Abstract:
A dot matrix system, which uses an electronic display panel as a diffractive optical device to produce two laser beams. The interference pattern of these two beams, at the focal plane of a lens, forms a grating spot with a shape and beam profile determined by the wavefronts diffracted by the electronic display device. The invention uniquely combines aspects of the interfering beam prior art and the prior art using an imaging display. Instead of simply reducing a diffraction image on a display device as in the imaging display prior art, the invention puts two different Fourier transforms on the display, the laser beam interacts with these Fourier transforms, and a lens focuses the two beams on the recording medium, with the two beams interfering with each other to produce the desired grating pattern. Because multiple orders of the wavefront will be produced by the display device, a light blocking element is used, with an aperture to pass only the desired order(s) of the beams.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
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     STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
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     REFERENCE TO A “SEQUENCE LISTING,” A TABLE, OR A COMPUTER PROGRAM LISTING APPENDIX SUBMITTED ON A COMPACT DISK. 
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     BACKGROUND OF THE INVENTION 
     A Hologram is recorded by the interference of two coherent wavefronts. When a hologram is illuminated by one of the beams used in its construction process, the light diffracted by the hologram reconstructs the other wavefront completely, including phase and amplitude information. As such, if one of the wavefronts is originated from a three-dimensional object, an image of this 3D object can be reconstructed from its hologram. The term “hologram” is not only used to describe a device that reproduces the image of a 3D object, it is now commonly used to describe any device that can diffract light into a multitude of colors. These diffractive devices are used in graphic design for wrapping papers, package covers, labels to authenticate products and many other applications. It is difficult to pinpoint when the commercialization of such holograms began. In searching patent literature, an early U.S. Pat. No. 3,567,561 issued in 1971 described the use of composite grating structures as surface ornaments. Holograms displayed on credit cards are probably the earliest commercial holograms used on a large scale. 
     There are many methods for producing holograms. The 3D holograms on credit cards are called rainbow holograms (see U.S. Pat. No. 3,633,989). This type of hologram can produce 3D images with only horizontal parallax and can be reconstructed with a white light source. Ornamental surface type holograms are made by the interference of two parallel laser beams or two diverging laser beams with the same divergence cone. When a graphic pattern is composed of many hologram segments having different angles of rotation and different periods, each segment in the pattern has to be recorded sequentially on the same recording surface. For this reason a technique similar to a dot matrix printer was developed and used grating dots to construct graphic patterns. A patent was granted in Taiwan (Taiwan Patent 263565 issued in 1984) for one such system (see also U.S. Pat. No. 6,043,913). This Taiwan patent could be one of the earlier patents describing a dot matrix grating system for producing holograms. FIG. 1 shows the optical system for recording a dot matrix grating according to Taiwan Patent 263565. An incoming laser beam  101  is split into two beams  105  and  106  by beam splitter  104 . These two beams are recombined at recording plane  108 . Since only one lens  102  is used to focus the laser beam on surface  108 , only one beam,  105  or  106 , can be focused perfectly on surface  108 . As a result, the diameter of the focused spots on surface  108  have to be sufficiently large so that both focused beams are within the depth of focus of lens  102 . The period of the fringes within the overlapping beams is given by        T   =       λ     sin                 ϑ       .                            
     The fringe period can be adjusted by changing the angle of the prism mirror  107 . The orientation of the interference fringes is set by rotating the optical assembly consisting of prism  104  and prism mirror  107 . There are a number of problems related to this early design: 
     (1) The required depth of focus results in a very large beam spot on the recording surface, 
     (2) The laser used in this system must have long coherent length because the optical path length of the two beams are not equal, 
     (3) The beams on the recording plane are circular in shape with non-uniform beam profiles. 
     (4) The fringes are not continuous across adjacent grating dots. 
     For these reasons, the resolution of the early dot matrix system was limited to about 400 dots per inch and not very efficient in diffracting light. 
