2.877088e−023 
               3.146892e−027 
               0.000000e+000 
             
             
                 
                9 
               −1.963400e−022 
               2.716627e−026 
               0.000000e+000 
             
             
                 
               12 
               −9.175707e−027 
               1.629370e−031 
               0.000000e+000 
             
             
                 
               13 
               1.160369e−023 
               −1.219551e−027 
               0.000000e+000 
             
             
                 
               16 
               −2.557773e−022 
               5.424698e−026 
               0.000000e+000 
             
             
                 
               18 
               3.623462e−022 
               −1.873086e−025 
               0.000000e+000 
             
             
                 
               20 
               2.639407e−022 
               −5.908244e−025 
               0.000000e+000 
             
             
                 
               22 
               7.408468e−021 
               −4.850248e−025 
               0.000000e+000 
             
             
                 
               24 
               1.061653e−020 
               −1.104395e−023 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 2 
             
             
                 
             
             
               EXAMPLE 2 
             
             
                 
             
           
           
             
               FIRST OBJECT TO FIRST SURFACE DISTANCE: 75.685 mm 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
             
             
                 
             
           
        
         
             
                1 
               297.627 
               19.775 
               1.56000 
                 
             
             
                2 
               −1115.696 
               328.484 
             
             
                3 
               −160.548 
               18.000 
               1.56000 
             
             
                4 
               2147.160 
               22.180 
             
             
                5 
               −203.139 
               −22.180 
                 
               M1 
             
             
                6 
               2147.160 
               −18.000 
               1.56000 
             
             
                7 
               −160.548 
               −313.164 
             
             
                8 
               0.000 
               365.344 
                 
               M2 
             
             
                9 
               1040.329 
               38.055 
               1.56000 
             
             
               10 
               −387.846 
               1.000 
             
             
               11 
               190.260 
               45.524 
               1.56000 
             
             
               12 
               634.071 
               120.149 
             
             
               13 
               249.471 
               18.000 
               1.56000 
             
             
               14 
               127.136 
               325.385 
             
           
        
         
             
               15 
               0.0 (stop) 
               1.000 
                 
             
           
        
         
             
               16 
               234.780 
               33.014 
               1.56000 
                 
             
             
               17 
               −336.281 
               1.000 
             
             
               18 
               144.606 
               35.000 
               1.56000 
             
             
               19 
               968.534 
               16.804 
             
             
               20 
               −793.316 
               35.000 
               1.56000 
             
             
               21 
               −100.000 
               1.000 
             
             
               22 
               88.381 
               25.000 
               1.56000 
             
             
               23 
               0.000 
             
             
                 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               1.372961e−008 
               3.473252e−013 
               −3.195720e−016 
               9.094243e−020 
             
             
                3 
               0.000000e+000 
               2.151239e−008 
               9.541648e−012 
               4.776084e−016 
               7.380865e−020 
             
             
                5 
               0.000000e+000 
               4.532898e−009 
               1.823606e−012 
               1.222571e−016 
               1.631434e−020 
             
             
                7 
               0.000000e+000 
               2.151239e−008 
               9.541648e−012 
               4.776084e−016 
               7.380865e−020 
             
             
               10 
               0.000000e+000 
               5.040814e−010 
               2.625973e−013 
               −1.989714e−017 
               9.422664e−022 
             
             
               11 
               0.000000e+000 
               −5.072499e−009 
               1.389868e−013 
               −1.647184e−017 
               3.468047e−022 
             
             
               14 
               0.000000e+000 
               3.310157e−008 
               2.186614e−012 
               3.087404e−016 
               −3.918557e−020 
             
             
               17 
               0.000000e+000 
               1.858529e−007 
               1.966297e−011 
               2.828536e−015 
               2.203369e−019 
             
             
               20 
               0.000000e+000 
               −1.667572e−007 
               −3.379925e−011 
               7.374563e−015 
               −5.503285e−019 
             
             
               22 
               0.000000e+000 
               −4.993819e−008 
               7.233187e−012 
               −2.042203e−015 
               3.653495e−020 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               −1.434764e−023 
               1.206555e−027 
               −4.210407e−032 
             
             
                 
                3 
               −2.063590e−023 
               4.825958e−027 
               −5.593776e−031 
             
             
                 
                5 
               −8.711867e−025 
               2.964757e−028 
               1.525109e−033 
             
             
                 
                7 
               −2.063590e−023 
               4.825958e−027 
               −5.593776e−031 
             
             
                 
               10 
               −2.700833e−026 
               4.650686e−031 
               −4.262218e−036 
             
             
                 
               11 
               3.873194e−028 
               −2.799981e−031 
               4.425078e−037 
             
             
                 
               14 
               1.130858e−023 
               −1.107497e−027 
               6.460332e−032 
             
             
                 
               17 
               1.188890e−022 
               −2.552801e−026 
               7.612208e−030 
             
             
                 
               20 
               1.402677e−023 
               2.115981e−027 
               −8.027962e−031 
             
             
                 
               22 
               −2.309114e−022 
               −5.309629e−026 
               5.804270e−030 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 3 
             
             
                 
             
             
               EXAMPLE 3 
             
             
                 
             
           
           
             
               FIRST OBJECT TO FIRST SURFACE DISTANCE: 72.674 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
             
             
                 
             
           
        
         
             
                1 
               −593.057 
               25.376 
               1.56000 
                 
             
             
                2 
               −320.774 
               1.000 
             
             
                3 
               463.082 
               27.632 
               1.56000 
             
             
                4 
               −613.991 
               281.867 
             
             
                5 
               −109.249 
               18.000 
               1.56000 
             
             
                6 
               −961.687 
               9.159 
             
             
                7 
               −178.361 
               −9.159 
                 
               M1 
             
             
                8 
               −961.687 
               −18.000 
               1.56000 
             
             
                9 
               −109.249 
               −266.071 
             
             
               10 
               1622.171 
               305.230 
                 
               M2 
             
             
               11 
               −1660.654 
               24.024 
               1.56000 
             
             
               12 
               −365.238 
               1.000 
             
             
               13 
               347.111 
               47.000 
               1.56000 
             
             
               14 
               −1881.176 
               410.002 
             
             
               15 
               8178.667 
               26.178 
               1.56000 
             
             
               16 
               −212.848 
               75.049 
             
           
        
         
             
               17 
               0.0 (stop) 
               15.536 
                 
             
           
        
         
             
               18 
               268.041 
               33.816 
               1.56000 
                 
             
             
               19 
               −186.462 
               1.000 
             
             
               20 
               87.102 
               20.173 
               1.56000 
             
             
               21 
               350.675 
               1.000 
             
             
               22 
               156.475 
               21.218 
               1.56000 
             
             
               23 
               86.116 
               6.639 
             
             
               24 
               168.945 
               20.602 
               1.56000 
             
             
               25 
               −165.909 
               1.000 
             
             
               26 
               105.283 
               20.915 
               1.56000 
             
             
               27 
               −743.988 
             
             
                 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               −7.252390e+000 
               −4.701121e−009 
               −6.090134e−013 
               −1.267089e−017 
               8.029170e−022 
             
             
                4 
               0.000000e+000 
               −4.766887e−008 
               2.462294e−012 
               −9.893034e−017 
               6.719603e−021 
             
             
                5 
               0.000000e+000 
               2.116808e−009 
               −1.611319e−013 
               1.025091e−015 
               5.091150e−019 
             
             
                7 
               0.000000e+000 
               −6.712584e−009 
               −8.093063e−013 
               2.887582e−017 
               9.870124e−020 
             
             
                9 
               0.000000e+000 
               2.116808e−009 
               −1.611319e−013 
               1.025091e−015 
               5.091150e−019 
             
             
               10 
               0.000000e+000 
               7.054971e−010 
               2.418241e−014 
               1.839107e−018 
               −7.963029e−023 
             
             
               12 
               0.000000e+000 
               4.707819e−009 
               −2.189427e−014 
               1.973642e−018 
               −1.068343e−023 
             
             
               13 
               0.000000e+000 
               8.092928e−010 
               −6.294695e−014 
               1.464461e−018 
               1.870403e−023 
             
             
               15 
               0.000000e+000 
               −1.344505e−007 
               1.853632e−012 
               1.650439e−016 
               −1.056871e−020 
             
             
               18 
               5.660213e+000 
               2.805319e−008 
               −5.963359e−011 
               5.837059e−017 
               8.483480e−019 
             
             
               20 
               −5.463452e−001 
               −1.335770e−007 
               −8.743479e−013 
               4.818362e−015 
               2.569222e−020 
             
             
               22 
               −1.401348e+000 
               −4.899966e−008 
               2.339115e−011 
               −1.429818e−014 
               −1.677957e−018 
             
             
               24 
               0.000000e+000 
               3.153044e−007 
               −8.376396e−012 
               1.928547e−014 
               −5.705932e−018 
             
             
               26 
               6.648275e−001 
               −1.189888e−007 
               6.781855e−012 
               −1.430235e−014 
               3.880028e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               −4.085486e−025 
               1.924786e−029 
               0.000000e+000 
             
             
                 
                4 
               −2.271393e−025 
               1.177205e−030 
               0.000000e+000 
             
             
                 
                5 
               −1.657547e−023 
               6.847636e−027 
               0.000000e+000 
             
             
                 
                7 
               −1.029026e−023 
               8.654760e−028 
               0.000000e+000 
             
             
                 
                9 
               −1.657547e−023 
               6.847636e−027 
               0.000000e+000 
             
             
                 
               10 
               4.433871e−028 
               2.201312e−032 
               0.000000e+000 
             
             
                 
               12 
               −2.065745e−027 
               5.118720e−032 
               0.000000e+000 
             
             
                 
               13 
               −3.513181e−027 
               7.676071e−032 
               0.000000e+000 
             
             
                 
               15 
               −1.436354e−025 
               −9.351577e−030 
               0.000000e+000 
             
             
                 
               18 
               −2.758585e−022 
               2.006196e−026 
               0.000000e+000 
             
             
                 
               20 
               −2.770624e−022 
               −8.035716e−026 
               0.000000e+000 
             
             
                 
               22 
               1.983183e−021 
               −1.380364e−025 
               0.000000e+000 
             
             
                 
               24 
               −4.390899e−023 
               5.287086e−026 
               0.000000e+000 
             
             
                 
               26 
               3.573891e−021 
               2.151859e−025 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 4 
             
             
                 
             
             
               EXAMPLE 4 
             
             
                 
             
           
           
             
               FIRST OBJECT TO FIRST SURFACE DISTANCE: 81.211 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
             
             
                 
             
           
        
         
             
                1 
               2240.555 
               47.000 
               1.56000 
                 
             
             
                2 
               −312.927 
               1.000 
             
             
                3 
               209.677 
               34.603 
               1.56000 
             
             
                4 
               −314.137 
               150.769 
             
             
                5 
               −819.717 
               −140.769 
                 
               M1 
             
             
                6 
               277.686 
               889.917 
                 
               M2 
             
             
                7 
               1806.318 
               19.445 
               1.56000 
             
             
                8 
               −583.025 
               1.000 
             
           
        
         
             
                9 
               0.0 (stop) 
               73.850 
                 
             
           
        
         
             
               10 
               197.078 
               35.504 
               1.56000 
                 
             
             
               11 
               879.977 
               1.000 
             
             
               12 
               126.409 
               28.494 
               1.56000 
             
             
               13 
               168.675 
               98.900 
             
             
               14 
               121.885 
               21.036 
               1.56000 
             
             
               15 
               905.776 
             
             
                 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               0.000000e+000 
               3.706794e−008 
               −5.144019e−012 
               6.973326e−017 
               −7.330968e−021 
             
             
                4 
               0.000000e+000 
               3.878903e−009 
               7.795334e−012 
               −6.781754e−016 
               5.265168e−020 
             
             
                5 
               0.000000e+000 
               8.445174e−009 
               3.143938e−011 
               −2.614011e−014 
               2.098089e−017 
             
             
                6 
               0.000000e+000 
               −2.863861e−009 
               −5.305438e−015 
               1.717130e−018 
               −3.511472e−023 
             
             
                7 
               0.000000e+000 
               −3.549063e−009 
               −1.408264e−013 
               1.931760e−019 
               5.091573e−023 
             
