Patent Publication Number: US-2015077724-A1

Title: Projection optical system and projection-type display apparatus

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority under 35 U.S.C. §119 to Japanese Patent Application No. 2013-193986, filed on Sep. 19, 2013. The above application is hereby expressly incorporated by reference, in its entirety, into the present application. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a projection optical system that uses a refractive optical system and a reflective optical system, and which forms, on a screen, an image of an image displayed on an image display device, and also to a projection-type display apparatus including the projection optical system. 
     2. Description of the Related Art 
     As a projection-type display apparatus including a projection optical system that uses a refractive optical system and a reflective optical system, and which forms, on a screen, an image of an image displayed on an image display device, apparatuses disclosed in Japanese Unexamined Patent Publication No. 2007-323047 (Patent Document 1), Japanese Unexamined Patent Publication No. 2007-334052 (Patent Document 2), Specification of Japanese Patent No. 4731808 (Patent Document 3) and Specification of Japanese Patent No. 4889289 (Patent Document 4) are known. 
     SUMMARY OF THE INVENTION 
     In the projection optical system and the projection-type display apparatus including the projection optical system, as described above, further reduction in the size and the cost of the apparatus and a shorter projection distance while a magnified video image in sufficient size is displayed on a screen are requested. 
     In view of the foregoing circumstances, it is an object of the present invention to provide a projection optical system that can display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of an apparatus, and also a projection-type display apparatus including the projection optical system. 
     A projection optical system of the present invention projects an image displayed on an image display device arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image. The projection optical system includes a refractive optical system and a reflective optical system having negative refractive power in this order from a reduction side, and the following conditional formula (1) is satisfied: 
       ( ZL+ZD )× Y min/ Y max 2 ≦3.2  (1), where
 
     ZL: a total length of the refractive optical system, 
     ZD: a distance on an optical axis between the refractive optical system and the reflective optical system, 
     Ymin: a minimum value of a distance from each point in the image display device to the optical axis, and 
     Ymax: a maximum value of the distance from each point in the image display device to the optical axis. 
     In the projection optical system of the present invention, it is desirable that the refractive optical system and the reflective optical system have a common optical axis. 
     Further, it is desirable that the refractive optical system and the reflective optical system are rotationally symmetric about the optical axis. 
     Further, it is desirable that the reflective optical system substantially consists of a mirror having negative refractive power. 
     It is desirable that the following conditional formula (2) is satisfied: 
         Y min/ Y max≦0.20  (2).
 
     It is desirable that the following conditional formula (3) is satisfied: 
       ( ZL+ZD )/ Y max≦21  (3).
 
     It is desirable that the following conditional formula (4) is satisfied: 
       |cos θ−2 cos φ cos ψ|≦0.6  (4), where
 
     θ: an angle between a chief ray from a most peripheral area on a display surface of the image display device and the optical axis when the chief ray exits from the refractive optical system, 
     φ: an angle between a normal to the reflective optical system and the optical axis at a point where the chief ray from the most peripheral area on the display surface enters the reflective optical system, and 
     ψ: an angle between the chief ray and the normal to the reflective optical system at the point where the chief ray from the most peripheral area on the display surface enters the reflective optical system. 
     It is desirable that the following conditional formula (5) is satisfied: 
       0.5≦( ZL+ZD )/ Hm≦ 2.1  (5), where
 
     Hm: a maximum effective diameter at a reflection surface of the reflective optical system. 
     It is desirable that the refractive optical system includes at least one aspheric lens between optical element Lp and the reflective optical system when an optical element (a single lens or a cemented lens) including one of a spherical surface or surfaces arranged closest to a magnification side in the refractive optical system is optical element Lp. 
     It is desirable that a second lens group, as a whole, has positive refractive power when a lens system (which does not include optical element Lp) arranged between optical element Lp and the reflective optical system is a first lens group in the refractive optical system and a lens system including optical element Lp, and which is arranged toward a reduction side of the optical element Lp, is the second lens group in the refractive optical system. 
     Further, the first lens group may substantially consist of two lenses of an aspheric lens having negative refractive power and an aspheric lens having positive refractive power in this order from the magnification side. Alternatively, the first lens group may substantially consist of an aspheric lens having negative refractive power. 
     Further, it is desirable that a most-magnification-side surface of optical element Lp has a convex shape toward the magnification side. 
     It is desirable that a most-reduction-side surface of optical element Lp has a concave shape facing the reduction side. 
     Further, it is desirable that optical element Lp has negative refractive power. 
     Further, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a positive lens with its convex surface facing the magnification side, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power. Alternatively, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power. 
     It is desirable that the 2a-th lens group, as a whole, has positive refractive power. 
     It is desirable that the 2b-th lens group, as a whole, has positive refractive power. 
     It is desirable that the 2b-th lens group includes at least one aspheric lens. 
     It is desirable that the following conditional formula (1-1) is satisfied: 
       ( ZL+ZD )× Y min/ Y max 2 ≦2.5  (1-1).
 
     Further, it is desirable that the following conditional formula (2-1) is satisfied: 
         Y min/ Y max≦0.17  (2-1).
 
     It is desirable that the following conditional formula (3-1) is satisfied: 
       ( ZL+ZD )/ Y max≦16  (3-1).
 
     Further, it is desirable that the following conditional formula (4-1) is satisfied: 
       |cos θ−2 cos φ cos ψ|≦0.4  (4-1).
 
     Further, it is desirable that the following conditional formula (5-1) is satisfied: 
       1.0≦( ZL+ZD )/ Hm≦ 1.6  (5-1).
 
     A projection-type display apparatus of the present invention includes a light source, a light valve on which light from the light source is incident, and the aforementioned projection optical system of the present invention, as a projection optical system that projects an optical image of light that has been optically modulated by the light valve onto a screen. 
     Here, the expression “substantially consisting of” means that lenses substantially without any refractive power, optical elements other than lenses, such as a stop, a mask, a cover glass and a filter, mechanism parts, such as a lens flange, a lens barrel, an imaging device and a hand shake blur correction mechanism, and the like may be included in addition to the lens groups mentioned as composition elements. 
     The surface shape of the lens and the sign of the refractive power of the lens are considered in a paraxial region when the lens includes an aspherical surface. 
     Further, the term “chief ray” means a ray crossing the optical axis at an entrance pupil position. 
     A projection optical system of the present invention projects an image displayed on an image display device arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image. The projection optical system includes a refractive optical system and a reflective optical system having negative refractive power in this order from a reduction side, and the following conditional formula (1) is satisfied. Therefore, it is possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. 
       ( ZL+ZD )× Y min/ Y max 2 ≦3.2  (1)
 
     The projection-type display apparatus of the present invention includes the projection optical system of the present invention. Therefore, it is possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the apparatus. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross section illustrating the structure of a projection optical system according to an embodiment of the present invention (common to Example 1); 
         FIG. 2  is a cross section illustrating the structure of a projection optical system in Example 2 of the present invention; 
         FIG. 3  is a cross section illustrating the structure of a projection optical system in Example 3 of the present invention; 
         FIG. 4  is a cross section illustrating the structure of a projection optical system in Example 4 of the present invention; 
         FIG. 5  is a cross section illustrating the structure of a projection optical system in Example 5 of the present invention; 
         FIG. 6  is a cross section illustrating the structure of a projection optical system in Example 6 of the present invention; 
         FIG. 7  is a cross section illustrating the structure of a projection optical system in Example 7 of the present invention; 
         FIG. 8  is a cross section illustrating the structure of a projection optical system in Example 8 of the present invention; 
         FIG. 9  is a cross section illustrating the structure of a projection optical system in Example 9 of the present invention; 
         FIG. 10  is a cross section illustrating the structure of a projection optical system in Example 10 of the present invention; 
         FIG. 11  is a cross section illustrating the structure of a projection optical system in Example 11 of the present invention; 
         FIG. 12  is a cross section illustrating the structure of a projection optical system in Example 12 of the present invention; 
         FIG. 13  is a cross section illustrating the structure of a projection optical system in Example 13 of the present invention; 
         FIG. 14  is a cross section illustrating the structure of a projection optical system in Example 14 of the present invention; 
         FIG. 15  is a cross section illustrating the structure of a projection optical system in Example 15 of the present invention; 
         FIG. 16  is a cross section illustrating the structure of a projection optical system in Example 16 of the present invention; 
         FIG. 17  is a cross section illustrating the structure of a projection optical system in Example 17 of the present invention; 
         FIG. 18  is a diagram illustrating distortion performance of the projection optical system in Example 1 of the present invention; 
         FIG. 19  is a diagram illustrating distortion performance of the projection optical system in Example 2 of the present invention; 
         FIG. 20  is a diagram illustrating distortion performance of the projection optical system in Example 3 of the present invention; 
         FIG. 21  is a diagram illustrating distortion performance of the projection optical system in Example 4 of the present invention; 
         FIG. 22  is a diagram illustrating distortion performance of the projection optical system in Example 5 of the present invention; 
         FIG. 23  is a diagram illustrating distortion performance of the projection optical system in Example 6 of the present invention; 
         FIG. 24  is a diagram illustrating distortion performance of the projection optical system in Example 7 of the present invention; 
         FIG. 25  is a diagram illustrating distortion performance of the projection optical system in Example 8 of the present invention; 
         FIG. 26  is a diagram illustrating distortion performance of the projection optical system in Example 9 of the present invention; 
         FIG. 27  is a diagram illustrating distortion performance of the projection optical system in Example 10 of the present invention; 
         FIG. 28  is a diagram illustrating distortion performance of the projection optical system in Example 11 of the present invention; 
         FIG. 29  is a diagram illustrating distortion performance of the projection optical system in Example 12 of the present invention; 
         FIG. 30  is a diagram illustrating distortion performance of the projection optical system in Example 13 of the present invention; 
         FIG. 31  is a diagram illustrating distortion performance of the projection optical system in Example 14 of the present invention; 
         FIG. 32  is a diagram illustrating distortion performance of the projection optical system in Example 15 of the present invention; 
         FIG. 33  is a diagram illustrating distortion performance of the projection optical system in Example 16 of the present invention; 
         FIG. 34  is a diagram illustrating distortion performance of the projection optical system in Example 17 of the present invention; 
         FIG. 35  is a diagram illustrating spot performance of the projection optical system in Example 1 of the present invention; 
         FIG. 36  is a diagram illustrating spot performance of the projection optical system in Example 2 of the present invention; 
         FIG. 37  is a diagram illustrating spot performance of the projection optical system in Example 3 of the present invention; 
         FIG. 38  is a diagram illustrating spot performance of the projection optical system in Example 4 of the present invention; 
         FIG. 39  is a diagram illustrating spot performance of the projection optical system in Example 5 of the present invention; 
         FIG. 40  is a diagram illustrating spot performance of the projection optical system in Example 6 of the present invention; 
         FIG. 41  is a diagram illustrating spot performance of the projection optical system in Example 7 of the present invention; 
         FIG. 42  is a diagram illustrating spot performance of the projection optical system in Example 8 of the present invention; 
         FIG. 43  is a diagram illustrating spot performance of the projection optical system in Example 9 of the present invention; 
         FIG. 44  is a diagram illustrating spot performance of the projection optical system in Example 10 of the present invention; 
         FIG. 45  is a diagram illustrating spot performance of the projection optical system in Example 11 of the present invention; 
         FIG. 46  is a diagram illustrating spot performance of the projection optical system in Example 12 of the present invention; 
         FIG. 47  is a diagram illustrating spot performance of the projection optical system in Example 13 of the present invention; 
         FIG. 48  is a diagram illustrating spot performance of the projection optical system in Example 14 of the present invention; 
         FIG. 49  is a diagram illustrating spot performance of the projection optical system in Example 15 of the present invention; 
         FIG. 50  is a diagram illustrating spot performance of the projection optical system in Example 16 of the present invention; 
         FIG. 51  is a diagram illustrating spot performance of the projection optical system in Example 17 of the present invention; 
         FIG. 52  is a diagram illustrating evaluation points in an image display device; 
         FIG. 53  is a diagram illustrating evaluation points in a magnified image on a magnification-side conjugate plane; and 
         FIG. 54  is a schematic diagram illustrating the configuration of a projection-type display apparatus according to an embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Embodiments of the present invention will be described in detail with reference to drawings.  FIG. 1  is a cross section illustrating the structure of a projection optical system according to an embodiment of the present invention. The example of structure illustrated in  FIG. 1  is common to the structure of a projection optical system in Example 1, which will be described later. In  FIG. 1 , the left side is a reduction side, and the right side is a magnification side. 
     As illustrated in  FIG. 1 , this projection optical system projects an image displayed on image display device D arranged on a reduction-side conjugate plane onto a magnification-side conjugate plane, as a magnified image. The projection optical system includes a refractive optical system substantially consisting of lenses L 1  through L 12  and reflective optical system R having negative refractive power in this order from a reduction side along optical axis Z. 
     Image display device D is arranged at a position of so-called full shift or more so that no part of a whole display surface of image display device D crosses optical axis Z. 
     When this projection optical system is applied to a projection-type display apparatus, it is desirable to arrange a cover glass, a prism, and various filters, such as an infrared-ray-cut filter and a low-pass filter, between image display device D and the refractive optical system based on the configuration of the apparatus. Therefore,  FIG. 1  illustrates an example in which parallel-flat-plate-shaped optical member PP, assuming these elements, is arranged between image display device D and the refractive optical system. 
     The projection optical system is structured in such a manner to satisfy the following conditional formula (1). Therefore, it is possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. When the following conditional formula (1-1) is satisfied, more excellent properties are achievable: 
       ( ZL+ZD )× Y min/ Y max 2 ≦3.2  (1); and
 
       ( ZL+ZD )× Y min/ Y max 2 ≦2.5  (1-1), where
 
     ZL: a total length of the refractive optical system, 
     ZD: a distance on an optical axis between the refractive optical system and the reflective optical system, 
     Ymin: a minimum value of a distance from each point in the image display device to the optical axis (illustrated in  FIG. 52 ), and 
     Ymax: a maximum value of the distance from each point in the image display device to the optical axis (illustrated in  FIG. 52 ). 
     In the projection optical system, it is desirable that the refractive optical system and reflective optical system R have a common optical axis. Further, it is desirable that the refractive optical system and the reflective optical system are rotationally symmetric about the optical axis. Further, it is desirable that the reflective optical system substantially consists of a mirror having negative refractive power. Accordingly, it is possible to simplify the structure of the projection optical system, and that contributes to reduction in cost. 
     Further, it is desirable that the following conditional formula (2) is satisfied. Accordingly, it becomes possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. When the following conditional formula (2-1) is satisfied, more excellent properties are achievable: 
         Y min/ Y max≦0.20  (2); and
 
         Y min/ Y max≦0.17  (2-1).
 
     Further, it is desirable that the following conditional formula (3) is satisfied. Accordingly, it becomes possible to reduce the size of the optical system. When the following conditional formula (3-1) is satisfied, more excellent properties are achievable: 
       ( ZL+ZD )/ Y max≦21  (3); and
 
       ( ZL+ZD )/ Y max≦16  (3-1).
 
     Further, it is desirable that the following conditional formula (4) is satisfied. Accordingly, it becomes possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. When the following conditional formula (4-1) is satisfied, more excellent properties are achievable: 
       |cos θ−2 cos φ cos ψ|≦0.6  (4); and
 
       |cos θ−2 cos φ cos ψ|≦0.4  (4-1), where
 
     θ: an angle between a chief ray from a most peripheral area on a display surface of the image display device and the optical axis when the chief ray exits from the refractive optical system, 
     φ: an angle between a normal to the reflective optical system and the optical axis at a point where the chief ray from the most peripheral area on the display surface enters the reflective optical system, and 
     ψ: an angle between the chief ray and the normal to the reflective optical system at the point where the chief ray from the most peripheral area on the display surface enters the reflective optical system. 
     Further, it is desirable to satisfy the following conditional formula (5). Accordingly, it becomes possible to display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. When the following conditional formula (5-1) is satisfied, more excellent properties are achievable: 
       0.5≦( ZL+ZD )/ Hm≦ 2.1  (5); and
 
       1.0≦( ZL+ZD )/ Hm≦ 1.6  (5-1), where
 
     Hm: a maximum effective diameter at a reflection surface of the reflective optical system. 
     Further, it is desirable that the refractive optical system includes at least one aspheric lens between optical element Lp and reflective optical system R when an optical element (a single lens or a cemented lens) including one of a spherical surface or surfaces arranged closest to a magnification side in the refractive optical system is optical element Lp. Accordingly, it is possible to excellently correct various aberrations generated in reflective optical system R. In the embodiment of the present invention, lens L 10  corresponds to optical element Lp, and the projection optical system includes two aspheric lenses L 11 , L 12  between optical element Lp and reflective optical system R. 
     It is desirable that a second lens group, as a whole, has positive refractive power when a lens system (which does not include optical element Lp) arranged between optical element Lp and reflective optical system R is a first lens group in the refractive optical system and a lens system including the optical element Lp, and which is arranged toward a reduction side of the optical element Lp, is the second lens group in the refractive optical system. Accordingly, it is possible to excellently correct various aberrations generated in reflective optical system R. 
     Further, the first lens group may substantially consist of two lenses of an aspheric lens having negative refractive power and an aspheric lens having positive refractive power in this order from the magnification side. Alternatively, the first lens group may substantially consist of an aspheric lens having negative refractive power. However, when the first lens group substantially consists of two lenses of a negative aspheric lens and a positive aspheric lens, it is possible to more excellently correct various aberrations generated in reflective optical system R. When the first lens group substantially consists of an aspheric lens having negative refractive power, it is possible to simplify the optical system, and to suppress a level of difficulty in assembly and adjustment. In the embodiment of the present invention, the first lens group substantially consists of two lenses of aspheric lens L 12  having negative refractive power and aspheric lens L 11  having positive refractive power in this order from the magnification side. 
     It is desirable that a most-magnification-side surface of optical element Lp has a convex shape toward the magnification side. Further, it is desirable that a most-reduction-side surface of optical element Lp has a concave shape facing the reduction side. Accordingly, it is possible to excellently correct various aberrations generated in reflective optical system R. 
     Further, it is desirable that optical element Lp has negative refractive power. Accordingly, it becomes possible to excellently correct various aberrations generated in reflective optical system R while displaying a magnified video image in sufficient size on a screen at a short projection distance. 
     Further, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a positive lens with its convex surface facing the magnification side, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power. Alternatively, the second lens group may substantially consist of a 2a-th lens group, in which optical element Lp, a negative lens with its concave surface facing the magnification side, a positive lens with its convex surface facing the reduction side and at least one positive lens having biconvex shape are arranged in this order from the magnification side, and a 2b-th lens group arranged toward the reduction side of the 2a-th lens group, and in which a most-magnification-side optical element (a single lens or a cemented lens) has negative refractive power. Accordingly, it becomes possible to excellently correct various aberrations generated in reflective optical system R. 
     It is desirable that the 2a-th lens group, as a whole, has positive refractive power. Further, it is desirable that the 2b-th lens group, as a whole, has positive refractive power. Further, it is desirable that the 2b-th lens group includes at least one aspheric lens. Accordingly, it becomes possible to excellently correct various aberrations generated in reflective optical system R. 
       FIG. 1  illustrates an example in which optical member PP is arranged between image display device D and the refractive optical system. Instead of arranging various filters, such as a low-pass filter and a filter that cuts a specific wavelength band, and the like between image display device D and the refractive optical system, the various filters and the like may be arranged between lenses. Alternatively, a coating having a similar action to the various filters and the like may be applied to a lens surface of one of the lenses, or a multi-layer coating for protection, an anti-reflection coating for reducing ghost light or the like, and the like may be applied to a lens surface of one of the lenses. 
     Next, numerical value examples of the projection optical system of the present invention will be described. 
     First, a projection optical system in Example 1 will be described.  FIG. 1  is a cross section illustrating the structure of the projection optical system in Example 1. In  FIG. 1  and  FIGS. 2 through 17  corresponding to Examples 2 through 17, which will be described later, optical member PP is also illustrated, and the left side of the diagrams is a reduction side, and the right side of the diagrams is a magnification side. 
     Table 1 shows basic lens data on the projection optical system in Example 1. Table 2 shows data about specification, and Table 3 shows data about aspherical surface coefficients. Next, the meanings of signs in the tables will be described using the tables in Example 1, as an example. The meanings are basically similar in Examples 2 through 17. 
     In the lens data of Table 1, column Si shows the surface number of the i-th surface (i=1, 2, 3, . . . ) when the most-reduction-side surface of composition elements is the first surface, and surface numbers sequentially increase toward the magnification side. Column Ri shows the curvature radius of the i-th surface, and column Di shows a distance between the i-th surface and the (i+1) th surface on optical axis Z. Column Ndj shows the refractive index of the j-th optical element (j=1, 2, 3, . . . ) for d-line (wavelength is 587.6 nm). The most reduction-side optical element is the first optical element, and the number j sequentially increases toward the magnification side. The column νdj shows the Abbe number of also the j-th optical element for d-line (wavelength is 587.6 nm). 
     Here, the sign of a curvature radius is positive when a surface shape is convex toward the reduction side, and negative when a surface shape is convex toward the magnification side. The basic lens data show data including optical member PP. 
     The data about specification in Table 2 show the value of F-number FNo. and the value of full angle of view 2ω. 
     In the basic lens data and data about specification, degree is used as the unit of an angle, and mm is used as the unit of a length. Since an optical system is usable by being proportionally enlarged or proportionally reduced, other appropriate units may be used. 
     In the lens data of Table 1, marks * are attached to the surface numbers of aspherical surfaces. Further, the numerical value of a paraxial curvature radius is shown as a curvature radius of an aspherical surface. The data about aspherical surface coefficients in Table 3 show surface numbers Si of aspherical surfaces and aspherical surface coefficients about the aspherical surfaces. The aspherical surface coefficients are values of coefficients KA, Am (m=4, 6, 8, . . . 20) in an aspherical surface equation represented by the following expression (A): 
         Zd=C·h   2 /{1+(1 −KA·C   2   ·h   2 ) 1/2   }+ΣAm·h   m   (A), where
 
     Zd: the depth of an aspherical surface (the length of a perpendicular from a point on the aspherical surface at height h to a flat plane that contacts with the vertex of the aspherical surface and is perpendicular to the optical axis), 
     h: a height (a length from the optical axis), 
     C: a reciprocal of a paraxial curvature radius, and 
     KA, Am: aspherical surface coefficients (m=3, 4, 5, . . . 20). 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 EXAMPLE 1 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURV- 
                 Di 
                 (RE- 
                 νdj 
               
