US20050018295A1

US20050018295A1 - Optical processor architecture

Info

Publication number: US20050018295A1
Application number: US10/922,394
Authority: US
Inventors: David Mendlovic; Naim Konforti; Aviram Sariel
Original assignee: Lenslet Ltd
Current assignee: Lenslet Ltd
Priority date: 1999-05-19
Filing date: 2004-08-19
Publication date: 2005-01-27
Also published as: EP1190286B1; US7119941B1; ATE288098T1; WO2000072267A1; JP2003500719A; EP1190288A1; AU4428600A; US20050149598A1; EP1190287A1; AU4608100A; AU5529299A; DE60017738D1; US7012749B1; AU4428500A; EP1190286A1; AU4608000A; AU4607900A; JP2003500698A; DE60017738T2; US7194139B1

Abstract

Apparatus for optically applying a transform to data, comprising: a spatially modulated light source, that generates a spatially modulated light beam; a diffractive element that replicates said light beam; and a lens that applies a Fourier transform to said replicated light beam.

Description

RELATED APPLICATIONS

This application is a Divisional filing of U.S. application Ser. No. 09/979,183, filed on Jul. 15, 2002 which is a U.S. national filing of PCT Application No. PCT/IL00/00283, filed on May 19, 2000, which is a continuation-in-part of U.S. application Ser. No. 09/926,547, filed on Mar. 5, 2002 which is a U.S. national filing of PCT Application No. PCT/IL99/00479, filed on Sep. 5, 1999, the disclosures of all of which are incorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to the field of optical processor architectures

BACKGROUND OF THE INVENTION

A general linear transformation (GLT) in its discrete form is defined by its kernel function W. The transformed function G as a function of a two dimensional input g(x,y) is thus:
G(ξ, η)=ΣΣg(x,y)W(x, y; ξ, η) (1)
For a two dimensional object having the size of 1000 by 1000 pixels, a general linear transformation requires 10¹²multiplications.
The equation (1) for a one dimensional vector is:
G(ξ)=Σg(x)W(x; ξ) (2)
In matrix formulation, equation (2) becomes $\begin{matrix} [\begin{matrix} G_{1} \\ G_{2} \\ ⋮ \\ ⋮ \\ G_{N} \end{matrix}] = [\begin{matrix} g_{1} & g_{2} & \dots & \dots & g_{N} \end{matrix}] \cdot [\begin{matrix} W_{11} & W_{12} & \dots & \dots & W_{1 N} \\ W_{21} & W_{22} & ⋮ \\ ⋮ & ⋰ & ⋮ \\ ⋮ & ⋰ & ⋮ \\ W_{N1} & \dots & \dots & \dots & W_{NN} \end{matrix}] & (3) \end{matrix}$
, showing that a GLT can be performed as a vector-matrix multiplication.
Dammann gratings are described, for example in “High Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms”, H. Damman, K. Gortler, Optics communications, 3(5), 321-315
The following is a partial list of publications that describe one or more of optical processing methods, optical processors and cross-bar switches: For example: “Cosinusoidal transforms in white light,” by N. George and S. Wang, in Applied Optics, Vol. 23, No 6, 1984; “Hartley transforms in hybrid pattern matching,” by Nomura, K. Itoh and Y. Ichioka, in Applied Optics, Vol. 29, No. 29, 1990; “Lens design for a white light cosine transform achromat,” by K. B. Farr and S. Wang, in Applied Optics, Vol. 34, No. 1, 1995; “Optical computing,” by Feitelson in a chapter titled, “Optical image and signal processing,” pp. 102-104 (general discrete linear transforms using lenslet array) and pp. 117-129 (which describe matrix multiplication), MIT press 1988; “Optical crossbar interconnected digital signal processor with basic algorithms,” by A. D. McAulay, in Optical engineering, Vol. 25, P. 25, 1986; “Historical perspectives: Optical crossbars and optical computing,” by R. Arrathoon, in Proc. SPIE, Vol. 752, P. 2, 1987; “Optoelectronic parallel computing system with optical image crossbar switch,” by M. Fukui, in Applied Optics 32, 6475-6481, 1993; “Optical crossbar elements used for switching networks,” by Y. Wu, L. Liu and Z. Wang, in Applied Optics, Vol. 33, No. 2, 175-178, 1994; “Implementation of an optical crossbar network based on directional switches,” by KH. Brenner and T. M. Merklein, in Applied Optics, Vol. 31, No. 14, 2446-2451, 1992; “Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms,” by J. W. Goodman, A. R. Dias and L. M. Woody, in Optics Letters, Vol. 2, No. 1, 1-3, 1978; “High throughput optical image crossbar switch that uses a point light source array,” by M. Fukui and K. Hitayama, Optics Letters, Vol. 18, No. 5, 376-378, 1993; “Performance of 4×4 optical crossbar switch utilising acousto optic deflector,” by P. C. Huang, W. E. Stephens. C. Banwell, and L. A. Reith, Electronics Letters, Vol. 25, No.4, 252-253, 1989; “Link analysis of a deformable mirror device based optical crossbar switch,” by R. W. Cohn, Optical Engineering Vol. 31, No. 1, 134-140, 1992; “Compact optical crossbar switch,” S. Reinhorn, Y. Amitai, A. A. Friesem, A. W. Lohmann and S. Gorodeisky, Applied Optics, Vol. 36, No. 5, 1039-1044, 1997; “Microlens array processor with programmable weight mask and direct optical input,” by V. Schmid, E. Lueder, G. Bader, G. Maier and J. Siegordner, Proc. SPIE Vol. 3715, 175-184, 1999; and European patent application publication 0577258 by Nakajima et. al. entitled: “Picture compressing and restoring system and record pattern forming method for a spatial light modulator.” The disclosures of all of the above publications are incorporated herein by reference.

