Patent Publication Number: US-2023137707-A1

Title: Magnification adjustable projection system using movable lens plates

Description:
This application claims the benefit of priority to U.S. Provisional Patent Application Ser. No. 63/274,684 filed on Nov. 2, 2021, the content of which is relied upon and incorporated herein by reference in its entirety. 
    
    
     FIELD OF THE DISCLOSURE 
     The present disclosure generally relates to optical projection systems, and more particularly relates to a magnification adjustable projection system for magnifying projected patterns. 
     BACKGROUND OF THE DISCLOSURE 
     Lithographic projection systems commonly project patterns onto substrates for selectively exposing photosensitive layers at multiple stages during the manufacture of microcircuits and micro devices. Image magnification of the projected patterns is finely controlled to relate the patterns in successive exposures. Lithography requires precise alignment of the current exposed layer to a previous exposed layer on a substrate. The overlay generally has been achieved by alignment of the substrate to the image and magnification of the image by adjustments in the projection lens or mask position. It may be desirable to provide an adjustment of the anamorphic magnification in any clocking direction around the optical axis without experiencing excessive degradation of the image properties. 
     SUMMARY OF THE DISCLOSURE 
     According to one embodiment of the disclosure, a magnification adjustable projection system is provided. The magnification adjustable projection system includes an imaging system having an object or image space, a first pair of cylindrical lens plates located within the object or image space for contributing a first amount of magnification power to the imaging system, wherein the first pair of cylindrical lens plates includes a first cylindrical lens plate linearly movable relative to a second cylindrical lens plate, and a second pair of cylindrical lens plates located within the object or image space in optical alignment with the first pair of cylindrical lens plates, the second pair of cylindrical lens plates contributing a second amount of magnification power to the imaging system, wherein the second pair of cylindrical lens plates comprises a third cylindrical lens plate linearly movable relative to a fourth cylindrical lens plates, wherein the first pair of cylindrical lens plates are separated along the optical axis relative to the second pair of cylindrical lens plates. The system also includes a first actuator that adjusts a first distance between the first cylindrical lens plate and the second cylindrical lens plates for adjusting the first amount of magnification power, and a second actuator that adjusts a second distance between the third cylindrical lens plate and the fourth cylindrical lens plate for adjusting the second amount of magnification power, wherein the first pair of cylindrical lens plates has a first cylindrical transverse axis that extends substantially normal to an optical axis of the imaging system and the second pair of cylindrical lens plates has a second cylindrical transverse axis that extends substantially normal to the optical axis in the imaging system, wherein the first and second pairs of cylindrical lens plates are oriented such that the first cylindrical transverse axis is approximately 45° relative to the second cylindrical transverse axis. 
     According to another embodiment of the disclosure, a magnification adjustable projection system is provided. The magnification adjustable projection system includes an imaging system having an object or image space, a first pair of cylindrical lens plates located within the object or image space for contributing a first amount of magnification power to the imaging system, wherein the first pair of cylindrical lens plates includes a first cylindrical lens plate linearly movable relative to a second cylindrical lens plate, and a second pair of cylindrical lens plates located within the object or image space in optical alignment with the first pair of cylindrical lens plates, the second pair of cylindrical lens plates contributing a second amount of magnification power to the imaging system, wherein the second pair of cylindrical lens plates comprises a third cylindrical lens plate linearly movable relative to a fourth cylindrical lens plate, wherein the first pair of cylindrical lens plates are separated along the optical axis relative to the second pair of cylindrical lens plates. The system also includes a first actuator that adjusts a first distance between the first cylindrical lens plate and the second cylindrical lens plates for adjusting the first magnification, a second actuator that adjusts a second distance between the third cylindrical lens plate and the fourth cylindrical lens plate for adjusting the second amount of magnification power, wherein the first pair of cylindrical lens plates has a first cylindrical transverse axis that extends substantially normal to an optical axis of the imaging system and the second pair of cylindrical lens plates have a second cylindrical transverse axis that extends substantially normal to the optical axis in the imaging system, wherein the first and second pairs of cylindrical lens plates are oriented such that the first cylindrical transverse axis is approximately 45° relative to the second cylindrical transverse axis, and a projection lens assembly and an illuminator for illuminating a beam of light through the projection system and onto the first and second pairs of cylindrical lens plates, wherein the projection lens assembly further comprises a first rotating corrector plate located substantially parallel to a second rotating corrector plate, wherein the first and second rotating corrector plates each have a shaped surface and are movable relative to each other to correct for astigmatism. 
