Abstract:
Disclosed are methods of producing obliquity corrected light beams, and holographic recording and retrieval systems that utilize a obliquity corrected reference beam. The obliquity correction is accomplished using off-center lenses.

Description:
FIELD OF THE INVENTION 
   The present invention relates to optical systems for correcting the variation in the area exposed by a light beam due to the beam&#39;s obliquity. More specifically this invention relates to optical systems that decrease the width of a light beam as the obliquity of the light beam increases. 
   BACKGROUND 
   Holographic storage systems are storage systems that use holographic storage media to store data. Holographic storage media includes photorefractive materials that can take advantage of the photorefractive effect described by David M. Pepper et al., in “The Photorefractive Effect,” Scientific American, October 1990 pages 62-74. 
   The index of refraction in photorefractive materials can be changed by light that passes through them. Holographic storage media also include photopolymers, such as those described in Coufal et al., “Photopolymers for Digital Holographic Storage” in Holographic Data Storage, 199-207 (2000), and photochromatic materials. By controllably changing the index of refraction in such materials, high-density, high-capacity, and high-speed storage of information in holographic storage media can be accomplished. 
   In the typical holographic storage system, two coherent light beams are directed onto a storage medium. The first coherent light beam is a data beam, which is used to encode data. The second coherent light beam is a reference light beam. The two coherent light beams intersect within the storage medium to produce an interference pattern. The storage medium records this interference pattern by changing its index of refraction to form an image of the interference pattern. 
   The recorded information, stored as a holographic image, can be read by illuminating the holographic image with a reference beam. When the holographic image is illuminated with a reference beam at an appropriate angle, a data beam containing the information stored is produced. Most often the appropriate angle for illuminating the holographic image will be the same as the angle of the reference beam used for recording the holographic image. 
   Information can be encoded within the data beam in a variety of ways. One way of encoding information into a data beam is by using an electronic mask, called a spatial-light modulator (SLM). Typically, a SLM is a two dimensional matrix of pixels. Each pixel in the matrix can be directed to transmit or reflect light, corresponding to a binary 1, or to block light, corresponding to a binary 0. The data beam, once encoded by the SLM, is relayed onto the storage medium, where it intersects with a reference beam to form an interference pattern. The interference pattern records the information encoded in the data beam to the holographic storage medium. 
   The information recorded in the holographic storage medium is read by illuminating the storage medium with a reference beam. The resulting data beam is then typically imaged onto a sensor, such as a Charge Coupled Device (CCD) array or a CMOS active pixel sensor. The sensor is attached to a decoder, which is capable of decoding the data. 
   A holographic storage medium includes the material within which a hologram is recorded and from which an image is reconstructed. A holographic storage medium may take a variety of forms. For example, it may comprise a film containing dispersed silver halide particles, photosensitive polymer films (“photopolymers”) or a freestanding crystal such as iron-doped LiNbO3 crystal. U.S. Pat. No. 6,103,454, entitled RECORDING MEDIUM AND PROCESS FOR FORMING MEDIUM, generally describes several types of photopolymers suitable for use in holographic storage media. The patent describes an example of creation of a hologram in which a photopolymer is exposed to information carrying light. A monomer polymerizes in regions exposed to the light. Due to the lowering of the monomer concentration caused by the polymerization, monomer from darker unexposed regions of the material diffuses to the exposed regions. The polymerization and resulting concentration gradient creates a refractive index change forming a hologram representing the information carried by the light. 
     FIG. 1  illustrates the basic components of a holographic system  100 . System  100  contains a SLM  112 , a holographic storage medium  114 , and a sensor  116 . SLM  112  encodes beam  120  with an object image. The image is stored by interfering the encoded data beam  120  with a reference beam  122  at a location on or within holographic storage medium  114 . The interference creates an interference pattern (or hologram) that is captured within medium  114  as a pattern of, for example, a holographic refractive index grating. 
   It is possible for more than one holographic image to be stored at a single location, or for a holographic image to be stored at a single location, or for holograms to be stored in overlapping positions, by, for example, varying the angle, the wavelength, or the phase of the reference beam  122 , depending on the particular reference beam employed. Data beam  120  typically passes through lenses  130  before being intersected with reference beam  122  in the medium  114 . It is possible for reference beam  122  to pass through lenses  132  before this intersection. Once data is stored in medium  114 , it is possible to retrieve the data by intersecting a reference beam  122  with medium  114  at the same location and at the same angle, wavelength, or phase at which a reference beam  122  was directed during storage of the data. The reconstructed data beam passes through one or more lenses  134  and is detected by sensor  116 . Sensor  116 , is for example, a charged coupled device or an active pixel sensor. Sensor  116  typically is attached to a unit that decodes the data. 
   Varying the angle of the reference beam during recording to store multiple holographic images in the same volume is called angle multiplexing. Each image is recorded in the same volume using a different reference beam angle. A large number of images can be stored in the same volume using angle multiplexing by varying the angle of the reference beam over a wide range. 
