Patent Application: US-29468505-A

Abstract:
a programmable optical processing device employing a plurality of controllable light modulator elements . first and second optical elements are positioned to create an optical region therebetween comprising a fourier transform plane and at least one non - fourier optical region from the fourier transform plane . in one embodiment at least one of these non - fourier optical regions comprises fractional fourier regions . multiple controllable light modulator elements located in a non - fourier optical region may be adjacently stacked , spatially separated , or separated by grin material . the controllable light modulator elements further implement optical transfer functions that are positive - definite or non - positive - definite , and which may be controlled by electrical and / or optical control signals . in one embodiment the system may comprise a monolithic device and / or be comprised by a monolithic device .

Description:
the invention is concerned with processing presented image data , either recorded or real - time provided by an exogenous system , means , or method . this image data can be presented by means of an electronic display ( such as an lcd panel , crt , led array , or other technologies ), films , slides , illuminated photographs , or the output of some exogenous system such as an optical computer , integrated optics device , etc . the presented image data will herein be referred to as the image source . the invention is also concerned with image data then produced by the invention which is presented to a person , sensor ( such as a ccd image sensor , photo - transistor array , etc . ), or some exogenous system such as an optical computer , integrated optics device , etc . the later image presentation receiving entity will herein be referred to as a observer , image observation entity , or observation entity . fig1 shows a general arrangement involving an image source 101 , lens or lens system or other equivalent 102 , and an image observation entity 103 , capable of classical geometric optics , classical fourier optics , and fractional fourier transform optics . the class of optics ( geometric , fourier , or fractional fourier ) is determined by the following : the separation distances 111 and 112 the “ focal length ” parameter “ f ” of the lens or lens system or other equivalent 102 . the type of image source ( lit object , projection screen , etc .) in so far as whether a plane or spherical wave is emitted . as is well known , the cases where the source image is a lit object and where the distances 111 , which shall be called “ a ”, and 112 , which shall be called “ b ,” fall into the “ lens - law relationship ” determined by the focal length f : gives the geometric optics case . in this case the observed image 103 is a vertically and horizontally inverted version of the original image from the source 101 scaled in size by a magnification factor “ m ” given by : the fourier transforming properties of simple lenses and related optical elements is also well known and heavily used in a branch of engineering known as “ fourier optics ” [ 2 , 3 ]. classical fourier optics [ 2 , 3 , 4 , 5 ] involves the use of a lens , lens - systems , or other means to take a first two - dimensional fourier transform of an optical wavefront , thus creating at a particular spatial location a “ fourier plane ” wherein the amplitude distribution of an original two - dimensional optical image becomes the two - dimensional fourier transform of itself . in the arrangement of fig1 with a lit object serving as the source image 101 , the fourier optics case is obtained when a = b = f . in this way , classical fourier optics [ 2 , 3 , 4 , 5 ] allows for easy , inexpensive , flexible signal processing of images . fig2 shows a classical fourier optics image processing arrangement with an optical transfer function element 103 introduced in the fourier plane 104 , using two lenses 102 , 105 to realize the fourier plane 104 . the optical transfer function element 103 is typically implemented via a translucent plate or similar means in this location to introduce an optical transfer function operation on the optical wavefront . the image source 101 and a first lens 102 are separated by a distance 111 which , based on the focal length of the lens , creates a fourier plane 104 at a distance 112 on the opposite side of the first lens 102 . the image source 102 may be natural image ( as with a camera ), produced by an optoelectric transducer , or some other type of image source element . a second lens 105 is positioned a distance 113 from the fourier plane on the plane &# 39 ; s opposite side . the distance 113 is selected , based on the focal length of the second lens 105 , together with distance 114 so that an observation element 106 receives a fourier transform of the image emanating from the fourier plane 104 . the observation element 106 may be natural ( such as a viewfinder , display surface , projection screen , or other means ), optoelectric ( as in a phototransistor or ccd array or other means ), or some other type of observing element . as an aside , note that is the translucent plate is perfectly clear so as to effectively not be present , the result is the composition of two fourier transform operations ; since an inverse fourier transform is a fourier transform with its transform variable replaced with its negative , the composition of two fourier transforms amounts to reversing the image coordinates , i . e ., flipping the image up for down and left for right , the result expected for a compound lens . further , the distances 111 , 112 , 113 , 114 to give these effects are not unique ; alternate distance selections result in variations in image size , which amounts to varying the magnification power of a compound lens and hence the image size . within then possible scaling and flipped - image orientation differences , the above arrangements amount to the convolution of the impulse response corresponding to the optical transfer function with the original image . the same results can be obtained in other optical arrangements and with alternate types of elements , either of which may obey the same mathematical