     It is to be understood that both the foregoing general description and the following detailed description are merely exemplary, and are intended to provide an overview or framework to understanding the nature and character of the claims. The accompanying drawings are included to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiments, and together with the description serve to explain principles and operation of the various embodiments. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a diagram of a lithographic projection system with two pairs of the movable lens plates within telecentric image space for providing magnification adjustment; 
         FIG.  2 A  is a side view of a first pair of movable lens plates shown in  FIG.  1    in a first position; 
         FIG.  2 B  is a side view of a second pair of movable lens plates shown in  FIG.  1    in a second position; 
         FIG.  2 C  is a perspective view of the two overlapping pairs of movable lens plates each having transverse axes arranged in different directions at forty-five degrees (45°) relative to each other; 
         FIG.  2 D  is a top exploded view of the first and second pair of movable lens plates oriented at a rotated transverse angle of forty-five degrees (45°); 
         FIG.  3 A  is a top view of a pair of rotating corrector plates for use in the projection system, according to one example; 
         FIG.  3 B  is a side view of the pair of rotating corrector plates shown in  FIG.  3 A ; 
         FIG.  4 A  is a field distortion map showing 0° clocking of anamorphic magnification distortion in the image space; 
         FIG.  4 B  is a field distortion map showing 90° clocking of anamorphic magnification distortion rotated as skew in the image space; 
         FIG.  5    is a graph illustrating the relative adjustments of cylinder axial shifts of the pairs of lens plates for anamorphic distortion throughout the anamorphic clocking; 
         FIG.  6    is a graph illustrating fitted distortion terms for 100 ppm anamorphic distortion throughout the anamorphic clocking; 
         FIG.  7    is a graph illustrating maximum residual distortion of the image over the field throughout the anamorphic clocking; 
         FIG.  8    is a graph illustrating resultant defocus value of the image over the field throughout the anamorphic clocking; 
         FIG.  9 A  is a graph illustrating resultant astigmatism without the rotating corrector plates throughout the anamorphic clocking; 
         FIG.  9 B  is a graph illustrating the resultant astigmatism with the rotating corrector plates throughout the anamorphic clocking; 
         FIG.  10    is a graph illustrating optimal rotations of the rotatable corrector plates throughout the anamorphic clocking; 
         FIG.  11 A  is a graph illustrating the resultant RMS wavefront error without the rotating corrector plates over the field throughout the anamorphic clocking; and 
         FIG.  11 B  is a graph illustrating the resultant RMS wavefront error with the rotating correcting plates over the field throughout the anamorphic clocking. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to the present preferred embodiments, examples of which are illustrated in the accompanying drawings. Whenever possible, the same reference numerals will be used throughout the drawings to refer to the same or like parts. 
     The following detailed description represents embodiments that are intended to provide an overview or framework for understanding the nature and character of the claims. The accompanied drawings are included to provide a further understanding of the claims and constitute a part of the specification. The drawings illustrate various embodiments, and together with the descriptions serve to explain the principles and operations of these embodiments as claimed. 
     Referring to  FIG.  1   , a microlithographic projection system (tool)  10  is illustrated, as an example of a projection system which includes a light source  12 , an illuminator  14 , and a projection lens assembly  16  that serves as an imaging system for projecting an image of a reticle  18  onto a substrate  20 . A horizontal X-Y-axis stage  22 , which is translatable in two orthogonal directions normal to a common optical axis  24  of the illuminator  14  and the projection lens assembly  16 , provides for relatively moving the substrate  20  with respect to the projection lens assembly  16  for exposing successive areas of the substrate  20 . A vertical Z-axis stage  26  provides for relatively translating the projection lens assembly  16  with respect to the substrate  20  along the optical axis  24  to provide for appropriately focusing the image of the reticle  18  onto the substrate  20 . 
     The light source  12  emits radiation in the form of a beam of light  28  appropriate for developing the photosensitive substrate  20 . A variety of known devices can be used for the light source  12  including a lamp source, such as a high-pressure mercury arc lamp targeting certain spectral lines, or a laser source, such as an excimer laser, particularly for operating within the ultraviolet spectrum. 
     The illuminator  14  provides for shaping and spatially distributing the light beam  28  and targeting angular and spatial irradiance profiles set for both the pupil and image plane of the projection lens assembly, the latter coinciding with the substrate  20 . Although not shown in detail in  FIG.  1   , typical illuminators for microlithographic operations include a profiler for collecting and shaping the beam  28 , a uniformizer (e.g., a kaleidoscope or fly&#39;s eye array) for integrating the light into a uniform irradiance field, and a relay lens for relaying an image of the output of the uniformizer to the reticle  18 , where an image plane of the illuminator  14  coincides with an object plane of the projection lens assembly  16 . 
