Abstract:
A method of manufacturing an exposure apparatus includes a step of providing a projection optical system that projects a pattern image formed on a mask onto a photosensitive substrate. Additionally, a surface of a correction member having a predetermined thickness is locally tooled or processed in order to correct random aberration that remains in the projection optical system. The tooled correction member is arranged between the mask and the substrate, irrespective of the mask. Furthermore, when the projection optical system is provided, an aberration caused due to the predetermined thickness of the correction member is taken into account in advance.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a projection exposure apparatus for illuminating a first object with light to reduction-project a pattern on the first object thus illuminated onto a substrate or the like as a second object. More particularly, the invention relates to a projection exposure apparatus suitable for projecting a circuit pattern formed on a reticle (mask) as the first object onto a substrate (wafer) as the second object to effect exposure thereon. 
     2. Related Background Art 
     As patterns for integrated circuits become finer, demands for performance of the projection exposure apparatus used in printing on a wafer are becoming increasingly tougher these days. 
     Under such circumstances, a projection optical system is required to have a higher resolving power, flatness of image plane, less distortion, etc. Because of those, attempt has been made to reduce the distortion by shortening an exposure wavelength λ, increasing the numerical aperture NA of the projection optical system, or decreasing the curvature of field. Some examples of such attempts are those described in U.S. Pat. No. 5,260,832, Japanese Laid-open Patent Application No. 5-173065, etc. 
     Also, Japanese Laid-open Patent Applications No. 59-144127 and No. 62-35620 describe methods for adjusting only a magnification error. The former describes a technique that a curved film, for example a pellicle, which is very thin and which does not affect imaging performance, is set in an optical path. The latter describes a technique that a rotationally symmetric plano-convex lens or a combination of rotationally symmetric plano-convex and plano-concave lenses is moved along the optical axis to isotropically adjust the overall magnification on the wafer surface. 
     The high-performance projection optical systems as disclosed in U.S. Pat. No. 5,260,832 and Japanese Laid-open Patent Application No. 5-173065, however, include a lot of constituent lenses, i.e., 15 to 24 lenses. Particularly, in the case of high-resolution projection optical systems with numerical aperture NA being at least 0.4, the number of constituent lenses is very large, i.e., 20 or more. Thus, as the demand performance becomes higher, the projection optical systems are further increasing the number of constituent lenses and are becoming very complicated in structure. Therefore, in order to actually produce these projection optical systems, to mount them on projection exposure apparatus, keeping aberrations such as the curvature of field, the astigmatism, the distortion, etc. within ranges as designed, and then to obtain high performance, the accuracy of individual lens components and the accuracy of assembling must be controlled very strictly, which would raise problems of poor yield, very long production period, or failing to deliver sufficient performance, etc. 
     Further, the method for correcting the magnification error as described in Japanese Laid-open Patent Application No. 59-144127 includes a step of curving a very thin film or the like not affecting the imaging performance of the optical system so as to correct the magnification error by the prism effect thereof, but it cannot make fine adjustment for a correction amount or a correction direction of an asymmetric magnification error component with directionality remaining in the projection optical system. In addition, because it employs the thin film, the film can be two-dimensionally held as bonded on a metal frame or the like for long and narrow exposure areas as in the mirror projection method, but it is very difficult for such a thin film to be three-dimensionally held and to reveal good reproducibility for rectangular or square exposure areas. If glass etc. is used instead of the thin film for holding the shape, it is also difficult to form a thin and uniform film without affecting the imaging performance. Further, there are serious problems, e.g., durability of the film etc. including breakage accident due to heat absorption or the like of exposure light in actual use of such films etc., a change in optical performance with heat absorption of exposure light or with an environmental change, etc. 
     Further, Japanese Laid-open Patent Application No. 62-35620 discloses the technique that the magnification error is adjusted using a rotationally symmetric lens, but only moving the rotationally symmetric lens along the optical axis can adjust only the overall magnification on the wafer surface only on an isotropic basis and cannot adjust the asymmetric magnification error component with directionality remaining in the projection optical system. 
     Moreover, the methods for correcting the magnification error as disclosed in Japanese Laid-open Patent Applications No. 59-144127 and No. 62-35620 can basically correct only the magnification error, but they cannot correct the astigmatism etc. as off-axial aberrations. Further, it was also difficult for the methods to handle rotationally asymmetric magnification error components or distortion components locally remaining at random in the projection optical system. 
     SUMMARY OF THE INVENTION 
     The present invention has been accomplished taking the above problems into account. It is, therefore, an object of the present invention to provide a high-performance projection exposure apparatus excellent in durability and reproducibility, which can adjust, without a very strict control of the accuracy of individual components and the accuracy of assembling, optical characteristics which are rotationally asymmetric with respect to the optical axis of projection optical system and which remain in the projection optical system, for example rotationally asymmetric off-axial aberration components (astigmatism, curvature of field, etc.), rotationally asymmetric magnification error components, etc. Further, an auxiliary object of the invention is to provide a projection exposure apparatus which can satisfactorily deal with correction of rotationally asymmetric distortion etc. locally remaining at random on a rotationally asymmetric basis in the projection optical system. 
     The above object and other objects will be further apparent from the following description. 
     Provided according to the present invention is a projection exposure apparatus comprising an illumination optical system for illuminating a first object, a projection optical system for projecting an image of the first object illuminated by the illumination optical system onto a second object under a predetermined magnification, and an optical means set between the first object and the second object, having rotationally asymmetric powers with respect to an optical axis of the projection optical system, for correcting an optical characteristic rotationally asymmetric with respect to the optical axis of the projection optical system, remaining in the projection optical system. 
     Also provided according to the present invention is a projection exposure apparatus comprising an illumination optical system for illuminating a first object, and a projection optical system for projecting an image of the first object illuminated by the illumination optical system onto a second object under a predetermined magnification, wherein the projection optical system has a lens, the surface thereof contributes to imaging performance of the projection optical system and has a rotationally asymmetric region having rotationally asymmetric powers with respect to the optical axis of the projection optical system, in order to correct an optical characteristic rotationally asymmetric with respect to the optical axis of the projection optical system, remaining in the projection optical system. 
     The present invention will become more fully understood from the detailed description given hereinbelow and the accompanying drawings which are given by way of illustration only, and thus are not to be considered as limiting the present invention. 
     Further scope of applicability of the present invention will become apparent from the detailed description given hereinafter. However, it should be understood that the detailed description and specific examples, while indicating preferred embodiments of the invention, are given by way of illustration only, since various changes and modifications within the spirit and scope of the invention will become apparent to those skilled in the art from this detailed description. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a drawing to illustrate the principle when a toric lens is a negative cylindrical lens; 
     FIG. 2 is a drawing to illustrate the principle when a toric lens is a positive cylindrical lens; 
     FIG. 3 is a drawing to show the effect by the negative cylindrical lens of FIG. 1; 
     FIG. 4 is a drawing to show the effect by the positive cylindrical lens of FIG. 2; 
     FIG. 5 is a plan view to show a state of beam cross section on a virtual plane shown in FIG. 3; 
     FIG. 6 is a plan view to show a state of beam cross section on a virtual plane shown in FIG. 4; 
     FIG. 7 is a drawing to show a geometrical-optic relation of the negative cylindrical lens shown in FIG. 3; 
     FIG. 8 is a drawing to show a geometrical-optic relation of the positive cylindrical lens shown in FIG. 4; 
     FIG. 9 is a drawing to show a geometrical-optic relation of a projection optical system; 
     FIG. 10 is a drawing to show a geometrical-optic relation where a cylindrical lens as a toric lens is placed between the projection optical system shown in FIG. 9 and a reticle; 
     FIG. 11 is a drawing to show a geometrical-optic relation where a cylindrical lens as a toric lens is placed in the vicinity of the pupil of the projection optical system shown in FIG. 9; 
     FIG. 12 is a drawing to show the overall structure of an embodiment according to the present invention; 
     FIG. 13 is a plan view to show the structure of a reference reticle; 
     FIG. 14A is a drawing to show a state where a positive cylindrical lens and a negative cylindrical lens as toric lenses are placed between the wafer and the projection lens; 
     FIG. 14B is a drawing to show a state where a positive cylindrical lens and a negative cylindrical lens as toric lenses are placed at or near the position of the pupil of the projection lens; 
     FIG. 14C is a drawing to show a state where positive cylindrical lenses as toric lenses are placed between the reticle and the projection lens and between the projection lens and the wafer, respectively; 
     FIG. 14D is a drawing to show a state where a pair of a positive cylindrical lens and a negative cylindrical lens as toric lenses are placed between the reticle and the projection lens and another pair thereof between the projection lens and the wafer; 
     FIG. 14E is a drawing to show a state where a pair of a positive cylindrical lens and a negative cylindrical lens as toric lenses are placed between the reticle and the projection lens and another pair thereof at or near the position of the pupil of the projection lens; 
     FIG. 14F is a drawing to show a state where a pair of a positive cylindrical lens and a negative cylindrical lens as toric lenses are placed between the reticle and the projection lens, another pair thereof at or near the position of the pupil of the projection lens, and another pair thereof between the projection lens and the wafer; 
     FIG. 15 is a structural drawing to show an embodiment in which some constituent lenses of the projection lens are toric optical members having a rotationally asymmetric lens power; 
     FIG. 16 is a lens constitutional drawing to show an appearance of the projection lens shown in FIG. 15 when it is seen along a direction parallel to the plane of FIG. 15; and 
     FIG. 17 is a drawing to show the overall structure of an embodiment using the projection lens shown in FIG.  15  and FIG.  16 . 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     As shown in FIG. 1, let f 1  be a focal length in the meridional direction (the direction of yy′ plane) of a cylindrical lens  1  having a negative refracting power, which is a kind of toric lens having different powers in orthogonal directions, d 11  be a distance from the cylindrical lens  1  to a reticle surface  4  (xy plane) as a first object, and d 11  be a position of an image point (virtual image) formed between the object point (reticle surface  4 ) and the cylindrical lens  1  by the cylindrical lens  1  where the object point is at the center position of the reticle surface  4  (a position of intersection between the reticle surface and the optical axis Ax). In this case, the below formulas (1) and (2) provide an image magnification β1 in the Y direction rotated by θ from the y axis (or in the direction of a plane including the optical axis Ax and the Y axis) by the cylindrical lens  1 , and the distance d 11  between the cylindrical lens  1  and the image point position (hereinafter simply referred to as an image position). Although not shown in FIG. 1, a projection optical system for projecting a pattern on a reticle onto a wafer is provided on the opposite side to the reticle surface  4  with respect to the cylindrical lens, which is the case as to FIG. 2 to FIG. 4 as detailed later. 
     