SUMMARY OF THE INVENTION

An aspect of some embodiments of the invention relates to using a diffractive optical replicator, for example a Dammann grid, or a Ronchi grating to replicate a light source. The replicated light source may be used, for example, to perform a DCT transform using a Fourier transforming system. In one exemplary embodiment, the light source comprises an array of VCELs or an SLM image. The replicated light is transformed using a lenslet array and the transformed light is detected by a photo-electric detector.
An aspect of some embodiments of the invention relates to applying a transform to a linear one dimensional source, by spreading the source in a direction perpendicular to the extent of the light source and optically processing the spread light. In one embodiment, the source, for example a one-dimensional array of VCELs is spread using a lens or a reflector, such as a parabolic reflector. In another embodiment, the source is spread using non-imaging optics, for example light guides.
In some embodiments of the invention the light source is spatially and/or temporally coherent. In other embodiments, an incoherent light source is used. Also, instead of electro-optical detection, in some embodiments the transformed light is used for further processing, optionally being detected by an array of optical fibers or by a lens or lenslet array.
There is thus provided in accordance with an exemplary embodiment of the invention, apparatus for optically applying a transform to data, comprising:

- a spatially modulated light source, that generates a spatially modulated light beam encoding said data by said modulation;
- a diffractive element that replicates said light beam; and
- a lens that applies a Fourier transform to said replicated light beam. Optionally, the apparatus comprises a detector that detects said transformed light. Optionally, the apparatus comprises electronic circuitry that converts said detected signals into a discrete transform of said data. Optionally, said transform is a linear transform. Optionally, said transform is a DCT transform.

In an exemplary embodiment of the invention, said replicating comprises replicating said beam to a two dimensional arrangement. Alternatively or additionally, said diffractive element comprises a Dammann grating. Alternatively, said diffractive element comprises a Ronchi grid.
There is also provided in accordance with an exemplary embodiment of the invention, apparatus for optically applying an transform to data, comprising:

- a linear array of light sources;
- at least one first optical element for converting light from said arrays into a two dimensional array of light, wherein each light source is a line in said two dimensional array of light;
- at least one transforming optical element that applies a transform to said spread light; and
- at least one second optical element that combines said transformed spread light onto a linear detector array,
- wherein said first optical element is one of reflective, anamorphic or non-imaging. Optionally, said first optical element is an anamorphic cylindrical lens having different focal lengths in two directions. Alternatively, said first optical element is an anamorphic reflector having different focal lengths in two directions. Alternatively, said first optical element is a curved reflector. Optionally, said first optical element is a parabolic reflector. Alternatively or additionally, said first optical element comprises a non-imaging optics element. Optionally, said first optical element comprises a leaky light guide.