   However, varying the reference beam angle can increase the area of the holographic storage medium exposed by the reference beam. The area exposed by a reference beam that strikes the surface of the holographic storage medium depends upon the reference beam&#39;s angle of incidence with the storage medium (“the obliquity”). This area is related to the capacity of the holographic storage medium since the larger area exposed by the reference beam, the smaller the capacity of the holographic storage medium per unit volume. Accordingly, a need exists for a optical system that is capable of maintaining the size of the area exposed by a reference beam as the obliquity of the reference beam changes. 
   In the past, obliquity has been corrected using a complex set of prisms. The use of these prisms is discussed in Coufal et al., “Tamarack Optical Head Holographic Sorage” in Holographic Data Storage, 343-357 (2000).  FIG. 2  shows an obliquity correction system using two prisms  226  and  228  and three lens component  230 ,  232  and  234 . In  FIG. 2 , light beams  224  are reflected off of scanning mirror  222  onto first prism  226 . The light beams exiting first prism  226  then proceed to second prism  228 . The light beams exiting second prism  228  then proceed through lens components  230 ,  232  and  234 . 
   The use of the complex prisms shown in  FIG. 2  have the drawback of being difficult to manufacture and align. Accordingly, a need exists for an obliquity correction system that does not require the use of complex prisms. 
   SUMMARY OF THE INVENTION 
   Disclosed are methods of producing obliquity corrected light beams, and holographic recording and retrieval systems that utilize a obliquity corrected reference beam. 
   In one embodiment, the method of producing an obliquity corrected light beam comprises projecting a light beam through one or more off-center lens components onto a surface with an angle of incidence. The off-center lens components vary the width of the light beam as a function of the angle of incidence on the surface. 
   Preferably, the lens components narrow the width of the light beam as the angle of incidence increases. Preferably, the projected light beam is a planar beam. Preferably, the incident light beam is a collimated beam. Preferably, the off-center lens components image the light beam anamorphically. 
   Preferably, the off-center lens components produce a wavefront error of less than 20 waves. Preferably, the surface comprises a holographic storage medium with a polymer matrix. 
   In another embodiment, the holographic recording system comprises a reference beam source, a lens system and a holographic storage medium. The reference beam source projects a reference beam that is incident upon the holographic storage medium and the lens system varies the width of the reference beam as a function of the angle of incidence upon the holographic storage medium. 
   Preferably, the incident reference beam is projected onto a planar surface of the holographic storage medium. Preferably, the holographic storage medium comprises a polymer matrix. Preferably, the reference beam source comprises a scanning mirror. Preferably, the reference beam intersects a data beam within the holographic storage medium to produce an interference pattern. Preferably, the interference pattern is recorded within the holographic storage medium. 
   Preferably, the reference beam that is incident upon the holographic storage medium with an angular range of at least 20 degrees to 50 degrees. 
   In yet another embodiment, the holographic retrieval system comprises a reference beam source, a lens system and a holographic storage medium. The reference beam source projects a reference beam that is incident upon the holographic storage medium and the lens system varies the width of the reference beam as a function of the angle of incidence upon the holographic storage medium. Preferably, the reference beam intersects a holographic image within the holographic storage medium to produce a data beam. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be better understood by reference to the Detailed Description of the Invention when taken together with the attached drawings, wherein: 
       FIG. 1  is a holographic storage and retrieval system; 
       FIG. 2  is a prior art obliquity correction system; 
       FIG. 3  is one embodiment of an obliquity correction system according to the present invention; and 
       FIG. 4  is another embodiment of an obliquity correction system according to the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   When a beam of light strikes a surface, the area exposed by the beam is dependent upon the incidence angle (the “obliquity”) of the beam of light. The greater the obliquity of the beam of light, the greater the surface area exposed by the beam. The area exposed by a beam of light striking a surface is also dependent upon the width of the beam of light. The wider the beam of light, the greater the surface area exposed by the beam. Accordingly, by decreasing the width of a beam of light as the obliquity increases, the surface area exposed by a beam of light can be maintained relatively constant. 
   Described are optical systems that help minimize the dispersion of a beam of light that is incident upon a surface. Particularly, the optical systems decrease the width of a light beam as the obliquity of the light beam upon a surface increases. 
   The disclosed optical systems can be used for a variety of applications where a surface is illuminated with a beam of light. A preferred application for the disclosed optical systems is in holographic data storage systems (HDSS). 
   An HDSS is composed of an optical system that directs and shapes coherent optical beams to intersect at a surface or volume where the interference pattern is recorded. The hologram constitutes the recorded pattern in the media. 
   In HDSS, an entire page of information is stored at once as an optical interference pattern within a holographic storage medium by intersecting two coherent laser beams within the holographic storage medium. The first beam is called the “data beam,” which contains the information to be stored. The second beam is called the “reference beam.” The reference beam is often (but not necessarily) an unmodulated beam, preferably a spherical beam or a collimated beam with a planar wave front. 
