Resonance domain diffraction gratings with local periods near the wavelength may have very high diffraction efficiencies. Unfortunately, they are difficult to fabricate, especially for use with light in visible and shorter wavelengths. We present several methods for fabricating surface relief resonance domain diffraction gratings used in the visible spectral region. We also optimize the relevant fabrication parameters and compare the resulting performance for each method. For the fabrication, we resort to e-beam lithography and reactive ion etching. Characterization is performed with environmental scanning electron microscopy, atomic force microscopy, and optical measurements on representative structures. Nearly 100% Bragg diffraction efficiency can be achieved with transmission resonance domain binary gratings formed in fused silica and having a period of 0.5 μm and a groove depth of 1 μm.
Selections from our recent developments in passive phase locking and coherent combining of lasers are presented. These
include the principles of our approaches, lasers configurations, experimental procedures and results with solid state lasers
and fiber lasers.
Structuring of optical surfaces with surface-relief diffractive optical elements is an enabling technology for achieving
considerable spatially varying changes in light propagation direction and wavefront curvature. This way, Bragg effects,
angular and spectral selectivity and nearly 100% diffraction efficiency usually attributed to volume optical holograms
can be achieved by surface relief computer generated holograms and diffractive optical elements. Several methods for
fabricating deep "resonance domain" diffraction structures with periods, exceeding the subwavelength limit but near to
the wavelength, were compared and optimized. Results of direct e-beam writing RIE etching, SEM and AFM
measurements for fused silica gratings with period of 520 nm and groove depth of 1000 nm, designed for nearly 100%
diffraction efficiency in the green 532 nm laser light, are presented.
We demonstrate an approach for stabilizing the transverse mode structure in cases where there is strong coupling between the longitudinal and the transverse modes. In this approach, an intracavity phase element that discriminates and selects a specific transverse mode is inserted into the laser resonator. We show that the discrimination can be so strong that the selection of the single transverse mode remains stable despite changes of the resonator length. We calculated the ratio of the small-signal gain and the gain threshold value for the fundamental and (1,0) Hermite-Gaussian modes, as function of a tiny change &Dgr;z of the resonator length, with and without the phase element. Without the phase element, the tiny change of the axial coordinate z of one of the mirrors of CO2 laser leads to periodical change of different transverse modes. Introducing intracavity phase element preserves a single transverse mode, which is kept practically unchanged with the change of the axial coordinate z, except for a slight periodical change of the output power and the beam quality, due to the periodicity of the resonance conditions.
In order to understand complex-hierarchical biomaterials such as bones and teeth, it is necessary to relate their structure and mechanical-properties. We have adapted electronic speckle pattern-correlation interferometry (ESPI) to make measurements of deformation of small water-immersed specimens of teeth and bones. By combining full-field ESPI with precision mechanical loading we mapped sub-micron displacements and determined material-properties of the samples. By gradually and elastically compressing the samples, we compensate for poor S/N-ratios and displacement differences of about 100nm were reliably determined along samples just 2~3mm long. We produced stress-strain curves well within the elastic performance range of these materials under biologically relevant conditions. For human tooth-dentin, Young's modulus in inter-dental areas of the root is 40% higher than on the outer sides. For cubic equine bone samples the compression modulus of axial orientations is about double the modulus of radial and tangential orientations (20 GPa versus 10 GPa respectively). Furthermore, we measured and reproduced a surprisingly low Poisson's ratio, which averaged about 0.1. Thus the non-contact and non-destructive measurements by ESPI produce high sensitivity analyses of mechanical properties of mineralized tissues. This paves the way for mapping deformation-differences of various regions of bones, teeth and other biomaterials.
Experimental and calculated characterization of resonance domain surface relief gratings with different groove shapes, groove depths, and groove slant angles are presented. Our results reveal that Bragg type diffraction, with efficiencies of about 90% can be achieved by properly choosing certain parameters of the resonance domain surface relief gratings.