relationships . in this way images can be relatively easily and inexpensively lowpass - filtered ( details softened ) and highpass - filtered ( details enhanced ) as well as multitude of other possibilities . these multitudes of possibilities have , due to properties of materials and fabrication limitations in transcending them in the construction of the transform element 103 , been limited to transfer functions that mathematically are “ positive - definite ,” i . e . those which affect only amplitude and do not introduce varying phase relationships . the apparatus and method of this invention utilizes fractional fourier transform [ 5 , 7 , 8 , 9 ] properties of lenses [ 5 , 6 ] or other means to introduce one or more positive - definite optical transfer functions at various locations outside the fourier plane to realize , or closely approximate , arbitrary non - positive - definite transfer functions . the fractional fourier transform properties of lenses cause complex but predictable phase variations to be introduced by each such located conventional positive - definite ( i . e ., amplitude variation without phase variation ) optical linear transfer function elements . by choice of the number of such elements , position of such elements , and the actual positive - definite transfer function used for each element , arbitrary non - positive - definite transfer functions can be approximated by the entire system . this is now explained in more detail below . as described in [ 5 ], for cases where a , b , and f do not satisfy the lens law of the fourier optics condition above , the amplitude distribution of the source image 101 as observed at the observation entity 103 experiences in general the action of a non - integer power of the fourier transform operator . as described in [ 5 ], this power , which shall be called α , varies between 0 and 2 and is determined by an arccosine function dependent on the lens focal length and the distances between the lens , image source , and image observer , specifically as α = 2 π ⁢ arccos ⁡ [ sgn ⁡ ( f - a ) ⁢ ( f - a ) ⁢ ( f - b ) f ] ( 3 ) for cases where ( f − a ) and ( f − b ) share the same sign . there are other cases which can be solved for from the more primitive equations in [ 5 ] ( at the bottom of pages the5 - 3 and the4 - 1 ). note simple substitutions show that the lens law relationship among a , b , and f indeed give a power of 2 and that the fourier optics conditions of a = b = f give a power of 1 ; as required . without loss of generally to other implementations , fig3 shows the exemplary realization of the invention introducing additional ( or alternate ) optical transfer function elements , here exemplified as 103 a and 103 b , introduced at additional ( or alternate ) locations , here exemplified as 104 a and 104 b , in a region outside the fourier plane , here exemplified with region 113 . it is understood that , depending on the desired transfer function to be realized with what degree of accuracy , arbitrary numbers of optical transfer function elements such as 103 a and 103 b could be located in any one or more of the regions 111 , 112 , 113 , 114 , and in fact the system may include or not include an element 103 in the fourier plane 104 . designs can be straightforwardly obtained by methods of approximation [ 11 , 12 ]. one embodiment of the approximation method leverages hermite function [ 16 ] expansions [ 17 , and more recently , 18 ] of the desired transfer function . this is advantageous in simplifying the approximation problem as the orthogonal hermite functions diagonalize the fourier transform [ 17 ] and fractional fourier transform [ 5 , 9 ]; the result is two - fold : throughout the entire optical system the amplitude and phase affairs of each hermite function are completely independent of those of the other hermite functions the hermite function expansion of a desired transfer function will naturally have coefficients that eventually tend to zero , meaning that to obtain an arbitrary degree of approximation only a manageable number of hermite functions need be handled explicitly . because of these properties it is simplest to explain the properties of the fractional fourier transform on the image in terms of the hermite function representation . it is understood that other methods for representing properties of the fractional fourier transform on an image as well as for approximation methodology are possible . a bounded ( non - infinite ) function k ( x ) can be represented as an infinite sum of hermite functions { h n ( x )} as : since the function is bounded the coefficients { a n } eventually become small and converge to zero . an image is a two dimensional entity , as is the amplitude variation of a translucent plate ; in either case the function can be represented in a two - dimensional expansion : for simplicity , consider the one - dimensional case . the fourier transform action on hermite expansion of the function k ( x ) with series coefficients { a n } is given by [ 16 ]: because the diagonal eigenfunction structure , fractional powers of the fourier transform operator can be obtained by taking the fractional power of each eigenfunction coefficient . the eigenfunction coefficients here are (− i ) n . complex branching artifact ambiguities that arise from taking the roots of complex numbers can be avoided through writing − i , as thus , for a given power α , the fractional fourier transform of the hermite expansion of the function k ( x ) with series coefficients { a n } is given by [ 5 ]: thus as the power α varies with separation distance ( via the arccosine relationship depending on separation distance ), the phase angle of the n th coefficient of the hermite expansion varies according to the relationship shown above . when α = 1 the result is the traditional fourier transform . the effect of the fourier plane on positive - definiteness is clear : with α = 1 the complex exponential is always either i , − i , 1 , or − 1 since n is an integer and with the { a n } all in the unit interval [ 0 , 1 ] there is no way to do anything with phase relationships . if α is not an integer than nα in general is not , and thus the complex exponential can attain other