   Multiple interference patterns can be stored within the same volume using angle multiplexing. In angle multiplexing, each interference pattern is stored using a specific reference beam angle. Multiple pages of information can be recorded within the same volume of holographic storage medium by changing the reference beam angle for each interference pattern. An angular spacing between reference beam angles is provided to help prevent the interference patterns from overlapping one another. 
   To store a large number of images within the same volume using angle multiplexing, preferably the angle of the reference beam is varied over a wide range. However, when a reference beam strikes the surface of the holographic storage medium with a large angle of incidence, the reference beam can spread out across the surface of the holographic storage medium exposing unintended regions of the holographic storage medium. 
   A common trait of typical holographic systems is the overlapping of two coherent beams inside a photosensitive medium. The interference pattern generated by the two beams is recorded in the material in the form of a hologram. The ratio of the intensity of the reference beam and the data beam at any point of overlap in the media controls the localized recording rate of the hologram. If the reference beam intensity varies over the media volume, then the quality of the hologram is degraded as different positions in the media record at different rates. 
   Preferably, the size of the reference beam is controlled so that when the reference beam spreads out as the angle of incidence increases, the size and intensity of the reference traveling through the optical material after striking the surface remains relatively constant, regardless of the angle of incidence. By narrowing the reference beam as the angle of incidence increases, the size and intensity of the reference beam within the optical material can be made to remain relatively constant. 
   Controlling the size of the of the reference beam as a function of angle of incidence can also improve the storage capacity of the optical material. When the reference beam spreads out at large angles of incidence, unintended areas of the optical material may be exposed. If these unintended areas of the optical material contain recorded interference patterns, or are used to record interference patterns, these interference patterns may become damaged. If these unintended areas are left empty, the loss of recording space in the optical material may result. 
   Many kinds of materials could be used as holographic storage media. Photopolymers are very promising because of their high sensitivity and dynamic range. Phenanthrenequinone-doped polymethylmethacrylate (PQ/PMMA) has excellent optical quality and is based on a photoreaction between the dopant and polymer followed by diffusion of unreacted chromophore. 
   Preferably the HDSS produces a planar reference beam. A “planar beam” is a beam that is characteristic of light emitted from a point source at infinity. In a planar beam, the propagating beam has a wavefront of plane waves propagating in a single direction. 
   In one embodiment, the reference beam is projected onto a scanning mirror. The scanning mirror can then be used to reflect the reference beam through an optical system which directs the reference beam onto the surface of a holographic storage medium. The optical system contains one or more lenses that “obliquity correct” the reference beam so that the width of the beam varies with the beam&#39;s obliquity to the surface of the holographic storage medium. 
   In an alternative embodiment, the reference beam is directly projected by a light source through the optical system onto a storage medium without the use of a scanning mirror. The optical system again can be used to obliquity correct the reference beam before directing it onto the holographic storage medium. 
   Whether the reference beam is directly projected through the optical system, or is reflected off of a scanning mirror through the optical system, preferably the reference beam can be projected onto the storage medium using a wide range of incident angles. 
   Preferably, the angle of the incident reference beam at an off-axis from the normal of a region of the medium is from about 20 degrees to about 50 degrees. More preferably, the angle of the incident reference beam is from about 10 degrees to about 60 degrees. Most preferably, the angle of the incident of the reference beam is from about −10 degrees to 70 degrees. 
   A preferred optical system for obliquely correcting the reference beam comprises one or more off-center lens elements. An off-center lens element has an optical axis which is not perpendicular to the surface onto which the light passing through the lens is projected, and in which the optical axis does not pass through the point being imaged or illuminated. In a HDSS the surface would be the surface of the holographic storage medium. 
   The aberrations of the off-center lens elements can be used to control the width of the reference beam as the angle of incidence of the reference beam relative to the holographic storage medium changes. The lenses are preferably designed to image plane waves anamorphically, that is the magnification is different in the two directions. Preferably, the lenses provide a different magnification in the scan direction, and the direction orthogonal to the scan direction. 
   Preferably, the anamorphic magnification varies over the angular range, by the amount needed to compensate for the obliquity effect. This can be achieved by balancing the aberrations that can affect the beam width) for example, distortion, field curvature, astigmatism, etc., such that they change the width of the beam as a function of the beam angle. Preferably, the lens system is designed to minimize the amount of deterioration in wave front quality. Preferably, the lens system is designed to minimize or prevent any lateral shift of the beam of light passing through the lens system. 
   Preferably, the change in width of the beam, as it changes incidence angle at the media, is such that the illuminated area remains constant. For thin media, this means that the width of the beam is proportional to the cosine of the incidence angle. A thin storage medium is preferably one that has a thickness less than about 30% of the diameter of the illuminating beam. 
   For example, if the system includes normal incidence, and if the beam width for normal/perpendicular incidence is defined to be 1 unit, then the following factors could be applied to the beam width as the angle changes for thin media: 
   