We demonstrate an ultra sensitive method for Two Photon Fluorescence (TPF) excitation using resonant Grating Waveguide Structures (GWS). In its basic configuration, a GWS consists of a substrate, a waveguide layer and an additional grating layer. When illuminated with laser light under resonant conditions, the GWS reflects all light and leads to very high local surface intensities. This field enhancement can be exploited for TPF spectroscopy, without the need for a highly intense, focused laser light. We present the enhanced TPF signal obtained from a 23 nM drop of tetramethylrhodamine (TMR) on the top of high-finesse resonant polymeric GWS. The resonant behaviour of the GWS was tested for normal incidence with TE polarization illumination. As expected, the transmission spectral profile has a dip at resonant wavelength. The TPF spectra of TMR molecules were observed for different excitation wavelengths. Close to resonance, TPF intensity increases and the maximum signal is obtained when the excitation wavelength coincides with the resonance wavelength of the GWS. These results clearly indicate that the huge field localization at grating surface is responsible for the TPF excitation. We obtained a detection limit down to picomolar concentration of the dye molecules, offering the possibility of a highly sensitive, compact and non-destructive tool for widespread biochemical applications.
Mineralized biological materials have complex hierarchical graded structures. It is therefore difficult to understand the relations between their structure and mechanical properties. We report the use of electronic speckle pattern-correlation interferometry (ESPI) combined with a mechanical compression apparatus to measure the strain and Young's modulus of root dentin compressed under water. We describe the optomechanical instrumentation, experimental techniques and procedures needed to measure cubes as small as 1×1×2 mm. Calibration of the method is performed using aluminum, which shows that the measurements are accurate within 3% of the compression modulus reported for standard aluminum 6061. Our results reveal that the compression moduli of root dentin from the buccal and lingual sides of the root are quite different from the moduli of the interproximal sides. Root dentin from interproximal locations is found to have an average modulus of 21.3 GPa, which is about 40% stiffer than root dentin from the buccal and lingual locations, found to have a modulus of 15.0 GPa. Our approach can be used to map deformations on irregular surfaces, and measure strain on wet samples of varying sizes. This can be extended to the study of other biological materials including bone and synthetic biomaterials.
Planar optical light guides that are suitable for compact, relatively large virtual image projection displays, of either see-through or non-see-through capabilities, are presented. Such light guides are comprised of three diffractive elements that are recorded on a single substrate. The basic principles, design methods, experimental procedures, calculated as well as experimental results are presented. The results reveal that a relatively large field of view and uniform luminance over the entire output image can be obtained, even when the distance from the light guide to the viewer is relatively large.
"Flatland" is the title of a science fiction story, written in 1880 by E.A. Abbott. The creatures of Flatland, living in their two-dimensional universe, are inspected and manipulated by 3D-people like we are. Here we show how the optics part of this science fiction story can be implemented -- for fun and profit.
A simple method for obtaining a nearly Gaussian laser beam from a high order Hermite-Gaussian mode is presented. The method is based on separating the equal lobes of the high order mode and combining them together coherently. The method was experimentally verified with an arrangement of three mirrors, a 50% beam splitter and a phase tuning plate. The beam quality factor calculated in x-direction for the resulting output beam is 1.045, being very close to that of ideal Gaussian beam. The calculated power leakage is only 1.5%. The experimental near-field and far-field intensity distributions of the output beam have nearly Gaussian cross sections in both the x and y directions, with M2x=1.34 and M2y=1.32. With some modifications, it is possible to obtain an output beam with M2x=1.15 and no power leakage.
The research of passive and active grating waveguide structures has been ongoing in our group for the last decade. We briefly review recent research activities, emphasizing how such structures can be exploited for optical communication and for biological sensing.