               
                 (SURFACE 
                 ATURE 
                 (SURFACE 
                 FRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.6987 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 19.9000 
                   
                   
               
               
                 4 
                 24.6586 
                 10.0091 
                 1.65960 
                 48.29 
               
               
                 5 
                 −15.6789 
                 1.0000 
                 1.80000 
                 48.00 
               
               
                 6 
                 15.7283 
                 0.1999 
                   
                   
               
               
                 7 
                 14.1414 
                 4.7519 
                 1.58587 
                 49.98 
               
               
                 8 
                 −38.7087 
                 1.9998 
                   
                   
               
               
                 9 
                 18.0461 
                 9.0902 
                 1.49007 
                 65.38 
               
               
                 10 
                 −12.2005 
                 0.1200 
                   
                   
               
               
                 11 
                 −11.5906 
                 1.0002 
                 1.90366 
                 31.31 
               
               
                 12 
                 65.2415 
                 3.4718 
                   
                   
               
               
                 13 
                 85.7210 
                 4.6078 
                 1.55557 
                 62.86 
               
               
                 14 
                 −25.2757 
                 4.9873 
                   
                   
               
               
                 15 
                 37.6964 
                 5.3799 
                 1.63028 
                 40.80 
               
               
                 16 
                 −57.2505 
                 14.6255 
                   
                   
               
               
                 17 
                 −20.3607 
                 2.6358 
                 1.55831 
                 62.76 
               
               
                 18 
                 40.3593 
                 1.0481 
                   
                   
               
               
                 19 
                 59.8280 
                 7.7872 
                 1.61102 
                 36.90 
               
               
                 20 
                 −30.9203 
                 4.6847 
                   
                   
               
               
                 21 
                 −17.8928 
                 1.7010 
                 1.75054 
                 49.35 
               
               
                 22 
                 −40.0374 
                 14.1767 
                   
                   
               
               
                 *23 
                 −13.1426 
                 5.0014 
                 1.49100 
                 57.58 
               
               
                 *24 
                 −10.8105 
                 29.9527 
                   
                   
               
               
                 *25 
                 −14.3833 
                 6.0000 
                 1.49100 
                 57.58 
               
               
                 *26 
                 −15301.9711 
                 25.7890 
                   
                   
               
               
                 *27 
                 34.0756 
                 −240.0000 
                 REFLECTION 
                   
               
               
                   
                   
                   
                 SURFACE 
                   
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 EXAMPLE 1 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.50 
               
               
                   
                 2ω[°] 
                 156.10 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 EXAMPLE 1 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 −4.6412961E−02 
               
               
                   
                 A3 
                 −3.2780215E−03 
               
               
                   
                 A4 
                 6.2262301E−04 
               
               
                   
                 A5 
                 −5.7798269E−06 
               
               
                   
                 A6 
                 −6.4964585E−06 
               
               
                   
                 A7 
                 4.2948136E−07 
               
               
                   
                 A8 
                 1.5028564E−08 
               
               
                   
                 A9 
                 −2.7888875E−09 
               
               
                   
                 A10 
                 9.6125863E−11 
               
               
                   
                 A11 
                 1.4890607E−12 
               
               
                   
                 A12 
                 −1.1758397E−13 
               
               
                   
                 A13 
                 −9.1203310E−16 
               
               
                   
                 A14 
                 −6.5840553E−17 
               
               
                   
                 A15 
                 1.2272777E−17 
               
               
                   
                 A16 
                 −2.6452600E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 1.6532179E−01 
               
               
                   
                 A3 
                 −2.1512871E−03 
               
               
                   
                 A4 
                 3.5886722E−04 
               
               
                   
                 A5 
                 −3.0768866E−05 
               
               
                   
                 A6 
                 9.3696535E−06 
               
               
                   
                 A7 
                 −1.7389268E−06 
               
               
                   
                 A8 
                 1.5561909E−07 
               
               
                   
                 A9 
                 −6.8935855E−09 
               
               
                   
                 A10 
                 6.6355189E−11 
               
               
                   
                 A11 
                 9.4534688E−12 
               
               
                   
                 A12 
                 −4.5745988E−13 
               
               
                   
                 A13 
                 −2.7719524E−15 
               
               
                   
                 A14 
                 8.9862999E−16 
               
               
                   
                 A15 
                 −2.9125420E−17 
               
               
                   
                 A16 
                 3.1248281E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
                   
               
               
                   
                 KA 
                 −5.0166516E−03 
               
               
                   
                 A3 
                 −2.6609567E−03 
               
               
                   
                 A4 
                 5.2802485E−04 
               
               
                   
                 A5 
                 −2.7498193E−05 
               
               
                   
                 A6 
                 −7.0818516E−07 
               
               
                   
                 A7 
                 6.2838432E−08 
               
               
                   
                 A8 
                 2.9559652E−09 
               
               
                   
                 A9 
                 −2.3843579E−10 
               
               
                   
                 A10 
                 3.8266963E−13 
               
               
                   
                 A11 
                 2.3662850E−13 
               
               
                   
                 A12 
                 −2.4988875E−15 
               
               
                   
                 A13 
                 −1.4401058E−16 
               
               
                   
                 A14 
                 3.6438603E−18 
               
               
                   
                 A15 
                 −2.0672982E−20 
               
               
                   
                 A16 
                 −6.8018496E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
                   
               
               
                   
                 KA 
                 1.2663467E+05 
               
               
                   
                 A3 
                 −9.1565413E−04 
               
               
                   
                 A4 
                 2.8728395E−05 
               
               
                   
                 A5 
                 −8.3301551E−07 
               
               
                   
                 A6 
                 −1.3025401E−07 
               
               
                   
                 A7 
                 8.8433551E−09 
               
               
                   
                 A8 
                 −1.0064131E−10 
               
               
                   
                 A9 
                 −2.5674450E−12 
               
               
                   
                 A10 
                 −1.2063025E−14 
               
               
                   
                 A11 
                 2.8003831E−15 
               
               
                   
                 A12 
                 −3.1931820E−17 
               
               
                   
                 A13 
                 −4.6032388E−19 
               
               
                   
                 A14 
                 1.5503710E−20 
               
               
                   
                 A15 
                 −1.9170291E−22 
               
               
                   
                 A16 
                 1.0120978E−24 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 27 
               
               
                   
                   
               
               
                   
                 KA 
                 −3.5372007E+00 
               
               
                   
                 A3 
                 3.6765137E−05 
               
               
                   
                 A4 
                 −1.0325833E−06 
               
               
                   
                 A5 
                 8.6090225E−09 
               
               
                   
                 A6 
                 −1.3764971E−10 
               
               
                   
                 A7 
                 3.6950491E−12 
               
               
                   
                 A8 
                 −2.7956965E−14 
               
               
                   
                 A9 
                 −2.8233783E−16 
               
               
                   
                 A10 
                 4.5775758E−18 
               
               
                   
                 A11 
                 3.8203822E−21 
               
               
                   
                 A12 
                 −3.8319158E−22 
               
               
                   
                 A13 
                 2.2811185E−24 
               
               
                   
                 A14 
                 −1.3780969E−27 
               
               
                   
                 A15 
                 −2.6728962E−29 
               
               
                   
                 A16 
                 6.6325098E−32 
               
               
                   
                   
               
            
           
         
       
     
     In Example 1, Surface 22 through Surface 21 are optical element Lp, Surface 26 through Surface 23 are a first lens group, Surface 22 through Surface 13 are a 2a-th lens group, and Surface 12 through Surface 4 are a 2b-th lens group. 
       FIG. 18  illustrates distortion performance of the projection optical system in Example 1, and  FIG. 35  illustrates spot performance of the projection optical system in Example 1. Evaluation points in the diagram illustrating spot performance correspond to point 1 through point 15 in  FIG. 52  and  FIG. 53 , and that is similar also in Examples 2 through 17. 
     Next, a projection optical system in Example 2 will be described.  FIG. 2  is a cross section illustrating the structure of the projection optical system in Example 2. Table 4 shows basic lens data on the projection optical system in Example 2, and Table 5 shows data about specification. Table 6 shows data about aspherical surface coefficients.  FIG. 19  is a diagram illustrating distortion performance, and  FIG. 36  is a diagram illustrating spot performance. 
     In Example 2, Surface 22 through Surface 21 are optical element Lp, Surface 26 through Surface 23 are a first lens group, Surface 22 through Surface 13 are a 2a-th lens group, and Surface 12 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 EXAMPLE 2 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURV- 
                 Di 
                 (RE- 
                 νdj 
               
               
                 (SURFACE 
                 ATURE 
                 (SURFACE 
                 FRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.7012 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 20.0002 
                   
                   
               
               
                 4 
                 23.7903 
                 6.9435 
                 1.71976 
                 40.01 
               
               
                 5 
                 −16.2245 
                 1.2008 
                 1.80001 
                 48.00 
               
               
                 6 
                 13.9036 
                 0.1998 
                   
                   
               
               
                 7 
                 13.1492 
                 5.0686 
                 1.55294 
                 62.96 
               
               
                 8 
                 −42.5195 
                 2.0002 
                   
                   
               
               
                 9 
                 18.9943 
                 10.1632 
                 1.48999 
                 65.39 
               
               
                 10 
                 −12.5556 
                 0.1491 
                   
                   
               
               
                 11 
                 −11.7473 
                 1.5008 
                 1.80001 
                 28.16 
               
               
                 12 
                 65.9312 
                 5.2755 
                   
                   
               
               
                 13 
                 56.7245 
                 4.8304 
                 1.53701 
                 63.58 
               
               
                 14 
                 −32.8901 
                 0.1990 
                   
                   
               
               
                 15 
                 41.9824 
                 5.0841 
                 1.58194 
                 39.81 
               
               
                 16 
                 −51.2078 
                 13.6442 
                   
                   
               
               
                 17 
                 −19.4317 
                 1.4998 
                 1.52280 
                 64.12 
               
               
                 18 
                 41.3726 
                 1.4655 
                   
                   
               
               
                 19 
                 90.1560 
                 6.8992 
                 1.67458 
                 31.82 
               
               
                 20 
                 −29.3643 
                 4.4550 
                   
                   
               
               
                 21 
                 −17.0768 
                 1.7007 
                 1.76427 
                 51.57 
               
               
                 22 
                 −40.1439 
                 13.3109 
                   
                   
               
               
                 *23 
                 −13.5347 
                 4.9990 
                 1.49100 
                 57.58 
               
               
                 *24 
                 −10.8237 
                 27.0600 
                   
                   
               
               
                 *25 
                 −15.3393 
                 5.0002 
                 1.49100 
                 57.58 
               
               
                 *26 
                 126.2269 
                 27.3740 
                   
                   
               
               
                 *27 
                 44.1765 
                 −290.0000 
                 REFLECTION 
                   
               
               
                   
                   
                   
                 SURFACE 
                   
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
               
                   
               
               
                 EXAMPLE 2 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                 2ω[°] 
                 153.10 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
               
                   
               
               
                 EXAMPLE 2 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 −6.1194506E−02 
               
               
                   
                 A3 
                 −2.5414362E−03 
               
               
                   
                 A4 
                 5.5231532E−04 
               
               
                   
                 A5 
                 −1.5278226E−05 
               
               
                   
                 A6 
                 −4.9756216E−06 
               
               
                   
                 A7 
                 4.1820671E−07 
               
               
                   
                 A8 
                 7.3790248E−09 
               
               
                   
                 A9 
                 −2.3384664E−09 
               
               
                   
                 A10 
                 9.6482227E−11 
               
               
                   
                 A11 
                 7.3185219E−13 
               
               
                   
                 A12 
                 −1.1947420E−13 
               
               
                   
                 A13 
                 3.7688650E−16 
               
               
                   
                 A14 
                 −3.3157198E−17 
               
               
                   
                 A15 
                 8.4666890E−18 
               
               
                   
                 A16 
                 −1.9786634E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 1.6789111E−01 
               
               
                   
                 A3 
                 −1.7002545E−03 
               
               
                   
                 A4 
                 3.3988322E−04 
               
               
                   
                 A5 
                 −3.5993263E−05 
               
               
                   
                 A6 
                 1.0101722E−05 
               
               
                   
                 A7 
                 −1.8489816E−06 
               
               
                   
                 A8 
                 1.6954470E−07 
               
               
                   
                 A9 
                 −7.6330064E−09 
               
               
                   
                 A10 
                 6.8605228E−11 
               
               
                   
                 A11 
                 1.0760666E−11 
               
               
                   
                 A12 
                 −5.0625644E−13 
               
               
                   
                 A13 
                 −3.3851910E−15 
               
               
                   
                 A14 
                 1.0260264E−15 
               
               
                   
                 A15 
                 −3.3857834E−17 
               
               
                   
                 A16 
                 3.7240880E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.1145789E−02 
               
               
                   
                 A3 
                 −3.1164922E−03 
               
               
                   
                 A4 
                 5.3886174E−04 
               
               
                   
                 A5 
                 −3.0073789E−05 
               
               
                   
                 A6 
                 −6.2682977E−07 
               
               
                   
                 A7 
                 7.3431696E−08 
               
               
                   
                 A8 
                 3.0089777E−09 
               
               
                   
                 A9 
                 −2.8755645E−10 
               
               
                   
                 A10 
                 1.0629670E−12 
               
               
                   
                 A11 
                 2.9732423E−13 
               
               
                   
                 A12 
                 −3.6042557E−15 
               
               
                   
                 A13 
                 −1.8764745E−16 
               
               
                   
                 A14 
                 4.9399102E−18 
               
               
                   
                 A15 
                 −2.6630863E−20 
               
               
                   
                 A16 
                 −1.2444372E−22 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
                   
               
               
                   
                 KA 
                 −1.3092026E+01 
               
               
                   
                 A3 
                 −1.3821578E−03 
               
               
                   
                 A4 
                 3.0252589E−05 
               
               
                   
                 A5 
                 3.8048965E−08 
               
               
                   
                 A6 
                 −1.6581558E−07 
               
               
                   
                 A7 
                 1.0168569E−08 
               
               
                   
                 A8 
                 −1.2622266E−10 
               
               
                   
                 A9 
                 −2.7089593E−12 
               
               
                   
                 A10 
                 −2.7249480E−14 
               
               
                   
                 A11 
                 3.9321784E−15 
               
               
                   
                 A12 
                 −4.6088715E−17 
               
               
                   
                 A13 
                 −6.9749411E−19 
               
               
                   
                 A14 
                 2.5446130E−20 
               
               
                   
                 A15 
                 −3.4239994E−22 
               
               
                   
                 A16 
                 1.9353451E−24 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 27 
               
               
                   
                   
               
               
                   
                 KA 
                 −4.3366875E+00 
               
               
                   
                 A3 
                 5.3926804E−05 
               
               
                   
                 A4 
                 −1.3391705E−06 
               
               
                   
                 A5 
                 9.8200425E−09 
               
               
                   
                 A6 
                 −2.0776567E−10 
               
               
                   
                 A7 
                 6.3809824E−12 
               
               
                   
                 A8 
                 −4.9798883E−14 
               
               
                   
                 A9 
                 −5.6057817E−16 
               
               
                   
                 A10 
                 9.3161027E−18 
               
               
                   
                 A11 
                 9.8245743E−21 
               
               
                   
                 A12 
                 −8.9078606E−22 
               
               
                   
                 A13 
                 5.5840605E−24 
               
               
                   
                 A14 
                 −3.3733947E−27 
               
               
                   
                 A15 
                 −7.5313252E−29 
               
               
                   
                 A16 
                 1.9838590E−31 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 3 will be described.  FIG. 3  is a cross section illustrating the structure of the projection optical system in Example 3. Table 7 shows basic lens data on the projection optical system in Example 3, and Table 8 shows data about specification. Table 9 shows data about aspherical surface coefficients.  FIG. 20  is a diagram illustrating distortion performance, and  FIG. 37  is a diagram illustrating spot performance. 
     In Example 3, Surface 22 through Surface 21 are optical element Lp, Surface 26 through Surface 23 are a first lens group, Surface 22 through Surface 13 are a 2a-th lens group, and Surface 12 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 EXAMPLE 3 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                   
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 Ndj 
                 νdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 (REFRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.7009 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 20.0010 
               
               
                 4 
                 25.5726 
                 6.7309 
                 1.73200 
                 39.48 
               
               
                 5 
                 −15.5584 
                 1.1999 
                 1.80001 
                 48.00 
               
               
                 6 
                 14.3760 
                 0.1991 
               
               
                 7 
                 13.3689 
                 5.0218 
                 1.54418 
                 63.30 
               
               
                 8 
                 −46.6808 
                 2.0002 
               
               
                 9 
                 19.3005 
                 10.4662 
                 1.48999 
                 65.38 
               
               
                 10 
                 −12.4734 
                 0.1490 
               
               
                 11 
                 −11.7144 
                 1.5000 
                 1.80001 
                 27.02 
               
               
                 12 
                 74.6714 
                 5.2910 
               
               
                 13 
                 60.8455 
                 4.8649 
                 1.66531 
                 41.40 
               
               
                 14 
                 −39.1599 
                 0.2005 
               
               
                 15 
                 40.2186 
                 5.3141 
                 1.60466 
                 60.97 
               
               
                 16 
                 −61.0762 
                 11.4801 
               
               
                 17 
                 −23.9550 
                 1.4997 
                 1.52511 
                 64.03 
               
               
                 18 
                 35.2385 
                 1.4771 
               
               
                 19 
                 71.7629 
                 5.3887 
                 1.74446 
                 27.78 
               
               
                 20 
                 −42.9540 
                 5.5497 
               
               
                 21 
                 −15.9111 
                 1.7000 
                 1.71640 
                 55.68 
               
               
                 22 
                 −42.0422 
                 11.2507 
               
               
                 *23 
                 −14.1095 
                 5.0001 
                 1.49100 
                 57.58 
               
               
                 *24 
                 −10.8434 
                 23.5897 
               
               
                 *25 
                 −15.7823 
                 5.1561 
                 1.49100 
                 57.58 
               
               
                 *26 
                 102.6229 
                 29.9990 
               
               
                 *27 
                 54.1512 
                 −345.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 EXAMPLE 3 • SPECIFICATION (d-LINE) 
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                   
               
               
                   
                 2ω[°] 
                 149.90 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 9 
               
               
                   
               
               
                 EXAMPLE 3 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.0639393E−02 
               
               
                   
                 A3 
                 −2.2428175E−03 
               
               
                   
                 A4 
                 7.0894582E−04 
               
               
                   
                 A5 
                 −3.5395657E−05 
               
               
                   
                 A6 
                 −7.5077644E−06 
               
               
                   
                 A7 
                 8.6886666E−07 
               
               
                   
                 A8 
                 1.1665169E−08 
               
               
                   
                 A9 
                 −5.7474932E−09 
               
               
                   
                 A10 
                 2.1668961E−10 
               
               
                   
                 A11 
                 6.1721628E−12 
               
               
                   
                 A12 
                 −3.7936224E−13 
               
               
                   
                 A13 
                 −6.7067101E−15 
               
               
                   
                 A14 
                 1.0982016E−16 
               
               
                   
                 A15 
                 2.9753518E−17 
               
               
                   
                 A16 
                 −7.6815219E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 1.7672298E−01 
               
               
                   
                 A3 
                 −1.8281729E−03 
               
               
                   
                 A4 
                 4.8935302E−04 
               
               
                   
                 A5 
                 −4.0200405E−05 
               
               
                   
                 A6 
                 7.8115439E−06 
               
               
                   
                 A7 
                 −1.7384392E−06 
               
               
                   
                 A8 
                 1.8293213E−07 
               
               
                   
                 A9 
                 −8.1403441E−09 
               
               
                   
                 A10 
                 9.9820032E−12 
               
               
                   
                 A11 
                 1.2464099E−11 
               
               
                   
                 A12 
                 −3.8041398E−13 
               
               
                   
                 A13 
                 −6.0465040E−15 
               
               
                   
                 A14 
                 8.8171579E−16 
               
               
                   
                 A15 
                 −3.1554069E−17 
               
               
                   
                 A16 
                 4.1570146E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
                   
               
               
                   
                 KA 
                 −9.1213395E−02 
               
               
                   
                 A3 
                 −3.1739315E−03 
               
               
                   
                 A4 
                 6.1510088E−04 
               
               
                   
                 A5 
                 −4.2429242E−05 
               
               
                   
                 A6 
                 −5.5034644E−07 
               
               
                   
                 A7 
                 1.1268926E−07 
               
               
                   
                 A8 
                 4.2515689E−09 
               
               
                   
                 A9 
                 −5.1007821E−10 
               
               
                   
                 A10 
                 3.1856576E−12 
               
               
                   
                 A11 
                 6.0179609E−13 
               
               
                   
                 A12 
                 −8.7928372E−15 
               
               
                   
                 A13 
                 −4.3662096E−16 
               
               
                   
                 A14 
                 1.2814644E−17 
               
               
                   
                 A15 
                 −7.4196538E−20 
               
               
                   
                 A16 
                 −3.9318034E−22 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
                   
               
               
                   
                 KA 
                 5.9764602E+00 
               
               
                   
                 A3 
                 −1.1980257E−03 
               
               
                   
                 A4 
                 6.5886160E−06 
               
               
                   
                 A5 
                 −2.1395820E−08 
               
               
                   
                 A6 
                 −1.6486329E−07 
               
               
                   
                 A7 
                 1.5717320E−08 
               
               
                   
                 A8 
                 −3.9497973E−10 
               
               
                   
                 A9 
                 −1.3833639E−12 
               
               
                   
                 A10 
                 5.4003304E−14 
               
               
                   
                 A11 
                 6.4540563E−15 
               
               
                   
                 A12 
                 −1.7110134E−16 
               
               
                   
                 A13 
                 −9.2439125E−19 
               
               
                   
                 A14 
                 9.0244609E−20 
               
               
                   
                 A15 
                 −1.3067207E−21 
               
               
                   
                 A16 
                 6.2798026E−24 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 27 
               
               
                   
                   
               
               
                   
                 KA 
                 −6.2052363E+00 
               
               
                   
                 A3 
                 7.2391590E−05 
               
               
                   
                 A4 
                 −1.5134281E−06 
               
               
                   