       
         β1 =f 1/( d 11.cos 2   θ+f 1)  (1) 
       
     
     
       
           d 12= d 11 .f 1/( d 11.cos 2   θ+f 1)  (2) 
       
     
     Similarly, the following formulas (3) and (4) provide an image magnification β1′ and an image position d 12 ′ in the X direction (or in the direction of a plane including the optical axis Ax and the X axis) perpendicular to the Y direction. 
     
       
         β1′ =f 1/( d 11.sin 2   θ+f 1)  (3) 
       
     
     
       
           d 12′= d 11 .f 1/( d 11.sin 2   θ+f 1)  (4) 
       
     
     Accordingly, an astigmatism amount AS 1  is given by the following formula (5). 
     
       
           AS 1 =d 12 −d 12′  (5) 
       
     
     It is thus understood that d 11  in formula (1) to formula (4) changes by moving the cylindrical lens  1 , which changes the astigmatism amount from formula (5) and which also changes the magnifications of formula (1) and formula (3). 
     On the other hand, it is also understood that θ in formula (1) to formula (4) changes by rotating the cylindrical lens  1 , which changes the astigmatism amount from formula (5) and which also changes the magnifications of formula (1) and formula (3). 
     Further, as shown in FIG. 2, let f 2  be a focal length in the meridional direction (or in the direction of yy′ plane) of a cylindrical lens  2  having a positive refracting power, which is a kind of toric lens, d 21  be a distance from the cylindrical lens  2  to the reticle surface  4  (xy plane) as a first object, and d 21  be a position of an image point formed by the cylindrical lens  2  where the object point is at the center position of the reticle surface  4  (a position of intersection between the reticle surface and the optical axis Ax). In this case, the below formulas (6) and (7) provide an image magnification β2 in the Y direction rotated by θ from the y axis (or in the direction of a plane including the optical axis Ax and the Y axis) by the cylindrical lens, and the distance d 21  between the cylindrical lens  2  and the image point position (hereinafter simply referred to as an image position). 
     
       
         β2 =f 2/( d 21.cos 2   θ+f 2)  (6) 
       
     
     
       
           d 22= d 21 .f 2/( d 21.cos 2   +f 2)  (7) 
       
     
     Similarly, the following formulas (8) and (9) provide an image magnification β2′ and an image position d 22 ′ in the X direction (or in the direction of a plane including the optical axis Ax and the X axis) perpendicular to the Y direction. 
     
       
         β2′ =f 2/( d 21.sin 2   θ+f 2)  (8) 
       
     
     
       
           d 22′= d 21 .f 2/( d 21.sin 2   θ+f 2)  (9) 
       
     
     Accordingly, an astigmatism amount AS 2  is given by the following formula. 
     
       
           AS 2 =d 22 −d 22′  (10) 
       
     
     It is thus understood that d 21  in formula (6) to formula (9) changes by moving the cylindrical lens  2 , which changes the astigmatism amount from formula (10) and which also changes the magnifications of formula (6) and formula (8). 
     On the other hand, it is also understood that θ in formula (6) to formula (9) changes by rotating the cylindrical lens  2 , which changes the astigmatism amount from formula (10) and which also changes the magnifications of formula (6) and formula (8). 
     Now, AS 1 , AS 2  expressed by the above formula (5) or formula (10) is an astigmatism amount which can be corrected by either cylindrical lens ( 1 ,  2 ). 
     In that case, a best focus plane is given by either one of the following formulas. 
     
       
         (d12+d12′)/2  (11) 
       
     
      (d22+d22′)/2  (12) 
     Since the best focus plane changes depending upon d 11 , d 21 , or θ, it is clear that an amount of the curvature of field also changes. 
     As described above, it is seen that amounts and directions of the image magnification, the astigmatism, and the curvature of field can be adjusted by moving a toric lens such as a cylindrical lens along the optical axis or rotating it. Another possible method is to change the focal length of the toric lens itself, other than the above method of adjustment. 
     Meanwhile, let θ=0 in order to estimate an amount of correction of maximum astigmatism when the cylindrical lens  2  shown in FIG. 2 is used. The maximum astigmatism in that case is given as follows. 
     