A CMOS-liquid crystal-based image transceiver device (ITD) is under development at the Holon Institute of Technology. The device combines both functions of imaging and display in a single array configuration. This unique structure allows the combination of see-through, aiming, imaging and the displaying of a superposed image to be combined in a single, compact, head mounted display. The CMOS-based pixel elements are designed to provide efficient imaging in the visible range as well as driver capabilities for the overlying liquid crystal modulator. The image sensor part of the pixel is based on an n-well photodiode and a three-transistor readout circuit. The imaging function is based on a back- illuminated sensor configuration. In order to provide a high imager fill-factor, two pixel configurations are proposed: 1) A p++/p-/p-well silicon structure using twin- well CMOS process; 2) An n-well processed silicon structure with a micro-lens array. The display portion of the IT device is to be fabricated on a silicon-based reflective, active matrix driver, using nematic liquid crystal material, in LCOS technology. The timing, sequencing and control of the IT device array are designed in a pipeline array processing scheme. A preliminary prototype system and device design have been performed and the first test device is currently undergoing testing. Details of the device design as well as its Smart Goggle applications are presented.
The propagation law of the Wigner distribution function in the first-order non-orthogonal optical systems is described by using the linear canonical transform integral. The Wigner matrices for the usual optical components (free space, spherical and cylindrical lenses, and linear phase filter) are presented in four-dimensional phase space domain. Then with Wigner algebra, we analyze basic and more general optical configurations for performing a set of linear unitary coordinate transformations. These configurations are comprised of refractive spherical and cylindrical lenses that are readily available.
Novel compact devices for wavelength division multiplexing and demultiplexing are presented. These devices are based on planar optics configurations. A method for designing and recording such planar devices is described. Experimental procedures and results for devices that can handle three closely separated wavelengths in the visible as well as near infrared radiation are presented.
An optical spatial filtering system, designed to operate with totally incoherent light sources is presented. When correlating with such polychromatic light sources, one major problem is the dependence of the correlation response scaling on wavelength. A theoretical system that exactly compensate for this problem is analyzed. A practical configuration for implementing such a system, satisfying the theoretical solution up to first order in wavelength, is proposed. This configuration includes a combination of diffractive and refractive lenses and a gray scale filter. The possibility of higher order approximations is considered.
An achromatic Fourier system (AFS) performs optically a Fourier transformation in spatially coherent white light, without color blurring. Our design method uses matrix algebra, applied upon the Wigner distribution function. The matrix procedure is similar to what is used in geometrical objects. However, our approach is valid also for wave optics. That is important because the AFS does contain not only refractive lenses, but also diffractive lenses (Fresnel zone plates).
We present a system in which it is possible to distort the intensity distribution of an object I(x,y) into I(Ax + By,Cx + Dy), where the ABCD matrix has a unit determinant. The coefficients A, B, C and D can be varied independent of each other by rotating some cylindrical lenses. The degree of coherence is arbitrary. The number of pixels is limited in the usual way by the size of the object, by the wavelength, and by the F-number of the lenses.
A novel compact planar configuration for correcting the asymmetric divergence of light emanating from diode lasers is presented. It is comprised of two holographic lenses that are recorded on one transparent substrate, where the light propagates form one lens to the other by means of total internal reflections. The design of the overall planar configuration is presented along with experimental result. The results reveal that it is possible to focus a collimated asymmetric beam to a circular spot.
A compact configuration for a real-time updatable optical correlator is considered. The correlator is designed to operate with incoherent illumination and efficient phase filters, which can be implemented with real-time, updatable, electronically addressed, liquid-crystal spatial light modulator. In order to obtain both a rigid and a compact correlator, a configuration which can be incorporated with planar optics is investigated. The overall correlator includes two pairs of diffractive lenses, each for performing a Fourier transformation, one spatial light modulator and input and output interface devices. The design consideration and fundamental limits of a compact updatable correlator using off-axis, diffractive lenses are presented, along with some experimental results.
A method for designing and fabricating optical systems based on planar holographic optics is presented. The planar optical system is usually composed of two (or more) holographic optical elements which are fabricated onto the same substrate. This paper compares and contrasts the two principal fabrication methods of holographic elements as Bragg volume holograms or as surface relief gratings. Various examples of planar holographic optical systems are presented, and their advantages over regular optical systems are illustrated.
A compact planar configuration for performing optical correlation is described. It is comprised of two pairs of identical holographic lenses and a holographic filter. Each pair of lenses is recorded on a single substrate and together perform exact Fourier transformation. The light between the lenses propagates inside the substrate by means of total internal reflection. The design and recording considerations for each of the lenses along with experimental results for the overall planar correlator are presented.