                 A5 
                 8.0683826E−09 
               
               
                   
                 A6 
                 −2.6461014E−10 
               
               
                   
                 A7 
                 9.2070275E−12 
               
               
                   
                 A8 
                 −7.1848366E−14 
               
               
                   
                 A9 
                 −8.7571201E−16 
               
               
                   
                 A10 
                 1.4440586E−17 
               
               
                   
                 A11 
                 1.8591265E−20 
               
               
                   
                 A12 
                 −1.4850227E−21 
               
               
                   
                 A13 
                 9.4753676E−24 
               
               
                   
                 A14 
                 −5.3295272E−27 
               
               
                   
                 A15 
                 −1.3916960E−28 
               
               
                   
                 A16 
                 3.7601655E−31 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 4 will be described.  FIG. 4  is a cross section illustrating the structure of the projection optical system in Example 4. Table 10 shows basic lens data on the projection optical system in Example 4, and Table 11 shows data about specification. Table 12 shows data about aspherical surface coefficients.  FIG. 21  is a diagram illustrating distortion performance, and  FIG. 38  is a diagram illustrating spot performance. 
     In Example 4, Surface 18 through Surface 17 are optical element Lp, Surface 22 through Surface 19 are a first lens group, Surface 18 through Surface 11 are a 2a-th lens group, and Surface 10 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 EXAMPLE 4 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                   
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 Ndj 
                 νdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 (REFRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.7087 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 20.0008 
               
               
                 4 
                 25.9189 
                 7.5621 
                 1.80001 
                 48.00 
               
               
                 5 
                 8.3415 
                 6.0621 
                 1.68841 
                 57.08 
               
               
                 6 
                 −225.5059 
                 6.2257 
               
               
                 7 
                 23.4804 
                 4.9370 
                 1.57886 
                 61.97 
               
               
                 8 
                 −14.0217 
                 0.9494 
               
               
                 9 
                 −13.0557 
                 1.5004 
                 1.68892 
                 30.79 
               
               
                 10 
                 43.3546 
                 7.4113 
               
               
                 11 
                 41.9575 
                 5.8914 
                 1.75513 
                 45.36 
               
               
                 12 
                 −44.8569 
                 7.7187 
               
               
                 13 
                 120.1457 
                 4.7104 
                 1.61001 
                 37.00 
               
               
                 14 
                 −44.2753 
                 1.7754 
               
               
                 15 
                 −25.7538 
                 1.5007 
                 1.51499 
                 64.42 
               
               
                 16 
                 326.9731 
                 10.7972 
               
               
                 17 
                 −16.1641 
                 1.7005 
                 1.49804 
                 65.08 
               
               
                 18 
                 −45.0924 
                 8.7789 
               
               
                 *19 
                 −12.6516 
                 5.2032 
                 1.49100 
                 57.58 
               
               
                 *20 
                 −9.3356 
                 16.1991 
               
               
                 *21 
                 −21.0963 
                 5.9848 
                 1.49100 
                 57.58 
               
               
                 *22 
                 22.8430 
                 35.1061 
               
               
                 *23 
                 57.4912 
                 −425.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 40.0 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 EXAMPLE 4 • SPECIFICATION (d-LINE) 
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.50 
               
               
                   
                   
               
               
                   
                 2ω[°] 
                 144.80 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
               
                   
               
               
                 EXAMPLE 4 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 19 
               
               
                   
                   
               
               
                   
                 KA 
                 −6.7156234E−02 
               
               
                   
                 A3 
                 1.0567713E−03 
               
               
                   
                 A4 
                 1.9219394E−04 
               
               
                   
                 A5 
                 −3.5906268E−05 
               
               
                   
                 A6 
                 −8.5470585E−07 
               
               
                   
                 A7 
                 5.6451265E−07 
               
               
                   
                 A8 
                 −2.0566226E−08 
               
               
                   
                 A9 
                 −3.2759567E−09 
               
               
                   
                 A10 
                 2.6972146E−10 
               
               
                   
                 A11 
                 −1.4475486E−12 
               
               
                   
                 A12 
                 −3.7746164E−13 
               
               
                   
                 A13 
                 4.9580039E−15 
               
               
                   
                 A14 
                 4.9548202E−18 
               
               
                   
                 A15 
                 2.0541125E−17 
               
               
                   
                 A16 
                 −5.9640374E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 20 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0579492E−01 
               
               
                   
                 A3 
                 2.5017462E−04 
               
               
                   
                 A4 
                 3.4537062E−04 
               
               
                   
                 A5 
                 −5.5802286E−05 
               
               
                   
                 A6 
                 7.9112290E−06 
               
               
                   
                 A7 
                 −1.1651071E−06 
               
               
                   
                 A8 
                 1.2252480E−07 
               
               
                   
                 A9 
                 −6.2224057E−09 
               
               
                   
                 A10 
                 3.7564237E−11 
               
               
                   
                 A11 
                 9.0614032E−12 
               
               
                   
                 A12 
                 −2.8240213E−13 
               
               
                   
                 A13 
                 −4.6937030E−15 
               
               
                   
                 A14 
                 5.4150234E−16 
               
               
                   
                 A15 
                 −1.6898556E−17 
               
               
                   
                 A16 
                 2.0937344E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 21 
               
               
                   
                   
               
               
                   
                 KA 
                 3.9545077E−01 
               
               
                   
                 A3 
                 −2.2688757E−03 
               
               
                   
                 A4 
                 1.5752495E−04 
               
               
                   
                 A5 
                 −8.8038289E−06 
               
               
                   
                 A6 
                 7.0147962E−08 
               
               
                   
                 A7 
                 9.4251735E−09 
               
               
                   
                 A8 
                 9.5959499E−10 
               
               
                   
                 A9 
                 −7.0382801E−11 
               
               
                   
                 A10 
                 1.3800570E−13 
               
               
                   
                 A11 
                 6.2556412E−14 
               
               
                   
                 A12 
                 −5.7014117E−16 
               
               
                   
                 A13 
                 −3.4866746E−17 
               
               
                   
                 A14 
                 8.0807199E−19 
               
               
                   
                 A15 
                 −5.2545272E−21 
               
               
                   
                 A16 
                 5.0591645E−24 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 22 
               
               
                   
                   
               
               
                   
                 KA 
                 −1.4636230E+00 
               
               
                   
                 A3 
                 −3.8320839E−03 
               
               
                   
                 A4 
                 1.3504916E−04 
               
               
                   
                 A5 
                 3.3822783E−06 
               
               
                   
                 A6 
                 −6.3274316E−07 
               
               
                   
                 A7 
                 3.1103619E−08 
               
               
                   
                 A8 
                 −6.2754133E−10 
               
               
                   
                 A9 
                 −2.7111426E−13 
               
               
                   
                 A10 
                 −3.0866385E−14 
               
               
                   
                 A11 
                 2.0258915E−14 
               
               
                   
                 A12 
                 −6.3486489E−16 
               
               
                   
                 A13 
                 −3.2260850E−18 
               
               
                   
                 A14 
                 4.5398157E−19 
               
               
                   
                 A15 
                 −7.3492347E−21 
               
               
                   
                 A16 
                 3.5784190E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 −4.3689790E+00 
               
               
                   
                 A3 
                 2.7225351E−05 
               
               
                   
                 A4 
                 −8.7775940E−07 
               
               
                   
                 A5 
                 1.7257081E−08 
               
               
                   
                 A6 
                 −7.5182563E−10 
               
               
                   
                 A7 
                 1.7040996E−11 
               
               
                   
                 A8 
                 −9.1515104E−14 
               
               
                   
                 A9 
                 −2.0808430E−15 
               
               
                   
                 A10 
                 2.8724682E−17 
               
               
                   
                 A11 
                 7.3195980E−20 
               
               
                   
                 A12 
                 −3.6670401E−21 
               
               
                   
                 A13 
                 2.4143458E−23 
               
               
                   
                 A14 
                 −1.3140987E−26 
               
               
                   
                 A15 
                 −4.1509346E−28 
               
               
                   
                 A16 
                 1.2055245E−30 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 5 will be described.  FIG. 5  is a cross section illustrating the structure of the projection optical system in Example 5. Table 13 shows basic lens data on the projection optical system in Example 5, and Table 14 shows data about specification. Table 15 shows data about aspherical surface coefficients.  FIG. 22  is a diagram illustrating distortion performance, and  FIG. 39  is a diagram illustrating spot performance. 
     In Example 5, Surface 23 through Surface 22 are optical element Lp, Surface 25 through Surface 24 are a first lens group, Surface 23 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                 EXAMPLE 5 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                   
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 Ndj 
                 νdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 (REFRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.7064 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 23.5000 
               
               
                 4 
                 24.3572 
                 5.9036 
                 1.48749 
                 70.23 
               
               
                 5 
                 −11.7048 
                 0.0397 
               
               
                 6 
                 −11.4784 
                 1.1360 
                 1.83400 
                 37.16 
               
               
                 7 
                 41.3595 
                 0.2001 
               
               
                 *8 
                 17.6321 
                 5.9987 
                 1.58313 
                 59.38 
               
               
                 *9 
                 −14.7819 
                 0.2008 
               
               
                 10 
                 532.1221 
                 7.4349 
                 1.51633 
                 64.14 
               
               
                 11 
                 −11.4305 
                 0.0604 
               
               
                 12 
                 −11.2711 
                 1.0506 
                 1.78590 
                 44.20 
               
               
                 13 
                 30.5625 
                 0.9942 
               
               
                 14 
                 57.7667 
                 14.2840 
                 1.51742 
                 52.43 
               
               
                 15 
                 −19.1849 
                 21.2107 
               
               
                 16 
                 120.1641 
                 8.1224 
                 1.80518 
                 25.42 
               
               
                 17 
                 −55.7119 
                 1.8827 
               
               
                 18 
                 36.4802 
                 6.1085 
                 1.80518 
                 25.42 
               
               
                 19 
                 167.9520 
                 2.1727 
               
               
                 20 
                 −144.0455 
                 1.3991 
                 1.80518 
                 25.42 
               
               
                 21 
                 24.6524 
                 14.7685 
               
               
                 22 
                 −18.4764 
                 5.4618 
                 1.84666 
                 23.78 
               
               
                 23 
                 −60.6146 
                 18.2285 
               
               
                 *24 
                 15.0773 
                 7.0000 
                 1.49100 
                 57.58 
               
               
                 *25 
                 9.2087 
                 51.3833 
               
               
                 *26 
                 113.6259 
                 −562.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 30.2 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 EXAMPLE 5 • SPECIFICATION (d-LINE) 
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                   
               
               
                   
                 2ω[°] 
                 140.20 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 15 
               
               
                   
               
               
                 EXAMPLE 5 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 8 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
               
               
                   
                 A4 
                 −5.8646571E−05 
               
               
                   
                 A6 
                 3.0074427E−07 
               
               
                   
                 A8 
                 1.0977627E−09 
               
               
                   
                 A10 
                 −3.0481514E−12 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 9 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
               
               
                   
                 A4 
                 3.0060642E−05 
               
               
                   
                 A6 
                 5.3583142E−08 
               
               
                   
                 A8 
                 1.9272085E−09 
               
               
                   
                 A10 
                 2.8311516E−11 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 −4.8530596E+00 
               
               
                   
                 A3 
                 −6.8078736E−04 
               
               
                   
                 A4 
                 −1.8886971E−05 
               
               
                   
                 A5 
                 −1.3974903E−06 
               
               
                   
                 A6 
                 −4.5172871E−08 
               
               
                   
                 A7 
                 1.1636985E−08 
               
               
                   
                 A8 
                 3.2713625E−11 
               
               
                   
                 A9 
                 −2.8750701E−11 
               
               
                   
                 A10 
                 4.2833732E−13 
               
               
                   
                 A11 
                 1.4527379E−14 
               
               
                   
                 A12 
                 5.4481976E−17 
               
               
                   
                 A13 
                 −1.2091389E−17 
               
               
                   
                 A14 
                 −2.3255189E−19 
               
               
                   
                 A15 
                 1.2626231E−20 
               
               
                   
                 A16 
                 −1.1360084E−22 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.7478619E+00 
               
               
                   
                 A3 
                 −8.4342662E−05 
               
               
                   
                 A4 
                 −7.0929113E−05 
               
               
                   
                 A5 
                 1.1930934E−06 
               
               
                   
                 A6 
                 1.3015805E−07 
               
               
                   
                 A7 
                 −5.7260652E−10 
               
               
                   
                 A8 
                 −4.9222461E−10 
               
               
                   
                 A9 
                 2.0850003E−11 
               
               
                   
                 A10 
                 −2.1174948E−13 
               
               
                   
                 A11 
                 −2.5709636E−15 
               
               
                   
                 A12 
                 −2.2162726E−17 
               
               
                   
                 A13 
                 3.8373323E−19 
               
               
                   
                 A14 
                 1.2458051E−19 
               
               
                   
                 A15 
                 −3.5196617E−21 
               
               
                   
                 A16 
                 2.7900258E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
                   
               
               
                   
                 KA 
                 −1.0143512E+01 
               
               
                   
                 A3 
                 −9.9531779E−06 
               
               
                   
                 A4 
                 1.2027936E−07 
               
               
                   
                 A5 
                 5.6799538E−09 
               
               
                   
                 A6 
                 −1.2021621E−10 
               
               
                   
                 A7 
                 3.0011813E−12 
               
               
                   
                 A8 
                 −1.5049754E−13 
               
               
                   
                 A9 
                 4.5218697E−15 
               
               
                   
                 A10 
                 −8.7270730E−17 
               
               
                   
                 A11 
                 1.2285732E−18 
               
               
                   
                 A12 
                 −1.2946242E−20 
               
               
                   
                 A13 
                 9.7693647E−23 
               
               
                   
                 A14 
                 −4.8799440E−25 
               
               
                   
                 A15 
                 1.4265937E−27 
               
               
                   
                 A16 
                 −1.8362336E−30 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 6 will be described.  FIG. 6  is a cross section illustrating the structure of the projection optical system in Example 6. Table 16 shows basic lens data on the projection optical system in Example 6, and Table 17 shows data about specification. Table 18 shows data about aspherical surface coefficients.  FIG. 23  is a diagram illustrating distortion performance, and  FIG. 40  is a diagram illustrating spot performance. 
     In Example 6, Surface 21 through Surface 20 are optical element Lp, Surface 23 through Surface 22 are a first lens group, Surface 21 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 16 
               
             
            
               
                   
               
               
                 EXAMPLE 6 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                   
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 Ndj 
                 νdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 (REFRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.7122 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 23.5000 
               
               
                 4 
                 24.2572 
                 5.0038 
                 1.48749 
                 70.23 
               
               
                 5 
                 −11.9259 
                 0.0409 
               
               
                 6 
                 −11.6867 
                 0.9634 
                 1.83400 
                 37.16 
               
               
                 7 
                 41.3064 
                 0.4546 
               
               
                 *8 
                 19.1138 
                 5.9124 
                 1.58313 
                 59.38 
               
               
                 *9 
                 −14.6324 
                 0.1991 
               
               
                 10 
                 167.0780 
                 6.4709 
                 1.48749 
                 70.23 
               
               
                 11 
                 −11.7776 
                 0.0600 
               
               
                 12 
                 −11.5974 
                 1.0501 
                 1.80400 
                 46.58 
               
               
                 13 
                 31.8087 
                 1.3550 
               
               
                 14 
                 59.1257 
                 13.8651 
                 1.49533 
                 64.48 
               
               
                 15 
                 −18.3239 
                 20.6040 
               
               
                 16 
                 126.3462 
                 6.7262 
                 1.79999 
                 25.00 
               
               
                 17 
                 −69.2194 
                 3.9097 
               
               
                 18 
                 27.4705 
                 8.3848 
                 1.51669 
                 64.36 
               
               
                 19 
                 18.8667 
                 16.2428 
               
               
                 20 
                 −18.0070 
                 5.5007 
                 1.83419 
                 24.27 
               
               
                 21 
                 −134.9902 
                 19.1604 
               
               
                 *22 
                 14.0814 
                 7.0001 
                 1.49100 
                 57.58 
               
               
                 *23 
                 8.9104 
                 52.1050 
               
               
                 *24 
                 119.1422 
                 −562.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 30.2 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 17 
               
             
            
               
                   
               
               
                 EXAMPLE 6 • SPECIFICATION (d-LINE) 
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                   
               
               
                   
                 2ω[°] 
                 140.00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 18 
               
               
                   
               
               
                 EXAMPLE 6 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 8 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
               
               
                   
                 A4 
                 −4.2839566E−05 
               
               
                   
                 A6 
                 1.5838606E−07 
               
               
                   
                 A8 
                 5.3108137E−09 
               
               
                   
                 A10 
                 −1.9739049E−11 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 9 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
               
               
                   
                 A4 
                 3.0351035E−05 
               
               
                   
                 A6 
                 1.4248812E−07 
               
               
                   
                 A8 
                 −7.9831740E−10 
               
               
                   
                 A10 
                 7.3628436E−11 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 22 
               
               
                   
                   
               
               
                   
                 KA 
                 −4.9675509E+00 
               
               
                   
                 A3 
                 −8.3564233E−04 
               
               
                   
                 A4 
                 2.7260068E−06 
               
               
                   
                 A5 
                 −1.5162176E−06 
               
               
                   
                 A6 
                 −1.1582365E−07 
               
               
                   
                 A7 
                 1.2896963E−08 
               
               
                   
                 A8 
                 1.4178798E−10 
               
               
                   
                 A9 
                 −3.0636011E−11 
               
               
                   
                 A10 
                 3.1856151E−13 
               
               
                   
                 A11 
                 1.6763884E−14 
               
               
                   
                 A12 
                 7.8227138E−17 
               
               
                   
                 A13 
                 −1.2591173E−17 
               
               
                   
                 A14 
                 −2.1397590E−19 
               
               
                   
                 A15 
                 1.1737565E−20 
               
               
                   
                 A16 
                 −1.0356158E−22 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 −3.1856063E+00 
               
               
                   
                 A3 
                 1.4615400E−04 
               
               
                   
                 A4 
                 −8.0637819E−05 
               
               
                   
                 A5 
                 1.0613018E−06 
               
               
                   
                 A6 
                 1.4639739E−07 
               
               
                   
                 A7 
                 −7.9152457E−10 
               
               
                   
                 A8 
                 −4.8778452E−10 
               
               
                   
                 A9 
                 2.0158050E−11 
               
               
                   
                 A10 
                 −1.9044707E−13 
               
               
                   
                 A11 
                 −2.6270917E−15 
               
               
                   
                 A12 
                 −2.3810326E−17 
               
               
                   
                 A13 
                 4.0749800E−19 
               
               
                   
                 A14 
                 1.1553271E−19 
               
               
                   
                 A15 
                 −3.2263399E−21 
               
               
                   
                 A16 
                 2.5278504E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 −1.1141359E+01 
               
               
                   
                 A3 
                 −1.0024196E−05 
               
               
                   
                 A4 
                 1.2358980E−07 
               
               
                   
                 A5 
                 5.5061450E−09 
               
               
                   
                 A6 
                 −1.2298128E−10 
               
               
                   
                 A7 
                 3.2343199E−12 
               
               
                   
                 A8 
                 −1.6444853E−13 
               
               
                   
                 A9 
                 4.9846709E−15 
               
               
                   
                 A10 
                 −9.6899945E−17 
               
               
                   
                 A11 
                 1.3763157E−18 
               
               
                   
                 A12 
                 −1.4673207E−20 
               
               
                   
                 A13 
                 1.1207577E−22 
               
               
                   
                 A14 
                 −5.6564215E−25 
               
               
                   
                 A15 
                 1.6666037E−27 
               
               
                   
                 A16 
                 −2.1575652E−30 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 7 will be described.  FIG. 7  is a cross section illustrating the structure of the projection optical system in Example 7. Table 19 shows basic lens data on the projection optical system in Example 7, and Table 20 shows data about specification. Table 21 shows data about aspherical surface coefficients.  FIG. 24  is a diagram illustrating distortion performance, and  FIG. 41  is a diagram illustrating spot performance. 
     In Example 7, Surface 23 through Surface 22 are optical element Lp, Surface 27 through Surface 24 are a first lens group, Surface 23 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 19 
               
             
            
               
                   
               
               
                 EXAMPLE 7 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                   
                   
               
               
                 Si 
                 (CURVA- 
                 Di 
                 Ndj 
                 νdj 
               
               
                 (SURFACE 
                 TURE 
                 (SURFACE 
                 (REFRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 1.1436 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 24.0000 
               
               
                 4 
                 26.4352 
                 4.6158 
                 1.48749 
                 70.23 
               
               
                 5 
                 −12.2017 
                 0.0408 
               
               
                 6 
                 −11.9544 
                 0.8998 
                 1.83400 
                 37.16 
               
               
                 7 
                 50.2341 
                 0.2469 
               
               
                 *8 
                 19.7081 
                 6.0697 
                 1.58313 
                 59.38 
               
               
                 *9 
                 −15.5249 
                 0.3641 
               
               
                 10 
                 86.6728 
                 5.7616 
                 1.48749 
                 70.23 
               
               
                 11 
                 −11.9472 
                 0.0594 
               
               
                 12 
                 −11.7832 
                 1.0508 
                 1.80400 
                 46.58 
               
               
                 13 
                 29.8102 
                 0.9315 
               
               
                 14 
                 50.9628 
                 16.0000 
                 1.51633 
                 64.14 
               
               
                 15 
                 −20.8828 
                 20.1857 
               
               
                 16 
                 79.7028 
                 8.4744 
                 1.80000 
                 29.84 
               
               
                 17 
                 −66.9751 
                 4.5035 
               
               
                 18 
                 41.7057 
                 5.4800 
                 1.80518 
                 25.42 
               
               
                 19 
                 233.4703 
                 2.6733 
               
               
                 20 
                 −91.1313 
                 1.3999 
                 1.68893 
                 31.07 
               
               
                 21 
                 23.7989 
                 14.9364 
               
               
                 22 
                 −18.0261 
                 1.9861 
                 1.84666 
                 23.78 
               
               
                 23 
                 −82.9595 
                 8.2553 
               
               
                 *24 
                 −41.5406 
                 5.4696 
                 1.49100 
                 57.58 
               
               
                 *25 
                 −54.9166 
                 10.0230 
               
               
                 *26 
                 7.3049 
                 5.9036 
                 1.49100 
                 57.58 
               