     
       
             
             
           
         
             
                 
             
             
               Incidence angle (degrees from normal) 
               cosine (width change factor) 
             
             
                 
             
           
           
             
                0 
               1.000 
             
             
               10 
               0.985 
             
             
               20 
               0.940 
             
             
               30 
               0.866 
             
             
               40 
               0.766 
             
             
               50 
               0.643 
             
             
               60 
               0.500 
             
             
               70 
               0.342 
             
             
                 
             
           
        
       
     
   
   Accordingly, a beam that is 10 degrees from normal would preferably have a thickness of about 0.985 units. 
   If the system does not include normal incidence, then the correct change factor at a given angle can be determined as the ratio of the cosines of different beam angles; for example: cosine(given angle)/cosine(smallest angle used). An example is a system that covers 10 to 60 degrees, for the following factors would be applied to the beam width as the angle changes: 
   
     
       
             
             
           
         
             
                 
             
             
               Incidence angle (degrees from 
                 
             
             
               normal) 
               cosine ratio (width change factor) 
             
             
                 
             
           
           
             
               10 
               1.000 
             
             
               20 
               0.954 
             
             
               30 
               0.879 
             
             
               40 
               0.778 
             
             
               50 
               0.653 
             
             
               60 
               0.508 
             
             
                 
             
           
        
       
     
   
   Preferably, the distortion of the reference beam produced by the optical system is minimized. Distortion can be qualified in terms of peak-to-valley wavefront error measured in wavelengths of the transmitted light. Limiting the distortion of the reference beam passing through the optical system is important for at least two reasons. 
   First, distortion of the wavefront can decrease the quality of the image produced by the optical system. In a holographic storage system, distortion of the reference beam can decrease the quality of the interference pattern produced by the storage system. 
   Second, minimizing the distortion of the wavefront is also important for creating a reproducible beam of light. In a HDSS a reproducible reference beam is preferable because a reference beam that is the same or similar to the reference beam used to create the interference pattern is typically used to reproduce the data beam from the interference pattern during the readout process. Accordingly, any distortion of the reference beam due to the optical system should be reproducible. By minimizing the amount of distortion, reproducibility of the reference beam is typically improved. 
   The wavefront error of the reference beam is preferably less than 20 waves, more preferably less than 10 waves, most preferably less than 0.25 waves. Distortion greater than the diffraction limit of 0.25 waves is still useful in a HDSS because the reference beam errors can be corrected to some extent during the readout process using a reference beam with the same or similar distortion. 
   Preferably, the optical system does not shift the position of a beam of light passing through the optical system. In a HDSS, a shift in position of the beam of light entering the optical system can cause unintended areas of the holographic storage medium to be illuminated, thereby wasting data storage capacity. To avoid this, the system preferably prevents the beam from shifting position while its width and/or angle is adjusted. 
   For a thin storage medium the optical system can be designed to constrain the edge rays to limit their lateral motion on the media surface while the beam angle changes. By constraining the edge rays in this manner, a constant area can be illuminated over a range of angles. 
