Coherent optical processing

The principles of communication theory were applied in the 1950's to optical imaging systems and to the analysis of images. Optical systems were analyzed in much the same way as linear systems (modulation transfer functions and channel capacities) and images were characterized in ways analogous to time signals (space-bandwidth products, spatial frequency content, etc.). Both coherently and incoherently illuminated optical systems can be treated using these concepts. Coherently illuminated systems are most useful for performing operation such as convolution, cross correlation, and spectral analysis because the Fourier transform of an optical signal physically exists and can, therefore, be measured or modified. The basic Fourier transform relationship for coherently illuminated systems is developed in this paper. It can be detected directly and used to estimate the distribution of spatial frequencies contained in the signal. Methods for constructing complex-valued spatial filters are described; these filters can be used to realize such operations as convolution or cross correlation, addition or subtraction, and differentiation or integration. Experimental results are given to illustrate the concepts and to susgest potential applications. To extend the range of applications, interface devices are needed to allow optical processing of two-dimensional raster-scanned time signals, wide bandwidth electrical signals, and incoherent optical signals. Interface devices are often needed to convert the output optical signal to an electrical signal for post-processing by a digital computer. For some applications, interface devices are needed to construct spatial filters in real time, so different operations can be performed on a given signal. The desired characteristics of these three interface devices and the current state of their development are briefly reviewed.

[1]  F P Carlson,et al.  Linear vector operations in coherent optical data processing systems. , 1970, Applied optics.

[2]  K. Preston.  A Coherent Optical Computer System Using the Membrane Light Modulator , 1970, IEEE Transactions on Aerospace and Electronic Systems.

[3]  J. D. Margerum,et al.  REVERSIBLE ULTRAVIOLET IMAGING WITH LIQUID CRYSTALS , 1970 .

[4]  B. McGlamery.  Restoration of Turbulence-Degraded Images* , 1967 .

[5]  Edward L. O'Neill,et al.  Spatial filtering in optics , 1956, IRE Trans. Inf. Theory.

[6]  H. Dammann,et al.  Restoration of Faulty Images of Periodic Objects by Means of Self-imaging. , 1971, Applied optics.

[7]  G. Groh,et al.  Information input in an optical pattern recognition system using a relay tube based on the pockels effect , 1970 .

[8]  A. Lugt,et al.  The use of film nonlinearities in optical spatial filtering. , 1970, Applied optics.

[9]  H. H. Hopkins,et al.  The concept of partial coherence in optics , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[10]  J. Elmer Rhodes.  Analysis and Synthesis of Optical Images , 1953 .

[11]  H Stark,et al.  Optical processing of radar signals with fresnel diffraction masks. , 1971, Applied optics.

[12]  N. Sheridon,et al.  The Ruticon family of erasable image recording devices , 1972 .

[13]  David Pearce MacAdam,et al.  Digital Image Restoration by Constrained Deconvolution , 1970 .

[14]  C E Thomas,et al.  Optical spectrum analysis of large space bandwidth signals. , 1966, Applied optics.

[15]  D. Slepian.  Linear Least-Squares Filtering of Distorted Images , 1967 .

[16]  E. I. Gordon,et al.  A review of acoustooptical deflection and modulation devices , 1966 .

[17]  C. W. Barnes.  Object Restoration in a Diffraction-Limited Imaging System , 1966 .

[18]  H Stark,et al.  Design considerations in power spectra measurements by diffraction of coherent light. , 1969, Applied optics.

[19]  R. Meier,et al.  Thermoplastic xerographic holography. , 1966, Applied optics.

[20]  W T Maloney,et al.  Lensless holographic recognition of spatially incoherent patterns in real time. , 1971, Applied optics.

[21]  G. D. Francia.  Degrees of Freedom of Image , 1969 .

[22]  C B Burckhardt,et al.  A Simplification of Lee's Method of Generating Holograms by Computer. , 1970, Applied Optics.

[23]  W. E. Glenn.  Principles of Simultaneous-Color Projection Television Using Fluid Deformation , 1970 .

[24]  A W Lohmann,et al.  Computer generated spatial filters for coherent optical data processiing. , 1968, Applied optics.