               
                 *27 
                 5.1475 
                 49.6818 
               
               
                 *28 
                 135.0387 
                 −562.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 20 
               
             
            
               
                   
               
               
                 EXAMPLE 7 • SPECIFICATION (d-LINE) 
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                   
               
               
                   
                 2ω[°] 
                 139.70 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 21 
               
               
                   
               
               
                 EXAMPLE 7 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 8 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
               
               
                   
                 A4 
                 −3.6369620E−05 
               
               
                   
                 A6 
                 2.8442859E−07 
               
               
                   
                 A8 
                 −2.2536981E−10 
               
               
                   
                 A10 
                 −2.4002750E−12 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 9 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0000000E+00 
               
               
                   
                 A4 
                 2.2149593E−05 
               
               
                   
                 A6 
                 −6.7326578E−09 
               
               
                   
                 A8 
                 3.0573301E−09 
               
               
                   
                 A10 
                 −3.6453768E−12 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 1.5583500E+00 
               
               
                   
                 A3 
                 −1.5401324E−03 
               
               
                   
                 A4 
                 9.6295783E−05 
               
               
                   
                 A5 
                 1.5917455E−05 
               
               
                   
                 A6 
                 −9.2729971E−07 
               
               
                   
                 A7 
                 −6.5352396E−08 
               
               
                   
                 A8 
                 3.6993206E−09 
               
               
                   
                 A9 
                 1.3928520E−10 
               
               
                   
                 A10 
                 −7.5961829E−12 
               
               
                   
                 A11 
                 −1.6273741E−13 
               
               
                   
                 A12 
                 8.3948834E−15 
               
               
                   
                 A13 
                 9.8648985E−17 
               
               
                   
                 A14 
                 −4.7521895E−18 
               
               
                   
                 A15 
                 −2.4171128E−20 
               
               
                   
                 A16 
                 1.0851097E−21 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
                   
               
               
                   
                 KA 
                 1.2510904E+00 
               
               
                   
                 A3 
                 −2.6851525E−03 
               
               
                   
                 A4 
                 1.0669764E−04 
               
               
                   
                 A5 
                 1.9861296E−05 
               
               
                   
                 A6 
                 −8.5838808E−07 
               
               
                   
                 A7 
                 −6.9757964E−08 
               
               
                   
                 A8 
                 3.1315071E−09 
               
               
                   
                 A9 
                 1.3167122E−10 
               
               
                   
                 A10 
                 −6.0404997E−12 
               
               
                   
                 A11 
                 −1.3718034E−13 
               
               
                   
                 A12 
                 6.4062963E−15 
               
               
                   
                 A13 
                 7.4185264E−17 
               
               
                   
                 A14 
                 −3.5372651E−18 
               
               
                   
                 A15 
                 −1.6271230E−20 
               
               
                   
                 A16 
                 7.9462615E−22 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
                   
               
               
                   
                 KA 
                 −5.6235108E+00 
               
               
                   
                 A3 
                 −2.9333167E−03 
               
               
                   
                 A4 
                 8.3296856E−05 
               
               
                   
                 A5 
                 4.6023512E−06 
               
               
                   
                 A6 
                 −4.5096481E−07 
               
               
                   
                 A7 
                 1.0073123E−09 
               
               
                   
                 A8 
                 8.8563150E−10 
               
               
                   
                 A9 
                 −1.2610404E−11 
               
               
                   
                 A10 
                 −7.2112729E−13 
               
               
                   
                 A11 
                 5.6478789E−15 
               
               
                   
                 A12 
                 6.4584300E−16 
               
               
                   
                 A13 
                 −5.5762994E−18 
               
               
                   
                 A14 
                 −3.1653003E−19 
               
               
                   
                 A15 
                 5.8095791E−21 
               
               
                   
                 A16 
                 −2.2969300E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 27 
               
               
                   
                   
               
               
                   
                 KA 
                 −4.0374968E+00 
               
               
                   
                 A3 
                 −6.5960709E−04 
               
               
                   
                 A4 
                 −4.4331836E−05 
               
               
                   
                 A5 
                 2.2207558E−06 
               
               
                   
                 A6 
                 4.6458610E−08 
               
               
                   
                 A7 
                 −1.8244784E−09 
               
               
                   
                 A8 
                 −2.9177789E−10 
               
               
                   
                 A9 
                 1.6823917E−11 
               
               
                   
                 A10 
                 −2.3813487E−13 
               
               
                   
                 A11 
                 −1.9087294E−15 
               
               
                   
                 A12 
                 1.6682888E−17 
               
               
                   
                 A13 
                 1.6807941E−19 
               
               
                   
                 A14 
                 7.7040757E−20 
               
               
                   
                 A15 
                 −2.2684215E−21 
               
               
                   
                 A16 
                 1.8118812E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 28 
               
               
                   
                   
               
               
                   
                 KA 
                 −1.8325942E+01 
               
               
                   
                 A3 
                 4.6594993E−06 
               
               
                   
                 A4 
                 2.7099017E−07 
               
               
                   
                 A5 
                 −2.4593862E−09 
               
               
                   
                 A6 
                 −9.4890899E−11 
               
               
                   
                 A7 
                 2.2823093E−12 
               
               
                   
                 A8 
                 −4.6562219E−14 
               
               
                   
                 A9 
                 1.1671872E−15 
               
               
                   
                 A10 
                 −2.1804927E−17 
               
               
                   
                 A11 
                 2.7641493E−19 
               
               
                   
                 A12 
                 −2.4781109E−21 
               
               
                   
                 A13 
                 1.5877131E−23 
               
               
                   
                 A14 
                 −6.9267939E−26 
               
               
                   
                 A15 
                 1.8238324E−28 
               
               
                   
                 A16 
                 −2.1615054E−31 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 8 will be described.  FIG. 8  is a cross section illustrating the structure of the projection optical system in Example 8. Table 22 shows basic lens data on the projection optical system in Example 8, and Table 23 shows data about specification. Table 24 shows data about aspherical surface coefficients.  FIG. 25  is a diagram illustrating distortion performance, and  FIG. 42  is a diagram illustrating spot performance. 
     In Example 8, Surface 24 through Surface 22 are optical element Lp, Surface 26 through Surface 25 are a first lens group, Surface 24 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 22 
               
             
            
               
                   
               
               
                 EXAMPLE 8 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                   
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 (REFRACTIVE 
                 νdj 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 (ABBE NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.7027 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 24.0000 
                   
                   
               
               
                 4 
                 25.3362 
                 5.9809 
                 1.51199 
                 64.54 
               
               
                 5 
                 −11.2080 
                 0.0409 
                   
                   
               
               
                 6 
                 −10.9968 
                 0.8991 
                 1.90366 
                 31.31 
               
               
                 7 
                 61.3664 
                 0.2004 
                   
                   
               
               
                 8 
                 21.9589 
                 4.9835 
                 1.56104 
                 50.24 
               
               
                 9 
                 −15.1724 
                 0.1991 
                   
                   
               
               
                 10 
                 34.6386 
                 4.6245 
                 1.51919 
                 51.40 
               
               
                 11 
                 −21.5342 
                 0.9936 
                   
                   
               
               
                 12 
                 −13.5703 
                 1.0492 
                 1.83400 
                 37.16 
               
               
                 13 
                 30.7732 
                 0.8494 
                   
                   
               
               
                 14 
                 53.5248 
                 13.5547 
                 1.56564 
                 44.58 
               
               
                 15 
                 −21.8172 
                 16.7220 
                   
                   
               
               
                 16 
                 149.3213 
                 7.5906 
                 1.80518 
                 25.42 
               
               
                 17 
                 −53.7445 
                 9.1930 
                   
                   
               
               
                 18 
                 35.5435 
                 6.2231 
                 1.80000 
                 29.64 
               
               
                 19 
                 265.5989 
                 2.5746 
                   
                   
               
               
                 20 
                 −80.3130 
                 1.3990 
                 1.80518 
                 25.42 
               
               
                 21 
                 27.4807 
                 14.6970 
                   
                   
               
               
                 *22 
                 −19.7727 
                 0.4010 
                 1.52437 
                 53.67 
               
               
                 23 
                 −19.2203 
                 1.7000 
                 1.80518 
                 25.42 
               
               
                 24 
                 −64.3321 
                 15.4613 
                   
                   
               
               
                 *25 
                 10.3764 
                 7.0009 
                 1.49100 
                 57.58 
               
               
                 *26 
                 6.8379 
                 53.6900 
                   
                   
               
               
                 *27 
                 120.1798 
                 −516.0000 
                 REFLECTION 
                   
               
               
                   
                   
                   
                 SURFACE 
                   
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 23 
               
               
                   
               
               
                 EXAMPLE 8 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                 2ω[°] 
                 139.70 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 24 
               
               
                   
               
               
                 EXAMPLE 8 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 22 
               
               
                   
               
               
                   
                 KA 
                 1.0000000E+00 
               
               
                   
                 A3 
                 0.0000000E+00 
               
               
                   
                 A4 
                 4.3301170E−05 
               
               
                   
                 A5 
                 −3.2557864E−06 
               
               
                   
                 A6 
                 −7.0340177E−08 
               
               
                   
                 A7 
                 7.7847644E−10 
               
               
                   
                 A8 
                 1.8653702E−10 
               
               
                   
                 A9 
                 7.0752174E−12 
               
               
                   
                 A10 
                 2.5778014E−13 
               
               
                   
                 A11 
                 −2.0204305E−14 
               
               
                   
                 A12 
                 −3.3943719E−16 
               
               
                   
                 A13 
                 −1.0284233E−16 
               
               
                   
                 A14 
                 −5.0935247E−18 
               
               
                   
                 A15 
                 1.9504046E−19 
               
               
                   
                 A16 
                 1.3198964E−21 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
               
               
                   
                 KA 
                 −2.0811958E+00 
               
               
                   
                 A3 
                 −1.1519904E−03 
               
               
                   
                 A4 
                 −4.0862512E−05 
               
               
                   
                 A5 
                 −1.0901039E−06 
               
               
                   
                 A6 
                 6.8913160E−08 
               
               
                   
                 A7 
                 1.1016458E−08 
               
               
                   
                 A8 
                 −2.0162098E−10 
               
               
                   
                 A9 
                 −2.3114343E−11 
               
               
                   
                 A10 
                 5.5827689E−13 
               
               
                   
                 A11 
                 1.0899909E−14 
               
               
                   
                 A12 
                 −1.5724241E−16 
               
               
                   
                 A13 
                 −7.2553162E−18 
               
               
                   
                 A14 
                 −6.1150901E−20 
               
               
                   
                 A15 
                 6.7240125E−21 
               
               
                   
                 A16 
                 −6.8609827E−23 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
               
               
                   
                 KA 
                 −1.7389678E+00 
               
               
                   
                 A3 
                 −9.1409111E−04 
               
               
                   
                 A4 
                 −4.5203813E−05 
               
               
                   
                 A5 
                 2.5559318E−06 
               
               
                   
                 A6 
                 5.1169398E−08 
               
               
                   
                 A7 
                 −1.1890333E−09 
               
               
                   
                 A8 
                 −3.8699943E−10 
               
               
                   
                 A9 
                 2.0163039E−11 
               
               
                   
                 A10 
                 −2.7472040E−13 
               
               
                   
                 A11 
                 −1.8935931E−15 
               
               
                   
                 A12 
                 −8.3881513E−19 
               
               
                   
                 A13 
                 1.2646365E−19 
               
               
                   
                 A14 
                 1.1997609E−19 
               
               
                   
                 A15 
                 −3.4318299E−21 
               
               
                   
                 A16 
                 2.7441423E−23 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 27 
               
               
                   
               
               
                   
                 KA 
                 −1.9228012E+01 
               
               
                   
                 A3 
                 2.4033356E−05 
               
               
                   
                 A4 
                 −4.3123308E−07 
               
               
                   
                 A5 
                 −7.6485930E−10 
               
               
                   
                 A6 
                 1.1464411E−10 
               
               
                   
                 A7 
                 3.7338832E−12 
               
               
                   
                 A8 
                 −2.7061878E−13 
               
               
                   
                 A9 
                 7.3336443E−15 
               
               
                   
                 A10 
                 −1.3677378E−16 
               
               
                   
                 A11 
                 2.0250792E−18 
               
               
                   
                 A12 
                 −2.3044680E−20 
               
               
                   
                 A13 
                 1.8483775E−22 
               
               
                   
                 A14 
                 −9.5824880E−25 
               
               
                   
                 A15 
                 2.8556539E−27 
               
               
                   
                 A16 
                 −3.7060729E−30 
               
               
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 9 will be described.  FIG. 9  is a cross section illustrating the structure of the projection optical system in Example 9. Table 25 shows basic lens data on the projection optical system in Example 9, and Table 26 shows data about specification. Table 27 shows data about aspherical surface coefficients.  FIG. 26  is a diagram illustrating distortion performance, and  FIG. 43  is a diagram illustrating spot performance. 
     In Example 9, Surface 25 through Surface 24 are optical element Lp, Surface 29 through Surface 26 are a first lens group, Surface 25 through Surface 14 are a 2a-th lens group, and Surface 13 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 25 
               
             
            
               
                   
               
               
                 EXAMPLE 9 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                   
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 (REFRACTIVE 
                 νdj 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 (ABBE NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.7048 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 24.0000 
                   
                   
               
               
                 4 
                 24.8239 
                 4.3703 
                 1.48749 
                 70.24 
               
               
                 5 
                 −15.3683 
                 0.0402 
                   
                   
               
               
                 6 
                 −15.9011 
                 1.0000 
                 1.80400 
                 46.58 
               
               
                 7 
                 27.7848 
                 0.1990 
                   
                   
               
               
                 8 
                 18.6030 
                 5.0117 
                 1.50581 
                 64.78 
               
               
                 9 
                 −19.1856 
                 0.1999 
                   
                   
               
               
                 10 
                 20.9264 
                 7.1571 
                 1.48749 
                 70.24 
               
               
                 11 
                 −12.1402 
                 0.0608 
                   
                   
               
               
                 12 
                 −11.9689 
                 1.9396 
                 1.80001 
                 43.85 
               
               
                 13 
                 26.3423 
                 0.5600 
                   
                   
               
               
                 14 
                 37.9928 
                 4.1565 
                 1.53060 
                 63.82 
               
               
                 15 
                 −58.8206 
                 13.2720 
                   
                   
               
               
                 16 
                 65.2172 
                 10.0808 
                 1.57193 
                 62.23 
               
               
                 17 
                 −41.7832 
                 0.2002 
                   
                   
               
               
                 18 
                 62.2668 
                 5.8088 
                 1.79443 
                 32.68 
               
               
                 19 
                 −241.9075 
                 13.6843 
                   
                   
               
               
                 20 
                 −27.3434 
                 2.0742 
                 1.51000 
                 53.13 
               
               
                 21 
                 29.1097 
                 4.5987 
                   
                   
               
               
                 22 
                 205.7866 
                 5.5512 
                 1.80000 
                 35.09 
               
               
                 23 
                 −51.6637 
                 5.8130 
                   
                   
               
               
                 24 
                 −20.1641 
                 1.7002 
                 1.84666 
                 23.78 
               
               
                 25 
                 −47.5862 
                 18.7680 
                   
                   
               
               
                 *26 
                 −55.7840 
                 5.0042 
                 1.49100 
                 57.58 
               
               
                 *27 
                 −36.4526 
                 22.7525 
                   
                   
               
               
                 *28 
                 −25.9278 
                 5.0006 
                 1.49100 
                 57.58 
               
               
                 *29 
                 19.4847 
                 30.0000 
                   
                   
               
               
                 *30 
                 94.4520 
                 −430.0000 
                 REFLECTION 
                   
               
               
                   
                   
                   
                 SURFACE 
                   
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 26 
               
               
                   
               
               
                 EXAMPLE 9 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                 2ω[°] 
                 144.80 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 27 
               
               
                   
               
               
                 EXAMPLE 9 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
               
               
                   
                 KA 
                 4.2742769E+00 
               
               
                   
                 A3 
                 −3.0679255E−03 
               
               
                   
                 A4 
                 1.3199878E−04 
               
               
                   
                 A5 
                 −2.1822209E−06 
               
               
                   
                 A6 
                 −7.9313815E−07 
               
               
                   
                 A7 
                 1.0887543E−07 
               
               
                   
                 A8 
                 −2.6572306E−09 
               
               
                   
                 A9 
                 −5.3262036E−10 
               
               
                   
                 A10 
                 3.9437503E−11 
               
               
                   
                 A11 
                 −3.9345972E−13 
               
               
                   
                 A12 
                 −2.7188425E−14 
               
               
                   
                 A13 
                 5.4193605E−16 
               
               
                   
                 A14 
                 −2.5653762E−17 
               
               
                   
                 A15 
                 1.6129763E−18 
               
               
                   
                 A16 
                 −2.5222424E−20 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 27 
               
               
                   
               
               
                   
                 KA 
                 8.4019028E−01 
               
               
                   
                 A3 
                 −1.4161064E−03 
               
               
                   
                 A4 
                 −7.6633531E−05 
               
               
                   
                 A5 
                 −7.2072345E−06 
               
               
                   
                 A6 
                 3.6477353E−06 
               
               
                   
                 A7 
                 −4.1235608E−07 
               
               
                   
                 A8 
                 2.3999573E−08 
               
               
                   
                 A9 
                 −8.3236016E−10 
               
               
                   
                 A10 
                 1.1848177E−11 
               
               
                   
                 A11 
                 6.7342354E−13 
               
               
                   
                 A12 
                 −3.7650201E−14 
               
               
                   
                 A13 
                 −4.6000900E−17 
               
               
                   
                 A14 
                 4.4791608E−17 
               
               
                   
                 A15 
                 −1.1105544E−18 
               
               
                   
                 A16 
                 8.3329621E−21 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 28 
               
               
                   
               
               
                   
                 KA 
                 −3.6940660E+00 
               
               
                   
                 A3 
                 1.2454970E−03 
               
               
                   
                 A4 
                 −4.5013280E−04 
               
               
                   
                 A5 
                 −9.0926391E−06 
               
               
                   
                 A6 
                 2.9038766E−06 
               
               
                   
                 A7 
                 −9.0182168E−08 
               
               
                   
                 A8 
                 7.7883408E−10 
               
               
                   
                 A9 
                 −8.9844580E−11 
               
               
                   
                 A10 
                 2.2275225E−12 
               
               
                   
                 A11 
                 1.5425791E−13 
               
               
                   
                 A12 
                 −3.6275698E−15 
               
               
                   
                 A13 
                 −2.1563571E−16 
               
               
                   
                 A14 
                 9.9890726E−18 
               
               
                   
                 A15 
                 −1.5051643E−19 
               
               
                   
                 A16 
                 7.9845950E−22 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 29 
               
               
                   
               
               
                   
                 KA 
                 −4.9082415E−01 
               
               
                   
                 A3 
                 −4.1301737E−03 
               
               
                   
                 A4 
                 9.0454113E−05 
               
               
                   
                 A5 
                 3.2145474E−05 
               
               
                   
                 A6 
                 −4.6721060E−07 
               
               
                   
                 A7 
                 2.5360824E−08 
               
               
                   
                 A8 
                 −4.1241893E−10 
               
               
                   
                 A9 
                 −5.1046458E−12 
               
               
                   
                 A10 
                 −1.2247544E−13 
               
               
                   
                 A11 
                 1.7277863E−14 
               
               
                   
                 A12 
                 −2.9701064E−16 
               
               
                   
                 A13 
                 −3.7764965E−18 
               
               
                   
                 A14 
                 2.1893241E−19 
               
               
                   
                 A15 
                 −3.6245785E−21 
               
               
                   
                 A16 
                 2.3488105E−23 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 30 
               
               
                   
               
               
                   
                 KA 
                 −2.0882647E+00 
               
               
                   
                 A3 
                 −8.3116592E−05 
               
               
                   
                 A4 
                 1.5285758E−06 
               
               
                   
                 A5 
                 −1.0936649E−08 
               
               
                   
                 A6 
                 −1.7665390E−09 
               
               
                   
                 A7 
                 4.3511488E−11 
               
               
                   
                 A8 
                 −1.3681297E−13 
               
               
                   
                 A9 
                 −6.5213847E−15 
               
               
                   
                 A10 
                 6.6348516E−17 
               
               
                   
                 A11 
                 3.7153014E−19 
               
               
                   
                 A12 
                 −9.7647580E−21 
               
               
                   
                 A13 
                 5.2574189E−23 
               
               
                   
                 A14 
                 2.2682052E−26 
               
               
                   
                 A15 
                 −1.0773951E−27 
               
               
                   
                 A16 
                 2.6966738E−30 
               
               
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 10 will be described.  FIG. 10  is a cross section illustrating the structure of the projection optical system in Example 10. Table 28 shows basic lens data on the projection optical system in Example 10, and Table 29 shows data about specification. Table 30 shows data about aspherical surface coefficients.  FIG. 27  is a diagram illustrating distortion performance, and  FIG. 44  is a diagram illustrating spot performance. 
     In Example 10, Surface 27 through Surface 26 are optical element Lp, Surface 31 through Surface 28 are a first lens group, Surface 27 through Surface 16 are a 2a-th lens group, and Surface 15 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 28 
               
             
            
               
                   
               
               
                 EXAMPLE 10 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                   
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 (REFRACTIVE 
                 νdj 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 (ABBE NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.0111 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 24.0000 
                   
                   
               
               
                 4 
                 39.8387 
                 2.7394 
                 1.67790 
                 55.34 
               
               
                 5 
                 −45.1095 
                 0.6703 
                   
                   
               
               
                 6 
                 −21.3338 
                 1.4820 
                 1.80518 
                 25.42 
               
               
                 7 
                 −50.4092 
                 0.1998 
                   
                   
               
               
                 8 
                 39.8543 
                 4.2090 
                 1.51633 
                 54.14 
               
               
                 9 
                 −12.1664 
                 1.0006 
                 1.77250 
                 49.60 
               
               
                 10 
                 40.1232 
                 0.2000 
                   
                   
               
               
                 11 
                 22.6870 
                 4.8931 
                 1.57099 
                 50.80 
               
               
                 12 
                 −17.3384 
                 0.2006 
                   
                   
               
               
                 13 
                 43.0088 
                 6.1940 
                 1.48749 
                 70.23 
               
               
                 14 
                 −11.7230 
                 1.1610 
                 1.80510 
                 40.92 
               