Grating formation in photoactive polymers are monitored by holographic recording. The photopolymers are based on acrylamide monomers, which are dissolved together with xanthine dyes in polyvinyl alcohol. Thin plastic coatings are obtained by casing on glass substrates. Photorecording occurs quasi-real-time and in-situ, meaning that no wet- chemical or post-thermal/photochemical processing is required. Formulations have been found, which produce large enough refractive index modulations, so that very high diffraction efficiencies can be obtained, when the recording beam angles are symmetric. Unfortunately, DEs significantly drop, when recording angles are highly asymmetric. The origin of this effect is shown to stem from grating anomalies, in that the slanted fringes bend due to nonlinear shrinkage effects during recording. The introduction of cross-linking and gelling agents stabilize the formed grating structures against dimensional distortions. These photopolymer layers have potential in photonics applications, such as holographic optical elements and waveguide structures.
Photoactive polymer matrices are investigated by and for holographic recording at 514 nm. The photopolymers are based on acrylamide monomers, which are dissolved together with xanthine dyes and other additives in polyvinylalcohol. Dry plastic coatings are obtained by casting the aqueous polymer solutions on glass substrates. Photorecording occurs in real-time and in-situ, without any post-exposure processing. This paper describes the influences of chemical additives on the photorecording process. Specifically, the addition of diphenyl iodonium chloride (DPI-Cl), in conjunction with triethanolamine (TEA), significantly increases the exposure sensitivities, by a factor of over three (to about 15 mJ/cm2). This sensitizing effect is shown to originate from a superadditive effect between TEA and DPI-Cl. The mechanism of the superadditive effect is discussed by a proposed reaction model. The exposure sensitivities are also significantly influenced by the PVA binder parameters, such as average molecular weights and degree of hydrolization. The present formulations produce large enough refractive index modulations, so that very high diffraction efficiencies (DEs > 90%) are obtained. The dynamic range of refractive index modulations was increased from 0.014 to 0.018 by the addition of glutaraldehyde crosslinking, which also improves the dimensional stability of the holograms.
In this work we propose a design procedure for producing an optical interconnection lens as a computer originated hologram. New methods for analyzing and designing holographic optical elements are developed. These are mainly based on the introduction of Taylor series expansion to solving the equations of holographic elements. Specifically, the Taylor expansion is exploited to solve the Bragg conditions after they are reformulated as a nonlinear partial differential equation. The expansion is also used for analyzing the propagation of a given wavefront in an optical system that can be comprised of several holographic and conventional elements. According to computer simulations, the spot size, calculated in accordance with geometrical optics, is several orders of magnitude less than the diffraction limited size, and the diffraction efficiency degradation is less than 0.01%.
A symmetric substrate mode holographic doublet that performs Fourier transformation is presented. This doublet is composed of two identical quadratic off-axis holographic lenses which were recorded on the same glass substrate. The first lens couples the light from the input into the glass substrate. The second lens, located at the back focal plane of the first one, couples the light out of the glass substrate and corrects the phase of the emerging wavefront in order to obtain the desired Fourier transformation. In such a configuration the input and the output planes are adjacent to the lenses, so the overall alignment is very convenient.
We investigated how best to record phase filters on a spatial light modulator (SLM) in a hybrid optic-electronic correlator that operates with incoherent light. The SLM used in our experiments was the Hughes liquid crystal light valve (LCLV), on which we recorded phase filters having 256 by 256 pixels. Two correlation configurations were tested in which the input scenes contained 512 by 512 pixels. In one, the input scene was introduced by means of a transparency that was illuminated by a laser beam that emerged from a rotating diffuser. In the other, the input scene was displayed on a miniature monochromatic cathode ray tube (CRT). The experimental results with both configurations reveal that real time updatability of optical filters for correlation with incoherent light is indeed possible. The analysis, correlation configurations and experimental procedures and results are presented.