In an exemplary embodiment of the invention, said second optical element comprises a lens. Optionally, said second optical element comprises an anamorphic lens.
In an exemplary embodiment of the invention, said second optical element comprises a reflector.
In an exemplary embodiment of the invention, said second optical element comprises a non-imaging optics light collector.
In an exemplary embodiment of the invention, said first optical element comprises an array of light guiding slabs. Alternatively or additionally, said transforming optical element comprises a mask. Alternatively or additionally, said transforming optical element comprises an SLM (spatial light modulator). Alternatively or additionally, said transforming optical element comprises a lenslet array. Alternatively or additionally, said detector is an electro-optic detector.

BRIEF DESCRIPTION OF THE FIGURES

Some embodiments of the present invention will be now be described in the following detailed description and with reference to the attached drawings, in which:
FIG. 1 is a general flowchart showing a processing method in accordance with an exemplary embodiment of the invention;
FIG. 2 is a general flowchart showing a fan-out and fan-in section of the method of FIG. 1;
FIG. 3 is a schematic flowchart of a combined optical and electronic processing method in accordance with an exemplary embodiment of the invention;
FIG. 4 is a schematic diagram of an optical processing system using a Dammann grating in accordance with an exemplary embodiment of the invention;
FIGS. 5A and 5B are a top and a side schematic views of a linear source optical processing system in accordance with an exemplary embodiment of the invention;
FIGS. 6A and 6B are a top and a side schematic views of a non-imaging optics optical processing system in accordance with an exemplary embodiment of the invention; and
FIG. 7 is a schematic view of a two dimensional optical processing system, in accordance with an exemplary embodiment of the invention.