     The projection lens assembly  16  is shown in a simplified view having a first lens element  16 A receiving the beam of light from the illuminator  14  and a second lens element  16 B outputting the light to the first and second pairs of movable lens plates  40 A and  40 B. The projection lens assembly  16  may include more than two lens elements such as twelve to thirty elements, for example. The first lens element  16 A has a posterior surface on the upper light input side and the second lens element  16 B has a posterior surface on the lower light output side. The first lens element  16 A is spaced from the second lens element  16 B so as to create a desired size beam of light entering the first and second pairs of movable lens plates  40 A and  40 B. Disposed between the first and second lens elements  16 A and  16 B are first and second corrector lens plates  60 A and  60 B which is in the pupil region of the projection. The projection lens assembly  16 , which may have an entrance numerical aperture (NA) larger than an exit numerical aperture of the illuminator  14  for providing partial coherent imaging, projects an image of the reticle  18  onto the substrate  20 . That is, a pupil (not shown) of the projection lens assembly  16 , which is typically conjugate to a pupil (also not shown) in the illuminator  14 , may be underfilled by the image of the illuminator pupil but is sized to collect angularly divergent light from illuminated features of the reticle  18  to produce a high resolution image of the reticle  18  on the substrate  20 . The projected image of the reticle  18  can be enlarged or reduced as required by shifting height of the reticle or one or more lens elements within the projection lens assembly  16 . Reduction or enlargement is a rotationally symmetrical magnification change which may be needed for achieving full clocking range of anamorphic magnification. The projection lens assembly  16  can include reflective or diffractive elements as well as refractive elements or combinations of such elements, such as in catadioptric optics. 
     The reticle  18 , also referred to as a “mask,” includes one or more patterns intended for projection onto the substrate  20  and can be sized within or beyond the field captured by the projector lens assembly  16 . Reticles with larger patterns can be relatively translated with respect to the projection lens assembly  16  to expose different parts of the reticle patterns in succession. 
     The photosensitive substrate  20  is shown generally in the form of a flat plate, such as a semiconductor wafer or glass panel treated with a photoresist to react to exposures of light. Often, the entire substrate  20  cannot be imaged at once, so the horizontal X-Y-axis translational stage  22  on a base  30  provides for translating the substrate  20  through a range of positions for collectively illuminating a desired working area of the substrate  20 . The projection lens assembly  16  is supported on a stage  26  above the base  30 . The substrate  20  may be adjusted vertically to adjust the image distance of the projection lens assembly  16  from the substrate  20  along the optical axis  24  to maintain focus. A controller  32  coordinates relative motions among the projection lens assembly  16 , the reticle  18 , and the substrate  20  as well as the exposure of the projection system  10 . 
     First and second pairs of movable cylindrical lens plates  40 A and  40 B are shown located below the projection lens assembly  16  within a telecentric image space  38  of the projection lens assembly  16 . The first and second pairs of movable cylindrical lens plates  40 A and  40 B each have two cylindrical lens plates with top and bottom curved cylindrical shaped surfaces having cylindrical transverse axes for the shaped surfaces with each pair of movable lens plates  40 A and  40 B, the individual lens plates move axially with respect to each other. Although shown in telecentric image space  38  adjacent to the substrate  20 , the first and second pairs of movable cylindrical lens plates  40 A and  40 B could also be located in telecentric object space  36 . The choice can be made largely on the basis of space and access considerations. In either or both locations, the first and second pairs of movable cylindrical lens plates  40 A and  40 B can control magnification in a lithographic projection system that is telecentric in both image and object space. 
     The first pair of movable cylindrical lens plates  42  includes a first cylindrical lens plate  42 A axially aligned with a second cylindrical lens plate  44 A. The first cylindrical lens plate  42 A is axially movable along the optical axis  24  relative to the second cylindrical lens plate  44 A. Similarly, the second pair of cylindrical lens plates  40 B includes a third cylindrical lens plate  42 B axially movable along the optical axis  24  relative to a fourth cylindrical lens plate  44 B. The first pair of cylindrical lens plates  40 A are located within the object or image space for contributing a first amount of magnification power to the imaging system. The second pair of cylindrical lens plates  40 B are located within the object or image space in optical alignment on optical axis  24  with the first pair of cylindrical lens plates  40 A and contribute a second amount of magnification power in the imaging system. The first pair of cylindrical lens plates  40 A are separated by an axial distance D in the range of about 2 to 10 mm, for example, along the optical axis  24  relative to the second pair of lens plates  40 B. 
     A first actuator  52 A is operatively coupled to one of the first pair of movable cylindrical lens plates, specifically shown operatively coupled to the second cylindrical lens plate  44 A. The first actuator  52 A may include an electric motor that actuates the second cylindrical lens plate  44 A to move relative to the first cylindrical lens plate  42 A axially along optical axis  24  between a first position shown in  FIG.  2 A  and an extended position separated and distanced from the first cylindrical lens plate  42 A by distance D 2 . Similarly, a second actuator  52 B is operatively coupled to the second pair of movable cylindrical lens plates  40 B, particularly shown operatively coupled to the fourth cylindrical lens plate  44 B for actuating the fourth cylindrical lens plate  44 B to move relative to the third cylindrical lens plate  42 B axially along optical axis  24 . The second actuator  52 B may include an electric motor for moving the fourth cylindrical lens plate  44 B from a position in close contact to the third cylindrical lens plate  42 B to an extended position separated from the third cylindrical lens plate  42 B by distance D 2  as shown in  FIG.  2 B . 