values not on the unit circle . referring now to the arrangement of fig3 , the above relationship can be used in sequence to calculate the phase contributions at each optical transfer function element 103 a , 103 b , etc . as well as any element in the fourier plane 104 : the distances between the elements can be used to calculate the power of the fractional fourier transform at the element location these powers are used to determine the phase variation introduced by that element the composite effect of all optical transfer function elements in the system can then be calculated . the phase shift introduced by n optical transfer function elements for image expansion coefficient f n , m and optical transfer function element expansion coefficients t 1 n , m . . . t n n , m with separation distances determining fractional fourier transform powers α 1 , . . . , α n is : approximation methods can then be used , based on a very small but sufficiently rich collection of easily implemented optical transfer function elements and a convenient range of separation distances dictated by physical considerations . a class of system embodiments of special interest provided for by the invention are those where a sequence or physically - adjacent stack of programmable light modulators , such as lcd panels , are used as the optical transfer function elements . electrical and / or computer and / or , with future materials , optical control could then be used to alter the individual transfer function of each optical transfer function element . the latter arrangement could be implemented as an integrated optics device , perhaps including storage capabilities to storage the transfer function pixel arrays and perhaps even an associated processor for computing the individual optical transfer function element transfer function pixel arrays . the result is a powerful , relatively low - cost , potentially high - resolution real - time integrated optics image processor which would perform optical transformations otherwise requiring many vast orders of magnitudes of computation power . further , the image source and observation elements may in fact be optoelectric transducers ( led arrays , lcds , ccds , crts , etc .) and may be further integrated into a comprehensive system which can further be abstracted into a more general purpose complex - number arithmetic optical computing array processor of tremendous processing power . the invention provides for the range of these integrated optical processor architectures to readily implemented through photolithography or beam - controlled fabrication methods . returning to the image processing application , such an integrated optics image processor could be realized for monochrome , visual color , or wide - spectrum images depending on the systems architecture and / or the components used . for example , a visual color image processor could be realized by three monochrome image processing sub - systems as described above , each monochrome image processing sub - systems dedicated to one of the three visual color components ( i . e ., “ red ,” “ green ,” and “ blue ”) as is commonly done in videographics and digital image processing systems . alternatively , color lcd panels may be used as the optical transfer function elements , allowing single image processing system as described in the previous paragraph to simultaneously process the entire visual range . both of these systems and method approaches may also be used for wide - spectrum images : a wide - spectrum image may be decomposed into multiple optical frequency bands which are processed separately ( and potentially , though not necessarily , recombined ), or wide - spectrum lcd optical transfer function elements can be used in a single channel system . it is noted that the multichannel system has the additional wide - spectrum advantage of permitting different materials to be used in each spectral band , thus allowing choices of materials each best matched for its associated band . it is also noted that another wide - spectrum advantage of the multichannel system is that splitting the spectrum potentially allows for approximate wavelength - dependent dispersion corrections and / or control . yet another wide - spectrum advantage of the multichannel system is that splitting the spectrum potentially allows for separate detector areas for each wavelength band , having potential applications in astronomical observation sensors and wavelength - division multiplexing . finally , it is noted that both dispersion compensation / control and separate detector partitions can be served with a large plurality of wavelength - partitioned channels readily implemented through photolithography or beam - controlled fabrication of the integrated optical processor . before continuing with additional aspects of these several types of integrated optical processors , it is noted that the systems and methods described herein can be applied to conventional lens - based optical image processing systems as well as to systems with other types of elements obeying fractional fourier optical models and as well to widely ranging environments such as integrated optics , optical computing systems , particle beam systems , radiation accelerators , and astronomical observation methods . in particular it is noted that an important class of optical systems obeying fractional fourier optical models are graded - index optical materials ( such as optical fibers ), in particular quadratic graded - index media . it is therefore noted that graded index materials can be used in the fabrication of the integrated optical processors described above , removing the need for any lenses . this allows further design options in the creation of both monolithic and hybrid physical realizations and fabrication of the integrated optical processors described above . for instance , fig4 shows the optics device of fig3 configured as a monolithic device 120 providing optical filtering according to various techniques disclosed herein . one alternative is to omit image source 101 and image observation element 106 , resulting in optics device 125 . if desired , as shown in fig5 , optics device 100 may be implemented within optics system 