     FIG. 2 shows a more recent system for recording dot matrix holograms. A laser beam  201  is directed by a mirror  202  to a beam splitter  203 , with output beams  204  and  205 . Beam  205  is directed to a prism mirror  206 . This system uses additional prism mirrors  207 ,  208 ,  209  and  210  to equalize the optical path length to reduce the coherence requirement of the laser source. A lens  213  is also used to simultaneously focus beams  204  and  205  on the recording surface  214 . The spot diameter on the recording surface is given by δ=λF/d, where λ is the wavelength of the laser light, F is the focal length of lens  213  and d is the diameter of the laser beams. Suppose that a spot diameter δ=10 μm is needed for the system and λ=0.5 μm, the ratio of        F   d                          
     is equal to 20. The period of the fringes is equal to          T   =     λ     2      sin                 θ         ,                          
     because both beams subtend an angle θ with respect to the optical axis. In FIG. 2 it can be seen that the focal length F and the diameter of the lens  213  is also related by          tan                 θ     =       D     2      F       .                            
     To obtain T=1 μm , the diffraction angle is equal to 14.5 degree. This angle determines that the lens  213  must be an f-2 lens. In this dot matrix system, prisms  211  and  212  can be moved up and down in unison to change the interference angle θ and hence the period of the fringes. In spite of the improvements in this more recent system over the system shown in FIG. 1, the problems related to beam shape, beam non-uniformity, and fringe continuity remained unsolved. 
     U.S. Pat. No. 5,291,317 proposed an optical system, which further resolved some of the aforementioned difficulties. FIG. 3 shows the optical system according to U.S. Pat. No. 5,291,317. A laser beam  301  illuminates a mask  302  and a grating  303 . The lens  307  produces a de-magnified image of the grating on the, recording surface  308 . The mask  302  defines an aperture so that the shape of the grating dot on the recording surface  308  can be rectangular, hexagonal or circular in shape. The laser beam  301  has been expanded so that its intensity profile, between its perimeters  304  and  305 , on the grating  303  is nearly uniform. The grating is mounted on a rotary stage so that its fringes can be rotated under computer control. This system is simple in concept but with a fundamental optical restriction on the lens  307 . Suppose that the lens  307  has focal length F=10 mm and it is used to de-magnify the grating image by a factor  10 . In order to record a grating dot with a fringe spacing of 1 μm, with a laser wavelength of λ=0.5 μm the period of the grating  303  is 10 μm. The diffraction angle of this grating according to relationship sin θ=λ/T is equal to 2.86 degree. To achieve the 10× reduction, the grating is approximately 100 mm from the lens. Therefore, 1 st  order beam will be at a distance 5 mm from the center of the lens  307 . This means that ratio of the focal length to the diameter of the lens (f-numer) is about 1. This lens is difficult to design, if not impractical. This difficulty can not be avoided by using smaller de-magnification. For example, reducing the de-magnification to 5 will reduce the distance between the grating  303  and the lens  307  to 50 mm. However, the diffraction angle will increase from 2.86 degrees to 5.74 degrees. The result is still that we need a lens aperture equal to the focal length of the lens. However, when a laser is used as the light source and a spatial filter  306  is used to block the 0 th  order wave from the grating  303 , the intensity variation on plane  308  has twice the spatial frequency of grating  303 . This phenomenon can be explained as follows. Suppose that the complex amplitude of the phase grating image on the recording plane is given by          i        (   x   )       =     1   +       sin        (       2      π                 x     T     )       .                              
     After the aperture  306  stops the 0 th  order of grating  303 , the intensity variation on the recording plane  308  is equal to          I        (   x   )       =         [     sin        (       2      π                 x     T     )       ]     2     =       1   2          [     1   +     cos        (       4      π                 x     T     )         ]                                
     Because of this coherent effect, the system as described in FIG. 3 can use an f-2 lens instead of an f-1 lens to record grating dot with 1 μm fringes. The fringes in adjacent grating dots produced by this system are still not contiguous. 
     Another method for producing grating patterns is shown in U.S. Pat. Nos. 4,510,575 and 6,268,893 show grating or hologram images being put on a display screen, with optics being used to reduce the image and focus it onto a recording substrate. The &#39;575 patent shows a microscope reducing an image from a CRT. The &#39;893 patent shows a laser beam being projected through a LCD (Liquid Crystal Display), which is then imaged onto a recording material. 