       
           AS 2 max =−( d 21) 2 /( d 21 +f 2)  (13) 
       
     
     It was found that the maximum astigmatism amount AS 2   max  to be corrected was not more than 10 −5  L from results of repetitive trial printings and studies with a projection exposure apparatus for printing a line width of 10 or less microns where L was a distance between a reticle as the first object and a wafer as the second object. 
     Accordingly, supposing d 21 &lt;10 −2  L, 
     
       
         |f2|≧10L  (14) 
       
     
     from formula (13). The focal length of the positive cylindrical lens  2  preferably satisfies the above condition of the range in formula (14). 
     For a combination of two or more toric lenses such as the cylindrical lenses as shown in FIG.  1  and FIG. 2 or for a combination with another optical element, a new object point is defined at an image position in a noted direction, of an image formed by a first toric lens or another optical element from the object point of reticle  4 , a distance is recalculated between the new object point and the next toric lens or another optical element, and the distance is put in d 11  or d 21 . 
     Next studied is a case wherein the negative cylindrical lens  1  shown in FIG.  1  and the positive cylindrical lens  2  shown in FIG. 2 are arranged in series along the optical axis. 
     Here, if directions of generatrices of the two cylindrical lenses  1 ,  2  are coincident with each other and if a product of the image magnifications of the two cylindrical lenses is  1 , that is, if |β1·β2|=1, combined powers of the two cylindrical lenses  1 ,  2  in all directions become approximately zero, thus not changing the optical characteristics such as the magnification and off-axial aberrations (astigmatism, curvature of field, etc.) at all. 
     On the other hand, if the directions of generatrices of the two cylindrical lenses  1 ,  2  are perpendicular to each other, they produces a maximum magnification and maximum off-axial aberrations. 
     Accordingly, it is understood that adjustment can be achieved by relatively rotating the two cylindrical lenses  1 ,  2 , for correction amounts or correction directions of asymmetric magnification error components and off-axial aberration components with directionality remaining in the projection optical system. 
     Where two negative cylindrical lenses  1  shown in FIG. 1 are arranged in series along the optical axis or where two positive cylindrical lenses  2  shown in FIG. 2 are arranged in series along the optical axis, the maximum magnification and maximum off-axial aberrations can be generated when the directions of generatrices of the respective cylindrical lenses are coincident with each other; whereas, they can have substantially the same lens effect as a single, rotationally symmetric, spherical lens, when the directions of generatrices of the respective cylindrical lenses are perpendicular to each other. 
     As described above, amounts and directions of the optical characteristics such as the magnification and off-axial aberrations (astigmatism, curvature of field, etc.) can be arbitrarily adjusted by using at least two cylindrical lenses each being a kind of toric lens and arranging at least one of the cylindrical lenses so as to be rotatable. 
     The above description mainly concerned the adjustment for the astigmatism and the curvature of field, but the adjustment of magnification error is next described in detail referring to FIG. 3 to FIG. 7 when the negative cylindrical lens  1  shown in FIG. 1 or the positive cylindrical lens  2  shown in FIG. 2 is rotated about the optical axis Ax. 
     FIG. 3 shows a state when a bundle of parallel rays in radius R around the optical axis Ax are let to enter the negative cylindrical lens  1  shown in FIG.  1 . Here, in FIG. 3, a circle  13  represents a locus when the bundle of parallel rays in radius R around the optical axis Ax pass the reticle surface  4  (xy plane), while an ellipse  11  is a locus when a beam diverged by the cylindrical lens  1  from the bundle of parallel rays in radius R around the optical axis Ax, passes the virtual plane (x′y′ plane). Also, FIG. 5 shows a state of beam size on the virtual plane (x′y′ plane) shown in FIG.  3 . 
     On the other hand, FIG. 4 shows a state when a bundle of parallel rays in radius R around the optical axis Ax are let to enter the positive cylindrical lens  2  shown in FIG.  2 . Here, in FIG. 4, a circle  13  represents a locus when the bundle of parallel rays in radius R around the optical axis Ax pass the reticle surface  4  (xy plane), while an ellipse  12  is a locus when a beam converged by the cylindrical lens  2  from the bundle of parallel rays in radius R around the optical axis Ax, passes the virtual plane (x′y′ plane). Also, FIG. 6 shows a state of beam size on the virtual plane (x′y′ plane) shown in FIG.  4 . 
     When the cylindrical lens  1 ,  2  is rotated about the optical axis, the ellipse  11  in FIG. 3 or the ellipse  12  in FIG. 4 also rotates with the rotation. 
     As shown in FIG. 7, letting ΔR 1  be a change amount of the beam size in the y′ direction (in the direction of a plane including the optical axis Ax and the y′ axis) being the meridional direction on the virtual plane (x′y′ plane) by the negative cylindrical lens  1 , and e 1  be a distance between the negative cylindrical lens  1  and the virtual plane (x′y′ plane), the following relation holds. 
     
       
         Δ R 1 =−R·e 1 /f 1  (15) 
       
     
     Similarly, as shown in FIG. 8, letting ΔR 2  be a change amount of the beam size in the y′ direction (in the direction of a plane including the optical axis Ax and the y′ axis) being the meridional direction on the virtual plane (x′y′ plane) by the positive cylindrical lens  2 , and e 2  be a distance between the positive cylindrical lens  2  and the virtual plane (x′y′ plane), the following relation holds. 
     
       
         Δ R 2 =−R·e 2 /f 2  (16) 
       
     
     As shown in FIG. 5 or FIG. 6, let R 1 , R 2  be a y′-directional length (a half of the major axis in FIG. 5 or a half of the minor axis in FIG. 6) represented by a solid line on the virtual plane (x′y′ plane). Then, they are given by the following formulas. 
     
       
           R   1   =R (1 −e 1 /f 1)  (17) 
       
     
     
       
           R   2   =R (1 −e 2 /f 2)  (18) 
       
     
     Since the x′-directional length is R in either case, the ellipse  11  and ellipse  12  indicated by the solid lines in FIG.  5  and in FIG. 6 can be expressed by the following formulas. 
     
       
           x′   2   /R   2   +y′   2 /[(1 −e 1 /f 1)· R]   2 =1  (19) 
       
     
     
       
           x′   2   /R   2   +y′   2 /[(1 −e 2 /f 2)· R]   2 =1  (20) 
       
     
     As described, where there is an asymmetric magnification error for example as shown in FIG. 6 inside the projection optical system, the beam size as shown in FIG. 6 can be arbitrarily changed from ellipse to circle by rotating the cylindrical lens  1  of FIG. 3 having the optical characteristics as shown in FIG. 5, whereby the asymmetric magnification error can be adjusted. Conversely, where there is an asymmetric magnification error for example as shown in FIG. 5 inside the projection optical system, the beam size as shown in FIG. 5 can be arbitrarily changed from ellipse to circle by rotating the cylindrical lens  2  of FIG. 4 having the optical characteristics shown in FIG. 6, whereby the asymmetric magnification error can be adjusted. 
     Here, when the negative cylindrical lens  1  as shown in FIG. 1 was used and when the distance is L between a reticle as the first object and a wafer as the second object, results of repetitive trial printings and studies with a projection exposure apparatus for printing a line width of 10 or less microns showed that a correction amount of maximum magnification error was preferably not more than 10 −4  (=100 ppm). 
     Modifying the above formula (1) showing the relation between the focal length f 1  of cylindrical lens  1  and the magnification β1 of cylindrical lens  1 , the following formula is obtained. 
     
       
           f 1=(− d 11·β1)/(β1−1)  (21) 
       