             
               10 
               0.000000e+000 
               −5.841539e−009 
               −2.405096e−013 
               4.288890e−018 
               −7.434790e−022 
             
             
               12 
               0.000000e+000 
               −5.913583e−009 
               −4.340165e−014 
               −1.651705e−017 
               −1.294295e−022 
             
             
               14 
               0.000000e+000 
               −8.534527e−008 
               −8.202426e−012 
               −7.411706e−016 
               −1.255475e−020 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               7.818988e−025 
               −1.099803e−029 
               0.000000e+000 
             
             
                 
                4 
               −3.124244e−024 
               7.960469e−029 
               0.000000e+000 
             
             
                 
                5 
               −1.054713e−020 
               2.300997e−024 
               0.000000e+000 
             
             
                 
                6 
               −1.813806e−028 
               5.037276e−032 
               0.000000e+000 
             
             
                 
                7 
               −4.316781e−027 
               8.877331e−032 
               0.000000e+000 
             
             
                 
               10 
               2.311772e−026 
               −5.842989e−031 
               0.000000e+000 
             
             
                 
               12 
               1.623655e−026 
               −3.143454e−030 
               0.000000e+000 
             
             
                 
               14 
               −2.566756e−024 
               −3.831608e−028 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 5 
             
             
                 
             
             
               EXAMPLE 5 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 281.857 
             
             
                 
             
             
                1 
               −276.517 
               −185.013 
               −1.0 
               M1 
             
             
                2 
               698.217 
               199.972 
                 
               M2 
             
             
                3 
               507.773 
               48.488 
               1.56000 
             
             
                4 
               −238.848 
               9.987 
                 
               FL1 
             
             
                5 
               253.725 
               25.649 
               1.56000 
             
             
                6 
               544.261 
               258.577 
             
             
                7 
               −100.183 
               10.000 
               1.56000 
             
             
                8 
               −348.125 
               108.113 
             
             
                9 
               −205.877 
               10.000 
               1.56000 
             
             
               10 
               −302.653 
               9.696 
             
             
               11 
               0.0 (stop) 
               11.356 
             
             
               12 
               388.065 
               23.350 
               1.56000 
             
             
               13 
               −153.114 
               45.670 
             
             
               14 
               227.862 
               40.204 
               1.56000 
             
             
               15 
               −163.407 
               1.004 
             
             
               16 
               82.650 
               12.336 
               1.56000 
             
             
               17 
               80.232 
               7.123 
             
             
               18 
               118.960 
               10.000 
               1.56000 
             
             
               19 
               54.261 
               1.597 
             
             
               20 
               56.346 
               44.698 
               1.56000 
             
             
               21 
               −655.354 
             
             
                 
             
           
        
         
             
               β = ⅙ 
             
             
               L = 1005 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               1.497949e+000 
               5.904355e−008 
               4.604214e−012 
               −6.840591e−016 
               −4.605410e−019 
             
             
                2 
               3.802520e+000 
               −2.958077e−008 
               −4.331805e−013 
               −3.956055e−017 
               1.351662e−020 
             
             
                3 
               0.000000e+000 
               −1.396795e−008 
               −2.011294e−013 
               9.452577e−019 
               3.436796e−022 
             
             
                6 
               0.000000e+000 
               −5.231213e−009 
               −3.200408e−013 
               −7.768341e−018 
               3.291916e−022 
             
             
                8 
               0.000000e+000 
               2.948640e−008 
               −6.137758e−012 
               −5.828601e−016 
               −1.299053e−019 
             
             
               10 
               0.000000e+000 
               1.391954e−007 
               −1.481745e−011 
               −9.656666e−016 
               2.464643e−020 
             
             
               13 
               0.000000e+000 
               9.988863e−008 
               1.676874e−011 
               −3.517423e−016 
               1.878125e−019 
             
             
               14 
               0.000000e+000 
               −1.684359e−009 
               −1.027341e−011 
               −6.807870e−016 
               4.062904e−019 
             
             
               16 
               0.000000e+000 
               −1.178575e−007 
               4.129293e−012 
               4.790552e−015 
               8.697392e−019 
             
             
               19 
               0.000000e+000 
               1.390299e−008 
               −3.249927e−010 
               −4.393543e−014 
               1.252755e−016 
             
             
               20 
               0.000000e+000 
               2.089833e−007 
               −3.169110e−010 
               −5.080159e−014 
               1.188278e−016 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               4.455246e−022 
               −9.166535e−026 
               0.000000e+000 
             
             
                 
                2 
               −3.311509e−024 
               2.709386e−028 
               0.000000e+000 
             
             
                 
                3 
               −1.264170e−026 
               1.297626e−031 
               0.000000e+000 
             
             
                 
                6 
               2.676252e−027 
               −1.441611e−031 
               0.000000e+000 
             
             
                 
                8 
               1.266055e−023 
               −2.859330e−027 
               0.000000e+000 
             
             
                 
               10 
               6.808416e−024 
               2.160253e−027 
               0.000000e+000 
             
             
                 
               13 
               −1.242980e−023 
               4.020013e−028 
               0.000000e+000 
             
             
                 
               14 
               −4.999088e−023 
               2.234236e−027 
               0.000000e+000 
             
             
                 
               16 
               −4.361816e−022 
               6.665268e−026 
               0.000000e+000 
             
             
                 
               19 
               −7.292427e−020 
               1.490664e−023 
               0.000000e+000 
             
             
                 
               20 
               −6.999891e−020 
               1.483259e−023 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 6 
             
             
                 
             
             
               EXAMPLE 6 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.000 
             
             
                 
             
           
        
         
             
                1 
               182.669 
               30.734 
               1.56000 
                 
             
             
                2 
               −503.082 
               207.487 
               −1.0 
               M1 
             
             
                3 
               −210.424 
               −187.803 
             
             
                4 
               659.854 
               198.194 
                 
               M2 
             
             
                5 
               444.311 
               36.819 
               1.56000 
               FL1 
             
             
                6 
               −268.965 
               10.000 
             
             
                7 
               453.477 
               20.965 
               1.56000 
             
             
                8 
               −50557.268 
               242.048 
             
             
                9 
               40075.824 
               10.000 
               1.56000 
             
             
               10 
               139.483 
               106.449 
             
             
               11 
               −315.120 
               10.000 
               1.56000 
             
             
               12 
               −568.730 
               9.619 
             
           
        
         
             
               13 
               0.0 (stop) 
               12.608 
                 
             
           
        
         
             
               14 
               594.545 
               31.653 
               1.56000 
                 
             
             
               15 
               −138.456 
               36.327 
             
             
               16 
               237.603 
               34.661 
               1.56000 
             
             
               17 
               −150.971 
               0.100 
             
             
               18 
               86.895 
               17.884 
               1.56000 
             
             
               19 
               114.792 
               5.157 
             
             
               20 
               161.292 
               10.000 
               1.56000 
             
             
               21 
               48.459 
               2.549 
             
             
               22 
               50.928 
               29.428 
               1.56000 
             
             
               23 
               −7294.344 
             
             
                 
             
           
        
         
             
               β = ⅕ 
             
             
               L = 956 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               0.000000e+000 
               2.099767e−008 
               9.783077e−013 
               −1.844192e−016 
               3.604034e−020 
             
             
                3 
               5.000000e+000 
               5.501181e−007 
               1.471305e−010 
               2.886973e−014 
               −5.770432e−017 
             
             
                4 
               −4.000000e+000 
               −9.108110e−009 
               −4.299510e−013 
               −1.602878e−017 
               3.309710e−021 
             
             
                5 
               0.000000e+000 
               −2.136611e−008 
               4.694331e−013 
               1.022387e−017 
               −1.167939e−021 
             
             
                8 
               0.000000e+000 
               −9.037445e−009 
               3.670281e−013 
               2.497754e−017 
               −1.935627e−021 
             
             
               10 
               0.000000e+000 
               1.834298e−007 
               −9.750639e−012 
               −4.421365e−015 
               −1.558851e−018 
             
             
               12 
               0.000000e+000 
               9.777784e−008 
               −1.873380e−012 
               −2.797369e−015 
               9.646417e−019 
             
             
               15 
               0.000000e+000 
               8.427543e−011 
               1.174046e−011 
               5.170272e−016 
               −9.544492e−020 
             
             
               16 
               0.000000e+000 
               3.081549e−008 
               −1.715163e−011 
               −1.340386e−015 
               4.768602e−019 
             
             
               18 
               0.000000e+000 
               −2.081579e−007 
               −2.247876e−011 
               7.527512e−015 
               2.070479e−018 
             
             
               21 
               0.000000e+000 
               2.662651e−007 
               −3.356811e−010 
               −5.994494e−014 
               9.695043e−017 
             
             
               22 
               0.000000e+000 
               3.826198e−007 
               −2.597161e−010 
               −5.670062e−014 
               7.056558e−017 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               −4.028724e−024 
               1.813820e−028 
               0.000000e+000 
             
             
                 
                3 
               2.143537e−020 
               −3.240090e−024 
               0.000000e+000 
             
             
                 
                4 
               −7.115890e−025 
               4.509207e−029 
               0.000000e+000 
             
             
                 
                5 
               3.965841e−026 
               −6.232492e−031 
               0.000000e+000 
             
             
                 
                8 
               9.346277e−026 
               −2.137993e−030 
               0.000000e+000 
             
             
                 
               10 
               −7.137854e−023 
               −1.911788e−026 
               0.000000e+000 
             
             
                 
               12 
               −2.470578e−022 
               3.056952e−026 
               0.000000e+000 
             
             
                 
               15 
               3.689421e−023 
               −4.096568e−027 
               0.000000e+000 
             
             
                 
               16 
               −4.768922e−023 
               1.934145e−027 
               0.000000e+000 
             
             
                 
               18 
               −5.194783e−022 
               1.217812e−025 
               0.000000e+000 
             
             
                 
               21 
               −1.088463e−019 
               3.144081e−023 
               0.000000e+000 
             
             
                 
               22 
               −9.170412e−020 
               2.592177e−023 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 7 
             
             
                 
             
             
               EXAMPLE 7 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.000 
             
             
                 
             
             
                1 
               586.085 
               16.642 
               1.56000 
             
             
                2 
               −710.026 
               244.154 
                 
               M1 
             
             
                3 
               −293.735 
               −213.130 
               −1.0 
             
             
                4 
               634.175 
               224.502 
                 
               M2 
             
             
                5 
               692.102 
               18.310 
               1.56000 
               FL1 
             
             
                6 
               −893.803 
               0.100 
             
             
                7 
               223.331 
               68.784 
               1.56000 
             
             
                8 
               726.029 
               73.396 
             
             
                9 
               244.650 
               29.831 
               1.56000 
             
             
               10 
               754.199 
               319.081 
             
             
               11 
               213.429 
               15.000 
               1.56000 
             
             
               12 
               104.913 
               106.241 
             
             
               13 
               0.0 (stop) 
               20.000 
             
             
               14 
               712.703 
               86.305 
               1.56000 
             
             
               15 
               −278.062 
               3.439 
             
             
               16 
               182.736 
               24.810 
               1.56000 
             
             
               17 
               −564.680 
               0.782 
             
             
               18 
               157.087 
               23.136 
               1.56000 
             
             
               19 
               1255.657 
               1.227 
             
             
               20 
               87.955 
               50.999 
               1.56000 
             
             
               21 
               123.472 
             
             
                 
             
           
        
         
             
               β = ⅕ 
             
             
               L = 1199 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               0.000000e+000 
               3.201613e−008 
               3.554666e−013 
               −3.442541e−016 
               8.565884e−020 
             
             
                3 
               −1.672235e+000 
               2.280202e−008 
               −7.033732e−013 
               3.718998e−017 
               −2.862300e−021 
             
             
                4 
               −1.049283e+000 
               1.235688e−008 
               −1.490507e−012 
               7.744144e−016 
               −3.612880e−019 
             
             
                6 
               0.000000e+000 
               2.918278e−008 
               4.292516e−015 
               6.272355e−018 
               −7.663849e−022 
             
             
                9 
               0.000000e+000 
               1.320709e−008 
               −8.609941e−013 
               1.501924e−017 
               −1.136497e−021 
             