               
                 15 
                 26.5498 
                 0.5784 
                   
                   
               
               
                 16 
                 37.4859 
                 4.9082 
                 1.51633 
                 64.14 
               
               
                 17 
                 −30.5336 
                 13.6869 
                   
                   
               
               
                 18 
                 95.5747 
                 6.9253 
                 1.72825 
                 28.46 
               
               
                 19 
                 −40.4376 
                 0.4014 
                   
                   
               
               
                 20 
                 43.7848 
                 4.0166 
                 1.51742 
                 52.43 
               
               
                 21 
                 124.1146 
                 7.4964 
                   
                   
               
               
                 22 
                 −47.9497 
                 1.5004 
                 1.62299 
                 58.16 
               
               
                 23 
                 37.0602 
                 7.5053 
                   
                   
               
               
                 *24 
                 −42.6101 
                 4.9120 
                 1.49100 
                 57.58 
               
               
                 *25 
                 −28.3253 
                 12.7739 
                   
                   
               
               
                 26 
                 −23.2771 
                 2.0003 
                 1.80518 
                 25.42 
               
               
                 27 
                 −47.4367 
                 15.1363 
                   
                   
               
               
                 *28 
                 −78.2426 
                 5.4470 
                 1.49100 
                 57.58 
               
               
                 *29 
                 −61.2421 
                 23.0176 
                   
                   
               
               
                 *30 
                 −818.9245 
                 5.0526 
                 1.49100 
                 57.58 
               
               
                 *31 
                 25.3056 
                 31.7038 
                   
                   
               
               
                 *32 
                 61.9999 
                 −290.0000 
                 REFLECTION 
                   
               
               
                   
                   
                   
                 SURFACE 
                   
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 29 
               
               
                   
               
               
                 EXAMPLE 10 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                 2ω[°] 
                 152.70 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 30 
               
               
                   
               
               
                 EXAMPLE 10 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
               
               
                   
                 KA 
                 4.0207962E+00 
               
               
                   
                 A3 
                 −6.2359574E−05 
               
               
                   
                 A4 
                 2.4260210E−05 
               
               
                   
                 A5 
                 3.0315217E−06 
               
               
                   
                 A6 
                 −8.7417236E−07 
               
               
                   
                 A7 
                 −6.8974126E−10 
               
               
                   
                 A8 
                 1.2266829E−08 
               
               
                   
                 A9 
                 −2.1874992E−10 
               
               
                   
                 A10 
                 −8.0518176E−11 
               
               
                   
                 A11 
                 1.5502178E−12 
               
               
                   
                 A12 
                 2.8919120E−13 
               
               
                   
                 A13 
                 −4.6056801E−15 
               
               
                   
                 A14 
                 −5.6744965E−15 
               
               
                   
                 A15 
                 5.1633933E−18 
               
               
                   
                 A16 
                 4.6857766E−19 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
               
               
                   
                 KA 
                 −9.6051245E−01 
               
               
                   
                 A3 
                 −3.8027998E−04 
               
               
                   
                 A4 
                 1.1179819E−04 
               
               
                   
                 A5 
                 −6.2142858E−06 
               
               
                   
                 A6 
                 −1.1736404E−06 
               
               
                   
                 A7 
                 1.3257522E−07 
               
               
                   
                 A8 
                 6.1593066E−09 
               
               
                   
                 A9 
                 −1.0000797E−09 
               
               
                   
                 A10 
                 −4.9879936E−12 
               
               
                   
                 A11 
                 3.6933649E−12 
               
               
                   
                 A12 
                 −6.4827940E−14 
               
               
                   
                 A13 
                 −6.5924532E−15 
               
               
                   
                 A14 
                 2.0139651E−16 
               
               
                   
                 A15 
                 4.9295873E−18 
               
               
                   
                 A16 
                 −1.9084085E−19 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 28 
               
               
                   
               
               
                   
                 KA 
                 7.0965628E+00 
               
               
                   
                 A3 
                 −4.6197923E−03 
               
               
                   
                 A4 
                 1.7413996E−04 
               
               
                   
                 A5 
                 3.5622953E−05 
               
               
                   
                 A6 
                 −2.1533506E−06 
               
               
                   
                 A7 
                 −1.4851853E−07 
               
               
                   
                 A8 
                 8.8928737E−09 
               
               
                   
                 A9 
                 3.5288730E−10 
               
               
                   
                 A10 
                 −1.3487677E−11 
               
               
                   
                 A11 
                 −1.0237058E−12 
               
               
                   
                 A12 
                 3.4187251E−14 
               
               
                   
                 A13 
                 8.4928668E−16 
               
               
                   
                 A14 
                 −3.9240931E−17 
               
               
                   
                 A15 
                 1.7216154E−19 
               
               
                   
                 A16 
                 4.2658955E−21 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 29 
               
               
                   
               
               
                   
                 KA 
                 2.8166231E+00 
               
               
                   
                 A3 
                 −4.2844184E−03 
               
               
                   
                 A4 
                 1.3184318E−04 
               
               
                   
                 A5 
                 1.3746538E−05 
               
               
                   
                 A6 
                 1.9540189E−06 
               
               
                   
                 A7 
                 −4.5661487E−07 
               
               
                   
                 A8 
                 2.7686005E−08 
               
               
                   
                 A9 
                 −6.2578676E−10 
               
               
                   
                 A10 
                 −8.7688938E−13 
               
               
                   
                 A11 
                 4.5769213E−13 
               
               
                   
                 A12 
                 −1.9380766E−14 
               
               
                   
                 A13 
                 4.2420170E−17 
               
               
                   
                 A14 
                 2.9958262E−17 
               
               
                   
                 A15 
                 −9.7725046E−19 
               
               
                   
                 A16 
                 9.5336091E−21 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 30 
               
               
                   
               
               
                   
                 KA 
                 3.3497301E+02 
               
               
                   
                 A3 
                 −4.8854643E−03 
               
               
                   
                 A4 
                 −5.4760381E−05 
               
               
                   
                 A5 
                 1.4991593E−05 
               
               
                   
                 A6 
                 2.6026984E−07 
               
               
                   
                 A7 
                 −4.2855670E−08 
               
               
                   
                 A8 
                 6.6724473E−10 
               
               
                   
                 A9 
                 1.6824790E−11 
               
               
                   
                 A10 
                 −3.4565251E−13 
               
               
                   
                 A11 
                 −4.1952599E−15 
               
               
                   
                 A12 
                 9.6643528E−17 
               
               
                   
                 A13 
                 −3.8039529E−18 
               
               
                   
                 A14 
                 1.9401136E−19 
               
               
                   
                 A15 
                 −3.4328223E−21 
               
               
                   
                 A16 
                 1.9764393E−23 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 31 
               
               
                   
               
               
                   
                 KA 
                 −9.8472941E−01 
               
               
                   
                 A3 
                 −3.5819758E−03 
               
               
                   
                 A4 
                 3.7884687E−05 
               
               
                   
                 A5 
                 5.8341491E−06 
               
               
                   
                 A6 
                 −2.6050838E−07 
               
               
                   
                 A7 
                 6.6284039E−09 
               
               
                   
                 A8 
                 −1.7831210E−10 
               
               
                   
                 A9 
                 4.9407516E−12 
               
               
                   
                 A10 
                 −1.2459978E−13 
               
               
                   
                 A11 
                 3.1126223E−15 
               
               
                   
                 A12 
                 −6.0462218E−17 
               
               
                   
                 A13 
                 −2.8060225E−19 
               
               
                   
                 A14 
                 5.3261544E−20 
               
               
                   
                 A15 
                 −1.1446516E−21 
               
               
                   
                 A16 
                 7.9423996E−24 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 32 
               
               
                   
               
               
                   
                 KA 
                 −2.2510641E+00 
               
               
                   
                 A3 
                 −2.4732774E−05 
               
               
                   
                 A4 
                 7.9262476E−07 
               
               
                   
                 A5 
                 1.6111326E−09 
               
               
                   
                 A6 
                 −8.9009744E−10 
               
               
                   
                 A7 
                 1.8699936E−11 
               
               
                   
                 A8 
                 −5.7013185E−14 
               
               
                   
                 A9 
                 −2.2690220E−15 
               
               
                   
                 A10 
                 2.1896828E−17 
               
               
                   
                 A11 
                 1.0114568E−19 
               
               
                   
                 A12 
                 −2.6031577E−21 
               
               
                   
                 A13 
                 1.3152983E−23 
               
               
                   
                 A14 
                 3.1117842E−27 
               
               
                   
                 A15 
                 −2.1551088E−28 
               
               
                   
                 A16 
                 5.0042640E−31 
               
               
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 11 will be described.  FIG. 11  is a cross section illustrating the structure of the projection optical system in Example 11. Table 31 shows basic lens data on the projection optical system in Example 11, and Table 32 shows data about specification. Table 33 shows data about aspherical surface coefficients.  FIG. 28  is a diagram illustrating distortion performance, and  FIG. 45  is a diagram illustrating spot performance. 
     In Example 11, Surface 27 through Surface 26 are optical element Lp, Surface 31 through Surface 28 are a first lens group, Surface 27 through Surface 16 are a 2a-th lens group, and Surface 15 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 31 
               
             
            
               
                   
               
               
                 EXAMPLE 11 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                   
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 (REFRACTIVE 
                 νdj 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 (ABBE NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.0102 
                   
                   
               
               
                 2 
                 ∞ 
                 1.0500 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 24.0000 
                   
                   
               
               
                 4 
                 37.1892 
                 2.5247 
                 1.74400 
                 44.78 
               
               
                 5 
                 −104.1925 
                 0.8964 
                   
                   
               
               
                 6 
                 −23.2256 
                 1.4769 
                 1.69895 
                 30.13 
               
               
                 7 
                 −60.3560 
                 0.2009 
                   
                   
               
               
                 8 
                 63.8991 
                 4.1462 
                 1.48749 
                 70.23 
               
               
                 9 
                 −11.7717 
                 1.0003 
                 1.77250 
                 49.60 
               
               
                 10 
                 48.9655 
                 0.2008 
                   
                   
               
               
                 11 
                 26.3175 
                 5.2294 
                 1.58267 
                 46.42 
               
               
                 12 
                 −17.1244 
                 0.2007 
                   
                   
               
               
                 13 
                 39.3962 
                 7.2641 
                 1.48749 
                 70.23 
               
               
                 14 
                 −12.1652 
                 1.1006 
                 1.80100 
                 34.97 
               
               
                 15 
                 31.2009 
                 0.5937 
                   
                   
               
               
                 16 
                 42.1666 
                 8.1904 
                 1.62299 
                 58.16 
               
               
                 17 
                 −39.7791 
                 12.5227 
                   
                   
               
               
                 18 
                 65.8979 
                 7.7887 
                 1.80000 
                 29.84 
               
               
                 19 
                 −57.0081 
                 7.7565 
                   
                   
               
               
                 20 
                 58.9087 
                 3.9579 
                 1.58913 
                 61.14 
               
               
                 21 
                 825.6641 
                 4.3518 
                   
                   
               
               
                 22 
                 −31.8577 
                 1.5001 
                 1.51633 
                 64.14 
               
               
                 23 
                 28.7855 
                 6.1834 
                   
                   
               
               
                 24 
                 −78.0750 
                 4.3560 
                 1.80518 
                 25.42 
               
               
                 25 
                 −34.8737 
                 5.2877 
                   
                   
               
               
                 26 
                 −18.9041 
                 2.8155 
                 1.84656 
                 23.78 
               
               
                 27 
                 −51.6913 
                 15.8918 
                   
                   
               
               
                 *28 
                 −78.3452 
                 4.9999 
                 1.49100 
                 57.58 
               
               
                 *29 
                 −39.7185 
                 24.5711 
                   
                   
               
               
                 *30 
                 −64.3891 
                 5.0000 
                 1.49100 
                 57.58 
               
               
                 *31 
                 15.6633 
                 30.0006 
                   
                   
               
               
                 *32 
                 98.2779 
                 −425.0000 
                 REFLECTION 
                   
               
               
                   
                   
                   
                 SURFACE 
                   
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 29.3 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 32 
               
               
                   
               
               
                 EXAMPLE 11 • SPECIFICATION(d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.40 
               
               
                   
                 2ω[°] 
                 144.20 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 33 
               
               
                   
               
               
                 EXAMPLE 11 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 28 
               
               
                   
               
               
                   
                 KA 
                 8.3580004E+00 
               
               
                   
                 A3 
                 −4.1116274E−03 
               
               
                   
                 A4 
                 1.7197848E−04 
               
               
                   
                 A5 
                 1.2682272E−05 
               
               
                   
                 A6 
                 −1.8503067E−06 
               
               
                   
                 A7 
                 2.4365158E−08 
               
               
                   
                 A8 
                 4.8192812E−09 
               
               
                   
                 A9 
                 −2.5340485E−10 
               
               
                   
                 A10 
                 1.3830305E−11 
               
               
                   
                 A11 
                 −8.9023525E−13 
               
               
                   
                 A12 
                 1.8296073E−14 
               
               
                   
                 A13 
                 1.0057412E−15 
               
               
                   
                 A14 
                 −6.6618797E−17 
               
               
                   
                 A15 
                 1.4071485E−18 
               
               
                   
                 A16 
                 −9.4814544E−21 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 29 
               
               
                   
               
               
                   
                 KA 
                 1.0860865E+00 
               
               
                   
                 A3 
                 −2.3075972E−03 
               
               
                   
                 A4 
                 −3.2577874E−05 
               
               
                   
                 A5 
                 −2.7132324E−06 
               
               
                   
                 A6 
                 4.1036319E−06 
               
               
                   
                 A7 
                 −5.8838142E−07 
               
               
                   
                 A8 
                 3.7463885E−08 
               
               
                   
                 A9 
                 −1.1736101E−09 
               
               
                   
                 A10 
                 9.5961186E−12 
               
               
                   
                 A11 
                 9.9510211E−13 
               
               
                   
                 A12 
                 −5.0513283E−14 
               
               
                   
                 A13 
                 2.3434680E−19 
               
               
                   
                 A14 
                 7.2298905E−17 
               
               
                   
                 A15 
                 −2.1835172E−18 
               
               
                   
                 A16 
                 2.0536684E−20 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 30 
               
               
                   
               
               
                   
                 KA 
                 −8.0863559E+00 
               
               
                   
                 A3 
                 2.7965765E−04 
               
               
                   
                 A4 
                 −3.6088477E−04 
               
               
                   
                 A5 
                 −6.1940485E−06 
               
               
                   
                 A6 
                 2.1517621E−06 
               
               
                   
                 A7 
                 −5.9063317E−08 
               
               
                   
                 A8 
                 2.9531977E−10 
               
               
                   
                 A9 
                 −6.9033466E−11 
               
               
                   
                 A10 
                 1.8660754E−12 
               
               
                   
                 A11 
                 1.0275935E−13 
               
               
                   
                 A12 
                 −2.5419951E−15 
               
               
                   
                 A13 
                 −1.1878350E−16 
               
               
                   
                 A14 
                 5.1585030E−18 
               
               
                   
                 A15 
                 −6.7583859E−20 
               
               
                   
                 A16 
                 2.8693193E−22 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 31 
               
               
                   
               
               
                   
                 KA 
                 −6.1758240E−01 
               
               
                   
                 A3 
                 −4.2929557E−03 
               
               
                   
                 A4 
                 8.4814161E−05 
               
               
                   
                 A5 
                 4.6605533E−06 
               
               
                   
                 A6 
                 −4.7564118E−07 
               
               
                   
                 A7 
                 2.1336645E−08 
               
               
                   
                 A8 
                 −3.3357299E−10 
               
               
                   
                 A9 
                 −1.2230526E−12 
               
               
                   
                 A10 
                 −2.0079317E−13 
               
               
                   
                 A11 
                 1.4327562E−14 
               
               
                   
                 A12 
                 −2.3111377E−16 
               
               
                   
                 A13 
                 −2.8978980E−18 
               
               
                   
                 A14 
                 1.9068446E−19 
               
               
                   
                 A15 
                 −3.5055118E−21 
               
               
                   
                 A16 
                 2.4174564E−23 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 32 
               
               
                   
               
               
                   
                 KA 
                 −1.8886101E+00 
               
               
                   
                 A3 
                 −8.1732739E−06 
               
               
                   
                 A4 
                 1.3580137E−06 
               
               
                   
                 A5 
                 −8.7838123E−09 
               
               
                   
                 A6 
                 −1.6535504E−09 
               
               
                   
                 A7 
                 4.0342143E−11 
               
               
                   
                 A8 
                 −1.2841316E−13 
               
               
                   
                 A9 
                 −5.9391024E−15 
               
               
                   
                 A10 
                 6.0544119E−17 
               
               
                   
                 A11 
                 3.3056836E−19 
               
               
                   
                 A12 
                 −8.7549642E−21 
               
               
                   
                 A13 
                 4.7148570E−23 
               
               
                   
                 A14 
                 1.8514268E−26 
               
               
                   
                 A15 
                 −9.4818523E−28 
               
               
                   
                 A16 
                 2.3700793E−30 
               
               
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 12 will be described.  FIG. 12  is across section illustrating the structure of the projection optical system in Example 12. Table 34 shows basic lens data on the projection optical system in Example 12, and Table 35 shows data about specification. Table 36 shows data about aspherical surface coefficients.  FIG. 29  is a diagram illustrating distortion performance, and  FIG. 46  is a diagram illustrating spot performance. 
     In Example 12, Surface 24 through Surface 22 are optical element Lp, Surface 28 through Surface 25 are a first lens group, and Surface 24 through Surface 4 are a second group. 
     
       
         
           
               
             
               
                 TABLE 34 
               
             
            
               
                   
               
               
                 EXAMPLE 12 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                 Si 
                 Ri 
                 Di 
                 Ndj 
                   
               
               
                 (SURFACE 
                 (CURVATURE 
                 (SURFACE 
                 (REFRACTIVE 
                 νdj 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 (ABBE NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 9.5189 
                   
                   
               
               
                 2 
                 ∞ 
                 22.8800 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 5.3800 
                   
                   
               
               
                 4 
                 39.1045 
                 8.2325 
                 1.80518 
                 25.42 
               
               
                 5 
                 2683.6464 
                 0.2000 
                   
                   
               
               
                 6 
                 73.2268 
                 3.3349 
                 1.80518 
                 25.42 
               
               
                 7 
                 182.5779 
                 0.4000 
                   
                   
               
               
                 *8 
                 167.2211 
                 3.7366 
                 1.49100 
                 57.58 
               
               
                 *9 
                 164.0477 
                 4.5646 
                   
                   
               
               
                 10 
                 33.8582 
                 13.3905 
                 1.49700 
                 81.54 
               
               
                 11 
                 −19.0114 
                 1.2001 
                 1.80518 
                 25.42 
               
               
                 12 
                 32.5474 
                 5.8328 
                   
                   
               
               
                 13 
                 47.9288 
                 6.4582 
                 1.58913 
                 61.14 
               
               
                 14 
                 −30.4974 
                 16.2777 
                   
                   
               
               
                 15 
                 62.8723 
                 12.7689 
                 1.64769 
                 33.79 
               
               
                 16 
                 −20.7981 
                 3.0778 
                 1.80000 
                 29.84 
               
               
                 17 
                 −42.4107 
                 0.2007 
                   
                   
               
               
                 18 
                 −704.3081 
                 9.9817 
                 1.75520 
                 27.51 
               
               
                 19 
                 −68.1613 
                 1.4396 
                   
                   
               
               
                 20 
                 −38.6682 
                 1.3000 
                 1.67003 
                 47.23 
               
               
                 21 
                 34.2547 
                 11.8778 
                   
                   
               
               
                 22 
                 −17.7538 
                 1.4100 
                 1.60311 
                 60.64 
               
               
                 23 
                 −43.2599 
                 7.1941 
                 1.80518 
                 25.42 
               
               
                 24 
                 −26.2228 
                 14.1293 
                   
                   
               
               
                 *25 
                 −11.9944 
                 6.0004 
                 1.49100 
                 57.58 
               
               
                 *26 
                 −10.4452 
                 19.8865 
                   
                   
               
               
                 *27 
                 −14.1202 
                 7.4467 
                 1.49100 
                 57.58 
               
               
                 *28 
                 253.6856 
                 40.6700 
                   
                   
               
               
                 *29 
                 115.5274 
                 −603.2000 
                 REFLECTION 
                   
               
               
                   
                   
                   
                 SURFACE 
                   
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 929.8 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 35 
               
               
                   
               
               
                 EXAMPLE 12 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 1.80 
               
               
                   
                 2ω[°] 
                 139.50 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 36 
               
               
                   
               
               
                 EXAMPLE 12 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 8 
               
               
                   
               
               
                   
                 KA 
                 −1.8729670E+01 
               
               
                   
                 A3 
                 −3.9026395E−05 
               
               
                   
                 A4 
                 2.5081689E−05 
               
               
                   
                 A5 
                 3.7858816E−06 
               
               
                   
                 A6 
                 −9.9024780E−07 
               
               
                   
                 A7 
                 1.1938756E−07 
               
               
                   
                 A8 
                 −8.2770926E−09 
               
               
                   
                 A9 
                 3.9347907E−10 
               
               
                   
                 A10 
                 −1.1809931E−11 
               
               
                   
                 A11 
                 −1.0337533E−12 
               
               
                   
                 A12 
                 1.7126594E−13 
               
               
                   
                 A13 
                 −8.0739882E−15 
               
               
                   
                 A14 
                 3.2305324E−17 
               
               
                   
                 A15 
                 7.8259687E−18 
               
               
                   
                 A16 
                 −1.6769954E−19 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 9 
               
               
                   
               
               
                   
                 KA 
                 3.7819359E+01 
               
               
                   
                 A3 
                 1.0854092E−04 
               
               
                   
                 A4 
                 −9.4324243E−06 
               
               
                   
                 A5 
                 9.7864768E−06 
               
               
                   
                 A6 
                 −4.8009532E−07 
               
               
                   
                 A7 
                 −1.5109562E−07 
               
               
                   
                 A8 
                 2.5554611E−08 
               
               
                   
                 A9 
                 −5.7919116E−10 
               
               
                   
                 A10 
                 −1.8176223E−10 
               
               
                   
                 A11 
                 1.5404820E−11 
               
               
                   
                 A12 
                 7.2416280E−14 
               
               
                   
                 A13 
                 −6.7967026E−14 
               
               
                   