     The first cylindrical lens plate  42 A has a slightly curved cylindrical upper posterior surface  48 A and a greater curved cylindrical lower anterior surface  46 A. The second cylindrical lens plate  44 A has a curved cylindrical upper posterior surface  46 A and a slightly cylindrical lower anterior surface  52 A. Each of the upper surface  48 A and lower surface  52 A are slightly curved in the shape of a partial cylinder having a transverse axis defining the longitudinal axis of the cylinder. The lower anterior surface  50 A of the first cylindrical lens plate  42 A and the posterior surface  46 A of the second cylindrical lens plate  44 A each have a curved cylindrical surface that is substantially similar or identical in shape with a substantially similar radius of curvature and conform to one another when the first and second cylindrical lens plates  42 A and  44 A abut one another as shown in  FIG.  2 A . Each of the anterior surface  50 A and posterior surface  46 A is curved in the shape of a partial cylindrical having radius of curvature and a transverse axis defining the longitudinal axis of the cylinder. 
     The third cylindrical lens plate  42 B has an upper posterior surface  48 B and a lower anterior surface  46 B. The fourth cylindrical lens plate  44 B has an upper posterior surface  46 B and a lower anterior surface  52 B. The upper surface  48 B and lower surface  52 B are slightly curved each with a partial cylindrical shape having a transverse axis. The lower anterior surface  46 B of the third cylindrical lens plate  42 B and the posterior surface  50 B of the fourth cylindrical lens plate  44 B each have a greater and substantially similar cylindrical shaped surface with a substantially similar radius of curvature and a transverse axis such that both surfaces conforms to one another such that the cylindrical surfaces  46 B and  50 B may abut one another. 
     Referring to  FIGS.  2 C and  2 D , the upper first pair of cylindrical lens plates  40 A is shown having both the first and second cylindrical lens plates  42 A and  44 A each having cylindrical shaped surfaces each curved about a cylindrical transverse axis  70 A extending substantially normal to the optical axis  24  and between a pair of opposing corners. The bottom pair of cylindrical lens plates  40 B are shown having the third and fourth cylindrical lens plates  42 B and  44 B each curved about a second cylindrical transverse axis  70 B extending substantially normal to the optical axis  24  and midway through opposite sides of the lens plates  42 B and  44 B. The first and second pairs of movable lens plates  40 A and  40 B are oriented such that the first cylindrical transverse axis  70 A is approximately forty-five degrees (45°) relative to the second cylindrical transverse axis  70 B. As seen, the first pair of movable lens plates  40 A may be larger in size than the second pair of movable plates  40 B due to the forty-five degree (45°) relative rotation in order to overlap and cover the entire same imaging field shown by dashed lines  75 . 
     The first pair of movable cylindrical lens plates  40 A is located within the object or image space for contributing a first magnification power to the imaging system as a function of the amount of cylindrical curvature of the first and second cylindrical lens plates  42 A and  44 A and the distance D 1  between the first and second cylindrical lens plates  42 A and  44 A. The second pair of movable cylindrical lens plates  40 B is also located within the object or image space for contributing a second amount of magnification power to the imaging system as a function of an amount of the cylindrical curvature of the third and fourth cylindrical lens plates  42 B and  44 B and the distance D 2  between the third and fourth cylindrical lens plates  42 B and  44 B. The first and second cylindrical lens plates  42 A and  44 B are movable axially relative to each other and a third and fourth cylindrical lens plates  42 B and  44 B are likewise movable axially relative to each other to change the magnification of light passing through the first and second pairs of movable lens plates  40 A and  40 B. With the first and second lens plates  42 A and  44 A abutting one another with distance D 1  equal to about zero as shown in  FIG.  2 A , an inner radii and air gap do not act on the rays significantly, and the outer radii form the equivalent of a glass bent plate, or cylindrical glass lens with little or no optical power. The anamorphic magnification decreases the image size in the Y direction, but not in the X direction. When the distance D 2  is increased between two of the movable lens plates as shown in  FIG.  2 B , the cylindrical power of an air lens formed between the two lens plates  42 B and  44 B will counteract the cylindrical power of the glass lenses. The air lens may operate as a bent plate of air or cylindrical air lens with little or no optical power. The radii may be designed to have no anamorphic magnification at midtravel of the elements. This enables the projection system  10  to generate continuously variable anamorphic magnification of both signs (inward and outward) by continuously varying the air space size. The static cylindrical glass lens generated by the outer radii provide an offset in anamorphic magnification that allows the various thickness cylindrical lenses to produce both signs of anamorphic magnification. It should be appreciated that one or the other or both of the first and second cylindrical lens plates  42 A and  44 A and that one or the other or both of the second cylindrical lens plates  42 B and  44 B may be moved to change the size of the air lens between the corresponding lens plates. 
     The projection system  10  shown in  FIG.  1    provides one example of an enlarging magnification. Each of lens plates  42 A and  42 B are configured as negative cylinder lenses and lens plates  44 A and  44 B are configured as positive cylinder lenses, in the example shown. However, the projection system  10  may likewise be applied to a reducing magnification system. Each of the first, second, third and fourth lens plates  42 A,  44 A,  42 B,  44 B may be made of optical glass, such as glass, in either an anamorphis or crystalline form to provide for the transmission of light without generating unnecessary wave front aberrations or departures from uniformity. 