             
               12 
               0.000000e+000 
               1.980383e−007 
               2.532422e−011 
               3.138382e−015 
               4.147537e−019 
             
             
               15 
               0.000000e+000 
               −1.871714e−008 
               −6.639558e−012 
               2.887450e−016 
               −2.996064e−020 
             
             
               16 
               0.000000e+000 
               −3.265199e−008 
               −6.424945e−012 
               −9.334562e−016 
               5.226456e−020 
             
             
               18 
               0.000000e+000 
               −2.362902e−008 
               −2.527146e−012 
               1.656380e−015 
               2.693269e−020 
             
             
               21 
               0.000000e+000 
               2.563403e−008 
               −8.361181e−011 
               −1.336716e−015 
               7.803202e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               −1.071073e−023 
               5.207120e−028 
               0.000000e+000 
             
             
                 
                3 
               1.492277e−025 
               −2.707991e−030 
               0.000000e+000 
             
             
                 
                4 
               9.419452e−023 
               −9.922151e−027 
               0.000000e+000 
             
             
                 
                6 
               4.479081e−026 
               −7.629337e−031 
               0.000000e+000 
             
             
                 
                9 
               4.453112e−026 
               −1.452102e−030 
               0.000000e+000 
             
             
                 
               12 
               2.365835e−023 
               1.782122e−026 
               0.000000e+000 
             
             
                 
               15 
               2.959532e−024 
               −6.298400e−029 
               0.000000e+000 
             
             
                 
               16 
               3.674846e−026 
               1.155101e−028 
               0.000000e+000 
             
             
                 
               18 
               −6.493817e−024 
               −4.440784e−028 
               0.000000e+000 
             
             
                 
               21 
               3.786297e−022 
               −7.589609e−025 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 8 
             
             
                 
             
             
               EXAMPLE 8 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.000 
             
             
                 
             
             
                1 
               283.541 
               20.452 
               1.56000 
             
             
                2 
               −1053.836 
               121.738 
             
             
                3 
               387.920 
               5.000 
               1.56000 
             
             
                4 
               229.873 
               124.483 
             
             
                5 
               −291.999 
               −124.483 
               −1.0 
               M1 
             
             
                6 
               229.873 
               −5.000 
               −1.56 
             
             
                7 
               387.920 
               −91.603 
               −1.0 
             
             
                8 
               881.192 
               91.603 
                 
               M2 
             
             
                9 
               387.920 
               5.000 
               1.56000 
             
             
               10 
               229.873 
               134.534 
             
             
               11 
               1316.372 
               24.857 
               1.56000 
               FL1 
             
             
               12 
               −643.793 
               0.100 
             
             
               13 
               290.336 
               45.391 
               1.56000 
             
             
               14 
               −3338.651 
               27.518 
             
             
               15 
               268.455 
               38.225 
               1.56000 
             
             
               16 
               708.139 
               372.871 
             
             
               17 
               145.801 
               15.000 
               1.56000 
             
             
               18 
               87.306 
               105.457 
             
             
               19 
               0.0 (stop) 
               20.000 
             
             
               20 
               794.943 
               80.807 
               1.56000 
             
             
               21 
               −245.392 
               1.206 
             
             
               22 
               219.487 
               25.203 
               1.56000 
             
             
               23 
               −440.290 
               0.297 
             
             
               24 
               156.783 
               20.641 
               1.56000 
             
             
               25 
               3004.077 
               0.391 
             
             
               26 
               91.029 
               52.047 
               1.56000 
             
             
               27 
               147.896 
             
             
                 
             
           
        
         
             
               β = ⅕ 
             
             
               L = 1198 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               0.000000e+000 
               1.670163e−008 
               −7.564550e−013 
               7.640310e−017 
               −8.895236e−021 
             
             
                4 
               0.000000e+000 
               −2.210204e−008 
               3.615438e−012 
               −2.715457e−016 
               1.987678e−020 
             
             
                5 
               −1.612890e+000 
               2.100848e−008 
               2.048446e−013 
               −9.687279e−017 
               9.141985e−021 
             
             
                6 
               0.000000e+000 
               −2.210204e−008 
               3.615438e−012 
               −2.715457e−016 
               1.987678e−020 
             
             
                8 
               2.782076e+000 
               1.108410e−008 
               8.595356e−013 
               −4.263225e−017 
               −8.502443e−020 
             
             
               10 
               0.000000e+000 
               −2.210204e−008 
               3.615438e−012 
               −2.715457e−016 
               1.987678e−020 
             
             
               12 
               0.000000e+000 
               4.440282e−009 
               −3.621140e−013 
               2.360928e−018 
               9.305637e−023 
             
             
               15 
               0.000000e+000 
               −1.135774e−008 
               −4.288698e−013 
               6.421899e−018 
               −2.225858e−022 
             
             
               18 
               0.000000e+000 
               1.483922e−007 
               1.741862e−011 
               2.796320e−015 
               3.491280e−019 
             
             
               21 
               0.000000e+000 
               1.354475e−008 
               −3.828203e−012 
               −1.671056e−016 
               3.582427e−020 
             
             
               22 
               0.000000e+000 
               −1.099866e−008 
               −2.113914e−012 
               −4.900979e−016 
               4.480872e−020 
             
             
               24 
               0.000000e+000 
               −2.754027e−008 
               −3.324771e−012 
               1.073083e−016 
               5.780353e−020 
             
             
               27 
               0.000000e+000 
               −2.478578e−008 
               1.119494e−011 
               −4.674713e−014 
               1.755113e−017 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               1.090188e−024 
               −5.939842e−029 
               0.000000e+000 
             
             
                 
                4 
               −1.063676e−024 
               2.691088e−030 
               0.000000e+000 
             
             
                 
                5 
               −5.265028e−025 
               1.391005e−029 
               0.000000e+000 
             
             
                 
                6 
               −1.063676e−024 
               2.691088e−030 
               0.000000e+000 
             
             
                 
                8 
               2.574157e−023 
               −2.657189e−027 
               0.000000e+000 
             
             
                 
               10 
               −1.063676e−024 
               2.691088e−030 
               0.000000e+000 
             
             
                 
               12 
               −7.574790e−027 
               1.413732e−031 
               0.000000e+000 
             
             
                 
               15 
               2.852148e−028 
               7.381569e−032 
               0.000000e+000 
             
             
                 
               18 
               8.679435e−024 
               1.093535e−026 
               0.000000e+000 
             
             
                 
               21 
               −2.719953e−024 
               1.131354e−028 
               0.000000e+000 
             
             
                 
               22 
               2.024346e−025 
               −8.888050e−029 
               0.000000e+000 
             
             
                 
               24 
               −1.099840e−023 
               2.651758e−028 
               0.000000e+000 
             
             
                 
               27 
               −5.370134e−021 
               8.559204e−025 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 9 
             
             
                 
             
             
               EXAMPLE 9 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 51.000 
             
             
                 
             
             
                1 
               −1815.127 
               22.814 
               1.56000 
             
             
                2 
               −265.701 
               23.300 
             
             
                3 
               1292.112 
               34.549 
               1.56000 
               LP1 
             
             
                4 
               −329.343 
               239.736 
             
             
                5 
               −126.569 
               15.000 
               1.56000 
               LN1 
             
             
                6 
               1807.475 
               23.600 
             
             
                7 
               −187.707 
               −23.600 
               −1.0 
               M1 
             
             
                8 
               1807.475 
               −15.000 
               −1.56 
               LN1 
             
             
                9 
               −126.569 
               −239.736 
               −1.0 
             
             
               10 
               −329.343 
               −34.549 
               −1.56 
               LP1 
             
             
               11 
               1292.112 
               −3.300 
               −1.0 
             
             
               12 
               −816.892 
               3.300 
                 
               M2 
             
             
               13 
               1292.112 
               34.549 
               1.56000 
               LP1 
             
             
               14 
               −329.343 
               292.223 
             
             
               15 
               2351.512 
               15.834 
               1.56000 
               FL1 
             
             
               16 
               −927.736 
               0.100 
             
             
               17 
               304.902 
               27.947 
               1.56000 
             
             
               18 
               1478.904 
               10.000 
             
             
               19 
               218.515 
               27.908 
               1.56000 
             
             
               20 
               527.237 
               169.549 
             
             
               21 
               278.804 
               10.000 
               1.56000 
             
             
               22 
               96.885 
               178.224 
             
             
               23 
               −147.170 
               10.000 
               1.56000 
             
             
               24 
               2898.421 
               31.011 
             
             
               25 
               415.702 
               30.726 
               1.56000 
             
             
               26 
               −182.240 
               9.109 
             
             
               27 
               0.0 (stop) 
               45.578 
             
             
               28 
               190.492 
               37.309 
               1.56000 
             
             
               29 
               −267.624 
               7.977 
             
             
               30 
               95.129 
               41.064 
               1.56000 
             
             
               31 
               116.210 
               15.986 
             
             
               32 
               91.034 
               43.273 
               1.56000 
             
             
               33 
               −471.423 
             
             
                 
             
           
        
         
             
               β = ⅕ 
             
             
               L = 1166 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               0.000000e+000 
               5.530494e−008 
               1.163655e−012 
               −6.282393e−017 
               −2.629751e−021 
             
             
                4 
               0.000000e+000 
               −1.892175e−008 
               4.266967e−013 
               1.121436e−017 
               −3.030043e−021 
             
             
                5 
               0.000000e+000 
               1.663615e−007 
               9.890835e−012 
               −1.309392e−015 
               6.427099e−019 
             
             
                7 
               9.165216e−004 
               2.675984e−008 
               1.316128e−012 
               2.694592e−017 
               −3.337487e−020 
             
             
                9 
               0.000000e+000 
               1.663615e−007 
               9.890835e−012 
               −1.309392e−015 
               6.427099e−019 
             
             
               10 
               0.000000e+000 
               −1.892175e−008 
               4.266967e−013 
               1.121436e−017 
               −3.030043e−021 
             
             
               12 
               5.000000e+000 
               −9.389111e−009 
               1.539504e−013 
               9.799722e−018 
               −2.247802e−021 
             
             
               14 
               0.000000e+000 
               −1.892175e−008 
               4.266967e−013 
               1.121436e−017 
               −3.030043e−021 
             
             
               16 
               0.000000e+000 
               1.255592e−008 
               −3.238808e−013 
               5.818116e−017 
               −7.054083e−021 
             
             
               17 
               0.000000e+000 
               4.718829e−009 
               −5.145063e−013 
               7.657683e−017 
               −9.189123e−021 
             
             
               22 
               0.000000e+000 
               −1.928999e−007 
               −1.154247e−011 
               4.702416e−017 
               −5.121045e−020 
             
             
               23 
               0.000000e+000 
               −3.035320e−007 
               −1.933933e−011 
               −2.138991e−015 
               −4.900557e−019 
             
             
               26 
               0.000000e+000 
               2.223625e−008 
               5.913986e−012 
               −1.487766e−016 
               4.859942e−020 
             
             
               28 
               0.000000e+000 
               1.714078e−008 
               1.881607e−012 
               −6.712043e−016 
               5.005422e−020 
             
             
               31 
               0.000000e+000 
               −1.372556e−008 
               7.658069e−011 
               −5.828110e−015 
               1.273953e−018 
             
             
               32 
               0.000000e+000 
               −5.643649e−007 
               1.451319e−011 
               −6.462196e−016 
               −8.490119e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               6.200738e−025 
               −2.301378e−029 
               0.000000e+000 
             
             
                 
                4 
               1.639180e−025 
               −3.981772e−030 
               0.000000e+000 
             
             
                 
                5 
               −2.796760e−022 
               4.335286e−026 
               0.000000e+000 
             
             
                 
                7 
               −4.892624e−024 
               1.494940e−027 
               0.000000e+000 
             
             
                 
                9 
               −2.796760e−022 
               4.335286e−026 
               0.000000e+000 
             
             
                 
               10 
               1.639180e−025 
               −3.981772e−030 
               0.000000e+000 
             
             
                 
               12 
               1.259049e−025 
               −3.392339e−030 
               0.000000e+000 
             
             
                 
               14 
               1.639180e−025 
               −3.981772e−030 
               0.000000e+000 
             