     
     Converting the above correction amount of maximum magnification error, 10 −4  (=100 ppm), into β1, β1=0.9999 (or 1.0001). Accordingly, supposing d 11 ≦10 −2  L, 
     
       
         |f1|≧10 2  L  (22) 
       
     
     from formula (21). Thus, it is preferred that the focal length of the negative cylindrical lens  1  satisfy the condition of the range of above formula (22). 
     The above description showed an example for correcting the magnification error by rotating a toric lens (cylindrical lens) about the optical axis, but it is apparent from the above formulas (1), (3), (6), and (8) that the magnification error can also be corrected by shifting a toric lens (cylindrical lens) along the optical axis. In this case, it is more preferable that the above formula (22) be satisfied. 
     Incidentally, the above description concerned that the magnification error was able to be corrected using a toric lens (cylindrical lens), but amounts and directions of the optical characteristics such as the magnification error can also arbitrarily be adjusted by using at least two cylindrical lenses each being a kind of toric lens and arranging at least one of the cylindrical lenses so as to be rotatable. 
     Thus, a possible arrangement is such that the negative cylindrical lens  1  shown in FIG.  1  and the positive cylindrical lens  2  shown in FIG. 2 are arranged in series along the optical axis of the projection optical system and that they are arranged as rotatable relative to each other. In this case, because the negative cylindrical lens  1  has the optical characteristics as shown in FIG.  5  and the positive cylindrical lens  2  has the optical characteristics as shown in FIG. 6, it is understood that a beam size formed by these cylindrical lenses ( 1 ,  2 ) becomes a combination of the beam sizes shown in FIG.  5  and FIG.  6  and that the combined beam size can be arbitrarily changed from ellipse to circle by relatively rotating them, whereby the asymmetric magnification error can be corrected. 
     Further, where the projection optical system has the asymmetric magnification error for example as shown in FIG. 5 or FIG. 6, the beam size as shown in FIG. 5 or FIG. 6 can be arbitrarily changed from ellipse to circle by arranging at least two or more cylindrical lenses in series along the optical axis and arranging at least one of the cylindrical lenses as rotatable, thereby enabling to adjust the asymmetric magnification error. 
     Where two or more toric lenses (cylindrical lenses) are combined or where a toric lens is combined with another optical element, pursuit may be done under such an assumption that a light beam obtained when a noted beam passes the first toric lens (cylindrical lens) or another optical element, is considered as a new beam and that the new beam enters the next toric lens (cylindrical lens) etc. 
     In a combination of two toric lenses (cylindrical lenses), where the negative cylindrical lens  1  as shown in FIG.  1  and the positive cylindrical lens  2  as shown in FIG. 2 are set as close to each other, the total lens power in each direction becomes nearly zero, thus, the beam shape is not changed, when the directions of generatrices of the lenses are coincident with each other; whereas, a change of the shape becomes maximum, when the directions of generatrices of the lenses are perpendicular to each other. 
     Further, where two negative cylindrical lenses  1  as shown in FIG. 1 are arranged in series along the optical axis, or where two positive cylindrical lenses  2  as shown in FIG. 2 are arranged in series along the optical axis, a maximum magnification and maximum off-axial aberrations can be generated when the directions of generatrices of the cylindrical lenses are coincident with each other; whereas, they can have the same lens effect as a single, rotationally symmetric, spherical lens, when the directions of generatrices of the cylindrical lenses are perpendicular to each other. 
     As described, using at least two cylindrical lenses each being a kind of toric lens and arranging at least one of them as rotatable, amounts and directions of the optical characteristics such as the magnification and off-axial aberrations (astigmatism, curvature of field, etc.) can be arbitrarily adjusted. 
     The above formula (14) and formula (22) can be expressed in a general form as follows, where fA is a focal length of a cylindrical lens effective for correction of astigmatism and fD a focal length of a cylindrical lens effective for correction of magnification error. 
     
       
         |fA|≧10 L  (23) 
       
     
     
       
         |fD|≧10 2  L  (24) 
       
     
     It is preferred that the above formula (23) be satisfied for effectively correcting the astigmatism, and that the above formula ( 24 ) be satisfied for effectively correcting the magnification error. It should be, however, noted that the focal length (fA, fD) of cylindrical lens in this case is not limited to a single cylindrical lens, but may be applied to a combination of a plurality of toric lenses such as cylindrical lenses, or toric reflecting members. Namely, the focal length (fA, fD) of cylindrical lens becomes a combined focal length of the plurality of cylindrical lenses in the case of a combination of the plurality of toric optical members. 
     Outside the relation of formula (23) or formula (24), a toric component is too strong, which affects other aberrations causing a problem. For example, in the case of correction of astigmatism, the curvature of field or the magnification error is degraded, or in the case of correction of magnification error, the telecentricity or the astigmatism is degraded. Therefore, the correction of asymmetric aberrations can be effectively made within the above ranges. 
     Incidentally, the above formula (23) or formula (24) showed the range of optimum focal length of toric optical member, and further the range of optimum focal length of toric optical member is next studied from another point of view. 
     First, FIG. 9 shows a projection optical system having a front group GF on the reticle  4  side and a rear group GR on the wafer  5  side with an aperture stop S in-between. Here, the front group GF has a focal length of f GF  and the rear group GR a focal length of f GR . The projection optical system is telecentric both on the reticle side and on the wafer side. 
     FIG. 10 shows a state where a cylindrical lens having a positive power as a toric optical member is placed between the front group GF in the projection optical system shown in FIG. 9, and the reticle  4 . The power of the cylindrical lens  2  is present in the direction of the plane of FIG. 10 (or in the meridional direction). 
     As shown in FIG. 10, letting f 2  be a focal length of cylindrical lens  2  and D 1  be a distance between the cylindrical lens  2  and the front group GF (a distance between the principal points of the two optical systems), a combined focal length F 1  of the cylindrical lens  2  and the front group GF is given by the following relation. 
     
       
           F   1 =( f 2 ·f   GF )/( f 2 +f   GF   −D   1 )  (25) 
       
     
     Also, letting B 1  be an image magnification of the projection optical system (GF, GR) and B 1 ′ be an image magnification of the combined system of the cylindrical lens  2  and the projection optical system (GF, GR), the following relations hold. 
     
       
           B   1   =−f   GR   /f   GF   (26) 
       
     
     
       
           B   1   ′=−f   GR   /F   1   =B   1 [1+( f   GF   −D   1 )/ f 2]  (27) 
       
     
     Accordingly, a magnification difference ΔB 1  between magnifications in the sagittal direction and in the meridional direction of the projection optical system is given as follows. 
     
       
         Δ B   1   =B   1   ′−B   1   =B   1 ( f   GF   −D   1 )/ f 2  (28) 
       
     
     On the other hand, letting H 1  be the reticle-side principal point by the combined system of the cylindrical lens  2  and the front group GF, P 1  be a reticle-side focus position by the combined system of the cylindrical lens  2  and the front group GF, Δs 1  be a distance between the focus position P 1  and the reticle  4 , and Δs 1 ′ be a distance between the wafer  5  and a position Q 1  of an image of reticle  4  by the combined system of the cylindrical lens  2  and the projection optical system (GF, GR), the following relations hold. 
     
       
         Δ s   1 =( f   GF   −D   1 ) 2 /( f 2 +f   GF   −D   1 )  (29) 
       
     
     
       
         Δ s   1 ′=( B   1 ′) 2   ·Δs   1   (30) 
       
     
     Here, Δs 1 ′ means a difference between image positions in the sagittal direction and in the meridional direction of the projection optical system, that is, an astigmatism amount (astigmatic difference). 
     Also, letting NA R  be a reticle-side numerical aperture of the projection optical system and λ be a wavelength of exposure light, a depth of focus DOF R  on the reticle side of the projection optical system is as follows. 
     