     A relatively pure magnification change accompanying a cylindrical distortion of the lens plates can be derived by considering how a tilted plate laterally deviates the telecentric rays. The deviation may be a function of the tilt, thickness and refractive index of the lens plate. The telecentric rays are the rays that pass through the center of the aperture stop of the imaging lens and are parallel in the telecentric image or object space. A lens plate with cylindrical shaped surfaces can be considered on a localized level as a plurality of individually tilted plates whose tilt increases by a sign function with distance from the optical axis, and the relationship between ray deviation and distance from the optical axis is highly linear for small curvatures. This linearity means that the deviations are proportional to the distance from the optical axis and the deviations have predominantly changed only the magnification of the image in the direction of the curvature and not the distortion. 
     The first and second pairs of movable cylindrical lens plates  40 A and  40 B may have no optical power, so as to maintain telecentricity across the field, and to avoid other aberrations. Spherical and axial color aberrations may occur when focusing through a glass plate. The projection lens assembly  16  can be designed to have the opposite spherical and axial color of that induced by the first and second pairs of movable cylindrical lens plates  40 A and  40 B so that the aberrations will cancel. Astigmatism may be produced when imaging through the cylindrical glass lens plates or air plates between each of the two pairs of cylindrical glass lens plates. This astigmatism may change the orientation as the first and second pairs of movable cylindrical lens plates  40 A and  40 B are actuated for different magnitudes and clockings of anamorphic magnification, such that dynamic correction may be needed. The astigmatism produced may be largely uniform over the field. 
     In order to correct for the astigmatism, the projection lens assembly  16  includes first and second rotating corrector plates  60 A and  60 B which are shown in more detail in  FIGS.  3 A and  3 B . The first and second rotating corrector plates  60 A and  60 B are located in the pupil space of the projection lens assembly  16  between lenses elements  16 A and  16 B and can generate the opposite astigmatism at any clocking over the image field that is created by the use of the first and second pairs of movable lens plates  40 A and  40 B. The interfacing surfaces of the first and second rotating corrector plates  60 A and  60 B have respective shaped surfaces  62 A and  62 B that depart from a planar surface. The opposing surface  64 A and  64 B are shown as generally planar. The shaped surfaces may each be in shape of a sag which is a shape of the astigmatism that is created. This may be a hyperbolic paraboloid or a saddle shape as shown in  FIG.  3 B . The shape may be the fifth Fringe Zernike term that is in cylindrical coordinates defined as Z 5 R 2  cos(2θ), where R is the distance from the optical axis and θ is the clocking around the perimeter of the round corrector plates  60 A and  60 B. The Z 5  is the Zernike coefficient that is a distance of half of the peak-to-valley (P-V) of the shape. The Sixth Zernike uses sine instead of cosine, so it is the same shape but rotated forty-five degrees (45°). The summation of both shapes with a set of these two coefficients can generate astigmatism of any magnitude and clocking. This summation is analgous to the use of zero degrees (0°) and forty-five degrees (45°) cylinder pairs to generate anamorphic astigmatism of varying magnitude and clocking. The two rotating corrector plates  60 A and  60 B have the saddle shapes rotated ninety degrees (90°) from each other, so that when they have the same clocking, they cancel and no astigmatism is generated. The first and second rotating corrector plates  60 A and  60 B are rotated relative to one another as seen in  FIG.  3 A . This may be achieved by rotating either the first or second rotating corrector plate with the other corrector plate fixed or rotating both corrector plates, with an actuator. As the difference in clocking increases, the magnitude of the generated astigmatism increases. The clocking of that astigmatism is set by the average of the two clockings. The amount of correction depends on the anamorphic magnification, the distance from the deformable lens plates from the image plane, and the numerical aperture of the imaging system. This correction method allows the projection system  10  to stay on a straight line optical axis (on-axis). Another method may be to introduce mirrors and produce an off-axis system with a MEMS deformable mirror. 
     The following is an example of a projection system that uses a numerical aperture of 0.065, an image field of 250×250 mm, and a spectral bandwidth from 363-370 nm (i-line of Hg). The terms magnification and anamorphic magnification are used to describe the relationship of image point placements over a field relative to the object. The calculations shown in Table 1 below use a 9×9 array of field points to create a field that is then fitted to 3 distortion terms multiplied by coefficients: magnification (Mag), anamorphic magnification (AnaMag) and Skew. Anything residual to this fitting is considered residual distortion. The Mag distortion term is the change in magnification from the system fundamental magnification. The Δx and Δy are the image displacement from the nominal positive of the image point based on the fundamental magnification of the system, and x and y are the distance in x and y to that nominal point on the image plane from the optical axis. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Distortion Term Name 
                 Equation 
               