   For a thick storage medium, maintaining the position of the beam can be more complicated. A thick storage medium is preferably one with a thickness greater than about 30% of the diameter of the illuminating beam. For a thick storage medium it is difficult to prevent the reference beam from illuminating at least some areas of the storage medium where the data beam is not present, so a preferable design criterion is to minimize this area. This can be done by finding the maximum media volume illuminated by the data beam, and then minimizing the size of the reference beam while still completely overlapping the data beam. In practice this is similar to what was done for a thin medium, except that the points where the edge rays are constrained to have no lateral shift occur on opposite sides (i.e., front and back) of the storage medium. 
   In a preferred embodiment, the constrained points for both a thin and thick storage medium are preferably anywhere from the front surface to the back surface of the media. 
   Preferably, the reference beam entering the optical system and exiting the optical system is collimated. A collimated light beam is a beam in which the rays are nearly parallel so that the beam does not converge or diverge appreciably. A laser, for example, is a collimated light source. 
   EXAMPLE 1 
     FIG. 3  shows an obliquity correction system  30  made up of four lens components  336 ,  342 ,  354  and  366 . All four lenses components  336 ,  342 ,  354  and  366  have spherical surfaces. A lens component is a single lens element, or two or more lens elements which are all held together in optical contact. Lens component  336  is a single lens element made out of B270, a lens material available from Schott Glass Technologies, Inc. Lens component  336  has a first outside surface  38  and a second outside surface  340 . 
   Lens component  342  has two lens elements  344  and  346 . Lens element  344  is made out of SF5, a lens material available from Schott Glass Technologies, Inc. Lens element  346  is made out of BK7, a lens material available from Schott Glass Technologies, Inc. Lens component  342  has a first outside surface  348 , an inside surface  350  and a second outside surface  352 . 
   Lens component  354  has two lens elements  356  and  358 . Lens element  356  is made out of BK7, a lens material available from Schott Glass Technologies, Inc. Lens element  358  is made out of F4, a lens material available from Schott Glass Technologies, Inc. Lens component  354  has a first outside surface  360 , an inside surface  362  and a second outside surface  364 . 
   Lens component  366  is a single lens element made out of 523586, a lens material available from Bausch and Lomb. Lens component  366  has a first outside surface  368  and a second outside surface  370 . 
   The system  300  has a collimated input beam which illuminates a scanning mirror  332 . Beams  334  exiting the mirror  332  are processed by lenses  336 ,  342 ,  354  and  366 , and relayed by them to the hologram location  372 . Together lenses  336 ,  342 ,  354  and  366  comprise a configuration known as a “4F scanner” (which is so called because, if two identical lens arrangements are used, the distance from the scanning mirror to the illuminated point is nominally four times F, the focal length of the lens arrangement). 
   The four lens elements can be divided into two groups of two lens elements. The first group of lens elements  374  contains lens elements  336  and  342 . The second group of lens elements  376  contains lens elements  354  and  366 . 
   The first lens group of lens elements  374  receives collimated light beams  334  at different angles, pivoting about a fixed point near the mirror  332 . The first group of lens elements  374  converts light beams  334  into converging light, with the central rays of each converging beam being approximately parallel to the optical axis. The light beams  334  then travel a distance great enough that they go past a focal point and are now diverging, but still with the central rays still essentially parallel to the axis. The second lens group  376  then receives these light beams  334 , converting them again into approximately collimated light. But now the central rays of light beams  334  (that is, each beam during the scan) are converging toward the center of the hologram location  372 . 
   In the obliquity correction system  300 , the mirror  332  and hologram (object and image) locations  372  are moved off the optical axis. This enables the astigmatism of the off-axis lenses  336 ,  342 ,  352  and  366  to change the beam width as a function of scan angle. The lens surface prescriptions are optimized to reduce aberrations that are not used to control obliquity, while allowing the beam width to change. The lenses are optimized using Zemax® an optical design program available from Focus Software Inc. The software program was directed to optimize the lens system with respect to three criteria: beam width, beam shift, and wavefront flatness. The characteristics of the lenses in obliquity correction system  300  are summarized in Table 1. 
   