130 , thus defining an integrated optics system according to an implementation of the present invention . it is next noted that the entire systems and methods developed thus far can now be generalized away from the fractional fourier transform and its associated hermite function basis and quadratic phase characteristics . for example , the integrated optical processor can , as just mentioned , be implemented with graded - index materials . to realize the fractional fourier transform and its associated hermite function basis and quadratic phase characteristics in the development so far , quadratic graded - index media must be used . if instead non - quadratic graded - index media are used , a similar but different mathematical framework can in general be employed : the hermite functions will be replaced with a different set of basis functions affiliated with the graded - index profile , and the fractional fourier transform will be replaced by a different operation affiliated with these replacement basis functions . this approach can prove important and advantageous in mass production at specific types of non - quadratic graded - index media may be found to more readily lend themselves to the fabrication of the same general form integrated optical processor architectures described above , as well as related ones . finally , returning now to the original fractional fourier transform approach and framework , note that it is also possible to effectively turn the original purpose of the framework on its head and admit controllable filtering elements that are indeed non - positive - definite in their transfer function , i . e ., shifting the phase of the light . such controllable optical phase - shifting filter elements may be , for example , realized as two - dimensional arrays of twisting liquid crystals or other electronically controllable optical material which varies the phase of transmitted light , for example , by changing its intrinsic optical properties such as its index of refraction , and / or changing the effective preparation length of the transmitted light , or by yet other methodologies . one case of an optical image processing or computation system involving this technology would involve electronically controllable optical phase - shifting filtering element arrays which can only vary the transmitted light phase over some range , perhaps a small one . a larger phase variation is therefore possible if a plurality of such arrays are ganged , i . e ., either stacked together or distributed in space . in general this will result in some or all of the arrays to lie outside the fourier plane , particularly if the overall optical system incorporating this array plurality is physically compact . the mathematical framework described earlier for calculating the overall transfer function assuming positive - definite optical filter elements can be used directly : the phase perturbations made possible by each phase - controllable element are incorporated by simply substituting the real - valued array parameters with complex - valued ones as is familiar in the common art of signal processing . the resulting mathematical expressions are then usable for transfer function synthesis as described earlier , but now with the additional degrees of freedom associated with the phase control made possible by these elements . a particularly useful application of this would be to use only all - pass phase - variable elements in a compound optical system set up to operate as an electronically adjustable lens . by varying the phase - shifts of the all - pass filter elements , the fractional fourier transform effects of a lens of varying focal length and / or varying separation distance from the affiliated optics can be synthesized . various compound optics arrangements can therefore be made utilizing this electronically controlled synthesis of effective focal length and / or varying separation distance . one important application would be the creation of an electronically adjustable lens with variable focus and variable zoom capabilities . the latter is a straightforward application of the electronically controlled variable phase - shift aspect of the invention . conventional optics rely on varying physical separation distances of movable optical elements to realize zoom and focus effects , thus the electronically controlled variable phase - shift realization of the invention would simply replace one or more such moving optical elements . particularly useful is an arrangement where the electronically controllable optical phase - shifting filter elements involve no moving parts , thus allowing electronically controllable variable focus and variable zoom capabilities to be realized with no moving parts . not only will this replace the need for today &# 39 ; s extensive precision optics and precision mechanics , but the resulting optical effects can be made very precise and operate with fast dynamics . because twisting liquid crystals today operate at full contrast at video rates ( 30 hz ), variations in zoom and focus would be executable in ˜ 30 msec or less . further , with the addition of electronic image sources and detectors on either side of the controllable optical phase - shifting filter element arrays , the more general purpose complex - number optical computing array processor of tremendous processing power described earlier may also be fabricated with an optical architecture similar to the electronically variable lens just described . finally , it is noted that as material methods advance , the invention provides for the variable phase elements described above to be controlled optically in part or whole rather than exclusively electrically . all publications and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication or patent application was specifically and individually indicated to be incorporated by reference . the invention now being fully described , it will be apparent to one of ordinary skill in the art that many changes and modifications can be made thereto without departing from its spirit or scope . l . levi , applied optics , volume 2 ( section 19 . 2 ), wiley , new york , 1980 . 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