       
           DOF   R =λ/( NA   R ) 2   (31) 
       
     
     Then, in order to control the astigmatism amount within the reticle-side depth of focus, the following formula is derived from the above formulas (29) and (31). 
     
       
           f 2≧−( f   GF   −D   1 )+[( NA   R ) 2 ( f   GF   −D   1 ) 2 ]/λ  (32) 
       
     
     Therefore, it is preferred that the cylindrical lens  2  be constructed so as to satisfy formula (32), whereby the astigmatism amount can be controlled within the depth of focus. 
     The following formula is a general expression of formula (32), where Δf is a power difference in orthogonal directions of the toric optical member. 
     
       
         Δ f ≧|−( f   GF   −D   1 )+[( NA   R ) 2 ( f   GF   −D   1 ) 2 ]/λ|  (33) 
       
     
     It is thus understood that the above formula (33) should be preferably satisfied in use of a toric optical member in order to control the astigmatism amount by this member within the reticle-side depth of focus of the projection optical system. It is needless to mention that the above relations of formulas (32) and (33) hold for any of projection optical systems having 1:1, reduction, or enlargement magnification. 
     As an example, suppose the reticle-side numerical aperture NA R  of the projection optical system is 0.1, the wavelength λ of exposure light is 436 nm, f GF =250 mm, f GR =250 mm, and D 1 =200 mm. From the above formula (32), the focal length f 2  in the meridional direction, of the cylindrical lens (generally speaking, from above formula (33), the power difference Δf in orthogonal directions of toric optical member) is not less than 5.7×10 4  mm, and a magnification correction amount (magnification difference ΔB 1 ) which can be variable in this case becomes not more than 870 ppm (=8.7×10 −4 ). 
     In the above description, formula (33) was derived assuming that the toric optical member was disposed between the reticle and the projection optical system, but, because the same relation holds even where the toric optical member is placed between the projection optical system and the wafer, the following relation should be preferably satisfied in that case. 
     
       
         Δ f ≧|−( f   GR   −D   1 ′)+[( NA   W ) 2 ( f   GR   −D   1 ′) 2 ]/λ|  (34) 
       
     
     Here, NA W  is the wafer-side numerical aperture of the projection optical system, and D 1 ′ is a distance between the toric optical member and the rear group GR (a distance between the principal points of the two optical systems). 
     Next studied referring to FIG. 11 is the range of optimum focal length of cylindrical lens  2  where a positive cylindrical lens  2  is placed between the front group GF and the rear group GR in the projection optical system, in other words, in the vicinity of the aperture stop S. 
     FIG. 11 shows a state where a cylindrical lens  2  having a positive power as a toric optical member is placed between the front group GF and the rear group GR in the projection optical system shown in FIG.  9 . The power of the cylindrical lens  2  is present in the direction of the plane of FIG. 11 (or in the meridional direction). 
     Here, as shown in FIG. 11, letting f 2  be a focal length of the cylindrical lens  2  and D 2  be a distance between the front group GF and the cylindrical lens  2  (a distance between the principal points of the two optical systems), the following relation holds for a combined focal length F 2  of the front group GF and the cylindrical lens  2 . 
     
       
           F   2 =( f 2 ·f   GF )/( f 2 +f   GF   −D   2 )  (35) 
       
     
     Also, letting B 2  be an image magnification of the projection optical system (GF, GR) and B 2 ′ be an image magnification of the combined system of the cylindrical lens  2  and the projection optical system (GF, GR), the following relations hold. 
     
       
           B   2   =−f   GR   /f   GF   (36) 
       
     
     
       
           B   2   ′=−f   GR   /F   2   =B   2 [1+( f   GF   −D   2 )/ f 2]  (37) 
       
     
     Accordingly, a magnification difference ΔB 2  between the magnifications in the sagittal direction and in the meridional direction of the projection optical system is as follows. 
     
       
         Δ B   2   =B   2   ′−B   2   =B   2 ( f   GF   −D   2 )/ f 2  (38) 
       
     
     On the other hand, letting H 2  be the reticle-side principal point by the combined system of the front group GF and the cylindrical lens  2 , P 2  be a reticle-side focus position by the combined system of the front group GF and the cylindrical lens  2 , Δs 2  be a distance between the focus position P 2  and the reticle  4 , and Δs 2 ′ be a distance between the wafer  5  and a position Q 2  of an image of reticle  4  by the combined system of the projection optical system (GF, GR) and the cylindrical lens  2 , the following relations hold. 
     
       
         Δ s   2 =( f   GF ) 2 /( f 2 +f   GF   −D   2 )  (39) 
       
     
     
       
         Δ s   2 ′=( B   2 ′) 2   ·Δs   2   (40) 
       
     
     Here, Δs 2 ′ means a difference between image positions in the sagittal direction and in the meridional direction of the projection optical system, that is, an astigmatism amount (astigmatic difference). 
     Then, in order to control the astigmatism amount within the reticle-side depth of focus of the projection optical system, the following formula is derived from the above formulas (31) and (39). 
     
       
           f 2≧−( f   GF   −D   2 )+[( NA   R ) 2 ( f   GF ) 2 ]/λ  (41) 
       
     
     Accordingly, the cylindrical lens  2  is preferably constructed so as to satisfy formula (41), whereby the astigmatism amount can be controlled within the depth of focus. 
     The following formula presents a general expression of formula (41) as a power difference Δf in orthogonal directions of the toric optical member. 
     
       
         Δ f ≧|−( f   GF   −D   2 )+[( NA   R ) 2 ( f   GF ) 2 ]/λ|  (42) 
       