               
                   
                   
               
             
            
               
                   
                 Magnification 
                 Δx = x * Mag 
               
               
                   
                   
                 Δy = y * Mag 
               
               
                   
                 Anamorphic Magnification 
                 Δx = x * AnaMag 
               
               
                   
                   
                 Δy = −y * AnaMag 
               
               
                   
                 Skew 
                 Δx = y * Skew 
               
               
                   
                   
                 Δy = x * Skew 
               
               
                   
                   
               
            
           
         
       
     
     Skew is anamorphic magnification rotated which is stretching the corners of the field, while AnaMag stretches the flats.  FIGS.  4 A and  4 B  show a field distortion map of both AnaMag and Skew. The sum of the AnaMag term and Skew terms can describe all 360° anamorphic clockings. The corners might be 45° from the flats, but note that each vector in the two maps has rotated 90° and the clocking of the anamorphic magnification is 0° and 90°. The field distortion maps are independent over 360° of clocking. The root sum square (RSS) of the coefficients gives the magnitude of the anamorphic astigmatism. The coefficients are relative to the size of the field in parts per million (ppm). According to one example, an adjustment of at least 100 ppm of anamorphic magnification may be achieved, which is the direction of max expansion is 100 ppm, and the perpendicular to that direction is contracted at −100 ppm. There is 200 ppm difference between the orthogonal directions, but is considered 100 ppm of anamorphic mag. 
     The weak outer radii of a cylinder lens plate pair defines the glass curved plate when the two lenses are close, and is an offset that allows the moving cylinder lens plate to start at one sign of anamorphic mag and reach the opposite sign at the end of the travel, and passing through 0 at mid-travel. The strong inner radii may need to be strong because the air bent space created by the gap needs to change the anamophic mag by twice as much as the glass curved plate, using air as a medium, and not glass. The starting parameters to start the design is the width of the lens plates (W), the strong inner radius R in , the total glass thickness of the pair (T), and the index (n) of the chosen glass. The total thickness is a compromise between difficulty of fabrication and total length of the two pairs of the lens plates. From this a first order design of one pair may be obtained. 
     