             
                 
               16 
               4.425044e−025 
               −1.068897e−029 
               0.000000e+000 
             
             
                 
               17 
               5.661917e−025 
               −1.358877e−029 
               0.000000e+000 
             
             
                 
               22 
               6.968981e−024 
               −1.633272e−027 
               0.000000e+000 
             
             
                 
               23 
               6.415923e−023 
               −3.092374e−026 
               0.000000e+000 
             
             
                 
               26 
               −3.316785e−024 
               1.932364e−028 
               0.000000e+000 
             
             
                 
               28 
               −2.320660e−024 
               6.485526e−029 
               0.000000e+000 
             
             
                 
               31 
               −4.331702e−023 
               6.899488e−027 
               0.000000e+000 
             
             
                 
               32 
               2.192732e−022 
               −3.846738e−026 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 10 
             
             
                 
             
             
               EXAMPLE 10 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.835 
             
             
                 
             
           
        
         
             
                1 
               146.528 
               21.753 
               1.56000 
                 
             
             
                2 
               279.100 
               29.521 
                 
             
             
                3 
               −775.358 
               24.514 
               1.56000 
               LP1 
             
             
                4 
               −290.509 
               319.054 
             
             
                5 
               −127.746 
               15.000 
               1.56000 
               LN1 
             
             
                6 
               901.597 
               15.068 
             
             
                7 
               −165.915 
               −15.068 
               −1.0 
               M1 
             
             
                8 
               901.597 
               −15.000 
               −1.56 
               LN1 
             
             
                9 
               −127.746 
               −319.054 
               −1.0 
             
             
               10 
               −290.509 
               −24.514 
               −1.56 
               LP1 
             
             
               11 
               −775.358 
               −2.093 
               −1.0 
             
             
               12 
               −1091.384 
               2.093 
                 
               M2 
             
             
               13 
               −775.358 
               24.514 
               1.56000 
               LP1 
             
             
               14 
               −290.509 
               366.602 
             
             
               15 
               −729.668 
               23.975 
               1.56000 
               FL1 
             
             
               16 
               −353.516 
               16.059 
             
             
               17 
               278.912 
               36.728 
               1.56000 
             
             
               18 
               1301.137 
               10.000 
             
             
               19 
               230.845 
               40.089 
               1.56000 
             
             
               20 
               858.078 
               145.157 
             
             
               21 
               −1139.792 
               10.000 
               1.56000 
             
             
               22 
               209.297 
               153.635 
             
             
               23 
               141.077 
               10.000 
               1.56000 
             
             
               24 
               77.386 
               30.123 
             
             
               25 
               291.198 
               29.071 
               1.56000 
             
             
               26 
               −210.751 
               4.057 
             
           
        
         
             
               27 
               0.0 (stop) 
               21.331 
                 
             
           
        
         
             
               28 
               204.073 
               51.876 
               1.56000 
                 
             
             
               29 
               −109.375 
               0.559 
             
             
               30 
               220.520 
               23.237 
               1.56000 
             
             
               31 
               552.592 
               4.737 
             
             
               32 
               63.753 
               26.644 
               1.56000 
             
             
               33 
               −13602.898 
             
             
                 
             
           
        
         
             
               β = ⅕ 
             
             
               L = 1160 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                2 
               0.000000e+000 
               8.655896e−008 
               −1.231783e−012 
               1.505671e−016 
               −1.994862e−020 
             
             
                4 
               0.000000e+000 
               −2.107372e−008 
               5.599304e−013 
               −3.486775e−017 
               4.285967e−021 
             
             
                5 
               0.000000e+000 
               1.483901e−007 
               −9.642930e−012 
               −1.428407e−016 
               −3.220462e−019 
             
             
                7 
               −1.883904e−001 
               3.492160e−008 
               2.674541e−013 
               −1.521679e−017 
               −4.134260e−020 
             
             
                9 
               0.000000e+000 
               1.483901e−007 
               −9.642930e−012 
               −1.428407e−016 
               −3.220462e−019 
             
             
               10 
               0.000000e+000 
               −2.107372e−008 
               5.599304e−013 
               −3.486775e−017 
               4.285967e−021 
             
             
               12 
               −3.641713e+000 
               −1.337813e−008 
               6.093453e−013 
               −2.932265e−017 
               3.056970e−021 
             
             
               14 
               0.000000e+000 
               −2.107372e−008 
               5.599304e−013 
               −3.486775e−017 
               4.285967e−021 
             
             
               16 
               0.000000e+000 
               −1.271307e−008 
               1.326186e−012 
               −6.548673e−017 
               2.762947e−021 
             
             
               19 
               0.000000e+000 
               −2.542101e−008 
               1.512560e−012 
               −3.198475e−017 
               3.416616e−021 
             
             
               22 
               0.000000e+000 
               −1.103975e−007 
               6.579457e−012 
               −1.251416e−016 
               −1.137648e−020 
             
             
               23 
               0.000000e+000 
               −6.584060e−007 
               −9.731531e−011 
               −4.923089e−015 
               −1.676955e−018 
             
             
               26 
               0.000000e+000 
               −2.178389e−007 
               −1.364187e−011 
               1.018419e−014 
               −1.147459e−018 
             
             
               28 
               0.000000e+000 
               −1.274240e−007 
               −3.607152e−011 
               8.050135e−015 
               −1.032749e−018 
             
             
               31 
               0.000000e+000 
               6.891976e−008 
               9.356366e−012 
               3.785313e−016 
               3.015742e−018 
             
             
               32 
               0.000000e+000 
               −1.469212e−007 
               −7.704012e−012 
               −3.664705e−015 
               3.444260e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                2 
               2.274640e−024 
               −9.987248e−029 
               0.000000e+000 
             
             
                 
                4 
               −2.059611e−025 
               2.643547e−031 
               0.000000e+000 
             
             
                 
                5 
               6.834179e−023 
               −3.369361e−027 
               0.000000e+000 
             
             
                 
                7 
               4.884293e−024 
               −2.923001e−028 
               0.000000e+000 
             
             
                 
                9 
               6.834179e−023 
               −3.369361e−027 
               0.000000e+000 
             
             
                 
               10 
               −2.059611e−025 
               2.643547e−031 
               0.000000e+000 
             
             
                 
               12 
               −1.866907e−025 
               2.516890e−030 
               0.000000e+000 
             
             
                 
               14 
               −2.059611e−025 
               2.643547e−031 
               0.000000e+000 
             
             
                 
               16 
               −7.218715e−026 
               8.926086e−031 
               0.000000e+000 
             
             
                 
               19 
               −9.166937e−026 
               1.136094e−030 
               0.000000e+000 
             
             
                 
               22 
               3.478710e−024 
               −1.372775e−028 
               0.000000e+000 
             
             
                 
               23 
               1.557766e−021 
               −4.766741e−025 
               0.000000e+000 
             
             
                 
               26 
               1.658131e−022 
               9.278466e−027 
               0.000000e+000 
             
             
                 
               28 
               9.644428e−023 
               −4.735347e−027 
               0.000000e+000 
             
             
                 
               31 
               −7.985615e−022 
               1.332556e−025 
               0.000000e+000 
             
             
                 
               32 
               −5.454904e−022 
               −8.938622e−026 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 11 
             
             
                 
             
             
               EXAMPLE 11 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.962 
             
             
                 
             
           
        
         
             
                1 
               549.485 
               18.225 
               1.56000 
                 
             
             
                2 
               −348.358 
               404.377 
             
             
                3 
               −117.591 
               15.000 
               1.56000 
               LN1 
             
             
                4 
               −11246.509 
               21.694 
             
             
                5 
               −181.192 
               −21.694 
               −1.0 
               M1 
             
             
                6 
               −11246.509 
               −15.000 
               −1.56 
               LN1 
             
             
                7 
               −117.591 
               −352.697 
               −1.0 
             
             
                8 
               −2026.523 
               −18.862 
               −1.56 
               LP1 
             
             
                9 
               461.050 
               −4.621 
               −1.0 
             
             
               10 
               −376.405 
               4.621 
                 
               M2 
             
             
               11 
               461.050 
               18.862 
               1.56000 
               LP1 
             
             
               12 
               −2026.523 
               398.890 
             
             
               13 
               1172.423 
               42.790 
               1.56000 
               FL1 
             
             
               14 
               −501.353 
               0.404 
             
             
               15 
               315.855 
               47.177 
               1.56000 
             
             
               16 
               1252.990 
               3.907 
             
             
               17 
               200.947 
               27.200 
               1.56000 
             
             
               18 
               240.640 
               296.917 
             
             
               19 
               −192.453 
               10.000 
               1.56000 
             
             
               20 
               602.106 
               179.501 
             
             
               21 
               −186.356 
               10.000 
               1.56000 
             
             
               22 
               438.885 
               32.245 
             
             
               23 
               541.516 
               30.056 
               1.56000 
             
             
               24 
               −149.805 
               8.704 
             
           
        
         
             
               25 
               0.0 (stop) 
               45.181 
                 
             
           
        
         
             
               26 
               179.275 
               33.860 
               1.56000 
                 
             
             
               27 
               −370.567 
               9.275 
             
             
               28 
               94.992 
               43.811 
               1.56000 
             
             
               29 
               81.799 
               18.120 
             
             
               30 
               68.314 
               41.095 
               1.56000 
             
             
               31 
               −681.697 
             
             
                 
             
           
        
         
             
               β = ¼ 
             
             
               L = 1430 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               4.575380e−008 
               7.817822e−013 
               −5.883907e−016 
               1.371733e−019 
             
             
                3 
               0.000000e+000 
               1.832675e−008 
               −2.154592e−013 
               −1.520651e−016 
               −8.218511e−021 
             
             
                5 
               8.415167e−001 
               1.155130e−008 
               1.103292e−013 
               −1.409211e−017 
               −1.720226e−021 
             
             
                7 
               0.000000e+000 
               1.832675e−008 
               −2.154592e−013 
               −1.520651e−016 
               −8.218511e−021 
             
             
                8 
               0.000000e+000 
               2.539857e−009 
               6.897518e−013 
               −2.706670e−016 
               2.977375e−020 
             
             
               10 
               6.525900e−001 
               −3.453255e−010 
               6.892838e−013 
               −1.705759e−016 
               1.444644e−020 
             
             
               12 
               0.000000e+000 
               2.539857e−009 
               6.897518e−013 
               −2.706670e−016 
               2.977375e−020 
             
             
               14 
               0.000000e+000 
               −2.178001e−009 
               4.103517e−013 
               −1.817801e−017 
               5.715837e−022 
             
             
               15 
               0.000000e+000 
               4.463480e−009 
               3.163776e−014 
               7.085203e−019 
               0.000000e+000 
             
             
               17 
               0.000000e+000 
               −1.282492e−008 
               3.641378e−013 
               −2.566752e−017 
               6.095086e−022 
             
             
               20 
               0.000000e+000 
               2.691714e−008 
               3.794681e−012 
               1.766293e−016 
               −1.533138e−020 
             
             
               21 
               0.000000e+000 
               −2.046926e−007 
               8.688717e−012 
               4.769864e−016 
               −8.554669e−020 
             
             
               24 
               0.000000e+000 
               1.946135e−008 
               5.791056e−012 
               −3.912959e−016 
               4.417233e−020 
             
             
               26 
               0.000000e+000 
               2.141413e−009 
               −8.073433e−013 
               −6.990201e−016 
               6.444734e−020 
             
             
               29 
               0.000000e+000 
               −2.143697e−008 
               3.327692e−011 
               −5.094587e−015 
               1.783172e−018 
             
             
               30 
               0.000000e+000 
               −2.020052e−007 
               −8.522637e−012 
               −7.090867e−015 
               1.840499e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               −1.760415e−023 
               8.840230e−028 
               0.000000e+000 
             
             
                 
                3 
               6.179683e−025 
               8.769913e−028 
               0.000000e+000 
             
             
                 
                5 
               −5.814168e−026 
               4.284447e−029 
               0.000000e+000 
             
             
                 
                7 
               6.179683e−025 
               8.769913e−028 
               0.000000e+000 
             
             
                 
                8 
               −1.502713e−024 
               2.475219e−029 
               0.000000e+000 
             