[25]  Joseph W. Goodman,et al.  Nonredundant Arrays and Postdetection Processing for Aberration Compensation in Incoherent Imaging , 1971 .

[26]  L. W. Nichols.  Optical Filtering , 1959, Proceedings of the IRE.

[27]  S H Lee,et al.  Synthesis of a spatial filter for the combined operations of subtraction and correlation. , 1971, Applied optics.

[28]  A. Walther.  Gabor’s Theorem and Energy Transfer through Lenses , 1967 .

[29]  A. Kozma,et al.  Tilted-plane optical processor. , 1972, Applied optics.

[30]  F. T. S. Yu,et al.  Synthesis of Optimum Complex Spatial Filters , 1972 .

[31]  J. Tsujiuchi.  IV Correction of Optical Images by Compensation of Aberrations and by Spatial Frequency Filtering , 1963 .

[32]  A. V. Lugt,et al.  Operational notation for the analysis and synthesis of optical data-processing systems , 1966 .

[33]  Thomas S. Huang,et al.  Digital Holography , 2003 .

[34]  A W Lohmann,et al.  Spatial pulse modulation. , 1971, Applied optics.

[35]  E. Leith,et al.  A High-Resolution Radar Combat-Surveillance System , 1961, IRE Transactions on Military Electronics.

[36]  A W Lohmann,et al.  Binary fraunhofer holograms, generated by computer. , 1967, Applied optics.

[37]  M Chang,et al.  Optical correlation of real-time signals. , 1971, Applied optics.

[38]  J. Burch.  A computer algorithm for the synthesis of spatial frequency filters , 1967 .

[39]  F T Yu,et al.  Optical correlation analysis of two-phase micrographs. , 1971, Applied optics.

[40]  Thomas M. Holladay,et al.  Phase Control by Polarization in Coherent Spatial Filtering , 1966 .

[41]  E B Felstead,et al.  Optical simulation of one-dimensional complex-valued functions. , 1971, Applied optics.

[42]  H. Hopkins.  On the diffraction theory of optical images , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[43]  H B Perkins.  Correlation signals produced by phase type matched filters. , 1969, Applied optics.

[44]  J. R. Maldonado,et al.  Strain-biased ferroelectric-photoconductor image storage and display devices , 1971 .

[45]  D G Falconer.  Optical processing of bubble chamber photographs. , 1966, Applied optics.

[46]  B J Pernick,et al.  An optical spectrum analyzer for power spectral density measurements. , 1969, Applied optics.

[47]  David Casasent,et al.  On-line Fourier transform of video images , 1968 .

[48]  M King,et al.  Holographic storage of electric signals. , 1969, Applied optics.

[49]  B. Frieden,et al.  OPTIMUM, NON-LINEAR PROCESSING OF NOISY IMAGES , 1968 .

[50]  D. Raso.  Simplified Method to Make Hologram Filters for Target Recognition , 1968 .

[51]  A. Papoulis,et al.  Approximations of Point Spreads for Deconvolution , 1972 .

[52]  Andrew H. Eschenfelder,et al.  Promise of Magneto‐Optic Storage Systems Compared to Conventional Magnetic Technology , 1970 .

[53]  Emmett N. Leith,et al.  Wavefront Reconstruction with Continuous-Tone Objects* , 1963 .

[54]  Albert B. Porter,et al.  XII. On the diffraction theory of microscopic vision , 1906 .

[55]  Z. J. Kiss,et al.  Photo erasable dark trace cathode-ray storage tube , 1968 .

[56]  J. R. Maldonado,et al.  Improved Aging and Switching of Lead Zirconate‐Lead Titanate Ceramics with Indium Electrodes , 1970 .

[57]  Paul G. Roetling.  Image Enhancement by Noise Suppression , 1970 .

[58]  J. Ator,et al.  Image velocity sensing by optical correlation. , 1966, Applied optics.

[59]  Emmett N. Leith,et al.  Wavefront Reconstruction with Diffused Illumination and Three-Dimensional Objects* , 1964 .

[60]  K. Preston.  An array optical spatial phase modulator , 1968 .