DETAILED DESCRIPTION OF SOME EMBODIMENTS

FIG. 1 is a general flowchart 100 showing a processing method in accordance with an exemplary embodiment of the invention. Stored data (102) is transferred to a processor (104), processed, preferably optically (106), transferred back to a memory (108) and stored again (110).
In accordance with some embodiments of the invention, optical means are used to parallelize the processing (106). FIG. 2 is a general flowchart 200 showing a fan-in and fan-out section of the method of FIG. 1. Many processes can be made parallel by fanning out the input (202), processing the fanned-out input in parallel (204) and the collating the results (fan in 206). In particular, a GLT can be performed as a plurality of simultaneous multiplications of various elements, followed by adding together of the multiplication results. In some exemplary embodiments of the invention, optical means are used to provide efficient fan in or fan out mechanisms.
FIG. 3 is a schematic flowchart 300 of a combined optical and electronic processing method in accordance with an exemplary embodiment of the invention. Prior to any optical processing, electronic preprocessing may be performed (302), for example to perform calculations more efficiently carried out electronically, calculations that utilize existing hardware, to match the data to the processing system and/or the processing to be performed and/or to prepare the data for parallel processing. However, in some embodiments, no pre-processing is performed, for example, an optical input image may be directly optically processed. The electronic data is then converted to an optical representation (304), for example using an SLM or an array of individually controllable light sources. The light is then optically processed (306), using various means, such as lens, holograms, SLMs, masks and/or lenslet arrays. The processed light may be directly utilized, for example in optical communications systems or for displaying or printing an image. Alternatively or additionally, the light is detected (308), for example using a CCD. Optionally, the detected signals are further electronically processed (310), for example to perform addition or other post processing more conveniently carried out using electrical circuitry. Alternatively or additionally, the detected signals are provided to an electronic circuitry.
In an exemplary application of the invention, a linear transform implemented is a Fourier based transform, for example JPEG-DCT. However, the following described optical processor architectures may be used for other linear transforms as well and/or for processing, such as switching, error correction and signal compression, for example using a ID wavelet transform. Alternatively or additionally, non-linear transforms and processing may also use a similar architecture or elements from the architectures described herein.
GLT can be used in many fields, including, for example, image compression, image enhancement, pattern recognition, signal identification, signal compression, optical interconnects and crossbar systems, morphologic operations, logical operations, image and signal transformation and modeling neural networks.
Although not required, in some embodiments of the invention, the input data set is processed as a series of bit planes, with the results of the transform of each bit plane being added together to yield the required transform of the input data. The following equation describes the relationship between the Fourier transforming of bit plane separated and unseparated data: $F (\sum_{i} 2^{i} a_{i}) = \sum_{i} 2^{i} F (a_{i})$
This equation is correct for all linear transformations and enables translation of a gray level (with M gray levels) linear transformation to a set of log₂M transforms of binary input data. It should be noted that in many cases, modulation of binary signals provides faster operation rates and better performance.
FIG. 4 is a schematic diagram of an optical processing system 400 using a Dammann grating 408 for image replication, in accordance with an exemplary embodiment of the invention. Alternatively, other diffractive elements may be used for replication, for example a Ronchi grating. The input source is a one or two dimensional array 404, which can be for example, a VCSEL array, a LED array, a laser array, and/or a light source combined with a spatial light modulator (SLM), for example, acousto-optic, liquid crystal, mechanical or MQW (multi quantum wells) modulators.
In an exemplary embodiment an 8 by 8 array of light sources is used for array source 404. Driver circuitry 402, which is typically electronic, but may also be of other types, such as optical, drives array source 404 in correspondence with the input data to system 400.
The image on array 404 is collimated a lens 406 and replicated by a replicating structure, for example a Dammann grating 408. The replicated images are then processed, for example using a masking convolution or using a lenslet array. One example of a masking convolution uses a mask array 410. Th results of the processing are optionally collected, for example using a lenslet array 412 onto an array of detectors 414. The signals generated by the detectors may be further processed by circuitry 416. Array 410 can be a standard half-tone mask or it may be a gray scale mask. A passive element may be used. Alternatively, an actively controllable element, such as an SLM (spatial light modulator) may be used. Although a linear response mask is preferred, in some embodiments, a non-linear response mask is used instead. Also it is noted that in some uses, such as JPEG image compression, not all the coefficients are strictly required, so they may be omitted from the mask.
A potential advantage of a Dammann grating is that the replication is almost identical to the original even if the input illumination is not uniform. A potential advantage of VCSELs is that even though each one of the sources is coherent, the sources are not coherent between themselves, so there may be fewer interference effects. However, neither a Darnmann grating nor a VCSEL are strictly required and they may be replaced by other elements, in accordance with some embodiments of the invention.
Typically, the GLT function W(x,y;ξ,η) to be performed is determined by masks 410 and/or lenslet array 412. Although fixed masks 410 may be used, in some embodiments of the invention, masks 410 are controllable, for example being SLMs, binary or gray level.
An analysis of an exemplary system 400 is as follows:
The imaging relation of the main lens provides: $\frac{1}{u} + \frac{1}{v} = \frac{1}{f},$
where U is the distance between array source 404 and lens 406 and v is the distance between Dammann grating 408 and mask array 410.
The magnification ratio is: $M = \frac{u}{v}$
The resolution condition: $2.44 λ f_{#} < \frac{250 μm}{M}$
when 250 μm is the pitch of the laser sources (in other embodiments, a different pitch may be available). A field of view (FOV) restriction in order to avoid spherical lens distortions may be applied as: $F O V = \frac{Δ x}{v} < 0.8 [rad]$
where Δx is the transaxial extent of detector array 414. Although system 400 is not rectangular, in some embodiments, it may be. Optionally, a reflective optical element is used to fold optical paths and/or shorten the system.
A volume V restriction condition may be defined, for example arbitrarily requiring a volume of less than 4000 cubic mm:
V=(u+v)·[max{Δx,D}] ²<4000 [mm ³]
where D is the diameter of the lens.
A cross talk condition can be defined as the interference between two neighbored replica: $2.44 λ f_{#} \cdot 20 < a \cdot \frac{250 μm}{M}$
where “a” is the required separation ratio between replica and 20 is an empirical constant. The “a” ratio may be extracted from this equation, assuming that each block is 8×8 pixels in size: $Δ x = 2 a \cdot 8 \cdot 8 \frac{250 μm}{M}$
In a particular implementation f=8 mm, f#=1, the light wavelength is 1 μm and M=5, a following setup configuration can be achieved:

- Δx=6.4 mm
- v=9.6 mm, u=48 mm
- FOV=38 [deg].
- V=3686.4 [mm³]

In another particular implementation: M=4, f=8 mm, f#=1, and the light wavelength is 1 μm. Resulting in:

- Δx=8 mm
- v=10 mm, u=40 mm
- FOV=46 [deg].
- V=3200 [mm³]

In some embodiments, the Dammann grating is a multi channel Dammann grating that replicates block portions of the input image, rather than the entire input image as a whole, which may be associated with a lenslet array instead of lens 406, for implementing a multi-channel system.
Another potential advantage of using a diffractive element is that a spatial shifting of the output can be achieved by varying the input wavelength. In one exemplary embodiment, a tunable laser input is used, with different wavelengths being used for different output positions and/or scales. Alternatively or additionally, a wavelength responsive reflector, lens or additional optical element may be used to shift the results for different wavelengths. Other wavelength shifting techniques can be used as well, for example, very fast modulators in combination with sensitive detection systems.
FIGS. 5A and 5B are a top and a side schematic views of a linear source optical processing system 500 in accordance with an exemplary embodiment of the invention.
In system 500, a linear light source 504, for example an array of VCSELs is driven by electronic circuitry 502 to generate a one dimensional pattern. Although a discrete source array is shown, in some embodiments, a continuous source array may be provided. It should be noted that although a straight one dimensional source is shown, the source may also be curved and/or folded with corresponding changes in other elements and/or their positioning. Alternatively, other methods of providing a one-dimensional light source may be provided. The spatially modulated light is spread in a transaxial direction by at least one lens 506, for example a single cylindrical lens. Optionally, the lens is an anamorphic lens, with different focal lengths for its two axes. The spread light is then processed by a two dimensional optical element 510, for example an array of masks. Alternatively or additionally, an active element may be used instead, for example an LCD or other type of light valve array. A second lens system 512, also optionally anamorphic collects the light onto a linear detector array 514, which is, for example, perpendicular to source array 504, so that it collects processed light from all of the sources together. Optional post processing may be performed by a processor 516 connected to detectors 514. The arrays may be, for example, 64 element long, to support an 8×8 block operation.
One possibly restriction of system 500 is generated by the resolution available in the Fourier plane. Assume a 256 gray level transformation mask 510 with a spatial production resolution of δ=0.5 μm. Then, the size of each pixel in the transformation mask ought to be: δL=δ{square root}{square root over (256)}=0.5 μg·16=8 [cm]
This size typically defines the maximal resolution in the Fourier plane. Such a resolution requires: $\frac{λ f}{64 \cdot δ x} = δ L$
where δox is the size of the VCSEL cell and f is the lens focal length.
In an exemplary embodiment of system 500, using a VCSEL vector of 64 pixels, δx=50 μm and λ=1 μm (the wavelength of the light):

f=50·64·8 μm=2.56 [cm]
resulting in a system length of 4f=10.24 [m]. If a f#=1 lens is used, a lens aperture of $D = \frac{f}{f_{#}} = 2.56 [cm]$
is obtained. A typical volume V of this exemplary system is:
V=(4f)·D ²=10.24·(2.56)²=6710 [mm ³]