       
         
           
             
               
                 The 
                 ⁢ 
                     
                 length 
                 ⁢ 
                     
                 of 
                 ⁢ 
                    
                 travel 
                 ⁢ 
                    
                 of 
                 ⁢ 
                     
                 one 
                 ⁢ 
                     
                 lens 
                 ⁢ 
                    
                 is 
               
               = 
               
                 2 
                 ⁢ 
                 
                   2 
                 
                 ⁢ 
                 
                   
                     
                       R 
                       in 
                     
                     ⁢ 
                     Δ 
                     ⁢ 
                     r 
                   
                   
                     W 
                     ⁡ 
                     ( 
                     
                       n 
                       - 
                       1 
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
     where Δr is the max displacement needed at the corner of the field, where n is the refractive index of the glass. The outer radius is 
     
       
         
           
             
               R 
               out 
             
             = 
             
               
                 
                   
                     W 
                     ⁡ 
                     ( 
                     
                       n 
                       - 
                       1 
                     
                     ) 
                   
                   ⁢ 
                   T 
                 
                 
                   
                     2 
                   
                   ⁢ 
                   n 
                   ⁢ 
                   Δ 
                   ⁢ 
                   r 
                 
               
               . 
             
           
         
       
     
     These equations provide a starting design that can be adjusted slightly in an optical design program for optical power and lens plate travel needed. Since the 45° pair of cylindrical lens plates has more sag for the same inner radius, more center thickness may be needed. The design provided in table 2 is for W=300 mm, Rin=5 m and a total glass thickness of 22 mm for the 45° pair of lens plates, and 16 mm for the 0° pair of lens plates. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Example design in the image space of a projection system 
               
            
           
           
               
               
               
               
            
               
                   
                 SURFACE DESCRIPTION 
                 THICKNESS 
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 RADIUS 
                   
                 OR 
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 ELT 
                 SUR NO. 
                 X 
                 Y 
                 SHAPE 
                 SEPARATION 
                 GLASS 
               
               
                   
               
            
           
           
               
            
               
                 45 deg pair of cylinder lenses 
               
            
           
           
               
               
               
               
            
               
                   
                 coordinates rotated −45 deg 
                   
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 45+ 
                 1 
                 INF 
                 −33045.00 
                 CC CYL 
                 13.0000 
                 Fused Silica 
               
               
                 45+ 
                 2 
                 INF 
                 −5002.000 
                 CX CYL 
                 0.1500* 
               
               
                 45− 
                 3 
                 INF 
                 −5002.000 
                 CC CYL 
                 9.0000 
                 Fused Silica 
               
               
                 45− 
                 4 
                 INF 
                 −33045.00 
                 CX CYL 
                 7.3000* 
               
            
           
           
               
               
               
               
            
               
                   
                 coordinates rotated +45 deg 
                   
                   
               
            
           
           
               
            
               
                 0 deg pair of cylinder lenses 
               
            
           
           
               
               
               
               
               
               
               
            
               
                  0+ 
                 5 
                 INF 
                 −24300.00 
                 CC CYL 
                 9.0000 
                 Fused Silica 
               
               
                  0+ 
                 6 
                 INF 
                 −5002.000 
                 CX CYL 
                 0.1500** 
               
               
                  0− 
                 7 
                 INF 
                 −5002.000 
                 CC CYL 
                 7.0000 
                 Fused Silica 
               
               
                  0− 
                 8 
                 INF 
                 −24300.00 
                 CX CYL 
                 21.0000** 
               
            
           
           
               
               
               
               
            
               
                 IMAGE 
                 INF 
                 FLT 
               
               
                   
               
               
                 Dimensions are given in millimeters 
               
               
                 *Internal air space adjusts from 0.15-5.15 mm and air space below lens adjusts 7.30-2.00 mm 
               
               
                 **Internal air space adjusts from 0.15-5.45 mm and air space below lens adjusts 21-15.7 mm 
               
            
           
         
       