                 A14 
                 3.7860548E−15 
               
               
                   
                 A15 
                 −8.8607650E−17 
               
               
                   
                 A16 
                 7.8537900E−19 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
               
               
                   
                 KA 
                 2.4533335E−01 
               
               
                   
                 A3 
                 5.0186041E−04 
               
               
                   
                 A4 
                 −1.2440749E−04 
               
               
                   
                 A5 
                 6.9122074E−05 
               
               
                   
                 A6 
                 −1.8472019E−05 
               
               
                   
                 A7 
                 2.3895483E−06 
               
               
                   
                 A8 
                 −1.5110369E−07 
               
               
                   
                 A9 
                 3.3737010E−09 
               
               
                   
                 A10 
                 7.4211020E−11 
               
               
                   
                 A11 
                 −1.7439111E−12 
               
               
                   
                 A12 
                 −2.6300717E−13 
               
               
                   
                 A13 
                 1.0279311E−14 
               
               
                   
                 A14 
                 4.7792073E−16 
               
               
                   
                 A15 
                 −6.1522373E−17 
               
               
                   
                 A16 
                 1.0512432E−18 
               
               
                   
                 A17 
                 1.8460378E−19 
               
               
                   
                 A18 
                 −1.3318964E−20 
               
               
                   
                 A19 
                 3.6090060E−22 
               
               
                   
                 A20 
                 −3.6248217E−24 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
               
               
                   
                 KA 
                 1.5214495E−01 
               
               
                   
                 A3 
                 7.7045392E−04 
               
               
                   
                 A4 
                 −3.8594787E−04 
               
               
                   
                 A5 
                 1.4711447E−04 
               
               
                   
                 A6 
                 −2.9170246E−05 
               
               
                   
                 A7 
                 3.2542107E−06 
               
               
                   
                 A8 
                 −1.9169657E−07 
               
               
                   
                 A9 
                 2.4325950E−09 
               
               
                   
                 A10 
                 4.7727624E−10 
               
               
                   
                 A11 
                 −3.5790688E−11 
               
               
                   
                 A12 
                 1.0854735E−12 
               
               
                   
                 A13 
                 −2.5918249E−14 
               
               
                   
                 A14 
                 1.9141082E−15 
               
               
                   
                 A15 
                 −8.4480869E−17 
               
               
                   
                 A16 
                 −2.1057922E−19 
               
               
                   
                 A17 
                 1.0455659E−19 
               
               
                   
                 A18 
                 −1.8044943E−21 
               
               
                   
                 A19 
                 −2.1874301E−23 
               
               
                   
                 A20 
                 5.8532230E−25 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 27 
               
               
                   
               
               
                   
                 KA 
                 −2.3279202E+00 
               
               
                   
                 A3 
                 −1.3112333E−03 
               
               
                   
                 A4 
                 −1.5483678E−04 
               
               
                   
                 A5 
                 1.1425286E−05 
               
               
                   
                 A6 
                 2.2637925E−06 
               
               
                   
                 A7 
                 −2.6489603E−07 
               
               
                   
                 A8 
                 6.4495222E−09 
               
               
                   
                 A9 
                 1.9350310E−10 
               
               
                   
                 A10 
                 −1.9088067E−12 
               
               
                   
                 A11 
                 −6.5926166E−13 
               
               
                   
                 A12 
                 1.5949064E−14 
               
               
                   
                 A13 
                 4.5438171E−16 
               
               
                   
                 A14 
                 −1.3263628E−17 
               
               
                   
                 A15 
                 −4.1734714E−19 
               
               
                   
                 A16 
                 1.4143953E−20 
               
               
                   
                 A17 
                 9.5491702E−23 
               
               
                   
                 A18 
                 −6.4078165E−24 
               
               
                   
                 A19 
                 3.8554102E−26 
               
               
                   
                 A20 
                 2.8671058E−28 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 28 
               
               
                   
               
               
                   
                 KA 
                 −2.1156382E+19 
               
               
                   
                 A3 
                 −1.7190824E−03 
               
               
                   
                 A4 
                 −4.3709076E−05 
               
               
                   
                 A5 
                 1.3310457E−05 
               
               
                   
                 A6 
                 −4.6023666E−07 
               
               
                   
                 A7 
                 −5.6047951E−09 
               
               
                   
                 A8 
                 −4.0074839E−10 
               
               
                   
                 A9 
                 7.1376825E−11 
               
               
                   
                 A10 
                 −1.0165856E−12 
               
               
                   
                 A11 
                 −9.4856881E−14 
               
               
                   
                 A12 
                 2.7822966E−15 
               
               
                   
                 A13 
                 5.0996261E−17 
               
               
                   
                 A14 
                 −2.7412501E−18 
               
               
                   
                 A15 
                 6.1018870E−21 
               
               
                   
                 A16 
                 8.9138916E−22 
               
               
                   
                 A17 
                 −4.0484579E−24 
               
               
                   
                 A18 
                 −2.3934231E−25 
               
               
                   
                 A19 
                 2.7988883E−27 
               
               
                   
                 A20 
                 −4.1314057E−30 
               
               
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 29 
               
               
                   
               
               
                   
                 KA 
                 1.0930970E+00 
               
               
                   
                 A3 
                 2.0500921E−04 
               
               
                   
                 A4 
                 −7.5522598E−06 
               
               
                   
                 A5 
                 −5.5985360E−08 
               
               
                   
                 A6 
                 8.9414144E−09 
               
               
                   
                 A7 
                 −1.5663911E−10 
               
               
                   
                 A8 
                 −2.7661297E−12 
               
               
                   
                 A9 
                 1.4653416E−13 
               
               
                   
                 A10 
                 −2.2231012E−15 
               
               
                   
                 A11 
                 1.3346813E−17 
               
               
                   
                 A12 
                 −3.6886813E−20 
               
               
                   
                 A13 
                 9.1565994E−22 
               
               
                   
                 A14 
                 −6.7799680E−24 
               
               
                   
                 A15 
                 −1.4084431E−25 
               
               
                   
                 A16 
                 1.6277053E−27 
               
               
                   
                 A17 
                 9.7981637E−30 
               
               
                   
                 A18 
                 −2.4320887E−31 
               
               
                   
                 A19 
                 1.4350978E−33 
               
               
                   
                 A20 
                 −2.9316381E−36 
               
               
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 13 will be described.  FIG. 13  is a cross section illustrating the structure of the projection optical system in Example 13. Table 37 shows basic lens data on the projection optical system in Example 13, and Table 38 shows data about specification. Table 39 shows data about aspherical surface coefficients.  FIG. 30  is a diagram illustrating distortion performance, and  FIG. 47  is a diagram illustrating spot performance. 
     In Example 13, Surface 18 through Surface 16 are optical element Lp, Surface 23 through Surface 19 are a first lens group, Surface 18 through Surface 11 are a 2a-th lens group, and Surface 10 through Surface 4 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 37 
               
             
            
               
                   
               
               
                 EXAMPLE 13 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURV- 
                 Di 
                 (RE- 
                 νdj 
               
               
                 (SURFACE 
                 ATURE 
                 (SURFACE 
                 FRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 9.5103 
                   
                   
               
               
                 2 
                 ∞ 
                 22.8800 
                 1.51633 
                 64.14 
               
               
                 3 
                 ∞ 
                 5.3800 
               
               
                 4 
                 33.7812 
                 9.3936 
                 1.79544 
                 25.64 
               
               
                 5 
                 −1401.6603 
                 0.4007 
               
               
                 *6 
                 159.8129 
                 4.3632 
                 1.49100 
                 57.58 
               
               
                 *7 
                 116.8669 
                 3.3723 
               
               
                 8 
                 25.2038 
                 13.5077 
                 1.49700 
                 81.54 
               
               
                 9 
                 −20.0000 
                 1.1991 
                 1.74929 
                 27.62 
               
               
                 10 
                 27.0040 
                 5.8682 
               
               
                 11 
                 39.0282 
                 8.5701 
                 1.58812 
                 61.61 
               
               
                 12 
                 −32.4013 
                 11.4317 
               
               
                 13 
                 51.3833 
                 11.0982 
                 1.57758 
                 42.19 
               
               
                 14 
                 −15.8531 
                 17.5326 
                 1.61001 
                 41.32 
               
               
                 15 
                 40.6474 
                 9.8325 
               
               
                 16 
                 −17.8029 
                 1.4091 
                 1.57662 
                 62.05 
               
               
                 17 
                 −157.5661 
                 9.2554 
                 1.80518 
                 25.42 
               
               
                 18 
                 −30.5930 
                 16.4458 
               
               
                 *19 
                 −12.2634 
                 6.1991 
                 1.49100 
                 57.58 
               
               
                 *20 
                 −10.3989 
                 19.9757 
               
               
                 *21 
                 −14.1305 
                 7.4901 
                 1.49100 
                 57.58 
               
               
                 *22 
                 164.3597 
                 43.6714 
               
               
                 *23 
                 116.1369 
                 −657.5000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 929.8 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 38 
               
               
                   
               
               
                 EXAMPLE 13 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 1.80 
               
               
                   
                 2ω[°] 
                 139.80 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 39 
               
               
                   
               
               
                 EXAMPLE 13 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 6 
               
               
                   
                   
               
               
                   
                 KA 
                 5.6079681E+01 
               
               
                   
                 A3 
                 −3.0172586E−05 
               
               
                   
                 A4 
                 6.6648587E−05 
               
               
                   
                 A5 
                 −2.2925425E−05 
               
               
                   
                 A6 
                 7.6878177E−06 
               
               
                   
                 A7 
                 −1.5411327E−06 
               
               
                   
                 A8 
                 1.8549282E−07 
               
               
                   
                 A9 
                 −1.1869984E−08 
               
               
                   
                 A10 
                 5.3265780E−11 
               
               
                   
                 A11 
                 5.8417915E−11 
               
               
                   
                 A12 
                 −5.1895274E−12 
               
               
                   
                 A13 
                 2.2664450E−13 
               
               
                   
                 A14 
                 −5.4161016E−15 
               
               
                   
                 A15 
                 6.3570357E−17 
               
               
                   
                 A16 
                 −2.3637700E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 7 
               
               
                   
                   
               
               
                   
                 KA 
                 4.4919516E+01 
               
               
                   
                 A3 
                 2.0232701E−04 
               
               
                   
                 A4 
                 −4.8331328E−05 
               
               
                   
                 A5 
                 2.6387613E−05 
               
               
                   
                 A6 
                 −4.9693371E−06 
               
               
                   
                 A7 
                 7.2148746E−07 
               
               
                   
                 A8 
                 −8.8623500E−08 
               
               
                   
                 A9 
                 8.7751911E−09 
               
               
                   
                 A10 
                 −5.6805488E−10 
               
               
                   
                 A11 
                 1.1903760E−11 
               
               
                   
                 A12 
                 1.2078073E−12 
               
               
                   
                 A13 
                 −9.6738296E−14 
               
               
                   
                 A14 
                 1.8727038E−15 
               
               
                   
                 A15 
                 4.3099568E−17 
               
               
                   
                 A16 
                 −1.5914424E−18 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 19 
               
               
                   
                   
               
               
                   
                 KA 
                 2.5868376E−01 
               
               
                   
                 A3 
                 5.5917339E−04 
               
               
                   
                 A4 
                 −1.5519518E−04 
               
               
                   
                 A5 
                 7.2651815E−05 
               
               
                   
                 A6 
                 −1.7936303E−05 
               
               
                   
                 A7 
                 2.3037907E−06 
               
               
                   
                 A8 
                 −1.5381578E−07 
               
               
                   
                 A9 
                 4.1841481E−09 
               
               
                   
                 A10 
                 6.7336594E−11 
               
               
                   
                 A11 
                 −5.4628815E−12 
               
               
                   
                 A12 
                 −1.6420420E−13 
               
               
                   
                 A13 
                 1.9814336E−14 
               
               
                   
                 A14 
                 1.1318652E−16 
               
               
                   
                 A15 
                 −7.5233481E−17 
               
               
                   
                 A16 
                 1.7097428E−18 
               
               
                   
                 A17 
                 1.9508630E−19 
               
               
                   
                 A18 
                 −1.3949266E−20 
               
               
                   
                 A19 
                 3.5930473E−22 
               
               
                   
                 A20 
                 −3.4276559E−24 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 20 
               
               
                   
                   
               
               
                   
                 KA 
                 1.5181721E−01 
               
               
                   
                 A3 
                 1.0354464E−03 
               
               
                   
                 A4 
                 −4.4828184E−04 
               
               
                   
                 A5 
                 1.5317401E−04 
               
               
                   
                 A6 
                 −2.9132927E−05 
               
               
                   
                 A7 
                 3.2585184E−06 
               
               
                   
                 A8 
                 −1.9896975E−07 
               
               
                   
                 A9 
                 2.9771466E−09 
               
               
                   
                 A10 
                 4.9299833E−10 
               
               
                   
                 A11 
                 −3.8787858E−11 
               
               
                   
                 A12 
                 1.1537217E−12 
               
               
                   
                 A13 
                 −2.3480232E−14 
               
               
                   
                 A14 
                 1.9178965E−15 
               
               
                   
                 A15 
                 −9.2927560E−17 
               
               
                   
                 A16 
                 −9.2616324E−20 
               
               
                   
                 A17 
                 1.1316315E−19 
               
               
                   
                 A18 
                 −2.0099967E−21 
               
               
                   
                 A19 
                 −2.3960966E−23 
               
               
                   
                 A20 
                 6.5388306E−25 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 21 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.1025943E+00 
               
               
                   
                 A3 
                 −5.4358481E−04 
               
               
                   
                 A4 
                 −1.5011214E−04 
               
               
                   
                 A5 
                 6.1317649E−06 
               
               
                   
                 A6 
                 2.3532540E−06 
               
               
                   
                 A7 
                 −2.6034715E−07 
               
               
                   
                 A8 
                 7.1740969E−09 
               
               
                   
                 A9 
                 1.5208492E−10 
               
               
                   
                 A10 
                 −2.7272479E−12 
               
               
                   
                 A11 
                 −6.4003421E−13 
               
               
                   
                 A12 
                 1.9351623E−14 
               
               
                   
                 A13 
                 4.1796412E−16 
               
               
                   
                 A14 
                 −1.7012515E−17 
               
               
                   
                 A15 
                 −4.2159324E−19 
               
               
                   
                 A16 
                 1.7887527E−20 
               
               
                   
                 A17 
                 9.0675967E−23 
               
               
                   
                 A18 
                 −8.1712742E−24 
               
               
                   
                 A19 
                 5.0082923E−26 
               
               
                   
                 A20 
                 4.2841319E−28 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 22 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.1156382E+19 
               
               
                   
                 A3 
                 −1.2390375E−03 
               
               
                   
                 A4 
                 −5.2229702E−05 
               
               
                   
                 A5 
                 1.1548327E−05 
               
               
                   
                 A6 
                 −4.1120450E−07 
               
               
                   
                 A7 
                 −3.3911485E−09 
               
               
                   
                 A8 
                 −4.8077604E−10 
               
               
                   
                 A9 
                 7.0992677E−11 
               
               
                   
                 A10 
                 −9.5083699E−13 
               
               
                   
                 A11 
                 −9.9091098E−14 
               
               
                   
                 A12 
                 2.8085486E−15 
               
               
                   
                 A13 
                 5.7737784E−17 
               
               
                   
                 A14 
                 −2.8338197E−18 
               
               
                   
                 A15 
                 9.6802790E−22 
               
               
                   
                 A16 
                 9.7931205E−22 
               
               
                   
                 A17 
                 −2.4185449E−24 
               
               
                   
                 A18 
                 −2.6776143E−25 
               
               
                   
                 A19 
                 2.5057504E−27 
               
               
                   
                 A20 
                 7.3999405E−31 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0887191E+00 
               
               
                   
                 A3 
                 1.9805169E−04 
               
               
                   
                 A4 
                 −7.5305630E−06 
               
               
                   
                 A5 
                 −4.8578661E−08 
               
               
                   
                 A6 
                 8.9996496E−09 
               
               
                   
                 A7 
                 −1.6355746E−10 
               
               
                   
                 A8 
                 −2.7815281E−12 
               
               
                   
                 A9 
                 1.5104119E−13 
               
               
                   
                 A10 
                 −2.2866996E−15 
               
               
                   
                 A11 
                 1.3362744E−17 
               
               
                   
                 A12 
                 −3.4956150E−20 
               
               
                   
                 A13 
                 9.8640041E−22 
               
               
                   
                 A14 
                 −7.4229990E−24 
               
               
                   
                 A15 
                 −1.4930115E−25 
               
               
                   
                 A16 
                 1.7247088E−27 
               
               
                   
                 A17 
                 1.0347675E−29 
               
               
                   
                 A18 
                 −2.5508970E−31 
               
               
                   
                 A19 
                 1.4948502E−33 
               
               
                   
                 A20 
                 −3.0311027E−36 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 14 will be described.  FIG. 14  is a cross section illustrating the structure of the projection optical system in Example 14. Table 40 shows basic lens data on the projection optical system in Example 14, and Table 41 shows data about specification. Table 42 shows data about aspherical surface coefficients.  FIG. 31  is a diagram illustrating distortion performance, and  FIG. 48  is a diagram illustrating spot performance. 
     In Example 14, Surface 19 through Surface 17 are optical element Lp, Surface 23 through Surface 20 are a first lens group, and Surface 19 through Surface 3 are a second group. 
     
       
         
           
               
             
               
                 TABLE 40 
               
             
            
               
                   
               
               
                 EXAMPLE 14 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURV- 
                 Di 
                 (RE- 
                 νdj 
               
               
                 (SURFACE 
                 ATURE 
                 (SURFACE 
                 FRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 26.0500 
                 1.51633 
                 64.14 
               
               
                 2 
                 ∞ 
                 11.9604 
               
               
                 3 
                 35.9778 
                 8.6085 
                 1.80518 
                 25.42 
               
               
                 4 
                 −154.8133 
                 0.5985 
               
               
                 *5 
                 148.3512 
                 3.8119 
                 1.51007 
                 56.24 
               
               
                 *6 
                 1465.2411 
                 3.4192 
               
               
                 7 
                 30.8141 
                 10.3963 
                 1.48749 
                 70.23 
               
               
                 8 
                 −24.6662 
                 1.1990 
                 1.80518 
                 25.42 
               
               
                 9 
                 23.6026 
                 5.7251 
               
               
                 10 
                 33.7511 
                 6.9859 
                 1.49700 
                 81.54 
               
               
                 11 
                 −26.2388 
                 15.2407 
               
               
                 12 
                 43.8218 
                 12.8945 
                 1.60342 
                 38.03 
               
               
                 13 
                 −17.9859 
                 1.3192 
                 1.80610 
                 33.27 
               
               
                 14 
                 −36.5003 
                 0.2009 
               
               
                 15 
                 −167.7121 
                 6.8460 
                 1.56883 
                 56.36 
               
               
                 16 
                 24.5133 
                 10.8406 
               
               
                 17 
                 −15.1471 
                 1.4107 
                 1.56384 
                 60.67 
               
               
                 18 
                 −39.7712 
                 6.5466 
                 1.80518 
                 25.42 
               
               
                 19 
                 −23.3517 
                 14.7892 
               
               
                 *20 
                 −11.2050 
                 5.5005 
                 1.49100 
                 57.58 
               
               
                 *21 
                 −9.8885 
                 19.0076 
               
               
                 *22 
                 −13.4510 
                 7.2437 
                 1.49100 
                 57.58 
               
               
                 *23 
                 −0.1067 
                 42.4438 
               
               
                 *24 
                 105.5388 
                 −562.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 709.0 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 41 
               
               
                   
               
               
                 EXAMPLE 14 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 2.00 
               
               
                   
                 2ω[°] 
                 140.00 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 42 
               
               
                   
               
               
                 EXAMPLE 14 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 5 
               
               
                   
                   
               
               
                   
                 KA 
                 6.5766135E+01 
               
               
                   
                 A3 
                 5.0795975E−05 
               
               
                   
                 A4 
                 −1.4539557E−05 
               
               
                   
                 A5 
                 5.7326791E−06 
               
               
                   
                 A6 
                 −9.6620064E−07 
               
               
                   
                 A7 
                 1.2733655E−07 
               
               
                   
                 A8 
                 −1.1771777E−08 
               
               
                   
                 A9 
                 8.2316678E−10 
               
               
                   
                 A10 
                 −3.0498203E−11 
               
               
                   
                 A11 
                 −2.0343848E−12 
               
               
                   
                 A12 
                 3.4705758E−13 
               
               
                   
                 A13 
                 −1.6495176E−14 
               
               
                   
                 A14 
                 5.7602520E−17 
               
               
                   
                 A15 
                 1.8371495E−17 
               
               
                   
                 A16 
                 −4.2229108E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 6 
               
               
                   
                   
               
               
                   
                 KA 
                 −3.3557820E+06 
               
               
                   
                 A3 
                 1.6549633E−04 
               
               
                   
                 A4 
                 −1.2388429E−05 
               
               
                   
                 A5 
                 4.8110204E−06 
               
               
                   
                 A6 
                 6.5251044E−08 
               
               
                   
                 A7 
                 −1.0249352E−07 
               
               
                   
                 A8 
                 1.5016992E−08 
               
               
                   
                 A9 
                 −3.9501197E−10 
               
               
                   
                 A10 
                 −1.1048561E−10 
               
               
                   
                 A11 
                 1.0848383E−11 
               
               
                   
                 A12 
                 −2.9971685E−14 
               
               
                   
                 A13 
                 −4.7325483E−14 
               
               
                   
                 A14 
                 2.8875139E−15 
               
               
                   
                 A15 
                 −6.8997086E−17 
               
               
                   
                 A16 
                 5.6348898E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 20 
               
               
                   
                   
               
               
                   
                 KA 
                 2.3216563E−01 
               
               
                   
                 A3 
                 2.1376251E−04 
               
               
                   
                 A4 
                 −6.8902504E−05 
               
               
                   
                 A5 
                 8.3269780E−05 
               
               
                   
                 A6 
                 −2.5249433E−05 
               
               
                   
                 A7 
                 3.4636962E−06 
               
               
                   
                 A8 
                 −2.2310818E−07 
               
               
                   
                 A9 
                 4.1030624E−09 
               
               
                   
                 A10 
                 1.6185204E−10 
               
               
                   
                 A11 
                 3.2943761E−12 
               
               
                   