It should be noted that in this and other exemplary estimated measurements, different manufacturing and/or design constrains will yield different results.
FIGS. 6A and 6B are a top and a side schematic views of a non-imaging optics optical processing system 600 in accordance with an exemplary embodiment of the invention. System 600 is characterized in that the light from a point source is spread using non-imaging means.
In system 600, an array of point sources 604, driven by circuitry is spread by non-imaging means, for example an array of planar light guides 606, which widen from a point to a line. Optionally, the use of light guides prevents or reduces cross-talk between channels. Alternatively, other means, such as mirrors or diffuse reflectors, may be used. Light sources 604 may be behind the effective linear source or they may be at a different angle, for example to the side. In one embodiment, the light is spread by scattering along a light guide to outside of the light guide. In another example, the light is conveyed along a light guide using total internal reflections, and exists the light guide via a diffraction grating or other non-uniformity of the surface. In a particular embodiment of the invention, each of light guides 606 comprises a distorted parabolic reflector, with a light source 604 so located in it that the light from the source is reflected by the reflector to extend the entire width of the light guide, at its end. In one dimension, the parabolic reflector generates a parallel beam of light from a point source placed in its focal point, so that the light does not exit the light guide. In some embodiments, no physical light guide is provided beyond a parabolic or other design reflector. The expansion of light in the other dimension may be supported by a distortion of the parabola or by using other suitable curves as known in the art of light reflecting. Alternatively or additionally, non-imaging optics techniques are used to spread the light, for example a suitably designed light guide. It should be noted that parabolic or other reflectors may also be used in conjunction with the embodiment of FIGS. 5A and 5B, for example for light collection.
Light exiting from light guides 606 is processed by an optical element 610, for example a mask or an SLM. The results of the processing are collected by a second set of light guides 612, to an array 614 of detectors. Alternatively, a lens may be used to collect the processed light. Optionally, a diffuser is placed adjacent element 610, to assist in imaging the processed light. In an alternative embodiment (also suitable for system 500) detectors 614 may be an array of linear detectors, for example, each element having a length equal to the width of the system. Alternatively or additionally, the light sources may be an array of linear light sources.
A potential advantage of not having imaging elements is that the resulting system may be more robust.
In an exemplary parametric design, if IL_FOVdenotes the illumination field of view of the light source, then: $Δ_{y} = 2 y_{0} = 2 \cdot \frac{1}{4 p}$
where Δy is the width of the optical processor. Assuming that δ is the size of the VCSEL: $p (64 \cdot δ) = \tan (\frac{{IL}_{FOV}}{4})$ $Thus :$ $Δ_{y} = \frac{64 \cdot δ}{2 \tan (\frac{{IL}_{FOV}}{4})}$
For an exemplary IL_FOVof 30 degrees and δ250 μm, a value of Δy=60 mm is obtain. An approximate volume for such an element is:
V=(64·ε)²Δ_y=15.5 [cm ³]
FIG. 7 is a schematic view of a two dimensional optical processing system 700, in accordance with a n exemplary embodiment of the invention.
A 2-D input (702) having N*N pixels requires a kernel having N²*N²pixels. In this case the space multiplexing may be more complex than the one in the 1-D input case. The transformation may be written as: $I_{o} (k, l) = \sum_{m} \sum_{n} I_{in} (m, n) K (m, n; k, l)$
In an exemplary embodiment, the kernel mask is divided into 2-D blocks and the index of each block will represent the output coordinate k,l while the location within each block m,n will represent the required kernel matrix. In this notation in order to perform the transformation the input I_in(m,n) is replicated to each block, multiplied by the value of the kernel there and summed to a single value k,l in the output plane.
In an incoherent illumination embodiment, the 2-D summation may be obtained using a lens attached to each block of the kernel, for example a lenslet array 710. The replication of the input may be done via a Dammann grating 706 or an array of prisms which are attached to the aperture of an imaging lens 704 (at 706, for example, instead of the grating). A direction correcting prism array may be provided at a replicated image plane 708.
In an embodiment using an incoherent illumination pattern, the kernel mask may be limited to being positive since the phase information is lost by the incoherence. Thus, in order to implement a general transformation kernel three or more parallel processing paths are optionally used. Each pixel of the input as well of the kernel may be represented in the following manner:
I _in(m,n)=a ₀ ^I(m,n)+a ₁ ^I(m,n)e ^2πi/3 +a ₂ ^I(m,n)e ^4πi/3
K(k,l,m,n)=a ₀ ^K(k,l;m,n)+a ₁ ^K(k,l;m,n)e ^2πi/3 +a ₂ ^K(k,l;m,n)e ^4πi/3