     
     It is thus understood that the above formula (42) should be preferably satisfied in use of a toric optical member in order to control the astigmatism amount by this member within the reticle-side depth of focus of the projection optical system. It is needless to mention that the above relations of formulas (41) and (42) hold for any of projection optical systems having 1:1, reduction, or enlargement magnification. 
     As an example, suppose the reticle-side numerical aperture NA R  of the projection optical system is 0.1, the wavelength λ of exposure light is 436 nm, f GF =250 mm, f GR =250 mm, and D 2 =200 mm. From the above formula (41), the focal length f 2  in the meridional direction, of the cylindrical lens (generally speaking, from above formula (42), the power difference Δf in orthogonal directions of toric optical member) is not less than 1.43×10 6  mm, and a magnification correction amount (magnification difference ΔB 1 ) which can be variable in this case becomes not more than 35 ppm (=3.5×10 −5 ). 
     From the results of the above analysis with FIG. 9 to FIG. 11, where the toric optical member is placed between the reticle and the projection optical system or between the projection optical system and the wafer, the contribution of correction to the magnification error can be increased while suppressing the contribution of correction to the astigmatism; while, where the toric optical member is placed at or near the pupil of the projection optical system, the contribution of correction to the astigmatism can be increased while suppressing the contribution of correction to the magnification error. 
     The toric optical member stated in the present invention may be replaced by a toric lens having different powers in orthogonal directions, obtained by polishing a rotationally symmetric spherical surface more in one direction. A projection optical system using such a toric lens will be described herein later. Further, the toric optical member may be a reflecting mirror having different powers in orthogonal directions, or a distributed index lens having different powers in orthogonal directions. 
     Incidentally, the above description concerned the correction of rotationally asymmetric aberrations such as the astigmatism, the curvature of field, the magnification error, etc. using the toric optical member having different powers in orthogonal directions as an aspherical surface rotationally asymmetric with respect to the optical axis of the projection optical system. If rotationally asymmetric magnification error components or distortion components locally remaining at random appear in the projection optical system in addition to these aberrations and magnification error appearing on a rotationally asymmetric basis, processing such as polishing is locally applied to a lens surface of a cylindrical lens as a kind of toric optical member slidable along the optical axis or rotatable about the optical axis. Locating the thus processed cylindrical lens between the reticle and the wafer, the magnification error components and distortion components appearing at random can be corrected in addition to the correction of the astigmatism, the curvature of field, and the magnification error appearing on a rotationally asymmetric basis. 
     Further, where the projection optical system has only the magnification error components or distortion components locally remaining at random on a rotationally asymmetric basis, the magnification error components or distortion components appearing at random can be corrected by applying local processing such as polishing to an optical element (lens or reflecting mirror) itself constituting the projection optical system. 
     Also, where the projection optical system has only the magnification error components or distortion components locally remaining at random on a rotationally asymmetric basis, the magnification error components or distortion components appearing at random can be corrected by such an arrangement that a plane-parallel plate having a certain thickness is subjected to local processing such as polishing and that the thus machined plane-parallel plate is placed either between the reticle and the projection optical system, inside the projection optical system, or between the projection optical system and the wafer. In this case, a spherical aberration appears because the plane-parallel plate has the certain thickness. Then, the projection optical system can be preliminarily arranged so as to correct the spherical aberration. 
     An embodiment of the present invention is next described in detail referring to FIG.  12 . 
     FIG. 12 shows the structure of a projection exposure apparatus according to the embodiment of the present invention. As shown in FIG. 12, a reticle  35  held on a reticle stage not shown is set above a both-side (or single-side) telecentric projection lens  36 , and a toric optical member having different powers in orthogonal directions is provided as optical means having rotationally asymmetric powers with respect to the optical axis of the projection lens  36  between the reticle  35  and the projection lens  36 . This toric optical member has, in order from the reticle side, a negative cylindrical lens  1  having a concave surface facing the projection lens and a negative power in the direction of the plane of the drawing, and a positive cylindrical lens  2  having a convex surface facing the reticle and a positive power in the direction of the plane of the drawing, wherein the cylindrical lens  1  and cylindrical lens  2  each are arranged as rotatable about the optical axis of the projection lens  36 . 
     Further, a wafer  38  mounted on a wafer stage  37  is set at a position conjugate with the reticle  35  with respect to the projection lens  36 , and the wafer stage  37  is composed of a two-dimensionally movable XY stage and a Z stage movable along the optical axis of the projection lens  36 . 
     Above the reticle  35  there is an illumination optical system  21 ,  22 ,  23 ,  24 ,  25 ,  32 ,  33 ,  34  for uniformly illuminating the reticle  35  by Köhler illumination, and the illumination optical system includes a measurement system  42  for measuring the optical characteristics of the projection lens, and a first alignment system  47  for optically performing detection of relative position between the reticle  35  and the wafer  38  with light of the same wavelength as exposure light IL described below. 
     Also, an off-axis type second alignment system  48  is set outside the projection lens  36 , and the second alignment system  48  optically detects a position of the wafer  38  with light of a wavelength different from the exposure light IL described below. 
     Specifically describing the embodiment shown in FIG. 12, the exposure light IL emitted from a light source  21  such as a mercury lamp is collected by an ellipsoidal mirror  22 , then is reflected by a reflection mirror  23 , thereafter is converted into a bundle of nearly parallel rays by a collimator lens  24 , and is incident into an optical integrator  25  consisting of a fly&#39;s eye lens. A shutter  26  is provided near the second focus of the ellipsoidal mirror  22 , and the illumination light IL can be arbitrarily interrupted by rotating the shutter  26  through a drive unit  27  such as a motor. 
     When the exposure light IL is interrupted by the shutter  26 , the illumination light IL reflected by the shutter  26  is guided in the direction approximately perpendicular to the optical axis of the ellipsoidal mirror  22 . The thus guided exposure light IL is put into one end of a light guide  29  by a condenser lens  28 . Accordingly, the exposure light IL emitted from the light source  21  enters either the optical integrator  25  or the light guide  29 . 
     When the exposure light IL is incident into the optical integrator  25 , there are a lot of secondary light source images (hereinafter simply referred to as secondary light sources) formed on the reticle-side focal plane of the optical integrator  25 . A variable aperture stop  30  is set on the plane where the secondary light sources are formed. The exposure light IL emitted from the secondary light sources passes through a half mirror  31  inclined at 45° relative to the optical axis, and thereafter travels via a first condenser lens  32 , a dichroic mirror  33 , and a second condenser lens  34  to illuminate a pattern area on the lower surface of reticle  35  with uniform illuminance. 
     Upon exposure an image of the pattern on the reticle  35  is formed on the wafer  38  through the toric optical member  1 ,  2  and the projection lens  36 . In this case, because the secondary light source plane of the optical integrator  25  is conjugate with the pupil plane of the projection lens  36 , the a value indicating coherency of the illumination optical system illuminating the reticle  35  can be changed by adjusting an aperture of the variable aperture stop  30  set on the secondary light source plane. When a maximum incident angle of the exposure light IL illuminating the reticle  35  is θ IL  and a half angular aperture of the projection lens  36  on the reticle  35  side is θ PL , the a value can be expressed by sinθ IL /sinθ PL . Here, the a value is set in the range of about 0.3 to 0.7. 
     Although not shown, an aperture stop is provided at the pupil position of the projection lens  36 , and an aperture of the aperture stop may be arranged as variable. 
     An adjustment plate  39  made for example of a glass plate is fixed near a wafer holder of wafer stage  37 , and a reference pattern is formed on the surface on the projection lens  36  side, of the adjustment plate  39 . Corresponding to it, a reticle mark RM is formed at a position conjugate with the reference pattern on the adjustment plate  39  with respect to the projection lens  36 , within an image field of projection lens  36  and near the pattern area of reticle  35 . As an example, the reference pattern on the adjustment plate  39  is a cross aperture pattern formed in a light shield portion, while the reticle mark RM on the wafer  35  is a pattern obtained by inverting the light and dark portions in a pattern obtained by multiplying the reference pattern by a projection magnification of the toric optical member  1 ,  2  and projection lens  36 . 
     A condenser lens  41  and a reflective mirror  40  are set below the adjustment plate  39  of wafer stage  37 , and an exit end of the light guide  29  is fixed at the rear focal plane of condenser lens  41 . Since the surface of the exit end of the light guide  29  is conjugate with the pupil plane of projection lens  36 , it is also conjugate with the variable aperture stop  30 . Also, because the emission surface at the exit end of the light guide  29  is sized so that the size of an image projected onto the variable aperture stop  30  is nearly equal to the aperture of variable aperture stop  30 , the reference pattern on the adjustment plate  39  is illuminated at an illumination a value nearly equal to that for exposure light IL. Further, in the illumination optical system of exposure light IL, a light-receiving portion of photomultiplier  42  is set at a position conjugate with the variable aperture stop  30  with respect to the half mirror  31 . Namely, the light-receiving portion of photomultiplier  42  is arranged as conjugate with the pupil plane of projection lens  36  and with the plane of the exit end of light guide  29 . A detection surface of the light-receiving portion is sized larger than an image of the light-emitting surface of the exit end of the light guide  29  projected thereon, thereby preventing a light quantity loss. Therefore, when the reference pattern on the adjustment plate  39  is illuminated from the bottom side, most of light emerging from the reference pattern on the adjustment plate  39  enters the projection lens  36  and toric optical member  1 ,  2  no matter where the adjustment plate  39  is located in the image field of projection lens  36 , thus impinging on the light-receiving surface of photomultiplier  42  through the reticle mark RM on reticle  35 . 
     A central processing unit  43  (hereinafter referred to as CPU) is electrically connected to the photomultiplier  42 , and photoelectrically converted signals output from the photomultiplier  42  are supplied to CPU  43 . A mirror for X direction and a mirror for Y direction not shown are fixed on the upper surface of wafer stage  37 , and, therefore, coordinates of a position on the wafer stage  37  can be always monitored using a laser interferometer  44  and the two mirrors. The coordinate information from the wafer stage  37  is supplied through the laser interferometer  44  to CPU  43 , and the CPU  43  can move the wafer stage  37  to a desired coordinate position through a stage drive unit  45 . 
     The operation of the present embodiment is next described. For measuring the rotationally asymmetric optical characteristics (astigmatism, curvature of field, magnification error, distortion) rotationally asymmetric with respect to the optical axis of the projection optical system and remaining in the projection lens  36  and toric optical member  1 ,  2  because of assembling errors etc., a reference reticle  35 ′ as shown in FIG. 13 is preliminarily set on the unrepresented reticle stage. As shown in FIG. 13, light-shielding patterns of cross chromium or the like are arranged at predetermined intervals on a two-dimensional basis in a pattern area of the reference reticle  35 ′. 