     BRIEF SUMMARY OF THE INVENTION 
     This invention describes a novel dot matrix system, which uses an electronic display panel as a diffractive optical device to produce two laser beams. The interference pattern of these two beams, at the focal plane of a lens, forms a grating spot with a shape and beam profile determined by the wavefronts diffracted by the electronic display device. 
     The invention uniquely combines aspects of the interfering beam prior art and the prior art using an imaging display. Instead of simply reducing a diffraction image on a display device as in the imaging display prior art, the invention puts two different Fourier transforms on the display, the laser beam interacts with these Fourier transforms, and a lens focuses the two beams on the recording medium, with the two beams interfering with each other to produce the desired grating pattern. Because multiple orders of the wavefront will be produced by the display device, a light blocking element is used, with an aperture to pass only the desired order(s) of the beams. 
     In one embodiment, the display device is a LCD. The laser can be projected onto the LCD through a beamsplitter from the front, then reflected back through the beamsplitter, aperture and lens to the recording medium. Alternately, the laser beam can be directed through the LCD from behind. By controlling the display, the two wavefronts are produced, with the middle portion of the laser beam being blocked, to result in two distinct beams emanating from the LCD. In one embodiment, the LCD modulates the amplitude of the laser wavefront, in other embodiment it modulates the phase. 
     The position of the recording medium relative to the optics can be moved after each spot, generating a grid of spots, each spot having its own grating pattern. Another feature of the present invention allows the fringes making up the grating for a spot to be slightly altered so that they line up with the fringes of an adjacent spot, making the fringes contiguous across the adjacent boundary. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a diagram of a prior art dot matrix grating device according to Taiwan Patent 263565. 
     FIG. 2 is a diagram of a more recent prior art dot matrix grating device. 
     FIG. 3 is a diagram of a prior art dot matrix grating device according to U.S. Pat. No. 5,291,317. 
     FIG.  4 ( a ) is a diagram of a first embodiment of the present invention using a polarization beamsplitter and reflecting a laser beam of an LCD. 
     FIG.  4 ( b ) is a modification of the diagram of FIG.  4 ( a ) illustrating the blocking of unwanted orders of the reflected beams. 
     FIG.  5 ( a ) is a diagram of a square aperture in the light blocking element. 
     FIG.  5 ( b ) is a diagram illustrating the Fourier transform of the beam on the square aperture of FIG.  5 ( a ). 
     FIG. 6 is a diagram illustrating the locations of the beam patterns on the display panel. 
     FIG.  7 ( a ) is a diagram of adjacent grating spots on the recording medium with the same fringe pattern. 
     FIG.  7 ( b ) is a diagram of adjacent grating spots on the recording medium with contiguous fringes. 
     FIG. 8 is a diagram of a second embodiment using a laser source behind the display panel with projects a beam through the display panel. 
     FIG. 9 is a diagram of a third embodiment using phase modulation instead of amplitude modulation. 
     FIG. 10 is a diagram of an embodiment wherein the patterns are focused beyond the recording medium to give a larger spot size. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     FIG.  4 ( a ) shows the top view of the optical system of one embodiment of the present invention. A collimated laser beam  402  with optical axis  401  is incident on a polarization beam splitter  403 , which reflects beam  402  towards a display panel  404 . LCD panels such as panel  404  are currently used in many image projection systems. The orientation of the molecules of the liquid crystal in the panel can be affected by a voltage applied on the liquid crystal layer. When a linear polarized light passes through the liquid crystal layer, its polarization is changed by the orientation of the molecules of the liquid crystal. As a result, when such a beam passes through an analyzer or a polarization beamsplitter, the brightness of the beam can be controlled by the voltage applied to the liquid crystal layer. 