The splitting into the three processing paths can be performed, for example, using a Dammann grating or a prisms set attached to an imaging lens. The transformation of each path is performed and then the three paths are summed to obtain the total output according to: $\begin{matrix} I_{o} (k, l) = \sum_{m} \sum_{n} ⌊ a_{0}^{I} (m, n) a_{0}^{K} (k, l; m, n) + a_{1}^{I} (m, n) a_{2}^{K} (m, n) + \\ a_{2}^{I} (m, n) a_{1}^{K} (m, n) ⌋ + ⅇ^{2 π ⅈ / 2} \sum_{m} \sum_{n} [a_{0}^{I} (m, n) a_{1}^{K} (k, l; m, n) + \\ a_{1}^{I} (m, n) a_{0}^{K} (m, n) + a_{2}^{I} (m, n) a_{2}^{K} (m, n)] + \\ ⅇ^{4 π ⅈ / 3} \sum_{m} \sum_{n} [a_{0}^{I} (m, n) a_{2}^{K} (k, l; m, n) + a_{1}^{I} (m, n) a_{1}^{K} (m, n) + \\ a_{2}^{I} (m, n) a_{0}^{K} (m, n)] \end{matrix}$
It should be noted that within each one of the three processing paths three sub processing operations are applied when the most general input representation is used. For a positive input each path contains only one sub-processing path.
It is noted that instead of three spatial processing paths, one or more of the three “paths” may be implemented by using a single system 700 multiple times, one for each processing path.
For a real input/kernel an embodiment with two main processing paths can be used: for the positive and the negative values. In this case the output distribution should be obtained as: $\begin{matrix} I_{o} (k, l) = \sum_{m} \sum_{n} [a_{0}^{I} (m, n) a_{0}^{K} (k, l; m, n) + a_{1}^{I} (m, n) a_{1}^{K} (m, n)] - \\ \sum_{m} \sum_{n} [a_{0}^{I} (m, n) a_{1}^{K} (k, l; m, n) + a_{1}^{I} (m, n) a_{0}^{K} (m, n)] \end{matrix}$
where a₀represents the positive values and a₁the negative ones.
It should be noted that the subtraction of the previous equation may be performed by using the same detector and performing the processing in two cycles. In the second cycle the voltage of the output detector is inverted. The first path is done in the first processing cycle and it loads the capacitor of the detector. In the second cycle the inversion starts to unload the capacitor and thus a subtraction between the two results is obtained.
The present application is related to the following four PCT applications filed on same date as the instant application in the IL receiving office, by applicant JTC2000 Development (Delaware), Inc.: attorney docket 141/01582 which especially describes matching of discrete and continuous optical elements, attorney docket 141/01541 which especially describes reflective and incoherent optical processor designs, attorney docket 141/01581 which especially describes a method of optical sign extraction and representation, and attorney docket 141/01542 which especially describes a method of processing by separating a data set into bit-planes and/or using feedback. The disclosures of all of these applications are incorporated herein by reference.
It will be appreciated that the above described methods and apparatus for optical processing may be varied in many ways, including, changing the order of steps, which steps are performed using electrical components and which steps are performed using optical components, the representation of the data and/or the hardware design. In addition, various distributed and/or centralized hardware configurations may be used to implement the above invention. In addition, a multiplicity of various features, both of methods and of devices, have been described. It should be appreciated that different features may be combined in different ways. In particular, not all the features shown above in a particular embodiment are necessary in every similar embodiment of the invention. Further, combinations of the above features are also considered to be within the scope of some embodiments of the invention. In addition, the scope of the invention includes methods of using, constructing, calibrating and/or maintaining the apparatus described herein. When used in the following claims, the terms “comprises”, “comprising”, “includes”, “including” or the like mean “including but not limited to”.

Claims

1. Apparatus for optically applying a transform to data, comprising:

a spatially modulated light source, that generates a spatially modulated light beam encoding said data by said modulation;

a diffractive element that replicates said light beam; and

a lens that applies a Fourier transform to said replicated light beam.

2. Apparatus according to claim 1, comprising a detector that detects said transformed light.

3. Apparatus according to claim 2, comprising electronic circuitry that converts said detected signals into a discrete transform of said data.

4. Apparatus according to claim 3, wherein said transform is a linear transform.

5. Apparatus according to claim 3, wherein said transform is a DCT transform.

6. Apparatus according to claim 1, wherein said replicating comprises replicating said beam to a two dimensional arrangement.

7. Apparatus according to claim 1, wherein said diffractive element comprises a Dammann grating.

8. Apparatus according to claim 1, wherein said diffractive element comprises a Ronchi grid.

9. Apparatus according to claim 1, wherein said spatially modulated light encodes said data as an array of blocks.