     After intercepting the exposure light IL by the shutter  26  through the drive unit  27 , CPU  43  moves the adjustment plate  39  on the wafer stage  37  into the image field of projection lens  36  through the stage drive unit  45 . By this, the exposure light IL (hereinafter simply referred to as illumination light) reflected by the shutter  26  is led through the condenser lens  28  and the light guide  29  into the wafer stage  37 . After being reflected by the reflective mirror  40 , the illumination light is converted into a bundle of nearly parallel rays by the condenser lens  41  so as to illuminate the reference pattern formed on the adjustment plate  39  from the bottom side. The reference pattern on the adjustment plate  39  is projected through the projection lens  36  and toric optical member  1 ,  2  onto the light-shielding patterns of reference reticle  35 ′, and the photomultiplier  42  photoelectrically detects a matching condition between the two patterns through the second condenser lens  34 , the dichroic mirror  33 , the first condenser lens  32 , and the half mirror  31 . Then, in order to successively detect coordinates of positions of plural light-shielding patterns two-dimensionally arranged in the reference reticle  35 ′ through the photomultiplier  42 , CPU  43  successively moves the wafer stage  37  through the wafer drive unit  45  while always monitoring the coordinate position of the wafer stage  37  through the laser interferometer  44 . By this, the photomultiplier  42  photoelectrically detects respective matching conditions of the reference pattern on the adjustment plate  39  with the plural light-shielding patterns two-dimensionally arranged in the reference reticle  35 ′, and CPU  43  successively stores the coordinate positions when matched, in a first memory unit not shown in CPU  43  through the laser interferometer  44 . Further, CPU  43  has a second memory unit and a first correction amount calculating unit inside, not shown, wherein the second memory unit preliminarily stores correlational information about relations between the optical characteristics (astigmatism, curvature of field, magnification error, distortion) rotationally asymmetric with respect to the optical axis of projection optical system and relative rotation amounts of toric optical member  1 ,  2 . Accordingly, the first correction amount calculating unit calculates an optimum amount of relative rotation for the toric optical member  1 ,  2  to correct, based on information from the first and second memory units. Then, based on the correction information from the first correction amount calculating unit, CPU  43  outputs a drive signal to the drive unit  46  such as a motor, so that the drive unit  46  relatively rotates the toric optical member  1 ,  2  by the determined correction amount (rotation amount). 
     After completion of the above operation, a normal reticle  35  used in actual process is set on the reticle stage not shown, and CPU  43  changes over the shutter  26  through the drive unit  27 . By this, the exposure light IL illuminates the reticle  35  through the illumination optical system, whereby an image of the pattern on the reticle  35  is faithfully transferred through the toric optical member  1 ,  2  and projection lens  36  onto the wafer  38 . Continuous exposure transfer with the projection exposure apparatus as described could accumulate thermal energy due to the exposure light IL in the projection lens  36 , which would change the optical characteristics of projection lens  36 . Thus, during operations of exposure transfer, the optical characteristics of projection lens  36  are periodically measured as described above and the toric optical member  1 ,  2  is rotated based on the measurement results. On this occasion, it is more preferable that the above adjustment be used in combination with the well-known technique to adjust the magnification of the projection lens  36  itself by controlling the pressure between constituent lenses of the projection lens  36 . 
     It is to be desired that it is checked whether the rotationally asymmetric optical characteristics (astigmatism, curvature of field, magnification error, distortion) remaining in the projection lens  36  are corrected in a perfectly optimized state by an amount of relative rotation of the toric optical member  1 ,  2 . In this case, more perfect correction can be achieved by repeating the above-described operations. 
     In measuring the magnification error and distortion remaining in the projection lens  36 , the wafer stage  37  is two-dimensionally moved to obtain coordinate positions of the respective light-shielding patterns in the reference reticle  35 ′. In more accurately measuring the astigmatism and curvature of field remaining in the projection lens  36 , coordinate positions of the respective light-shielding patterns in the reference reticle  35 ′ are obtained so as to maximize the contrast of an output signal from the photomultiplier  42  while moving the wafer stage  37  along the optical axis of the projection lens  36 . 
     The projection exposure apparatus of the present embodiment is fully effective for nonlinear extension or contraction of wafer  38  in the semiconductor fabrication process etc., or for cases where semiconductors are fabricated by a plurality of projection exposure apparatus and there are differences of magnification error and distortion between the projection exposure apparatus. Specifically, first, in order to successively optically detect coordinate positions of plural wafer marks formed on the wafer through the second alignment system  48  set outside the projection lens  36 , CPU  43  successively moves the wafer stage  37  through the stage drive unit  45  while always monitoring the coordinate position of wafer stage  37  through the laser interferometer  44 . By this, CPU  43  successively stores the coordinate positions of respective wafer marks formed on the wafer, as obtained from the second alignment system  48  and laser interferometer  44 , in a third memory unit not shown inside CPU  43 . Further, CPU  43  has a fourth memory unit and a second correction amount calculating unit inside, not shown, wherein the fourth memory unit preliminarily stores correlational information about relations between the optical characteristics (astigmatism, curvature of field, magnification error, distortion) rotationally asymmetric with respect to the optical axis of projection optical system and amounts of relative rotation of the toric optical member  1 ,  2 . Accordingly, the second correction amount calculating unit calculates an optimum amount of relative rotation for the toric optical member  1 ,  2  to correct, based on the information from the third and fourth memory units. Then, based on the correction information from the correction amount calculating unit, CPU  43  outputs a drive signal to the drive unit  46  such as a motor, so that the drive unit  46  relatively rotates the toric optical member  1 ,  2  by the determined correction amount (rotation amount). 
     Although the above embodiment shown in FIG. 12 showed an example to correct the rotationally asymmetric optical characteristics (astigmatism, curvature of field, magnification error, distortion) remaining in the projection lens  36  by an amount of relative rotation of the toric optical member  1 ,  2 , it is needless to mention that the correction may be made by relatively moving the toric optical member  1 ,  2  along the optical axis of projection lens  36 . Also, the embodiment of FIG. 12 showed an example to automatically correct the rotationally asymmetric optical characteristics (astigmatism, curvature of field, magnification error, distortion) remaining in the projection lens  36 , but the rotation or movement of the toric optical member  1 ,  2  can be manually performed. 
     Further, the light source  21 , ellipsoidal mirror  22 , and collimator lens  24  in the present embodiment may be replaced by a laser light source such as an excimer laser etc. for supplying a bundle of parallel rays. Moreover, this laser may be combined with a beam expander for converting the laser light into a light beam having a selected beam cross section. 
     The embodiment shown in FIG. 12 showed an example in which the toric optical member  1 ,  2  is placed between the reticle and the projection lens, but the present invention is by no means limited to this arrangement. For example, arrangements as shown in FIGS. 14A to  14 F may also be employed. 
     FIG. 14A shows an example in which the toric optical member  1 ,  2  is placed between the projection lens  36  and the wafer  38 . As shown, the toric optical member  1 ,  2  has, in order from the side of wafer  38 , a negative cylindrical lens  1  with a concave surface facing the reticle  35  and a positive cylindrical lens  2  with a convex surface facing the wafer  38 . This arrangement can exert greater contribution on correction of magnification error with little affecting the astigmatism, as in the embodiment shown in FIG.  12 . Accordingly, this arrangement is effective (as the embodiment shown in FIG. 12 is similarly effective) to cases where a large magnification error remains in the projection lens  36 . 
     FIG. 14B shows an example where the projection lens  36  is composed of a front group  36 A and a rear group  36 B, and the toric optical member  1 ,  2  is placed between the front group  36 A and the rear group  36 B, i.e., at or near the pupil position of the projection lens  36 . As shown, the toric optical member  1 ,  2  has a negative cylindrical lens  1  with a concave surface facing the wafer  38  and a positive cylindrical lens  2  with a convex surface facing the reticle  35 . This arrangement can exert greater contribution on the correction of astigmatism with little affecting the magnification error. Accordingly, this arrangement is effective to cases where a large astigmatism remains in the projection lens  36 . 
     FIG. 14C shows an example where the toric optical member  2 A,  2 B is separately arranged, one on the reticle  35  side and the other on the wafer  38  side with the projection lens  36  in-between. As shown, a first positive cylindrical lens  2 A with a convex surface facing the wafer  38  is set between the reticle  35  and the projection lens  36  and a second positive cylindrical lens  2 B with a convex surface facing the reticle  35  is set between the projection lens  36  and the wafer  38 . Similarly as in the examples shown in FIG.  12  and FIG. 14A, this arrangement can exert greater contribution on the correction of magnification error with little affecting the astigmatism. 
     FIG. 14D shows an example of application of FIG. 14C, wherein negative cylindrical lenses  1 A,  1 B are combined with associated positive cylindrical lenses  2 A,  2 B set on the reticle  35  side and on the wafer  38  side, respectively, with the projection lens  36  in-between. This arrangement can exert greater contribution on the correction of magnification error with little affecting the astigmatism. In this case, out of the first toric optical member  1 A,  2 A and the second toric optical member  1 B,  2 B, one is mainly used to correct the magnification error remaining in the projection lens  36  while the other is used to correct the magnification error due to expansion or contraction of wafer  38 . Further, if, based on this arrangement, the first toric optical member  1 A,  2 A and the second toric optical member  1 B,  2 B are arranged so that one of them has a strong power but the other a weak power, the one toric optical member with strong power can be used to coarsely adjust the magnification error with little affecting the astigmatism, while the other toric optical member with weak power can be used to finely adjust the magnification error with little affecting the astigmatism. 
     FIG. 14E shows another example of application based on a combination of FIG. 14A with FIG.  14 B. As shown, a first toric optical member  1 A,  2 A composed of a negative cylindrical lens  1 A and a positive cylindrical lens  2 A is set between the reticle  35  and the projection lens (front group  36 A), and a second toric optical member  1 B,  2 B composed of a negative cylindrical lens  1 B and a positive cylindrical lens  2 B is set between the front group  36 A and the rear group  36 B (at or near the pupil position of projection lens  36 ) in the projection lens  36 . According to this arrangement, the first toric optical member  1 A,  2 A can adjust the magnification error with little affecting the astigmatism, while the second toric optical member  1 B,  2 B can adjust the astigmatism with little affecting the magnification error. Namely, the magnification error and the astigmatism can be corrected independent of each other. 
     FIG. 14F shows an example of a combination of FIG.  14 D with FIG. 14E, which can correct the magnification error and the astigmatism independently of each other and which can perform coarse adjustment and fine adjustment of each of the magnification error and the astigmatism. 
     In the above description, the cylindrical lenses  1 ,  2  etc. as the toric optical member are provided separately from the projection lens  36 , but some lenses constituting the projection lens  36  may be arranged to have a rotationally asymmetric power. A projection lens  36  having such structure is next described. 
     In the projection lens  36  shown in FIG. 15, one surface of each of lenses L 1 , L 2  is processed into a toric surface to have a curvature r am , r bm  in the direction of the plane of FIG.  15 . 
     FIG. 16 shows a state where the projection lens  36  shown in FIG. 15 is observed in the direction of the plane of FIG. 15 (or in the direction parallel to the plane of FIG.  15 ). 
     The lenses L 1 , L 2  processed into a toric surface have respective curvatures r as , r bs  in the direction of the plane of FIG. 16, as keeping the following relations. 
     