     
       FIG.  5    shows the motions in relative adjustments of cylinder axial shift of the lens plates needed to obtain the anamorphic mag in all clockings as shown in  FIG.  6   . The RSS of the Skew and AnaMag coefficients give the magnitude of the anamorphic magnification. To obtain an anamorphic mag of 100 pm at all clockings with no mag residual, the mag needs to adjust ±√{square root over (2)}×100 ppm. This mag adjust can be accomplished by shifting elements in the projection lens axially, or shifting the mask axially. 
     The 0.5 relative adjustment is the mid-travel of the movable cylindrical lens plates, where there is no anamorphic contribution. If less than 100 ppm of anamorphic mag is desired, then the sinusoidal cylinder shift curves in  FIG.  5    would decrease in amplitude to the 0.5 relative adjustment line, and the mag adjustment to the 0 line. 
     The addition of the cylinders in the image space, is similar to adding plates. In telecentric imaging, there is spherical and axial color aberration introduced, that is easily corrected in the projection lens design. The max vector produced in the field for the resultant fits in  FIG.  6    is 17.7 um. The residual distortion from these fits are shown in  FIG.  7   . 
       FIG.  7    is the residual distortion which is 0.07/17.7=0.004 of the generated anamorphic mag, which is generally acceptable. If some improvement is desired, some 3rd order radial distortion could be removed in the projection lens design. The design of cylindrical lens plates based on the inner radii=10 m has a max residual distortion of 0.017 um, which is 4 times better. The longer radius designs require more travel of the cylinders, and thus more image space. 
     The min, max and average values of  FIG.  8    for the distribution of defocus values over the whole field. For each setting of anamorphic mag, the projection system  10  may adjust the height of the wafer to best focus. This is a routine correction used in all precise lithography systems. What cannot be corrected is the variation of focus over the field, which is the focal plane deviation (FPD) which is defined here as the max minus min focus. The quarter wave depth of focus for this projection system may be ±44 um in one example, and 8 um of FPD generated by the cylindrical lens plates may be acceptable. 
     The wavefront aberration without corrector plates  60 A and  60 B is dominated by astigmatism generated by the cylinder lenses. The amount of astigmatism produced by the cylinder lenses increases by the square of the NA and proportional to the distance from the image plane to the cylinders. The unit mWvs is milli-waves, or 1/1000 of a wave. The comparison of  FIGS.  9 A and  9 B  show a significant improvement. The R in =10 m solution has one-half the astigmatism with the corrector plates than for the R in =5 m design. 
     The rotating corrector plates in the pupil have a hyperbolic paraboloid, or saddle shape on the inner surfaces. For this design, the peak-to-valley (P-V) of the plates is 53 nm. These can be fabricated by deterministic polishing techniques. The P-V is independent of the diameter of the plates, since this is the wavefront correction that is needed in the pupil. The difference in clocking of the two plates generate the magnitude of the correction, and the average of the two generates the clocking of the correction. 
     One example of optimal rotations of the rotating corrector plates is shown in  FIG.  10   . The precision of the rotations is not demanding to the opto-mechanical design, though the speed could be depending on the diameter of the pupil space. The difference is the angular separation from the nulled clockings of the two rotating corrector plates. The average is the average clockings of the two. The motions may fit to sinusoidal equations. 
     Without the rotating corrector plates  60 A and  60 B, the wavefront error shown in  FIG.  11 A  is dominated by astigmatism. The residual left from the first and second cylindrical lens plates  40 A and  40 B is extremely low when the rotating corrector plates are used as shown in  FIG.  11 B . These calculated residuals are for the designed cylindrical lens plates  40 A and  40 B plus rotating corrector plates  60 A and  60 B, but does not include any unwanted contributions from the projection lens assembly  16 . These are design residuals and do not take into account the errors from fabrication. All residuals are for generating ±100 ppm of anamorphic distortion, and will decrease for cases where less anamorphic distortion is needed. 
     The projection system  10  advantageously generates anamorphic magnification adjustment for all clockings and a range of magnitudes in a projection system  10  without producing unacceptable amount of focal plane deviation such as may be experienced with other lens arrangements. The projection system  10  may achieve a full range of anamorphic magnification adjustment with a mechanical motion that is small in distance for the movable lens plates in the field space and rotations of rotating corrector plates  60 A and  60 B in the pupil space. This is a results in a simpler, more robust, lower cost, faster full range of travel, and impart a minimal lateral vibration to the imaging system. The projection system  10  may achieve anamorphic magnification adjustment with minimal parasitic aberration effects with the addition of the rotating corrector plates  60 A and  60 B. 
     The described embodiments are preferred and/or illustrated, but are not limiting. Various modifications are considered within the purview and scope of the appended claims.