     
       
             
             
             
             
           
             
             
             
             
             
           
         
             
               TABLE 1 
             
             
                 
             
             
                 
                 
               Central Thickness/ 
                 
             
             
               Surface # 
               Radius(mm) 
               Air Space(mm) t* 
               Glass 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               338 
               Infinity 
               4.0 
               (y = 338, x = 340) 
               B270 
             
             
               340 
               −19.8700 
               12.33 
               (y = 340, y = 348) 
               air 
             
             
               348 
               93.5716 
               1.5 
               (y = 348, x = 350) 
               SF5 
             
             
               350 
               32.1937 
               5.0 
               (y = 350, x = 352) 
               BK7 
             
             
               352 
               −43.5142 
               20.79 
               (y = 352, x = 360) 
               air 
             
             
               360 
               55.3710 
               6.10 
               (y = 360, x = 362) 
               BK7 
             
             
               362 
               −17.9600 
               3.2 
               (y = 362, x = 364) 
               F4 
             
             
               364 
               −48.3092 
               4.0 
               (y = 364, x = 368) 
               air 
             
             
               368 
               13.2850 
               10.4 
               (y = 368, x = 370) 
               523586 
             
             
               370 
               Infinity 
               9.7 
               (y = 370, x = 372) 
               air 
             
             
                 
             
             
               *t = distance between positions y and x, wherein x and y are positions in  FIG. 3.    
             
           
        
       
     