             
                 
               10 
               −1.403417e−025 
               −3.422820e−029 
               0.000000e+000 
             
             
                 
               12 
               −1.502713e−024 
               2.475219e−029 
               0.000000e+000 
             
             
                 
               14 
               −1.027112e−026 
               8.042716e−032 
               0.000000e+000 
             
             
                 
               15 
               3.066558e−028 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               17 
               −8.993226e−027 
               −1.018383e−031 
               0.000000e+000 
             
             
                 
               20 
               6.283744e−024 
               −5.389611e−028 
               0.000000e+000 
             
             
                 
               21 
               5.836557e−024 
               −1.386454e−027 
               0.000000e+000 
             
             
                 
               24 
               −3.359010e−024 
               9.801933e−029 
               0.000000e+000 
             
             
                 
               26 
               −3.453019e−024 
               7.077619e−029 
               0.000000e+000 
             
             
                 
               29 
               −4.057529e−022 
               2.496099e−026 
               0.000000e+000 
             
             
                 
               30 
               −1.434596e−021 
               −8.941485e−027 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
             
             
             
             
           
             
             
             
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 12 
             
             
                 
             
             
               EXAMPLE 12 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 63.346 
             
             
                 
             
           
        
         
             
                1 
               973.794 
               19.006 
               1.56000 
                 
             
             
                2 
               −274.730 
               408.564 
             
             
                3 
               −117.937 
               15.000 
               1.56000 
               LN1 
             
             
                4 
               −21944.448 
               22.129 
             
             
                5 
               −183.531 
               −22.129 
               −1.0 
               M1 
             
             
                6 
               −21944.448 
               −15.000 
               −1.56 
               LN1 
             
             
                7 
               −117.937 
               −391.508 
               −1.0 
             
             
                8 
               −2342.325 
               −16.507 
               −1.56 
               LP1 
             
             
                9 
               447.067 
               −0.506 
               −1.0 
             
             
               10 
               −376.377 
               0.506 
                 
               M2 
             
             
               11 
               447.067 
               16.507 
               1.56000 
               LP1 
             
             
               12 
               −2342.325 
               373.416 
             
             
               13 
               1097.080 
               47.121 
               1.56000 
               FL1 
             
             
               14 
               −515.510 
               27.362 
             
             
               15 
               280.430 
               47.913 
               1.56000 
             
             
               16 
               718.618 
               7.108 
             
             
               17 
               198.349 
               27.611 
               1.56000 
             
             
               18 
               249.428 
               300.922 
             
             
               19 
               −216.473 
               10.000 
               1.56000 
             
             
               20 
               445.322 
               181.217 
             
             
               21 
               −171.590 
               10.000 
               1.56000 
             
             
               22 
               666.307 
               32.257 
             
             
               23 
               625.617 
               30.422 
               1.56000 
             
             
               24 
               −151.533 
               8.809 
             
           
        
         
             
               25 
               0.0 (stop) 
               47.280 
                 
             
           
        
         
             
               26 
               180.626 
               36.149 
               1.56000 
                 
             
             
               27 
               −335.594 
               9.318 
             
             
               28 
               100.005 
               44.237 
               1.56000 
             
             
               29 
               88.936 
               17.909 
             
             
               30 
               70.805 
               41.541 
               1.56000 
             
             
               31 
               −1049.267 
             
             
                 
             
           
        
         
             
               β = ¼ 
             
             
               L = 1430 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               4.255133e−008 
               1.395979e−013 
               −1.009633e−016 
               4.472929e−021 
             
             
                3 
               0.000000e+000 
               1.715982e−008 
               1.867849e−013 
               1.918570e−017 
               −5.826782e−020 
             
             
                5 
               8.550872e−001 
               1.081079e−008 
               1.551602e−013 
               7.022939e−018 
               −6.098034e−021 
             
             
                7 
               0.000000e+000 
               1.715982e−008 
               1.867849e−013 
               1.918570e−017 
               −5.826782e−020 
             
             
                8 
               0.000000e+000 
               3.098651e−009 
               2.787833e−013 
               −1.677261e−016 
               1.684901e−020 
             
             
               10 
               9.872928e−001 
               1.142429e−009 
               4.039291e−013 
               −8.905924e−017 
               4.728326e−021 
             
             
               12 
               0.000000e+000 
               3.098651e−009 
               2.787833e−013 
               −1.677261e−016 
               1.684901e−020 
             
             
               14 
               0.000000e+000 
               −8.058628e−009 
               5.469068e−013 
               −1.863316e−017 
               4.646973e−022 
             
             
               15 
               0.000000e+000 
               8.819915e−010 
               1.397684e−013 
               −9.400188e−019 
               0.000000e+000 
             
             
               17 
               0.000000e+000 
               −1.822365e−008 
               3.451273e−013 
               −2.486759e−017 
               4.418373e−022 
             
             
               20 
               0.000000e+000 
               3.055326e−008 
               4.873760e−012 
               2.383916e−016 
               −6.806035e−021 
             
             
               21 
               0.000000e+000 
               −1.728562e−007 
               1.235438e−011 
               8.006503e−016 
               −6.090344e−020 
             
             
               24 
               0.000000e+000 
               3.819315e−008 
               6.635548e−012 
               −2.544128e−016 
               3.425391e−020 
             
             
               26 
               0.000000e+000 
               5.160883e−009 
               −9.687870e−013 
               −5.829555e−016 
               5.807106e−020 
             
             
               29 
               0.000000e+000 
               −8.273895e−009 
               2.604783e−011 
               −4.590743e−015 
               2.375151e−018 
             
             
               30 
               0.000000e+000 
               −1.430127e−007 
               −8.553894e−012 
               −7.235770e−015 
               4.163768e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               1.933908e−024 
               −3.573554e−028 
               0.000000e+000 
             
             
                 
                3 
               9.440074e−024 
               1.973849e−028 
               0.000000e+000 
             
             
                 
                5 
               4.929424e−025 
               1.438389e−029 
               0.000000e+000 
             
             
                 
                7 
               9.440074e−024 
               1.973849e−028 
               0.000000e+000 
             
             
                 
                8 
               −7.086691e−025 
               6.530829e−030 
               0.000000e+000 
             
             
                 
               10 
               2.776075e−025 
               −3.188109e−029 
               0.000000e+000 
             
             
                 
               12 
               −7.086691e−025 
               6.530829e−030 
               0.000000e+000 
             
             
                 
               14 
               −6.797904e−027 
               4.4013259e−032 
               0.000000e+000 
             
             
                 
               15 
               1.176176e−027 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               17 
               −5.160404e−027 
               −1.986704e−031 
               0.000000e+000 
             
             
                 
               20 
               7.977247e−024 
               −8.335599e−028 
               0.000000e+000 
             
             
                 
               21 
               −4.004980e−024 
               −5.894950e−028 
               0.000000e+000 
             
             
                 
               24 
               −2.492308e−024 
               4.150762e−029 
               0.000000e+000 
             
             
                 
               26 
               −3.458190e−024 
               9.835304e−029 
               0.000000e+000 
             
             
                 
               29 
               −7.369796e−022 
               6.477749e−026 
               0.000000e+000 
             
             
                 
               30 
               −2.463212e−021 
               2.053279e−025 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 13 
             
             
                 
             
             
               EXAMPLE 13 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 385.595 
             
             
                 
             
             
                1 
               −459.459 
               −335.573 
               −1.0 
               M1 
             
             
                2 
               3067.293 
               748.381 
                 
               M2 
             
             
                3 
               −739.933 
               −391.713 
               −1.0 
               FM1 
             
             
                4 
               −573.829 
               392.713 
                 
               FM2 
             
             
                5 
               0.0 (stop) 
               60.000 
             
             
                6 
               −130.197 
               54.213 
               1.56000 
             
             
                7 
               −119.178 
               0.100 
             
             
                8 
               117.405 
               51.990 
               1.56000 
             
             
                9 
               519.563 
               6.291 
             
             
               10 
               78.099 
               41.649 
               1.56000 
             
             
               11 
               1057.227 
               0.100 
             
             
               12 
               1050.175 
               15.000 
               1.56000 
             
             
               13 
               87.469 
               11.904 
             
             
               14 
               326.920 
               29.310 
               1.56000 
             
             
               15 
               −1292068.739 
             
             
                 
             
           
        
         
             
               β = ⅕ 
             
             
               L = 1100 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               2.151232e+000 
               2.074850e−008 
               1.028497e−012 
               1.000198e−016 
               −1.543777e−020 
             
             
                2 
               1.565028e+000 
               −1.030439e−008 
               −8.656324e−014 
               1.017720e−017 
               −3.830427e−021 
             
             
                3 
               −1.579007e−001 
               −1.873321e−010 
               −2.793967e−016 
               −3.564540e−021 
               7.688159e−026 
             
             
                4 
               −1.552277e+000 
               −9.150769e−009 
               −8.581363e−014 
               −1.464695e−017 
               2.978012e−021 
             
             
                7 
               0.000000e+000 
               −1.113320e−008 
               6.313114e−012 
               −4.925043e−016 
               6.437342e−020 
             
             
                8 
               0.000000e+000 
               5.404994e−009 
               −2.805582e−012 
               1.463407e−016 
               −4.789462e−020 
             
             
               10 
               0.000000e+000 
               −1.606239e−007 
               1.691804e−012 
               −2.762745e−015 
               1.781576e−019 
             
             
               13 
               0.000000e+000 
               2.498212e−007 
               1.350239e−011 
               2.359108e−014 
               5.612084e−019 
             
             
               14 
               0.000000e+000 
               4.979099e−007 
               −1.344689e−010 
               4.588479e−014 
               −2.537504e−017 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               3.311515e−024 
               −2.995664e−028 
               0.000000e+000 
             
             
                 
                2 
               5.161873e−025 
               −2.729459e−029 
               0.000000e+000 
             
             
                 
                3 
               −1.127394e−030 
               7.746168e−036 
               0.000000e+000 
             
             
                 
                4 
               −3.412103e−025 
               1.755156e−029 
               0.000000e+000 
             
             
                 
                7 
               −4.171136e−024 
               1.891343e−028 
               0.000000e+000 
             
             
                 
                8 
               4.264568e−024 
               −3.356973e−028 
               0.000000e+000 
             
             
                 
               10 
               −4.525225e−023 
               −2.846830e−028 
               0.000000e+000 
             
             
                 
               13 
               −2.105753e−021 
               1.040548e−024 
               0.000000e+000 
             
             
                 
               14 
               7.650574e−021 
               −1.459197e−024 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 14 
             
             
                 
             
             
               EXAMPLE 14 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 397.959 
             
             
                 
             
             
                1 
               −447.799 
               −347.959 
               −1.0 
               M1 
             
             
                2 
               11489.229 
               811.432 
                 
               M2 
             
             
                3 
               −804.784 
               −422.009 
               −1.0 
               FM1 
             
             
                4 
               −1121.103 
               −15.000 
               −1.56 
               LF 
             
             
                5 
               −431.869 
               −5.561 
               −1.0 
             
             
                6 
               −1235.236 
               5.561 
                 
               FM2 
             
             
                7 
               −431.869 
               15.000 
               1.56000 
               LF 
             
             
                8 
               −1121.103 
               423.009 
             
             
                9 
               0.0 (stop) 
               56.691 
             
             
               10 
               −128.913 
               19.560 
               1.56000 
             
             
               11 
               −108.272 
               0.309 
             
             
               12 
               124.318 
               28.713 
               1.56000 
             
             
               13 
               694.622 
               0.100 
             
             
               14 
               78.512 
               42.819 
               1.56000 
             
             
               15 
               219.566 
               9.184 
             
             
               16 
               −741.750 
               15.000 
               1.56000 
             
             
               17 
               92.545 
               14.848 
             
             
               18 
               73.579 
               20.344 
               1.56000 
             
             
               19 
               −2120.514 
             
             
                 
             
           
        
         
             
               β = /5 
             
             
               L = 1100 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               1.651069e+000 
               2.374926e−008 
               1.702835e−012 
               1.390779e−017 
               2.614732e−020 
             
             
                2 
               −4.000000e+000 
               −1.043013e−008 
               −1.517620e−013 
               4.986190e−018 
               −2.371680e−021 
             