     In FIG.  4 ( a ) two regions  405  and  406  of the liquid crystal display have voltages applied. Therefore, beams reflected back from regions  405  and  406  of the liquid crystal display panel can pass through the polarization beam splitter  403  toward lens  407 . Light reflected back from regions of the liquid crystal display where voltage has not been applied will be reflected by polarization beamsplitter towards the laser source (this is the middle, shaded area between the two beams  420 ,  421 . This produces two separate beams,  420 ,  421 , each with a different pattern from the LCD panel. The two beams, after passing through an aperture  408 , are then focused on a recording medium  409 . The two beams interfere on the surface of medium  409  to produce the desired grating pattern. The recording medium can then be moved so the next spot can be recorded, and the process continued until the recording medium has stepped through all the spots of a desired area on the recording medium. FIG.  4 ( b ) is a side view of the optical system which shows a display  404  emitting diffracted beams of light of multiple orders, which pass through beamsplitter  403 , and are focused by lens  407  on recording medium  409 , with some of the diffracted orders being blocked by a blocking element  408  with an aperture on the right side. The +1 st  order,  410 , a 0 th  order,  411  and a −1 st  order  412  are diffracted waves from the LCD panel. Blocking element  408  blocks beams  411  and  412 . Only beam  410  is focused by lens  407  on the recording plane  409 . The image suitable for recording is not on the optical axis of the lens. 
     In the first embodiment of the present invention, the LCD panel is used to shape the beam profile on the recording plane. The beam profile is the Fourier transform of the desired grating pattern on the recording medium. Lens  407  acts as a Fourier transform lens to generate the desired grating pattern. 
     For example, if a beam profile with a square shape such as shown in FIG.  5 ( a ) is required for the matrix recording, the pattern displayed on the panel is in the form of the function below:            f   1          (     x   ,   y   ,   ϕ     )       =     1   +       (       sin                 π                 x       π                 x       )          (       sin                 π                 y       π                 y       )            cos        (         2      π                 x     Λ     +   φ     )       .                                
     FIG. 5 ( b ) shows the variation of this function. The cosine function        cos        (         2      π                 x     Λ     +   φ     )                            
     in f 1 (x, y, φ) is used as a carrier to preserve the phase information of the function          (       sin                 π                 x       π                 x       )            (       sin                 π                 y       π                 y       )     .                            
     The two beams reflected from the display panels have wavefronts proportional to 
     f 1 (x+x 1 , y+y 1 , φ 1 )and f 1 (x+x 2 , y+Y 2 ,φ 2 ) respectively, where            x   1     =       D   2        cos                 ω       ,       y   1     =       D   2        sin                 ω                   x   2     =         -   D     2        cos                 ω       ,       y   2     =         -   D     2        sin                 ω                              
     and ω is the orientation of the two beams on the display panel (see FIG.  6 ). In FIG. 6 601 , and  602  are the locations of the functions 
     f 1 (x+x 1 , y+y 1 ,φ 1 ,) and f 1 (x+x 2 , y+y 2 , φ 2 ) on the LCD surface. It is well known that lens  407  performs a Fourier transformation on the wavefront of the beams. Therefore, the intensity pattern on the back focal plane of lens  407  is proportional to            I        (     u   ,   v     )       =                  F   1          (     u   ,   v     )                 (         j                 π                 D       λ                 F            (       ucso                 ω     +     v                 sin                 ω       )       )         +         F   1          (     u   ,   v     )                 (           -   j                   π                 D       λ                 F            (       ucso                 ω     +     v                 sin                 ω       )       )                2       ,                          
     where F 1 (u, v) is the Fourier transform of f 1 (x, y, φ) 
     Then the intensity pattern I(u,v) on the back focal plane of lens  407  becomes          I        (     u   ,   v     )       =                  F   1          (     u   ,   v     )                 (           j                 π                 D       λ                 F            (       ucso                 ω     +     v                 sin                 ω       )       +     ϕ   1       )         +         F   1          (     u   ,   v     )                 (             -   j                   π                 D       λ                 F            (       ucso                 ω     +     v                 sin                 ω       )       +     ϕ   2       )                2               I        (     u   ,   v     )       =                F   1          (     u   ,   v     )            2          [     1   +     2        cos        (           2      π                 D       λ                 F            (       u                 cos                 ω     +     v                 sin                 ω       )       +       (       ϕ   1     -     ϕ   2       )     /   2       )           ]                              
     As can be seen, the shape of the dot is determined by the function                 F   1          (     u   ,   v     )            2                          
     and the period of the fringes is equal to            λ                 F       2      D       .                          