                 A12 
                 −8.0224409E−13 
               
               
                   
                 A13 
                 2.8220375E−16 
               
               
                   
                 A14 
                 2.1568531E−15 
               
               
                   
                 A15 
                 −9.8454713E−17 
               
               
                   
                 A16 
                 8.1026974E−20 
               
               
                   
                 A17 
                 4.1787310E−19 
               
               
                   
                 A18 
                 −3.2242135E−20 
               
               
                   
                 A19 
                 1.0152879E−21 
               
               
                   
                 A20 
                 −1.1785269E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 21 
               
               
                   
                   
               
               
                   
                 KA 
                 1.5168053E−01 
               
               
                   
                 A3 
                 4.5751265E−04 
               
               
                   
                 A4 
                 −3.6314202E−04 
               
               
                   
                 A5 
                 1.7636739E−04 
               
               
                   
                 A6 
                 −3.8717709E−05 
               
               
                   
                 A7 
                 4.6103336E−06 
               
               
                   
                 A8 
                 −2.8168682E−07 
               
               
                   
                 A9 
                 3.0426406E−09 
               
               
                   
                 A10 
                 8.0671914E−10 
               
               
                   
                 A11 
                 −5.9079226E−11 
               
               
                   
                 A12 
                 1.8450683E−12 
               
               
                   
                 A13 
                 −5.5668675E−14 
               
               
                   
                 A14 
                 4.2112037E−15 
               
               
                   
                 A15 
                 −1.7373035E−16 
               
               
                   
                 A16 
                 −9.1389725E−19 
               
               
                   
                 A17 
                 2.4492393E−19 
               
               
                   
                 A18 
                 −4.2508924E−21 
               
               
                   
                 A19 
                 −5.6710702E−23 
               
               
                   
                 A20 
                 1.5564849E−24 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 22 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.1185681E+00 
               
               
                   
                 A3 
                 −1.4168490E−03 
               
               
                   
                 A4 
                 −1.2997025E−04 
               
               
                   
                 A5 
                 8.0589444E−06 
               
               
                   
                 A6 
                 2.3169271E−06 
               
               
                   
                 A7 
                 −2.6082024E−07 
               
               
                   
                 A8 
                 6.8538683E−09 
               
               
                   
                 A9 
                 1.1999319E−10 
               
               
                   
                 A10 
                 1.2988798E−12 
               
               
                   
                 A11 
                 −5.9782089E−13 
               
               
                   
                 A12 
                 9.8184110E−15 
               
               
                   
                 A13 
                 3.5839679E−16 
               
               
                   
                 A14 
                 −3.3782258E−18 
               
               
                   
                 A15 
                 −4.1301875E−19 
               
               
                   
                 A16 
                 8.4197246E−21 
               
               
                   
                 A17 
                 8.5859106E−23 
               
               
                   
                 A18 
                 −4.7022379E−24 
               
               
                   
                 A19 
                 6.1175937E−26 
               
               
                   
                 A20 
                 −2.8705141E−28 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.5885870E+43 
               
               
                   
                 A3 
                 −1.9163843E−03 
               
               
                   
                 A4 
                 −3.1954410E−05 
               
               
                   
                 A5 
                 1.3490083E−05 
               
               
                   
                 A6 
                 −6.0802460E−07 
               
               
                   
                 A7 
                 1.1962785E−09 
               
               
                   
                 A8 
                 −2.2746525E−10 
               
               
                   
                 A9 
                 5.9891347E−11 
               
               
                   
                 A10 
                 −1.4087958E−12 
               
               
                   
                 A11 
                 −7.5740967E−14 
               
               
                   
                 A12 
                 3.4062567E−15 
               
               
                   
                 A13 
                 2.4977620E−17 
               
               
                   
                 A14 
                 −3.3162351E−18 
               
               
                   
                 A15 
                 3.2287212E−20 
               
               
                   
                 A16 
                 9.7984659E−22 
               
               
                   
                 A17 
                 −1.3094848E−23 
               
               
                   
                 A18 
                 −2.5996999E−25 
               
               
                   
                 A19 
                 5.2010051E−27 
               
               
                   
                 A20 
                 −1.9673513E−29 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0510424E+00 
               
               
                   
                 A3 
                 2.5690923E−04 
               
               
                   
                 A4 
                 −9.4651289E−06 
               
               
                   
                 A5 
                 −9.0558146E−08 
               
               
                   
                 A6 
                 1.2630792E−08 
               
               
                   
                 A7 
                 −2.2305821E−10 
               
               
                   
                 A8 
                 −4.4849446E−12 
               
               
                   
                 A9 
                 2.4469888E−13 
               
               
                   
                 A10 
                 −3.9883739E−15 
               
               
                   
                 A11 
                 2.6675877E−17 
               
               
                   
                 A12 
                 −8.4614751E−20 
               
               
                   
                 A13 
                 1.8762077E−21 
               
               
                   
                 A14 
                 −1.4559126E−23 
               
               
                   
                 A15 
                 −3.3975502E−25 
               
               
                   
                 A16 
                 4.2215174E−27 
               
               
                   
                 A17 
                 2.7262688E−29 
               
               
                   
                 A18 
                 −7.3432046E−31 
               
               
                   
                 A19 
                 4.6908597E−33 
               
               
                   
                 A20 
                 −1.0374796E−35 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 15 will be described.  FIG. 15  is a cross section illustrating the structure of the projection optical system in Example 15. Table 43 shows basic lens data on the projection optical system in Example 15, and Table 44 shows data about specification. Table 45 shows data about aspherical surface coefficients.  FIG. 32  is a diagram illustrating distortion performance, and  FIG. 49  is a diagram illustrating spot performance. 
     In Example 15, Surface 21 through Surface 20 are optical element Lp, Surface 25 through Surface 22 are a first lens group, Surface 21 through Surface 12 are a 2a-th lens group, and Surface 11 through Surface 5 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 43 
               
             
            
               
                   
               
               
                 EXAMPLE 13 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURV- 
                 Di 
                 (RE- 
                 νdj 
               
               
                 (SURFACE 
                 ATURE 
                 (SURFACE 
                 FRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 0.0958 
                   
                   
               
               
                 2 
                 ∞ 
                 10.6000 
                 1.84666 
                 23.78 
               
               
                 3 
                 ∞ 
                 1.5500 
                 1.51633 
                 64.14 
               
               
                 4 
                 ∞ 
                 4.9000 
               
               
                 5 
                 14.6561 
                 3.7457 
                 1.78903 
                 26.14 
               
               
                 6 
                 224.0807 
                 0.1990 
               
               
                 *7 
                 45.2769 
                 1.9747 
                 1.49100 
                 57.58 
               
               
                 *8 
                 55.4989 
                 0.2230 
               
               
                 9 
                 9.3094 
                 6.5792 
                 1.49700 
                 81.54 
               
               
                 10 
                 −9.7310 
                 1.0992 
                 1.80240 
                 25.55 
               
               
                 11 
                 12.5029 
                 3.5528 
               
               
                 12 
                 19.0029 
                 2.8979 
                 1.48999 
                 56.88 
               
               
                 13 
                 −20.8854 
                 1.1459 
               
               
                 14 
                 34.1576 
                 10.7550 
                 1.51456 
                 52.27 
               
               
                 15 
                 −35.1796 
                 0.1991 
               
               
                 16 
                 62.8567 
                 7.2308 
                 1.80004 
                 25.65 
               
               
                 17 
                 −21.0449 
                 0.4473 
               
               
                 18 
                 −16.6402 
                 6.5929 
                 1.61752 
                 60.48 
               
               
                 19 
                 74.1682 
                 4.4443 
               
               
                 20 
                 −8.9472 
                 4.5015 
                 1.72973 
                 33.26 
               
               
                 21 
                 −19.5169 
                 9.2447 
               
               
                 *22 
                 −5.9583 
                 3.0955 
                 1.49100 
                 57.58 
               
               
                 *23 
                 −5.2468 
                 9.0046 
               
               
                 *24 
                 −44.9244 
                 4.5009 
                 1.49100 
                 57.58 
               
               
                 *25 
                 −0.0781 
                 13.5744 
               
               
                 *26 
                 57.7501 
                 −110.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 461.7 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 44 
               
               
                   
               
               
                 EXAMPLE 15 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 4.00 
               
               
                   
                 2ω[°] 
                 146.60 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 45 
               
               
                   
               
               
                 EXAMPLE 15 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 7 
               
               
                   
                   
               
               
                   
                 KA 
                 −4.6392765E+01 
               
               
                   
                 A3 
                 −7.0478565E−04 
               
               
                   
                 A4 
                 7.9972373E−04 
               
               
                   
                 A5 
                 −6.8306513E−05 
               
               
                   
                 A6 
                 −3.3554150E−05 
               
               
                   
                 A7 
                 1.5736232E−05 
               
               
                   
                 A8 
                 −1.9261250E−06 
               
               
                   
                 A9 
                 −1.0830313E−07 
               
               
                   
                 A10 
                 2.8004572E−08 
               
               
                   
                 A11 
                 1.4510131E−09 
               
               
                   
                 A12 
                 −1.8672656E−10 
               
               
                   
                 A13 
                 −4.5534704E−11 
               
               
                   
                 A14 
                 3.9684816E−12 
               
               
                   
                 A15 
                 1.5237886E−13 
               
               
                   
                 A16 
                 −1.5355110E−14 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 8 
               
               
                   
                   
               
               
                   
                 KA 
                 −1.7956130E+02 
               
               
                   
                 A3 
                 −1.1305315E−04 
               
               
                   
                 A4 
                 5.4684152E−04 
               
               
                   
                 A5 
                 1.7861424E−04 
               
               
                   
                 A6 
                 −6.0430901E−05 
               
               
                   
                 A7 
                 −4.4997542E−06 
               
               
                   
                 A8 
                 6.5886420E−06 
               
               
                   
                 A9 
                 −9.0401925E−07 
               
               
                   
                 A10 
                 −1.7580192E−07 
               
               
                   
                 A11 
                 5.0394622E−08 
               
               
                   
                 A12 
                 −5.4998562E−10 
               
               
                   
                 A13 
                 −9.0064904E−10 
               
               
                   
                 A14 
                 1.0208012E−10 
               
               
                   
                 A15 
                 −4.0958032E−12 
               
               
                   
                 A16 
                 5.0163064E−14 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 22 
               
               
                   
                   
               
               
                   
                 KA 
                 2.3716576E−01 
               
               
                   
                 A3 
                 1.0579370E−02 
               
               
                   
                 A4 
                 2.0387995E−03 
               
               
                   
                 A5 
                 1.5249766E−03 
               
               
                   
                 A6 
                 −7.8852791E−04 
               
               
                   
                 A7 
                 1.5158835E−04 
               
               
                   
                 A8 
                 −1.4814481E−05 
               
               
                   
                 A9 
                 8.2667132E−07 
               
               
                   
                 A10 
                 −3.7586489E−08 
               
               
                   
                 A11 
                 2.4173434E−09 
               
               
                   
                 A12 
                 8.5914805E−12 
               
               
                   
                 A13 
                 −2.9466682E−11 
               
               
                   
                 A14 
                 3.1966324E−12 
               
               
                   
                 A15 
                 −4.4109745E−13 
               
               
                   
                 A16 
                 2.1625020E−14 
               
               
                   
                 A17 
                 1.0261536E−14 
               
               
                   
                 A18 
                 −1.7760618E−15 
               
               
                   
                 A19 
                 1.0667902E−16 
               
               
                   
                 A20 
                 −2.2510132E−18 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 1.5246062E−01 
               
               
                   
                 A3 
                 5.1331499E−04 
               
               
                   
                 A4 
                 −4.9706280E−03 
               
               
                   
                 A5 
                 2.7705955E−03 
               
               
                   
                 A6 
                 −8.2845093E−04 
               
               
                   
                 A7 
                 1.8323949E−04 
               
               
                   
                 A8 
                 −2.7192802E−05 
               
               
                   
                 A9 
                 1.2388616E−06 
               
               
                   
                 A10 
                 2.8897079E−07 
               
               
                   
                 A11 
                 −4.5117632E−08 
               
               
                   
                 A12 
                 1.7215740E−09 
               
               
                   
                 A13 
                 −3.2848767E−11 
               
               
                   
                 A14 
                 1.8675233E−11 
               
               
                   
                 A15 
                 −1.7157086E−12 
               
               
                   
                 A16 
                 −1.9601438E−14 
               
               
                   
                 A17 
                 7.6670049E−15 
               
               
                   
                 A18 
                 −2.0417022E−16 
               
               
                   
                 A19 
                 −6.6340849E−18 
               
               
                   
                 A20 
                 2.7355201E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 −3.1856395E+00 
               
               
                   
                 A3 
                 −3.1013559E−02 
               
               
                   
                 A4 
                 −3.7060674E−04 
               
               
                   
                 A5 
                 7.7918887E−04 
               
               
                   
                 A6 
                 4.2213449E−05 
               
               
                   
                 A7 
                 −2.5863509E−05 
               
               
                   
                 A8 
                 1.3681830E−06 
               
               
                   
                 A9 
                 1.3375653E−07 
               
               
                   
                 A10 
                 −6.4057864E−09 
               
               
                   
                 A11 
                 −1.1905894E−09 
               
               
                   
                 A12 
                 6.6479437E−11 
               
               
                   
                 A13 
                 3.8430832E−12 
               
               
                   
                 A14 
                 −2.3889387E−13 
               
               
                   
                 A15 
                 −1.1560425E−14 
               
               
                   
                 A16 
                 7.7155480E−16 
               
               
                   
                 A17 
                 1.2488066E−17 
               
               
                   
                 A18 
                 −1.2455464E−18 
               
               
                   
                 A19 
                 6.7736438E−21 
               
               
                   
                 A20 
                 3.7111248E−22 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.1156382E+19 
               
               
                   
                 A3 
                 −2.7451387E−03 
               
               
                   
                 A4 
                 −1.7950739E−03 
               
               
                   
                 A5 
                 1.7288434E−04 
               
               
                   
                 A6 
                 1.3247307E−05 
               
               
                   
                 A7 
                 2.2070499E−07 
               
               
                   
                 A8 
                 −4.7314308E−07 
               
               
                   
                 A9 
                 2.8325839E−08 
               
               
                   
                 A10 
                 1.9788122E−09 
               
               
                   
                 A11 
                 −2.0092837E−10 
               
               
                   
                 A12 
                 −2.1331870E−12 
               
               
                   
                 A13 
                 6.2559028E−13 
               
               
                   
                 A14 
                 −1.0814452E−14 
               
               
                   
                 A15 
                 −4.9865013E−16 
               
               
                   
                 A16 
                 9.1838832E−18 
               
               
                   
                 A17 
                 4.2227044E−19 
               
               
                   
                 A18 
                 −2.5894931E−20 
               
               
                   
                 A19 
                 1.2137733E−21 
               
               
                   
                 A20 
                 −2.3623223E−23 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
                   
               
               
                   
                 KA 
                 1.0921890E+00 
               
               
                   
                 A3 
                 8.9836331E−04 
               
               
                   
                 A4 
                 −5.8899357E−05 
               
               
                   
                 A5 
                 −1.1346015E−06 
               
               
                   
                 A6 
                 2.8167686E−07 
               
               
                   
                 A7 
                 −9.3986473E−09 
               
               
                   
                 A8 
                 −3.5136649E−10 
               
               
                   
                 A9 
                 3.6240681E−11 
               
               
                   
                 A10 
                 −1.1064024E−12 
               
               
                   
                 A11 
                 1.3759930E−14 
               
               
                   
                 A12 
                 −8.2027665E−17 
               
               
                   
                 A13 
                 3.4859873E−18 
               
               
                   
                 A14 
                 −4.9439235E−20 
               
               
                   
                 A15 
                 −2.2026962E−21 
               
               
                   
                 A16 
                 5.0266169E−23 
               
               
                   
                 A17 
                 6.1761378E−25 
               
               
                   
                 A18 
                 −3.0508431E−26 
               
               
                   
                 A19 
                 3.6132882E−28 
               
               
                   
                 A20 
                 −1.4835427E−30 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 16 will be described.  FIG. 16  is a cross section illustrating the structure of the projection optical system in Example 16. Table 46 shows basic lens data on the projection optical system in Example 16, and Table 47 shows data about specification. Table 48 shows data about aspherical surface coefficients.  FIG. 33  is a diagram illustrating distortion performance, and  FIG. 50  is a diagram illustrating spot performance. 
     In Example 16, Surface 29 through Surface 28 are optical element Lp, Surface 33 through Surface 30 are a first lens group, and Surface 29 through Surface 5 are a second group. 
     
       
         
           
               
             
               
                 TABLE 46 
               
             
            
               
                   
               
               
                 EXAMPLE 16 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURV- 
                 Di 
                 (RE- 
                 νdj 
               
               
                 (SURFACE 
                 ATURE 
                 (SURFACE 
                 FRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 1.5500 
                 1.51680 
                 64.20 
               
               
                 2 
                 ∞ 
                 0.0000 
               
               
                 3 
                 ∞ 
                 10.6000 
                 1.84666 
                 23.78 
               
               
                 4 
                 ∞ 
                 5.7991 
               
               
                 5 
                 40.9778 
                 2.5739 
                 1.78111 
                 49.89 
               
               
                 6 
                 −105.4155 
                 0.1991 
               
               
                 7 
                 24.6916 
                 2.0956 
                 1.74756 
                 53.24 
               
               
                 8 
                 141.7015 
                 0.1995 
               
               
                 9 
                 26.9099 
                 1.6650 
                 1.77620 
                 26.19 
               
               
                 10 
                 16.5703 
                 2.4744 
                 1.69946 
                 56.53 
               
               
                 11 
                 226.7436 
                 1.9797 
               
               
                 *12 
                 122.2666 
                 4.1250 
                 1.51007 
                 56.24 
               
               
                 *13 
                 318.7030 
                 1.2375 
               
               
                 14 
                 −107.0069 
                 2.2600 
                 1.84481 
                 29.86 
               
               
                 15 
                 16.9691 
                 3.5363 
                 1.48746 
                 64.27 
               
               
                 16 
                 −49.0550 
                 3.2975 
               
               
                 17 
                 27.7522 
                 1.5008 
                 1.48751 
                 57.34 
               
               
                 18 
                 −4594.9840 
                 13.2789 
               
               
                 19 
                 38.8081 
                 2.2341 
                 1.66731 
                 32.33 
               
               
                 20 
                 161.2215 
                 0.3549 
               
               
                 21 
                 46.0541 
                 2.2326 
                 1.74816 
                 33.08 
               
               
                 22 
                 338.6393 
                 0.4569 
               
               
                 23 
                 −244.7909 
                 2.2650 
                 1.50881 
                 63.43 
               
               
                 24 
                 62.9054 
                 3.0902 
                 1.59385 
                 39.18 
               
               
                 25 
                 −67.2985 
                 0.5741 
               
               
                 26 
                 −42.8970 
                 2.7000 
                 1.73160 
                 53.18 
               
               
                 27 
                 −441.1616 
                 6.5765 
               
               
                 28 
                 −18.4239 
                 3.3000 
                 1.80991 
                 44.62 
               
               
                 29 
                 −42.4857 
                 11.6576 
               
               
                 *30 
                 −17.2281 
                 3.4991 
                 1.49100 
                 57.58 
               
               
                 *31 
                 −11.4306 
                 16.3210 
               
               
                 *32 
                 −13.6384 
                 5.0986 
                 1.49100 
                 57.58 
               
               
                 *33 
                 64.8825 
                 25.9045 
               
               
                 *34 
                 21.2202 
                 −150.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 314.3 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 47 
               
               
                   
               
               
                 EXAMPLE 16 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 3.97 
               
               
                   
                 2ω[°] 
                 159.60 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 48 
               
               
                   
               
               
                 EXAMPLE 16 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 12 
               
               
                   
                   
               
               
                   
                 KA 
                 −1.1587015E+03 
               
               
                   
                 A3 
                 −2.6120665E−05 
               
               
                   
                 A4 
                 −1.2695991E−04 
               
               
                   
                 A5 
                 1.9368835E−06 
               
               
                   
                 A6 
                 −5.0028444E−06 
               
               
                   
                 A7 
                 2.2995257E−07 
               
               
                   
                 A8 
                 2.1441755E−07 
               
               
                   
                 A9 
                 −5.8922525E−09 
               
               
                   
                 A10 
                 −8.4981907E−10 
               
               
                   
                 A11 
                 −1.1921538E−09 
               
               
                   
                 A12 
                 2.3295231E−11 
               
               
                   
                 A13 
                 3.4382533E−12 
               
               
                   
                 A14 
                 7.6230019E−12 
               
               
                   
                 A15 
                 −3.8817751E−13 
               
               
                   
                 A16 
                 −8.5102663E−15 
               
               
                   
                 A17 
                 3.4120894E−15 
               
               
                   
                 A18 
                 −4.7152682E−15 
               
               
                   
                 A19 
                 −3.8078062E−17 
               
               
                   
                 A20 
                 7.5497357E−17 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 13 
               
               
                   
                   
               
               
                   
                 KA 
                 −6.2744169E+03 
               
               
                   
                 A3 
                 −7.9005711E−05 
               
               
                   
                 A4 
                 −1.0207015E−05 
               
               
                   
                 A5 
                 −2.5931068E−05 
               
               
                   
                 A6 
                 5.6204196E−07 
               
               
                   
                 A7 
                 1.9536046E−07 
               
               
                   
                 A8 
                 5.3545102E−08 
               
               
                   
                 A9 
                 2.1293548E−07 
               
               
                   
                 A10 
                 3.3607326E−09 
               
               
                   
                 A11 
                 −2.3031204E−08 
               
               
                   
                 A12 
                 −1.7951249E−09 
               
               
                   
                 A13 
                 1.8379720E−10 
               
               
                   
                 A14 
                 3.8264717E−10 
               
               
                   
                 A15 
                 3.3715107E−11 
               
               
                   
                 A16 
                 −1.5400874E−11 
               
               
                   
                 A17 
                 −7.8824681E−14 
               
               
                   
                 A18 
                 −5.0117454E−13 
               
               
                   
                 A19 
                 1.8841489E−14 
               
               
                   
                 A20 
                 1.7154792E−14 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 30 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.9503762E−01 
               
               
                   
                 A3 
                 −5.8491507E−05 
               
               
                   
                 A4 
                 −7.8146781E−05 
               
               
                   