[61]  Olof Bryngdahl,et al.  Holographic Compensation of Motion Blur by Shutter Modulation , 1969 .

[62]  M Gottlieb,et al.  Optoacoustic processing of large time-bandwidth signals. , 1972, Applied optics.

[63]  J. Horner.  Optical Spatial Filtering with the Least Mean-Square-Error Filter* , 1969 .

[64]  A W Lohmann,et al.  Matched filtering with self-luminous objects. , 1968, Applied Optics.

[65]  A. B. Vander Lugt,et al.  Signal detection by complex spatial filtering , 1964, IEEE Trans. Inf. Theory.

[66]  R J Doyle,et al.  Remote real-time reconstruction of holograms using the lumatron. , 1972, Applied optics.

[67]  J L Horner.  Optical restoration of images blurred by atmospheric turbulence using optimum filter theory. , 1970, Applied optics.

[68]  E B Felstead.  A simplified coherent optical correlator. , 1968, Applied optics.

[69]  C. K. Rushforth,et al.  Restoration, Resolution, and Noise , 1968 .

[70]  J. K. Hawkins,et al.  Image Processing by Electron-Optical Techniques , 1967 .

[71]  M Gottlieb,et al.  Design and construction of an optoacoustic signal processor. , 1973, Applied optics.

[72]  G. O. Reynolds,et al.  Optical synthetic aperture analogues of two radio interferometers. , 1971 .

[73]  Leonard J. Porcello,et al.  Optical data processing and filtering systems , 1960, IRE Trans. Inf. Theory.

[74]  M. Dakss,et al.  A fast digitalized scan laser , 1968 .

[75]  E Marom,et al.  Real-time strain measurements by optical correlation. , 1970, Applied optics.

[76]  Frank R. Whitehead,et al.  Coherent Optical Parallel Processing , 1971 .

[77]  W. Duane Montgomery,et al.  Self-Imaging Objects of Infinite Aperture* , 1967 .

[78]  C. Helstrom.  Image Restoration by the Method of Least Squares , 1967 .

[79]  D. B. Fraser,et al.  Image storage and display devices using fine-grain, ferroelectric ceramics , 1970, Bell Syst. Tech. J..

[80]  F T Yu,et al.  Coherent optical target recognition through a phase distorting medium. , 1971, Applied optics.

[81]  William E. Good.  A New Approach to Color Television Display and Color Selection Using a Sealed Light Valve , 1969 .

[82]  H. Beauchamp,et al.  Write-read-erase in situ optical memory using thermoplastic holograms. , 1970, Applied optics.

[83]  Robert Hickling.  Scattering of Light by Spherical Liquid Droplets Using Computer-Synthesized Holograms , 1968 .

[84]  A. Vander Lugt,et al.  A Review of Optical Data-processing Techniques , 1968 .

[85]  R A Gabel,et al.  Minimization of reconstruction errors with computer generated binary holograms. , 1970, Applied optics.

[86]  J W Goodman,et al.  The optical convolution of time functions. , 1970, Applied optics.

[87]  K S Pennington,et al.  Filtering of defects in integrated circuits with orientation independence. , 1971, Applied optics.

[88]  S. H. Lee,et al.  Spatial Differentiation and Integration by Coherent Optical-Correlation Method , 1971 .

[89]  H. Kogelnik,et al.  Holographic Imaging Through a Random Medium , 1968 .

[90]  J. E. Rau.  Real-Time Complex Spatial Modulation , 1967 .

[91]  W. T. Maloney,et al.  Acoustooptical approaches to radar signal processing , 1969, IEEE Spectrum.

[92]  G. Turin,et al.  An introduction to matched filters , 1960, IRE Trans. Inf. Theory.

[93]  L. S. Watkins.  Inspection of integrated circuit photomasks with intensity spatial filters , 1969 .

[94]  W. H. Lee,et al.  Sampled fourier transform hologram generated by computer. , 1970, Applied optics.

[95]  A W Lohmann,et al.  Incoherent matched filtering with fourier holograms. , 1971, Applied optics.

[96]  J. L. Harris,et al.  Image Evaluation and Restoration , 1966 .