     The fringes are rotated by an angle ω with respect to the coordinates of the recording plane. The phase (φ 1 -φ 2 ) can be used to provide the continuity of the fringes across the recording dot. 
     In dot matrix systems such as shown in FIG. 1 to FIG. 3, grating spots are recorded consisting of a plurality of fringes, each fringe formed from a number of dots, or pixels. The medium is moved to step the desired pattern across the medium. A problem arises when the identical pattern is desired for multiple spots. When the adjacent grating spots have identical period and orientation, the fringes are not usually contiguous across the boundary of the spots as shown in FIG.  7 ( a ). As can be seen, fringes  701  and  703  do not line up. This is a fundamental limitation of all the dot matrix systems today. 
     In the present invention, the relative phase of the two beams can be changed from one grating spot to the next. As a result, when the adjacent spots have the same grating period and orientation, the fringes can be made contiguous as though the grating is formed as one large grating and not consisting of spots. The continuity of the fringes across adjacent spots is demonstrated in FIG.  7 ( b ). As can be seen, fringes  702  and  704  are aligned. 
     This first embodiment of the present invention can further be understood through some basic relationships among the various optical parameters. Suppose that the width of beams  405  and  406  is equal to W, the distance of separation between the two beams is D, and the focal length of lens  407  is F. 
     The incident angle of the two beams at the recording surface is equal to        θ   =       tan     -   1            (     D     2      F       )                              
     The period of the interference fringes is equal to        T   =       λ     2      sin                 θ       .                            
     The spot size on the recording plane is given by        δ   =         λ                 F     W     .                            
     Using F=10 mm, W=2 mm, λ=0.5 μm, the spot resolution δ=2.5 μm. The image on the recording plane will be composed of multiple of this resolution dots. The pattern displayed on the panel is the Fourier transform F(x,y) of the image of an aperture of arbitrary shape on the recording plane. A typical pattern on the display panel will take the following mathematical form          f        (     x   ,   y   ,   ϕ     )       =     1   +            F        (     x   ,   y     )                   cos        (         2      π                 x     Λ     +     φ        (     x   ,   y     )         )       .                                
     When the distance D separating the two patterns on the display panel is equal to 5.16 mm, the fringe period on the recording plane is equal to 1 μm. 
     FIG. 8 show a second embodiment of the present invention. The LCD panel  802  is a transmission type display. Incident beam  801  passes through LCD panel  802 . The portions of the incident passing through the activated regions  805 ,  806  will be transmitted through the polarization beam splitter  803 . The portion of the beam passing through inactivated regions of the LCD panel will be reflected as indicated by beam  804 . The two beams pass through lens  807  and blocking element  808  to have the +1 orders of the beam combined on the surface of recording medium  809 . The principle of operation of this embodiment is identical to that as shown in FIG.  4 . 
     FIG. 9 shows a third embodiment of the present invention. In this embodiment the LCD panel is a reflective device, and the structure is similar to FIG.  4 ( a ). An incident laser beam  901  is directed by polarization beamsplitter  903  to LCD  902 . Regions  905  and  906  of the LCD provide the Fourier transform of the desired pattern. The reflected light passes again through polarization beamsplitter  903 , resulting in two beams. The two beams pass through lens  907 , blocking element  908  and are combined on recording medium  909 . Note that blocking element  908  allows the 0 order beam to pass in this embodiment. 