             
                3 
               −7.638388e−002 
               −1.823532e−010 
               −2.150504e−016 
               −1.108786e−021 
               1.340316e−026 
             
             
                6 
               −3.827967e+000 
               −8.674101e−009 
               −1.051516e−013 
               −5.752138e−018 
               6.145431e−022 
             
             
               11 
               0.000000e+000 
               4.892931e−008 
               −5.416482e−013 
               5.381903e−016 
               1.678633e−020 
             
             
               12 
               0.000000e+000 
               7.048042e−008 
               2.284679e−012 
               −9.626527e−016 
               3.338522e−019 
             
             
               14 
               0.000000e+000 
               −3.924140e−008 
               −8.582640e−012 
               1.843538e−015 
               −3.326077e−019 
             
             
               17 
               0.000000e+000 
               8.970756e−007 
               3.402220e−011 
               3.720934e−014 
               1.395150e−017 
             
             
               18 
               0.000000e+000 
               7.110875e−007 
               −5.771239e−011 
               5.210874e−014 
               −9.240921e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               −7.722632e−024 
               7.560718e−028 
               0.000000e+000 
             
             
                 
                2 
               2.760856e−025 
               −1.354385e−029 
               0.000000e+000 
             
             
                 
                3 
               −1.379314e−031 
               5.943291e−037 
               0.000000e+000 
             
             
                 
                6 
               −5.871993e−026 
               2.213211e−030 
               0.000000e+000 
             
             
                 
               11 
               −6.073286e−024 
               6.405299e−028 
               0.000000e+000 
             
             
                 
               12 
               −4.157626e−023 
               2.508234e−027 
               0.000000e+000 
             
             
                 
               14 
               2.612172e−024 
               2.192107e−027 
               0.000000e+000 
             
             
                 
               17 
               −5.673999e−021 
               3.032464e−024 
               0.000000e+000 
             
             
                 
               18 
               6.249971e−021 
               9.050086e−031 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 15 
             
             
                 
             
             
               EXAMPLE 15 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.000 
             
             
                 
             
             
                1 
               204.213 
               15.833 
               1.56000 
             
             
                2 
               3825.784 
               413.292 
             
             
                3 
               −106.572 
               15.000 
               1.56000 
               LN1 
             
             
                4 
               −857.552 
               17.304 
             
             
                5 
               −187.562 
               −17.304 
               −1.0 
               M1 
             
             
                6 
               −857.552 
               −15.000 
               −1.56 
               LN1 
             
             
                7 
               −106.572 
               −408.626 
               −1.0 
             
             
                8 
               −1909.161 
               951.629 
                 
               M2 
             
             
                9 
               −858.848 
               −459.710 
               −1.0 
               FM1 
             
             
               10 
               −214.544 
               −26.074 
               −1.56 
               LF 
             
             
               11 
               −423.622 
               −4.701 
               −1.0 
             
             
               12 
               −291.919 
               4.701 
                 
               FM2 
             
             
               13 
               −423.622 
               26.074 
               1.56000 
               LF 
             
             
               14 
               −214.544 
               400.010 
             
             
               15 
               0.0 (stop) 
               59.759 
             
             
               16 
               424.663 
               15.005 
               1.56000 
             
             
               17 
               −637.707 
               0.101 
             
             
               18 
               135.307 
               20.950 
               1.56000 
             
             
               19 
               482.071 
               0.101 
             
             
               20 
               86.180 
               31.425 
               1.56000 
             
             
               21 
               180.516 
               9.606 
             
             
               22 
               108.812 
               15.000 
               1.56000 
             
             
               23 
               55.211 
               16.293 
             
             
               24 
               82.713 
               23.334 
               1.56000 
             
             
               25 
               −343.416 
             
             
                 
             
           
        
         
             
               β = ¼ 
             
             
               L = 1190 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               7.845851e−008 
               3.480979e−012 
               −2.192632e−016 
               2.652275e−020 
             
             
                2 
               0.000000e+000 
               1.287363e−007 
               5.213100e−012 
               −3.909292e−016 
               −2.757054e−020 
             
             
                3 
               0.000000e+000 
               5.511695e−008 
               2.742398e−012 
               2.976607e−016 
               −8.135784e−020 
             
             
                5 
               9.757356e−001 
               2.245223e−008 
               4.961650e−013 
               4.876359e−017 
               −9.218124e−021 
             
             
                7 
               0.000000e+000 
               5.511695e−008 
               2.742398e−012 
               2.976607e−016 
               −8.135784e−020 
             
             
                8 
               −2.324211e−001 
               −3.741519e−009 
               −2.965745e−014 
               3.165593e−019 
               −1.721869e−022 
             
             
                9 
               −1.351560e−001 
               −4.438792e−012 
               4.120307e−018 
               6.561688e−023 
               1.639361e−026 
             
             
               10 
               0.000000e+000 
               1.134555e−008 
               −5.474633e−013 
               −1.044929e−016 
               1.349222e−020 
             
             
               12 
               2.922694e+000 
               2.325940e−008 
               −2.396438e−013 
               −1.043028e−016 
               2.382476e−020 
             
             
               14 
               0.000000e+000 
               1.134555e−008 
               −5.474633e−013 
               −1.044929e−016 
               1.349222e−020 
             
             
               16 
               0.000000e+000 
               −5.994350e−008 
               −4.756412e−012 
               −8.685536e−017 
               −1.026534e−019 
             
             
               18 
               0.000000e+000 
               −8.290830e−008 
               −4.984870e−012 
               1.936271e−015 
               8.131779e−021 
             
             
               20 
               0.000000e+000 
               4.860989e−008 
               1.213638e−011 
               −2.550341e−015 
               9.673512e−020 
             
             
               23 
               0.000000e+000 
               −4.300839e−007 
               −3.408055e−011 
               −3.710689e−015 
               −2.158579e−018 
             
             
               24 
               0.000000e+000 
               −3.101203e−007 
               −4.766363e−011 
               1.545142e−015 
               1.795645e−020 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               −1.461145e−023 
               1.281999e−027 
               0.000000e+000 
             
             
                 
                2 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                3 
               3.995845e−023 
               −2.211509e−027 
               0.000000e+000 
             
             
                 
                5 
               3.224225e−024 
               −1.287665e−028 
               0.000000e+000 
             
             
                 
                7 
               3.995845e−023 
               −2.211509e−027 
               0.000000e+000 
             
             
                 
                8 
               1.248827e−026 
               −4.508298e−032 
               0.000000e+000 
             
             
                 
                9 
               −3.247603e−031 
               1.929812e−036 
               0.000000e+000 
             
             
                 
               10 
               −5.294016e−025 
               −6.522725e−030 
               0.000000e+000 
             
             
                 
               12 
               −1.683354e−024 
               3.413090e−029 
               0.000000e+000 
             
             
                 
               14 
               −5.294016e−025 
               −6.522725e−030 
               0.000000e+000 
             
             
                 
               16 
               2.849939e−023 
               −2.173374e−027 
               0.000000e+000 
             
             
                 
               18 
               −3.631059e−023 
               2.226964e−027 
               0.000000e+000 
             
             
                 
               20 
               −3.275165e−023 
               5.637523e−027 
               0.000000e+000 
             
             
                 
               23 
               −3.457497e−021 
               4.909090e−025 
               0.000000e+000 
             
             
                 
               24 
               −1.908395e−021 
               8.087019e−025 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 16 
             
             
                 
             
             
               EXAMPLE 16 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.267 
             
             
                 
             
             
                1 
               282.936 
               21.255 
               1.56000 
             
             
                2 
               3684.211 
               449.103 
             
             
                3 
               −267.457 
               15.000 
               1.56000 
               LN1 
             
             
                4 
               −1371.221 
               5.446 
             
             
                5 
               −321.384 
               −5.446 
               −1.0 
               M1 
             
             
                6 
               −1371.221 
               −15.000 
               −1.56 
               LN1 
             
             
                7 
               −267.457 
               −338.525 
               −1.0 
             
             
                8 
               −1540.132 
               368.971 
                 
               M2 
             
             
                9 
               440.699 
               35.890 
               1.56000 
               FL1 
             
             
               10 
               −1887.670 
               362.966 
             
             
               11 
               −922.802 
               −332.666 
               −1.0 
               FM1 
             
             
               12 
               8422.125 
               −15.000 
               −1.56 
               LF 
             
             
               13 
               −462.452 
               −5.300 
               −1.0 
             
             
               14 
               −1026.228 
               5.270 
                 
               FM2 
             
             
               15 
               −462.452 
               15.000 
               1.56000 
               LF 
             
             
               16 
               8422.125 
               268.193 
             
             
               17 
               0.0 (stop) 
               64.503 
             
             
               18 
               237.890 
               23.809 
               1.56000 
             
             
               19 
               2990.697 
               12.038 
             
             
               20 
               135.928 
               34.579 
               1.56000 
             
             
               21 
               622.051 
               3.846 
             
             
               22 
               144.391 
               38.185 
               1.56000 
             
             
               23 
               205.170 
               2.454 
             
             
               24 
               114.728 
               15.000 
               1.56000 
             
             
               25 
               72.687 
               9.881 
             
             
               26 
               78.971 
               64.113 
               1.56000 
             
             
               27 
               2179.982 
             
             
                 
             
           
        
         
             
               β = ⅕ 
             
             
               L = 1190 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               4.950479e−008 
               −1.556107e−012 
               1.719144e−017 
               2.105431e−021 
             
             
                3 
               0.000000e+000 
               −5.113917e−009 
               −2.873876e−012 
               2.602766e−017 
               6.788996e−020 
             
             
                5 
               7.999895e−001 
               −1.716298e−009 
               −1.163867e−012 
               2.214635e−018 
               2.170496e−020 
             
             
                7 
               0.000000e+000 
               −5.113917e−009 
               −2.873876e−012 
               2.602766e−017 
               6.788996e−020 
             
             
                8 
               5.000000e+000 
               3.994191e−009 
               −6.866541e−014 
               −1.799842e−018 
               −3.213142e−023 
             
             
                9 
               0.000000e+000 
               −4.745677e−009 
               9.727308e−015 
               −1.323010e−019 
               1.552321e−024 
             
             
               11 
               −3.742879e−001 
               −9.987061e−011 
               −8.267759e−016 
               2.319422e−020 
               −3.735582e−026 
             
             
               12 
               0.000000e+000 
               1.256240e−008 
               2.224328e−012 
               −1.743188e−015 
               1.674418e−019 
             
             
               14 
               3.922730e+000 
               −2.955486e−008 
               −3.015675e−013 
               −1.303534e−015 
               8.709164e−020 
             
             
               16 
               0.000000e+000 
               1.256240e−008 
               2.224328e−012 
               −1.743188e−015 
               1.674418e−019 
             
             
               20 
               0.000000e+000 
               −4.228533e−008 
               −1.756337e−012 
               −1.341137e−016 
               −8.216530e−021 
             
             
               22 
               0.000000e+000 
               1.397442e−008 
               −6.652675e−013 
               1.180182e−016 
               1.951605e−020 
             
             
               25 
               0.000000e+000 
               4.243718e−008 
               1.008140e−011 
               −5.060486e−016 
               −5.298502e−020 
             
             
               26 
               0.000000e+000 
               −1.152710e−007 
               4.633120e−012 
               −7.184290e−016 
               −1.928268e−019 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                3 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                5 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                7 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                8 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                9 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               11 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               12 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               14 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               16 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               20 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               22 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               25 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               26 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 17 
             
             
                 
             
             
               EXAMPLE 17 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 64.302 
             
             
                 
             
             