[97]  S I Ragnarsson.  A new Holographic Method of Generating a High Efficiency, Extended Range Spatial Filter with Application to Restoration of Defocussed Images , 1970 .

[98]  W T Maloney.  Real-time optical filtering of autocorrelation functions. , 1971, Applied optics.

[99]  M King,et al.  Real-time electrooptical signal processors with coherent detection. , 1967, Applied optics.

[100]  J. Goodman,et al.  A technique for optically convolving two functions. , 1966, Applied optics.

[101]  D. S. Oliver,et al.  IMAGE STORAGE AND OPTICAL READOUT IN A ZnS DEVICE , 1970 .

[102]  I. Gorog,et al.  Cathodochromic image displays. , 1970, Applied optics.

[103]  W H Lee,et al.  Matched filter optical processor. , 1974, Applied optics.

[104]  G. W. Taylor,et al.  Phase holograms in a ferroelectric-photoconductor device. , 1970, Applied optics.

[105]  John A. van Raalte.  A New Light Valve for Television Projection , 1971 .

[106]  H. Weinberger,et al.  Interference method for pattern comparison. , 1971, Applied optics.

[107]  A. W. Lohmann,et al.  Holographic production of spatial filters for code translation and image restoration , 1967 .

[108]  H J Caulfield,et al.  Improved discrimination in optical character recognition. , 1969, Applied optics.

[109]  S. Som.  Analysis of the Effect of Linear Smear on Photographic Images , 1971 .

[110]  W. E. Glenn,et al.  Low Friction of Metals in Reciprocating Sliding , 1959 .

[111]  A. Lohmann,et al.  Complex spatial filtering with binary masks. , 1966, Applied optics.

[112]  R. G. Zech,et al.  A posteriori image-correcting ''deconvolution'' by holographic Fourier-transform division. , 1967 .

[113]  Joseph P. Kirk,et al.  Phase-Only Complex-Valued Spatial Filter* , 1971 .

[114]  Olof Bryngdahl,et al.  Interferograms are Image Holograms , 1968 .

[115]  Neil J. Bershad,et al.  Resolution, Optical-Channel Capacity and Information Theory* , 1969 .

[116]  L. Rosen.  Moiré effects in computer-generated holograms , 1967 .

[117]  R. V. Pole,et al.  Electron beam writing of spatial filters , 1969 .

[118]  George O. Reynolds,et al.  Imaging with Optical Synthetic Apertures (Mills-Cross Analog)* , 1970 .

[119]  S H Lee,et al.  New method of producing gradient correlation filters for signal detection. , 1971, Applied optics.

[120]  Dennis Gabor,et al.  Interference Microscope with Total Wavefront Reconstruction , 1966 .

[121]  C. E. Land,et al.  Ferroelectric ceramic electrooptic materials and devices , 1969 .

[122]  N. Uchida,et al.  Acoustooptic deflection materials and techniques , 1973 .

[123]  A. Spencer,et al.  Thermoplastic recording , 1961, Electrical Engineering.

[124]  J E Wasielewski.  Optical filter analysis as a function of nonoptimum noise conditions. , 1971, Applied optics.

[125]  George G. Goetz.  REAL‐TIME HOLOGRAPHIC RECONSTRUCTION BY ELECTRO‐OPTIC MODULATION , 1970 .

[126]  Henri H. Arsenault,et al.  Optical Filter Synthesis by Holographic Methods , 1968 .

[127]  A V Lugt.  Practical considerations for the use of spatial carrier-frequency filters. , 1966, Applied optics.

[128]  E. N. Leith,et al.  Quasi-holographic techniques in the microwave region , 1971 .

[129]  S. H. Lee,et al.  Optical Image Synthesis (Complex Amplitude Addition and Subtraction) in Real Time by a Diffraction-Grating Interferometric Method , 1970 .

[130]  R E Williams,et al.  Combined beam forming and cross correlation of broadband signals from a multidimensional array using coherent optics. , 1971, Applied optics.

[131]  Joseph W. Goodman,et al.  Increasing the Dynamic Range of Coherent Optical Filters by Means of Modulating Gratings. , 1973 .

[132]  D. Gabor.  Microscopy by Reconstructed Wave Fronts: II , 1951 .