     This embodiment uses phase modulation by the LCD, instead of amplitude modulation as in the previous embodiments. The light beam reflected through the liquid crystal layer will acquire a phase shift proportional to the voltage applied to the liquid crystal layer. As a result, this particular LCD panel is a phase modulator, whereas the previous LCD panels are amplitude modulators. When a function f(x,y)+φ is displayed on the LCD panel, the light beam reflected off the LCD panel is now characterized by function 
     
       
         s(x,y,φ)=e jf(x,y)     +jφ     
       
     
     The intensity pattern on the recording surface is proportional to the Fourier transform of s(x,y,φ). The hologram which has only phase variation is called a kinoform (U.S. Pat. No. 4,510,575). The unique property of the kinoform is that it has only 0th order diffraction. Hence, the theoretical diffraction efficiency can be as much as 94%. There will be a few percentage of light scattered about the image. Since the LCD panel is a phase modulator, all the light incident on the LCD panel will be reflected from its surface. In the region outside regions  905  and  906  a linear phase will be applied so that the reflected beam  904  will be diffracted away from the optical axis of the lens. The stop  908  is used to block out the off-axis diffracted light. 
     FIG. 10 shows a 4th embodiment of the present invention. The incident laser beam  1001  is directed to LCD  1004  as in FIG.  4 ( a ). However, the patterns on the LCD cause the reflected beams to diverge, as if originating from points  1005  and  1006 . The beams pass through beamsplitter  1003  and are thus focused by lens  1007  behind recording medium  1009 , resulting in a larger spot. Unwanted diffracted orders are blocked by blocking element  1008  as before. 
     In this embodiment the pattern displayed on the electronic display panel is proportional to            f        (     x   ,   y   ,   ϕ     )       =     1   +       B        (     x   ,   y     )       ⊗     cos        (         2      π                 x     Λ     +       π        (       x   2     +     y   2       )         λ                 Z       +   φ     )             ,                          
     where B(x, y) is a beam shaping function, ⊕ is the symbol denoting a convolution operation between the two functions on either side of the symbol, the quadratic phase function          π        (       x   2     +     y   2       )         λ                 Z                            
     in the argument of the cosine function is that of a thin lens with focal length Z and the function φ(x,y) is used to shape the interference fringes. To form a square shape the function B(x,y) is equal to          (       sin                 πx     πx     )          (       sin                 πy     πy     )                            
     as discussed earlier. Because of the quadratic phase function            π        (       x   2     +     y   2       )         λ                 Z       ,                          
     the beams from the electronic display panel focus at a plane slightly further from the true focal plane of lens  1007 . The shift in distance is approximately equal to δZ=F 2 /Z. The size of the overlapping beams at the focal plane of lens  1007  is approximately equal to        δ   =       δ                   Z        (     F   /   W     )         =         F   3     ZW     .                              
     This relationship shows that the quadratic phase function allows the adjustment of the spot size on the recording plane. For example, for F=20 mm, W=1 mm, and δ=0.04 mm, the focal length Z in the quadratic phase function is equal to 200 meters. A larger spot size has been accomplished without changing the distance between the recording plane  1009  and the lens  1007 . The fringes within the grating dot is given by          I        (   x   )       =         [     sin        (         2      π                 x     T     +     φ   2     -     φ   1       )       ]     2     =       1   2          [     1   +     cos        (         4      π                 x     T     +     φ   2     -     φ   1       )         ]                                
     where        T   =       λ     2      sin                 θ       .                            
     The phase functions in the argument can be used to shape the fringes inside the grating dot ad make the fringes across the fringes continuous across the grating dots. 
     The advantages of embodiments of the present invention include: 
     1. The LCD panel modulates the phase or the amplitude of the light beam. Hence no light shutter or attenuator is needed. 
     2. The distance D between the two beams on the display panel can be used to control the period of the fringes on the recording material. 
     3. The spot size and shape of the beam on the recording medium is controlled by the function f(x,y) displayed on the LCD panel. 
     4. The phase difference φ in the displayed function f(x,y) can produce contiguous fringes across adjacent dots. 
     5. The adjustments of system parameters are all done by electronic means. 
     As will be understood by those of skill in the art, the present invention can be embodied in other specific forms or embodiments without departing from the essential characteristics thereof. For example, the beamsplitter in FIG. 8 could be replaced with a polarization filter. Accordingly, the foregoing description is intended to be illustrative, but not limiting, of the scope of the invention which is set forth in the following claims.