                1 
               145.868 
               15.654 
               1.56000 
             
             
                2 
               277.033 
               421.902 
             
             
                3 
               −331.764 
               15.000 
               1.56000 
               LN1 
             
             
                4 
               427.187 
               37.533 
             
             
                5 
               −243.163 
               −37.533 
               −1.0 
               M1 
             
             
                6 
               427.187 
               −15.000 
               −1.56 
               LN1 
             
             
                7 
               −331.764 
               −400.174 
               −1.0 
             
             
                8 
               −1050.590 
               462.707 
                 
               M2 
             
             
                9 
               1082.335 
               45.592 
               1.56000 
               FL1 
             
             
               10 
               −506.181 
               419.093 
             
             
               11 
               −556.173 
               −340.231 
               −1.0 
               FM1 
             
             
               12 
               890.632 
               −49.792 
               −1.56 
               LF 
             
             
               13 
               129.563 
               −12.279 
               −1.0 
             
             
               14 
               503.066 
               12.279 
                 
               FM2 
             
             
               15 
               129.563 
               49.792 
               1.56000 
               LF 
             
             
               16 
               890.632 
               308.936 
             
             
               17 
               0.0 (stop) 
               34.831 
             
             
               18 
               212.603 
               15.000 
               1.56000 
             
             
               19 
               358.696 
               0.100 
             
             
               20 
               154.082 
               17.867 
               1.56000 
             
             
               21 
               14558.550 
               0.107 
             
             
               22 
               233.915 
               24.251 
               1.56000 
             
             
               23 
               −182.460 
               0.246 
             
             
               24 
               102.219 
               15.000 
               1.56000 
             
             
               25 
               70.401 
               6.731 
             
             
               26 
               78.313 
               40.387 
               1.56000 
             
             
               27 
               −274.349 
             
             
                 
             
           
        
         
             
               β = ¼ 
             
             
               L = 1188 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               −4.543384e−008 
               2.008795e−013 
               −5.987597e−017 
               −7.178408e−022 
             
             
                3 
               0.000000e+000 
               −1.396774e−008 
               −1.312696e−012 
               −4.099589e−017 
               −1.204130e−021 
             
             
                5 
               2.136452e+000 
               7.442417e−009 
               1.306120e−013 
               2.191394e−018 
               −3.414108e−023 
             
             
                7 
               0.000000e+000 
               −1.396774e−008 
               −1.312696e−012 
               −4.099589e−017 
               −1.204130e−021 
             
             
                8 
               3.674765e−001 
               −5.080134e−009 
               −2.169803e−013 
               −7.383666e−018 
               −2.178985e−022 
             
             
                9 
               0.000000e+000 
               −3.096618e−009 
               6.122885e−015 
               −3.324130e−020 
               −2.496687e−026 
             
             
               11 
               −6.480972e−001 
               7.109927e−010 
               −3.912529e−015 
               3.016030e−021 
               −2.009020e−027 
             
             
               13 
               0.000000e+000 
               −1.535424e−008 
               −4.271143e−013 
               −5.423533e−017 
               2.156146e−021 
             
             
               14 
               −2.947254e−001 
               1.369848e−009 
               −1.353039e−013 
               1.572367e−017 
               −1.209804e−021 
             
             
               15 
               0.000000e+000 
               −1.535424e−008 
               −4.271143e−013 
               −5.423533e−017 
               2.156146e−021 
             
             
               20 
               0.000000e+000 
               −1.254255e−007 
               −3.689620e−012 
               −1.110656e−015 
               1.994369e−019 
             
             
               22 
               0.000000e+000 
               −1.374196e−007 
               −1.437806e−011 
               3.602627e−015 
               −3.618777e−019 
             
             
               25 
               0.000000e+000 
               8.431891e−008 
               −2.787295e−011 
               −9.578735e−015 
               −5.255927e−018 
             
             
               26 
               0.000000e+000 
               7.697163e−008 
               1.013236e−011 
               −6.851146e−015 
               −4.256775e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                3 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                5 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                7 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                8 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                9 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               11 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               13 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               14 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               15 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               20 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               22 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               25 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               26 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 18 
             
             
                 
             
             
               EXAMPLE 18 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 51.375 
             
             
                 
             
             
                1 
               294.105 
               24.410 
               1.56000 
             
             
                2 
               −2765.072 
               417.053 
             
             
                3 
               −116.294 
               15.000 
               1.56000 
               LN1 
             
             
                4 
               −2872.831 
               20.722 
             
             
                5 
               −186.216 
               −20.722 
               −1.0 
               M1 
             
             
                6 
               −2872.831 
               −15.000 
               −1.56 
               LN1 
             
             
                7 
               −116.294 
               −383.291 
               −1.0 
             
             
                8 
               −1505.962 
               429.623 
                 
               M2 
             
             
                9 
               444.041 
               63.934 
               1.56000 
               FL1 
             
             
               10 
               −3099.408 
               334.815 
             
             
               11 
               −948.436 
               −300.896 
               −1.0 
               FM1 
             
             
               12 
               −314.227 
               −16.435 
               −1.56 
               LF 
             
             
               13 
               −824.068 
               −7.484 
               −1.0 
             
             
               14 
               −325.089 
               7.484 
                 
               FM2 
             
             
               15 
               −824.068 
               16.435 
               1.56000 
               LF 
             
             
               16 
               −314.227 
               301.796 
             
             
               17 
               0.0 (stop) 
               55.267 
             
             
               18 
               654.524 
               17.101 
               1.56000 
             
             
               19 
               −493.112 
               0.100 
             
             
               20 
               127.646 
               36.817 
               1.56000 
             
             
               21 
               9721.169 
               9.587 
             
             
               22 
               124.513 
               19.292 
               1.56000 
             
             
               23 
               107.027 
               11.036 
             
             
               24 
               94.369 
               15.000 
               1.56000 
             
             
               25 
               93.351 
               9.999 
             
             
               26 
               115.073 
               47.374 
               1.56000 
             
             
               27 
               −373.527 
             
             
                 
             
           
        
         
             
               β = ¼ 
             
             
               L = 1197 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               3.270469e−008 
               −2.618357e−012 
               4.062834e−016 
               −5.211535e−020 
             
             
                3 
               0.000000e+000 
               4.411046e−009 
               −5.444659e−013 
               −4.482642e−017 
               1.266365e−019 
             
             
                5 
               9.780048e−001 
               1.163827e−008 
               2.616720e−013 
               −9.065597e−019 
               1.119604e−020 
             
             
                7 
               0.000000e+000 
               4.411046e−009 
               −5.444659e−013 
               −4.482642e−017 
               1.266365e−019 
             
             
                8 
               −1.539537e+000 
               3.786900e−009 
               −9.453622e−014 
               3.248795e−018 
               −2.012056e−022 
             
             
                9 
               0.000000e+000 
               −4.149266e−009 
               2.307771e−015 
               −1.751852e−021 
               −1.213130e−024 
             
             
               11 
               −3.776756e+000 
               −4.342111e−010 
               −2.394400e−015 
               5.496039e−020 
               −1.406823e−024 
             
             
               12 
               0.000000e+000 
               −1.673853e−009 
               −3.281730e−012 
               6.683323e−016 
               −8.393102e−020 
             
             
               14 
               −3.600157e+000 
               −3.076829e−008 
               −3.309550e−012 
               6.132785e−016 
               −1.002042e−019 
             
             
               16 
               0.000000e+000 
               −1.673853e−009 
               −3.281730e−012 
               6.683323e−016 
               −8.393102e−020 
             
             
               19 
               0.000000e+000 
               1.130381e−008 
               1.048332e−012 
               −2.689716e−016 
               1.609677e−020 
             
             
               20 
               0.000000e+000 
               −2.363339e−008 
               −1.791151e−012 
               −4.488565e−016 
               −3.302356e−020 
             
             
               22 
               0.000000e+000 
               4.460228e−009 
               −2.267365e−012 
               −2.653562e−016 
               2.051402e−020 
             
             
               25 
               0.000000e+000 
               3.016193e−007 
               2.151092e−011 
               −3.603828e−016 
               −2.089239e−018 
             
             
               26 
               0.000000e+000 
               2.718387e−007 
               2.254954e−011 
               −7.855692e−016 
               −2.167393e−018 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               3.766459e−024 
               −1.147383e−028 
               0.000000e+000 
             
             
                 
                3 
               −1.676440e−023 
               2.206450e−027 
               0.000000e+000 
             
             
                 
                5 
               −9.520370e−025 
               9.545144e−029 
               0.000000e+000 
             
             
                 
                7 
               −1.676440e−023 
               2.206450e−027 
               0.000000e+000 
             
             
                 
                8 
               1.042016e−026 
               −2.633116e−031 
               0.000000e+000 
             
             
                 
                9 
               1.190683e−029 
               −3.996052e−035 
               0.000000e+000 
             
             
                 
               11 
               1.831918e−029 
               −9.562670e−035 
               0.000000e+000 
             
             
                 
               12 
               4.958336e−024 
               −1.328994e−028 
               0.000000e+000 
             
             
                 
               14 
               7.328052e−024 
               −3.110175e−028 
               0.000000e+000 
             
             
                 
               16 
               4.958336e−024 
               −1.328994e−028 
               0.000000e+000 
             
             
                 
               19 
               −7.303308e−025 
               3.915870e−029 
               0.000000e+000 
             
             
                 
               20 
               −6.049533e−025 
               −2.110230e−029 
               0.000000e+000 
             
             
                 
               22 
               5.955447e−023 
               −4.660843e−027 
               0.000000e+000 
             
             
                 
               25 
               7.756637e−022 
               −7.997079e−027 
               0.000000e+000 
             
             
                 
               26 
               7.445927e−022 
               −4.578951e−026 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 19 
             
             
                 
             
             
               EXAMPLE 19 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
                 
               i 
               ri 
               di 
               ni 
               Obj-distance = 51.000 
             
             
                 
                 
             
             
                 
               1 
               351.655 
               16.754 
               1.56000 
             
             
                 
               2 
               −8365.385 
               1.500 
                 
             
             
                 
               3 
               200.954 
               22.369 
               1.56000 
             
             
                 
               4 
               591.866 
               247.671 
             
             
                 
               5 
               −88.814 
               15.000 
               1.56000 
               LN1 
             
             
                 
               6 
               −402.056 
               7.000 
             
             
                 
               7 
               −151.144 
               −7.000 
               −1.0 
               M1 
             
             
                 
               8 
               −402.056 
               −15.000 
               −1.56 
               LN1 
             
             
                 
               9 
               −88.814 
               −240.671 
               −1.0 
             
             
                 
               10 
               1366.187 
               349.374 
                 
               M2 
             
             
                 
               11 
               19831.441 
               26.737 
               1.56000 
               FL1 
             
             
                 
               12 
               −735.739 
               244.705 
             
             
                 
               13 
               −566.816 
               −219.048 
               −1.0 
               FM1 
             
             
                 
               14 
               −133.579 
               −14.510 
               −1.56 
               LF 
             
             
                 
               15 
               −205.618 
               −1.148 
               −1.0 
             
             
                 
               16 
               −202.153 
               1.148 
                 
               FM2 
             
             
                 
               17 
               −205.618 
               14.510 
               1.56000 
               LF 
             
             
                 
               18 
               −133.579 
               224.997 
             
             
                 
               19 
               0.0(stop) 
               −4.929 
             
             
                 
               20 
               −119.907 
               20.312 
               1.56000 
             
             
                 
               21 
               −246.626 
               7.094 
             
             
                 
               22 
               153.705 
               24.772 
               1.56000 
             
             
                 
               23 
               −385.679 
               18.913 
             
             
                 
               24 
               97.386 
               43.291 
               1.56000 
             
             
                 
               25 
               177.767 
               7.651 
             
             
                 
               26 
               95.442 
               31.717 
               1.56000 
             
             
                 
               27 
               364.058 
               6.848 
             
             
                 
               28 
               103.255 
               19.448 
               1.56000 
             
             
                 
               29 
               −1048.656 
             
             
                 
                 
             
           
        
         
             
               β = 1/5 
             
             
               L = 934 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               −8.093313e−008   
               4.522834e−012 
               −2.018073e−016   
                 2.267148e−020 
             
             
                3 
               0.000000e+000 
               6.511812e−008 
               −3.723599e−012   
               1.013032e−016 
               −2.501488e−021 
             
             
                5 
               0.000000e+000 
               2.476497e−008 
               −5.194074e−012   
               2.934576e−014 
               −6.771024e−018 
             
             
                7 
               −8.634921e−002   
               5.766118e−008 
               1.400403e−011 
               1.171617e−014 
               −2.406379e−018 
             
             
                9 
               0.000000e+000 
               2.476497e−008 
               −5.194074e−012   
               2.934576e−014 
               −6.771024e−018 
             