       
         r am ≠r as   
       
     
     
       
         r bm ≠r bs   
       
     
     The lenses L 1 , L 2  processed into a toric surface are rotatable about the optical axis Ax and rotatable by the drive unit  46 . 
     If formula (33) is satisfied by a power difference Δf in two mutually orthogonal directions of the toric surface in the lens L 1 , L 2 , the rotationally asymmetric magnification error can be corrected well while controlling the astigmatism amount within the reticle-side depth of focus of the projection lens  36 . 
     Similarly, one surface of lens L 8 , L 9  in the projection lens  36  is processed into a toric surface, and the lenses L 8 , L 9  are rotatable about the optical axis Ax by the drive unit  46 . 
     The toric surfaces have respective curvatures r cm , r dm  in the direction of the plane of FIG.  15  and respective curvatures r cs , r ds  in the direction of the plane of FIG.  16 . Also, there are the following relations between the curvatures. 
     
       
         r cm ≠r cs   
       
     
     
       
         r dm ≠r ds   
       
     
     If the power difference Δf in two mutually orthogonal directions of the toric surface in each lens L 8 , L 9  is selected so as to decrease the rotationally asymmetric magnification error given by formula (38), the astigmatism can be corrected well while suppressing generation of the rotationally asymmetric magnification error. 
     FIG. 17 shows the structure of an entire system using such a projection lens  36 . The drive unit  46  rotates either one pair out of the pair of lenses L 1 , L 2  and the pair of lenses L 8 , L 9 . 
     In the projection lens system  36  shown in FIG.  15  and FIG. 16, lenses other than the lenses L 1 , L 2 , L 8 , L 9 , that is, some of lenses L 3  to L 7 , L 10  to L 14  may be arranged as a toric optical member. 
     From the invention thus described, it will be obvious that the invention may be varied in many ways. Such variations are not to be regarded as a departure from the spirit and scope of the invention, and all such modifications as would be obvious to one skilled in the art are intended to be included within the scope of the following claims. 
     The basic Japanese Application No. 5-323721 filed on Dec. 22, 1993 is hereby incorporated by reference.