                 A5 
                 1.2934056E−05 
               
               
                   
                 A6 
                 8.9089980E−07 
               
               
                   
                 A7 
                 −1.8450519E−07 
               
               
                   
                 A8 
                 5.9930360E−09 
               
               
                   
                 A9 
                 −1.5846249E−10 
               
               
                   
                 A10 
                 2.5029599E−11 
               
               
                   
                 A11 
                 −1.0327021E−12 
               
               
                   
                 A12 
                 −8.4867084E−14 
               
               
                   
                 A13 
                 6.0251682E−15 
               
               
                   
                 A14 
                 3.0893042E−17 
               
               
                   
                 A15 
                 1.4113052E−18 
               
               
                   
                 A16 
                 −5.1330874E−19 
               
               
                   
                 A17 
                 −7.4152610E−20 
               
               
                   
                 A18 
                 7.6488837E−21 
               
               
                   
                 A19 
                 −2.5272112E−22 
               
               
                   
                 A20 
                 1.8072971E−24 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 31 
               
               
                   
                   
               
               
                   
                 KA 
                 1.6797579E−01 
               
               
                   
                 A3 
                 −1.6611232E−04 
               
               
                   
                 A4 
                 9.4682232E−05 
               
               
                   
                 A5 
                 −1.3829502E−05 
               
               
                   
                 A6 
                 4.6355743E−06 
               
               
                   
                 A7 
                 −5.3633840E−07 
               
               
                   
                 A8 
                 3.9219226E−08 
               
               
                   
                 A9 
                 −1.7717638E−09 
               
               
                   
                 A10 
                 −3.4187551E−11 
               
               
                   
                 A11 
                 6.7006420E−12 
               
               
                   
                 A12 
                 3.5926093E−14 
               
               
                   
                 A13 
                 −2.2073744E−14 
               
               
                   
                 A14 
                 1.5657581E−16 
               
               
                   
                 A15 
                 5.9195497E−17 
               
               
                   
                 A16 
                 −2.4024388E−18 
               
               
                   
                 A17 
                 2.1095060E−20 
               
               
                   
                 A18 
                 1.3148771E−22 
               
               
                   
                 A19 
                 1.3131270E−23 
               
               
                   
                 A20 
                 −3.5014132E−25 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 32 
               
               
                   
                   
               
               
                   
                 KA 
                 −9.8418190E+00 
               
               
                   
                 A3 
                 −4.0624612E−03 
               
               
                   
                 A4 
                 −9.9250632E−05 
               
               
                   
                 A5 
                 2.4118088E−06 
               
               
                   
                 A6 
                 3.7110006E−07 
               
               
                   
                 A7 
                 3.5789032E−07 
               
               
                   
                 A8 
                 −4.2590496E−08 
               
               
                   
                 A9 
                 8.9262884E−10 
               
               
                   
                 A10 
                 7.1518698E−11 
               
               
                   
                 A11 
                 −1.6592929E−12 
               
               
                   
                 A12 
                 −1.9885938E−13 
               
               
                   
                 A13 
                 7.3679429E−15 
               
               
                   
                 A14 
                 3.3057642E−16 
               
               
                   
                 A15 
                 −2.9874900E−17 
               
               
                   
                 A16 
                 8.3135603E−19 
               
               
                   
                 A17 
                 −1.5274389E−20 
               
               
                   
                 A18 
                 7.1776388E−22 
               
               
                   
                 A19 
                 −2.6263932E−23 
               
               
                   
                 A20 
                 3.2336776E−25 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 33 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.7572211E+03 
               
               
                   
                 A3 
                 −1.9905092E−03 
               
               
                   
                 A4 
                 −1.1637874E−04 
               
               
                   
                 A5 
                 −2.7098745E−06 
               
               
                   
                 A6 
                 2.5884194E−06 
               
               
                   
                 A7 
                 −2.2640692E−07 
               
               
                   
                 A8 
                 6.1093455E−09 
               
               
                   
                 A9 
                 3.4354415E−10 
               
               
                   
                 A10 
                 −3.5202993E−11 
               
               
                   
                 A11 
                 7.7541210E−13 
               
               
                   
                 A12 
                 3.5282913E−14 
               
               
                   
                 A13 
                 −1.7134594E−15 
               
               
                   
                 A14 
                 −1.5495969E−17 
               
               
                   
                 A15 
                 9.4419789E−19 
               
               
                   
                 A16 
                 5.7476033E−20 
               
               
                   
                 A17 
                 −1.7457513E−21 
               
               
                   
                 A18 
                 −5.2028340E−23 
               
               
                   
                 A19 
                 2.4924611E−24 
               
               
                   
                 A20 
                 −2.6080823E−26 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 34 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.5240145E+00 
               
               
                   
                 A3 
                 −1.9286019E−05 
               
               
                   
                 A4 
                 1.7668451E−07 
               
               
                   
                 A5 
                 3.9992188E−09 
               
               
                   
                 A6 
                 −2.4527463E−10 
               
               
                   
                 A7 
                 1.5311011E−12 
               
               
                   
                 A8 
                 4.5638539E−14 
               
               
                   
                 A9 
                 −4.6896864E−16 
               
               
                   
                 A10 
                 3.5785627E−18 
               
               
                   
                 A11 
                 −1.3751802E−19 
               
               
                   
                 A12 
                 1.3911262E−21 
               
               
                   
                 A13 
                 −4.0646214E−24 
               
               
                   
                 A14 
                 1.1081513E−25 
               
               
                   
                 A15 
                 −1.1139248E−27 
               
               
                   
                 A16 
                 −4.6280612E−29 
               
               
                   
                 A17 
                 1.5204343E−30 
               
               
                   
                 A18 
                 −1.8772399E−32 
               
               
                   
                 A19 
                 1.0063718E−34 
               
               
                   
                 A20 
                 −1.7551965E−37 
               
               
                   
                   
               
            
           
         
       
     
     Next, a projection optical system in Example 17 will be described.  FIG. 17  is a cross section illustrating the structure of the projection optical system in Example 17. Table 49 shows basic lens data on the projection optical system in Example 17, and Table 50 shows data about specification. Table 51 shows data about aspherical surface coefficients.  FIG. 34  is a diagram illustrating distortion performance, and  FIG. 51  is a diagram illustrating spot performance. 
     In Example 17, Surface 21 through Surface 20 are optical element Lp, Surface 25 through Surface 22 are a first lens group, Surface 21 through Surface 15 are a 2a-th lens group, and Surface 14 through Surface 5 are a 2b-th lens group. 
     
       
         
           
               
             
               
                 TABLE 49 
               
             
            
               
                   
               
               
                 EXAMPLE 17 • LENS DATA (n, ν FOR d-LINE) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Ri 
                   
                 Ndj 
                   
               
               
                 Si 
                 (CURV- 
                 Di 
                 (RE- 
                 νdj 
               
               
                 (SURFACE 
                 ATURE 
                 (SURFACE 
                 FRACTIVE 
                 (ABBE 
               
               
                 NUMBER) 
                 RADIUS) 
                 DISTANCE) 
                 INDEX) 
                 NUMBER) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 1 
                 ∞ 
                 1.5500 
                 1.51680 
                 64.20 
               
               
                 2 
                 ∞ 
                 0.0000 
               
               
                 3 
                 ∞ 
                 10.6000 
                 1.84666 
                 23.78 
               
               
                 4 
                 ∞ 
                 6.0005 
               
               
                 5 
                 18.9205 
                 3.2903 
                 1.75345 
                 52.66 
               
               
                 6 
                 −169.5404 
                 0.1990 
               
               
                 7 
                 28.4640 
                 1.6650 
                 1.84500 
                 22.75 
               
               
                 8 
                 14.7639 
                 3.1274 
                 1.82319 
                 45.68 
               
               
                 9 
                 −143.2185 
                 0.4787 
               
               
                 *10 
                 58.9029 
                 4.1250 
                 1.51007 
                 56.24 
               
               
                 *11 
                 59.0005 
                 0.7877 
               
               
                 12 
                 −68.7558 
                 2.2600 
                 1.84502 
                 22.75 
               
               
                 13 
                 18.4710 
                 1.7129 
                 1.65893 
                 58.55 
               
               
                 14 
                 −76.5603 
                 5.8046 
               
               
                 15 
                 32.7560 
                 1.3427 
                 1.71841 
                 32.31 
               
               
                 16 
                 −179.3248 
                 5.5780 
               
               
                 17 
                 40.7001 
                 2.3222 
                 1.83194 
                 23.40 
               
               
                 18 
                 −36.2430 
                 0.9991 
                 1.48749 
                 65.48 
               
               
                 19 
                 107.6291 
                 4.3351 
               
               
                 20 
                 −13.2419 
                 3.3000 
                 1.83484 
                 29.89 
               
               
                 21 
                 −68.6753 
                 5.1774 
               
               
                 *22 
                 −14.7770 
                 3.5010 
                 1.49100 
                 57.58 
               
               
                 *23 
                 −8.3245 
                 13.5225 
               
               
                 *24 
                 −11.3030 
                 4.4994 
                 1.49100 
                 57.58 
               
               
                 *25 
                 60.9090 
                 30.6513 
               
               
                 *26 
                 37.6466 
                 −150.0000 
                 REFLECTION 
               
               
                   
                   
                   
                 SURFACE 
               
               
                   
               
               
                 ENTRANCE PUPIL POSITION: 450.0 FROM FIRST SURFACE 
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 50 
               
               
                   
               
               
                 EXAMPLE 17 • SPECIFICATION (d-LINE) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                 FNo. 
                 3.78 
               
               
                   
                 2ω[°] 
                 147.40 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 51 
               
               
                   
               
               
                 EXAMPLE 17 • ASPHERICAL SURFACE COEFFICIENT 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 10 
               
               
                   
                   
               
               
                   
                 KA 
                 −2.0000001E+02 
               
               
                   
                 A3 
                 −2.0608485E−06 
               
               
                   
                 A4 
                 −2.2367059E−04 
               
               
                   
                 A5 
                 −2.4777364E−07 
               
               
                   
                 A6 
                 −2.1566237E−06 
               
               
                   
                 A7 
                 3.5005867E−07 
               
               
                   
                 A8 
                 −3.1394773E−07 
               
               
                   
                 A9 
                 1.9989087E−07 
               
               
                   
                 A10 
                 −4.3110702E−08 
               
               
                   
                 A11 
                 −2.3089218E−09 
               
               
                   
                 A12 
                 3.4509613E−09 
               
               
                   
                 A13 
                 −8.7868845E−10 
               
               
                   
                 A14 
                 1.1533089E−10 
               
               
                   
                 A15 
                 −8.0572036E−12 
               
               
                   
                 A16 
                 2.3712436E−13 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 11 
               
               
                   
                   
               
               
                   
                 KA 
                 9.8589363E+01 
               
               
                   
                 A3 
                 −1.1031376E−04 
               
               
                   
                 A4 
                 −2.3161674E−04 
               
               
                   
                 A5 
                 −5.3127939E−06 
               
               
                   
                 A6 
                 −1.4741562E−05 
               
               
                   
                 A7 
                 1.3487739E−05 
               
               
                   
                 A8 
                 −3.7148720E−06 
               
               
                   
                 A9 
                 1.3162064E−07 
               
               
                   
                 A10 
                 6.4016856E−08 
               
               
                   
                 A11 
                 1.6986505E−08 
               
               
                   
                 A12 
                 −4.0186408E−09 
               
               
                   
                 A13 
                 −2.3297468E−09 
               
               
                   
                 A14 
                 8.8545192E−10 
               
               
                   
                 A15 
                 −1.1144580E−10 
               
               
                   
                 A16 
                 4.9506701E−12 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 22 
               
               
                   
                   
               
               
                   
                 KA 
                 9.0926128E−06 
               
               
                   
                 A3 
                 −2.8227329E−05 
               
               
                   
                 A4 
                 −2.4729788E−05 
               
               
                   
                 A5 
                 1.5310496E−05 
               
               
                   
                 A6 
                 2.5974141E−07 
               
               
                   
                 A7 
                 −2.4627082E−07 
               
               
                   
                 A8 
                 −4.9697654E−09 
               
               
                   
                 A9 
                 3.0455089E−09 
               
               
                   
                 A10 
                 4.7094904E−11 
               
               
                   
                 A11 
                 −3.4004259E−11 
               
               
                   
                 A12 
                 1.9970819E−12 
               
               
                   
                 A13 
                 −1.1995782E−13 
               
               
                   
                 A14 
                 1.6375356E−14 
               
               
                   
                 A15 
                 −1.0568710E−15 
               
               
                   
                 A16 
                 2.2938782E−17 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 23 
               
               
                   
                   
               
               
                   
                 KA 
                 1.7871517E−01 
               
               
                   
                 A3 
                 −1.8662288E−04 
               
               
                   
                 A4 
                 1.6820070E−04 
               
               
                   
                 A5 
                 −1.4740000E−05 
               
               
                   
                 A6 
                 3.6348908E−06 
               
               
                   
                 A7 
                 −3.7716615E−07 
               
               
                   
                 A8 
                 3.4224910E−08 
               
               
                   
                 A9 
                 −2.7347524E−09 
               
               
                   
                 A10 
                 8.9405987E−11 
               
               
                   
                 A11 
                 −3.8618208E−12 
               
               
                   
                 A12 
                 5.6698147E−13 
               
               
                   
                 A13 
                 6.7031004E−14 
               
               
                   
                 A14 
                 −1.6432750E−14 
               
               
                   
                 A15 
                 1.0214001E−15 
               
               
                   
                 A16 
                 −2.1230747E−17 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 24 
               
               
                   
                   
               
               
                   
                 KA 
                 −5.9145369E+00 
               
               
                   
                 A3 
                 −4.1853991E−03 
               
               
                   
                 A4 
                 −2.9526853E−04 
               
               
                   
                 A5 
                 −1.9583792E−07 
               
               
                   
                 A6 
                 4.1682669E−06 
               
               
                   
                 A7 
                 1.8217440E−07 
               
               
                   
                 A8 
                 −4.2361684E−08 
               
               
                   
                 A9 
                 −2.3791647E−09 
               
               
                   
                 A10 
                 4.5146294E−10 
               
               
                   
                 A11 
                 −5.0525982E−12 
               
               
                   
                 A12 
                 −1.2113652E−12 
               
               
                   
                 A13 
                 2.0487937E−14 
               
               
                   
                 A14 
                 3.1280781E−15 
               
               
                   
                 A15 
                 −1.4729329E−16 
               
               
                   
                 A16 
                 1.9269750E−18 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 25 
               
               
                   
                   
               
               
                   
                 KA 
                 −5.0000001E+02 
               
               
                   
                 A3 
                 −2.7819326E−03 
               
               
                   
                 A4 
                 −1.3760975E−04 
               
               
                   
                 A5 
                 1.5886030E−06 
               
               
                   
                 A6 
                 4.2566726E−06 
               
               
                   
                 A7 
                 −5.5623976E−07 
               
               
                   
                 A8 
                 3.2449967E−08 
               
               
                   
                 A9 
                 −1.4404690E−09 
               
               
                   
                 A10 
                 1.4126691E−10 
               
               
                   
                 A11 
                 −1.4620887E−11 
               
               
                   
                 A12 
                 9.0638146E−13 
               
               
                   
                 A13 
                 −3.4143557E−14 
               
               
                   
                 A14 
                 8.4125438E−16 
               
               
                   
                 A15 
                 −1.4197753E−17 
               
               
                   
                 A16 
                 1.3267372E−19 
               
               
                   
                   
               
               
                   
                   
                 SURFACE NUMBER 
               
               
                   
                   
                 26 
               
               
                   
                   
               
               
                   
                 KA 
                 −3.1118883E+00 
               
               
                   
                 A3 
                 2.0340631E−05 
               
               
                   
                 A4 
                 −1.3965350E−05 
               
               
                   
                 A5 
                 2.6181849E−06 
               
               
                   
                 A6 
                 −2.4143206E−07 
               
               
                   
                 A7 
                 1.3148226E−08 
               
               
                   
                 A8 
                 −4.4574735E−10 
               
               
                   
                 A9 
                 8.8689764E−12 
               
               
                   
                 A10 
                 −7.1990857E−14 
               
               
                   
                 A11 
                 −6.9016277E−16 
               
               
                   
                 A12 
                 1.3883358E−17 
               
               
                   
                 A13 
                 2.0275535E−19 
               
               
                   
                 A14 
                 −7.2527639E−21 
               
               
                   
                 A15 
                 7.2481660E−23 
               
               
                   
                 A16 
                 −2.5849556E−25 
               
               
                   
                   
               
            
           
         
       
     
     Table 52 shows values corresponding to conditional formulas (1) through (5) about projection optical systems in Examples 1 through 17. In all of the examples, d-line is reference wavelength, and the following Table 52 shows values at this reference wavelength. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 52 
               
               
                   
               
             
            
               
                   
                 EXAMPLE 1 
                 EXAMPLE 2 
                 EXAMPLE 3 
                 EXAMPLE 4 
                 EXAMPLE 5 
                 EXAMPLE 6 
               
               
                   
               
               
                 (ZL + ZD) × Ymin/Ymax 2   
                 1.42 
                 1.49 
                 1.59 
                 1.61 
                 2.17 
                 2.17 
               
               
                 Ymin/Ymax 
                 0.11 
                 0.12 
                 0.14 
                 0.14 
                 0.16 
                 0.16 
               
               
                 (ZL + ZD)/Ymax 
                 13.21 
                 12.22 
                 11.66 
                 11.17 
                 13.78 
                 13.78 
               
               
                 |cosθ − 2cosφcosψ| 
                 0.21 
                 0.23 
                 0.26 
                 0.30 
                 0.34 
                 0.34 
               
               
                 (ZL + ZD)/Hm 
                 1.23 
                 1.20 
                 1.21 
                 1.27 
                 1.59 
                 1.46 
               
               
                   
               
               
                   
                 EXAMPLE 7 
                 EXAMPLE 8 
                 EXAMPLE 9 
                 EXAMPLE 10 
                 EXAMPLE 11 
                 EXAMPLE 12 
               
               
                   
               
               
                 (ZL + ZD) × Ymin/Ymax 2   
                 2.17 
                 2.11 
                 1.94 
                 1.77 
                 2.08 
                 2.27 
               
               
                 Ymin/Ymax 
                 0.16 
                 0.16 
                 0.14 
                 0.13 
                 0.15 
                 0.15 
               
               
                 (ZL + ZD)/Ymax 
                 13.78 
                 13.39 
                 13.55 
                 14.17 
                 13.82 
                 15.11 
               
               
                 |cosθ − 2cosφcosψ| 
                 0.34 
                 0.34 
                 0.30 
                 0.24 
                 0.31 
                 0.35 
               
               
                 (ZL + ZD)/Hm 
                 1.36 
                 1.42 
                 1.48 
                 1.34 
                 1.48 
                 1.96 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 EXAMPLE 13 
                 EXAMPLE 14 
                 EXAMPLE 15 
                 EXAMPLE 16 
                 EXAMPLE 17 
               
               
                   
                   
               
               
                   
                 (ZL + ZD) × Ymin/Ymax 2   
                 2.27 
                 2.12 
                 1.81 
                 1.22 
                 1.50 
               
               
                   
                 Ymin/Ymax 
                 0.15 
                 0.14 
                 0.13 
                 0.06 
                 0.10 
               
               
                   
                 (ZL + ZD)/Ymax 
                 15.11 
                 14.77 
                 13.83 
                 19.20 
                 14.55 
               
               
                   
                 |cosθ − 2cosφcosψ| 
                 0.34 
                 0.34 
                 0.29 
                 0.18 
                 0.28 
               
               
                   
                 (ZL + ZD)/Hm 
                 1.95 
                 2.07 
                 1.93 
                 1.60 
                 1.74 
               
               
                   
                   
               
            
           
         
       
     
     As the above data show, all of the projection optical systems in Examples 1 through 17 satisfy conditional formulas (1) through (5). It is recognizable that all of the projection optical systems can display a magnified video image in sufficient size on a screen at a short projection distance while achieving reduction in the size and the cost of the optical system. 
     Next, embodiments of a projection-type display apparatus according to the present invention will be described with reference to  FIG. 54 .  FIG. 54  is a schematic diagram illustrating the configuration of a projection-type display apparatus according to an embodiment of the present invention. 
     A projection-type display apparatus  100  illustrated in  FIG. 54  includes the projection optical system  10  according to an embodiment of the present invention, a light source  20 , transmission-type display devices  11   a  through  11   c , as light valves corresponding to light of respective colors, and an illumination optical unit  30  for guiding rays from the light source  20  to the light valves. The illumination optical unit  30  includes dichroic mirrors  12  and  13  for color separation, a cross-dichroic prism  14  for color combination, condenser lenses  16   a  through  16   c , and total reflection mirrors  18   a  through  18   c . In  FIG. 54 , the projection optical system  10  is schematically illustrated. Further, an integrator, such as a fly-eye integrator, is arranged between the light source  20  and the dichroic mirror  12 . However, the integrator is not illustrated in  FIG. 54 . 
     White light that has been output from the light source  20  is separated into rays of three colors (G light, B light and R light) by the dichroic mirrors  12  and  13  in the illumination optical unit  30 . After then, optical paths of the separated rays of respective colors are deflected by the total reflection mirrors  18   a  through  18   c , respectively. Further, the separated rays enter transmission-type display devices  11   a  through  11   c  corresponding to the rays of respective colors through condenser lenses  16   a  through  16   c , respectively, and are optically modulated. After the colors are combined by the cross-dichroic prism  14 , the light enters the projection optical system  10 . The projection optical system  10  projects an optical image of the light that has been optically modulated by the transmission-type display devices  11   a  through  11   c  onto a screen, which is not illustrated. 
     As the transmission-type display devices  11   a  through  11   c , for example, transmission-type liquid crystal display devices or the like may be used.  FIG. 54  illustrates an example in which transmission-type display devices are used as light valves. However, light valves provided in the projection-type display apparatus of the present invention are not limited to the transmission-type display devices. Other light modulation means, such as a reflection-type liquid crystal display device or a DMD, may be used. 
     So far, the present invention has been described by using embodiments and examples. However, the present invention is not limited to the aforementioned embodiments nor examples, and various modifications are possible. For example, a curvature radius, a distance between surfaces, a refractive index, an Abbe number and the like of each lens element are not limited to the values in each of the above numerical value examples, but may be other values.