             
               10 
               3.403605e+000 
               −2.532676e−009   
               4.911669e−014 
               1.807856e−018 
               −2.255506e−022 
             
             
               13 
               −5.700272e−001   
               1.734919e−010 
               1.781213e−015 
               −7.464135e−021   
                 1.125815e−024 
             
             
               14 
               0.000000e+000 
               6.268611e−009 
               9.790240e−013 
               5.096073e−017 
               −4.749646e−020 
             
             
               16 
               −9.969546e−001   
               4.762518e−009 
               8.200176e−013 
               6.576997e−018 
               −5.959712e−020 
             
             
               18 
               0.000000e+000 
               6.268611e−009 
               9.790240e−013 
               5.096073e−017 
               −4.749646e−020 
             
             
               21 
               0.000000e+000 
               7.500151e−008 
               −2.370496e−011   
               −1.965330e−015   
                 3.913950e−019 
             
             
               23 
               0.000000e+000 
               −5.983025e−009   
               2.383340e−011 
               −4.396313e−016   
               −2.197526e−019 
             
             
               24 
               0.000000e+000 
               4.080007e−008 
               −9.297261e−012   
               1.873727e−015 
               −1.418320e−019 
             
             
               26 
               0.000000e+000 
               −3.783040e−007   
               −1.883182e−012   
               −8.030466e−016   
               −7.057718e−019 
             
             
               28 
               0.000000e+000 
               −9.452418e−008   
               −1.957493e−011   
               −1.244651e−014   
                 0.000000e+000 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               −3.670991e−024   
                 2.228767e−028 
               0.000000e+000 
             
             
                 
                3 
               1.383272e−024 
               −1.154892e−028 
               0.000000e+000 
             
             
                 
                5 
               4.483389e−021 
               −9.723939e−025 
               0.000000e+000 
             
             
                 
                7 
               8.068244e−022 
               −6.319119e−026 
               0.000000e+000 
             
             
                 
                9 
               4.483389e−021 
               −9.723939e−025 
               0.000000e+000 
             
             
                 
               10 
               1.792109e−026 
               −6.218030e−031 
               0.000000e+000 
             
             
                 
               13 
               −3.288087e−029   
                 4.085249e−034 
               0.000000e+000 
             
             
                 
               14 
               1.007847e−023 
                 2.645246e−029 
               0.000000e+000 
             
             
                 
               16 
               1.769682e−023 
               −1.119411e−027 
               0.000000e+000 
             
             
                 
               18 
               1.007847e−023 
                 2.645246e−029 
               0.000000e+000 
             
             
                 
               21 
               −1.267664e−023   
               −8.319497e−028 
               0.000000e+000 
             
             
                 
               23 
               1.954211e−023 
               −3.173836e−029 
               0.000000e+000 
             
             
                 
               24 
               1.171050e−023 
               −3.681475e−028 
               0.000000e+000 
             
             
                 
               26 
               8.165762e−023 
                 1.411746e−026 
               0.000000e+000 
             
             
                 
               28 
               −2.398432e−022   
               −4.378158e−025 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 20 
             
             
                 
             
             
               EXAMPLE 20 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.000 
             
             
                 
             
             
                1 
               245.198 
               40.746 
               1.56000 
             
             
                2 
               565.312 
               378.944 
             
             
                3 
               −198.743 
               15.000 
               1.56000 
               LN1 
             
             
                4 
               −553.813 
               2.806 
             
             
                5 
               −383.608 
               −2.806 
               −1.0 
               M1 
             
             
                6 
               −553.813 
               −15.000 
               −1.56 
               LN1 
             
             
                7 
               −198.743 
               −358.732 
               −1.0 
             
             
                8 
               6976.362 
               386.889 
                 
               M2 
             
             
                9 
               355.685 
               51.490 
               1.56000 
               FL1 
             
             
               10 
               −12321.788 
               369.283 
             
             
               11 
               −1028.093 
               −343.512 
               −1.0 
               FM1 
             
             
               12 
               730.908 
               −15.000 
               −1.56 
               LF 
             
             
               13 
               −1511.630 
               −0.100 
               −1.0 
             
             
               14 
               −1023.030 
               0.070 
                 
               FM2 
             
             
               15 
               −1511.630 
               15.000 
               1.56000 
               LF 
             
             
               16 
               730.908 
               323.513 
             
             
               17 
               0.0 (stop) 
               39.007 
             
             
               18 
               302.719 
               22.983 
               1.56000 
             
             
               19 
               −6847.780 
               21.360 
             
             
               20 
               145.723 
               31.514 
               1.56000 
             
             
               21 
               618.670 
               8.713 
             
             
               22 
               147.653 
               25.174 
               1.56000 
             
             
               23 
               391.950 
               8.285 
             
             
               24 
               121.433 
               15.000 
               1.56000 
             
             
               25 
               80.944 
               14.809 
             
             
               26 
               94.829 
               68.564 
               1.56000 
             
             
               27 
               −806.611 
             
             
                 
             
           
        
         
             
               β = ⅛ 
             
             
               L = 1190 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               2.707002e−008 
               −8.717359e−013 
               1.291774e−017 
               −8.046083e−023 
             
             
                3 
               0.000000e+000 
               −1.285216e−008 
               −4.644289e−012 
               −1.098284e−015 
               4.074896e−020 
             
             
                5 
               1.853481e+000 
               −5.942386e−009 
               −1.921556e−012 
               −3.991601e−016 
               3.066166e−020 
             
             
                7 
               0.000000e+000 
               −1.285216e−008 
               −4.644289e−012 
               −1.098284e−015 
               4.074896e−020 
             
             
                8 
               4.692105e+000 
               6.776075e−009 
               −1.213133e−013 
               2.083765e−018 
               −3.379785e−023 
             
             
                9 
               0.000000e+000 
               −7.268271e−009 
               3.352308e−015 
               −1.357278e−019 
               −1.824547e−024 
             
             
               11 
               1.213373e+000 
               −1.515625e−010 
               −6.598956e−015 
               2.230167e−019 
               −3.018642e−024 
             
             
               12 
               0.000000e+000 
               2.663004e−009 
               −5.964634e−012 
               −3.132031e−015 
               3.139422e−019 
             
             
               14 
               3.818120e+000 
               −5.339360e−008 
               −6.525763e−012 
               −2.026068e−015 
               1.112273e−019 
             
             
               16 
               0.000000e+000 
               2.663004e−009 
               −5.964634e−012 
               −3.132031e−015 
               3.139422e−019 
             
             
               20 
               0.000000e+000 
               −4.537132e−008 
               −1.444034e−012 
               −6.237537e−017 
               −1.225622e−020 
             
             
               22 
               0.000000e+000 
               2.258810e−008 
               −2.784423e−012 
               −4.694218e−017 
               4.207858e−020 
             
             
               25 
               0.000000e+000 
               1.033200e−007 
               −6.071918e−012 
               −2.759843e−015 
               −3.195258e−019 
             
             
               26 
               0.000000e+000 
               −2.135939e−008 
               −6.495251e−012 
               −2.642392e−015 
               −2.963340e−019 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                3 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                5 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                7 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                8 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                9 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               11 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               12 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               14 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               16 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               20 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               22 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               25 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               26 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   
     
       
             
           
             
             
             
             
             
           
             
           
             
           
             
             
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 21 
             
             
                 
             
             
               EXAMPLE 21 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               i 
               ri 
               di 
               ni 
               Obj-distance = 50.487 
             
             
                 
             
             
                1 
               248.654 
               45.879 
               1.56000 
             
             
                2 
               2498.279 
               433.450 
             
             
                3 
               −430.357 
               17.451 
               1.56000 
               LN1 
             
             
                4 
               1258.317 
               2.793 
             
             
                5 
               −320.814 
               −2.793 
               −1.0 
               M1 
             
             
                6 
               1258.317 
               −17.451 
               −1.56 
               LN1 
             
             
                7 
               −430.357 
               −170.466 
               −1.0 
             
             
                8 
               −566426.061 
               200.710 
                 
               M2 
             
             
                9 
               −1563.039 
               37.005 
               1.56000 
               FL1 
             
             
               10 
               −250.953 
               361.172 
             
             
               11 
               −765.976 
               −329.940 
               −1.0 
               FM1 
             
             
               12 
               244.884 
               −15.000 
               −1.56 
               LF 
             
             
               13 
               549.490 
               −6.231 
               −1.0 
             
             
               14 
               −701.208 
               6.201 
                 
               FM2 
             
             
               15 
               549.490 
               15.000 
               1.56000 
               LF 
             
             
               16 
               244.884 
               283.488 
             
             
               17 
               0.0 (stop) 
               46.600 
             
             
               18 
               244.341 
               23.507 
               1.56000 
             
             
               19 
               57346.724 
               0.100 
             
             
               20 
               138.156 
               28.770 
               1.56000 
             
             
               21 
               561.247 
               3.336 
             
             
               22 
               145.732 
               37.036 
               1.56000 
             
             
               23 
               260.318 
               4.990 
             
             
               24 
               111.587 
               15.000 
               1.56000 
             
             
               25 
               70.790 
               33.292 
             
             
               26 
               75.408 
               49.617 
               1.56000 
             
             
               27 
               5689.128 
             
             
                 
             
           
        
         
             
               β = 1/10 
             
             
               L = 1190 mm 
             
             
               NA = 0.6 
             
           
        
         
             
               aspherical surfaces 
             
             
                 
             
           
        
         
             
               i 
               K 
               A 
               B 
               C 
               D 
             
             
                 
             
             
                1 
               0.000000e+000 
               −2.521478e−009 
               −8.451485e−014 
               5.214505e−019 
               −2.685571e−023 
             
             
                3 
               0.000000e+000 
               −3.993741e−008 
               2.044280e−012 
               1.954603e−014 
               4.016803e−018 
             
             
                5 
               4.706536e+000 
               −4.082512e−008 
               −1.158264e−011 
               7.155566e−015 
               −2.269483e−019 
             
             
                7 
               0.000000e+000 
               −3.993741e−008 
               2.044280e−012 
               1.954603e−014 
               4.016803e−018 
             
             
                8 
               5.000000e+000 
               −3.971095e−009 
               −7.223454e−014 
               −1.084017e−018 
               6.587792e−024 
             
             
                9 
               0.000000e+000 
               −4.759165e−009 
               1.313843e−014 
               1.109392e−019 
               −1.230866e−024 
             
             
               11 
               3.289899e−001 
               −3.568080e−010 
               −1.380316e−015 
               1.016681e−020 
               −6.587533e−026 
             
             
               12 
               0.000000e+000 
               −2.613402e−008 
               −9.198710e−013 
               −1.784868e−016 
               2.018156e−020 
             
             
               14 
               −4.000000e+000 
               −3.882997e−008 
               −1.433855e−012 
               −1.916913e−016 
               4.859577e−022 
             
             
               16 
               0.000000e+000 
               −2.613402e−008 
               −9.198710e−013 
               −1.784868e−016 
               2.018156e−020 
             
             
               20 
               0.000000e+000 
               −4.145601e−008 
               −2.245516e−012 
               −8.585230e−017 
               −7.216150e−021 
             
             
               22 
               0.000000e+000 
               1.029827e−008 
               −4.482490e−015 
               1.152103e−017 
               1.349052e−020 
             
             
               25 
               0.000000e+000 
               1.056111e−007 
               8.819533e−012 
               3.490901e−016 
               2.003722e−020 
             
             
               26 
               0.000000e+000 
               −3.282437e−008 
               3.472717e−012 
               −3.391125e−016 
               −1.465019e−019 
             
             
                 
             
           
        
         
             
                 
               i 
               E 
               F 
               G 
             
             
                 
                 
             
             
                 
                1 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                3 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                5 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                7 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                8 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                9 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               11 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               12 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               14 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               16 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               20 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               22 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               25 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
               26 
               0.000000e+000 
               0.000000e+000 
               0.000000e+000 
             
             
                 
                 
             
           
        
       
     
   
   While the invention has been described with reference to the structures disclosed herein, it is not confined to the details set forth and this application is intended to cover such modifications or changes as may come within the purposes of the improvements or the scope of the following claims.