   
   The scanning mirror  332  is 20 mm from the first outside surface  338  of first component  336 , and is 2.63 mm off axis. The top surface of the scanned media  378  is 9.7 mm from second outside surface  370  of lens component  366 . The center of the volume being illuminated  372  is approximately 2.2 mm off axis. 
     FIG. 4  shows an obliquity correction system  400  made up of two lens components  406  and  412 . Both lens components  406  and  412  have single lens elements with aspherical surfaces. Lens component  406  is a single lens element made out of C0550, a lens material available from Coming Inc. Lens component  406  has a first outside surface  408  and a second outside surface  410 . Lens component  412  is a single lens element made out of C0550. Lens component  412  has a first outside surface  414  and a second outside surface  416 . 
   The system  400  has a collimated input beam which illuminates a scanning mirror  402 . Beams  404  exiting the mirror  402  are processed by lenses  406  and  412 , and relayed by them to the hologram location  418 . 
   Lens component  406  receives collimated light beams  334  at different angles pivoting about a fixed point near the mirror  402 . Lens component  406  converts light beams  404  into converging light, with the central rays of each converging beam being approximately parallel to the optical axis. The light beams  404  then travel a distance great enough that they go past a focal point and are now diverging, but still with the central rays still essentially parallel to the axis. Lens component  412  then receives these light beams  404 , converting them again into approximately collimated light. But now the central rays of light beams  404  (that is, each beam during the scan) are converging toward the center of the hologram location  418 . 
   In the obliquity correction system  400 , the mirror  402  and hologram (object and image) locations  418  are moved off the optical axis. This enables the astigmatism of the off-axis lenses  406  and  412  to change the beam width as a function of scan angle. The lens surface prescriptions are optimized to reduce aberrations that are not used to control obliquity, while allowing the beam width to change. The lenses are optimized using Zemax®. The software program was directed to optimize the lens system with respect to three criteria: beam width, beam shift, and wavefront flatness. The characteristics of the lenses in obliquity correction system  400  are summarized in Table 2. 
   
     
       
             
             
             
             
           
             
             
             
             
             
           
             
           
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE 2 
             
             
                 
             
             
                 
                 
               Central Thickness/ 
                 
             
             
               Surface # 
               Radius(mm) 
               Air Space(mm) t* 
               Glass 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               408 
               −4.856e−28** 
               8.0 
               (y = 408, x = 410) 
               C0550 
             
             
               410 
               −14.639** 
               33.91 
               (y = 410, y = 414) 
               air 
             
             
               414 
               13.265** 
               12.0 
               (y = 414, x = 416) 
               C0550 
             
             
               416 
               —23.395** 
               11.52 
               (y = 416, x = 418) 
               air 
             
             
                 
             
           
        
         
             
               *t = distance between positions y and x, wherein x and y are positions in  FIG. 4.   
             
             
               **The aspheric coefficients are: 
             
           
        
         
             
               Surface 408: 
               k = 
               −9.799e40 
               a4 = 
               −6.35e−5 
               a6 = 
               −3.539−7 
               a8 = 
               −1.152e−8 
             
             
               Surface 410: 
               k = 
               0.749 
               a4 = 
               0.000121 
               a6 = 
               2.187e−7 
               a8 = 
               −4.790e−9 
             
             
               Surface 414: 
               k = 
               −0.213 
               a4 = 
               −7.116e−5 
               a6 = 
               −3.874e−7 
               a8 = 
               1.440e−9 
             
             
               Surface 416: 
               k = 
               −0.262 
               a4 = 
               9.926e−6 
               a6 = 
               −5.145e−8 
               a8 = 
               −8.74e−11 
             
             
                 
             
           
        
       
     
   
   The scanning mirror  402  is 15 mm from the first outside surface  408  of first component  406 . First component  406  is tilted 2.72 degrees and is and is 1.58 mm off axis. The top surface of the scanned media  420  is 11.52 mm from second outside surface 416 of lens component  412 . Second component  412  is tilted 2.21 degrees and is approximately 0.458 off axis. 
   The above description is presented to enable a person skilled in the art to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the preferred embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the invention. Thus, this invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein. 
   This application discloses several numerical range limitations. Persons skilled in the art would recognize that the numerical ranges disclosed inherently support any range within the disclosed numerical ranges even though a precise range limitation is not stated verbatim in the specification because this invention can be practiced throughout the disclosed numerical ranges. A holding to the contrary would “let form triumph over substance” and allow the written description requirement to eviscerate claims that might be narrowed during prosecution simply because the applicants broadly disclose in this application but then might narrow their claims during prosecution. Finally, the entire invention of the patents and publications referred in this application are hereby incorporated herein by reference.