An optical resonance phenomena, based on an interference effect that occurs when a plane wave is incident on a dielectric grating/waveguide structure, is presented. The incident wave excites a guided mode in the waveguide which in turn is partially diffracted by the grating in the direction of the transmitted zero order beam, interfering destructively. As a result most of the light energy is contained in the reflected zero order beam. This resonance phenomena is explained with a ray picture of the multiple interference and analyzed by solving Maxwell's equations for the exact eigenfunctions in a grating/waveguide structure. Some basic structures have been fabricated and experimentally tested. The results reveal that the resonance beamwidth and bandwidth depend strongly on the parameters of the grating/waveguide structure. Measurements indicate that the bandwidth of the resonances can be as narrow as 1 nm, with a corresponding angular beamwidth on the order of minutes of arc.
Planar optical configurations combine holographic elements with a substrate mode planar structure where the light is trapped inside the structure by total internal reflections. As a result, usual free space propagation can be replaced by guided propagation in the planar structures on which holographic elements are recorded on either side. These configurations can thus be very compact and readily modularized so as to eliminate the, usually needed, extreme alignment accuracies between input light sources, holographic elements, and output detectors. The principles and examples of how such elements can be incorporated into display and data processing applications are presented.
This paper describes optical systems which compensate for the wavelength dispersion and distortion that arise in diffractive fan-out elements. Two approaches are investigated, a space variant and a space invariant. In the space variant approach, microlenses or diffractive optical elements were introduced in the system correcting the wavefronts. In the space invariant approach refractive and diffractive lenses compensates for the chromatic aberrations and shifts in beam direction that are caused by the fan-out element. Several designs for such compensating optical systems are presented, along with simulated results.
Optical correlators with incoherent light offer many of the advantages of correlators with coherent light, yet they are not as sensitive to coherent noise and alignment errors. Moreover, sophisticated and complex spatial modulators are not needed. The correlation is performed by comparing the input scene with some predefined reference object that was recorded earlier in a single holographic filter. To increase the number of objects that can be simultaneously correlated, or, alternatively, allow rotation and scale changes of one object, we investigated how best to record holographically a multiplicity of different objects in one composite filter. We determined that for high SNR it is necessary to illuminate the recorded object with diffuse light. Results from computer simulation and laboratory experiments reveal that 16 different objects can be holographically recorded in one composite filter and then used for simultaneous correlation giving sharp correlation peak with good peak to background ratio. Alternatively, the range of rotation invariant correlation can be increased from a few degrees for a single filter to 160 deg for a composite filter of 16 objects.
A method for designing and recording Fourier transform holographic lenses, in the presence of a recording-readout wavelength shift, using a substrate-mode holographic doublet, is presented. The system is composed of two holographic optical elements (HOEs) which were recorded on the same plate. The first one couples the various spatial frequencies of the input into plane waves which are trapped inside the plate by total internal reflection. The second HOE focuses the collimated waves into the Fourier plane. Since the chromatic dispersion of the first hologram can be corrected by the dispersion of the second hologram, this system is much less sensitive to source wavelength shifts. The method is illustrated with a compact system, recorded at 458 nm and reconstructed at 633 nm. Near diffraction limited performance and a comparatively low chromatic sensitivity over a wide field of view has been obtained.
Real-time recording of mid-infrared laser radiation in photochromic spiropyran-MMA copolymer materials is investigated. The laser radiation, derived from a CO2 laser, bleached pre-colored merocyanine, thereby converting it back to spiropyran. The exposure sensitivity at 50 percent of the initial merocyanine optical density was about 0.1 J/mm2 at 10.6 micrometers laser wavelength and 0.2 J/mm2 at 10.5 micrometers . The difference of sensitivity at the two laser wavelengths points to differences in thermal energy dissipation mechanisms. The characteristics and examples of imagery, recorded in these photochromics, are presented. A resolution equal or better than 40 lines/mm was achieved.
Surface photodeposition is a photon assisted process, by which thin films can be formed on substrates immersed in colloidal solutions. Holographic gratings of various spatial frequencies have been recorded by photodeposition of amorphous selenium colloids. The holographic surface relief grating formation is described in relation to the modulation transfer function of colloidal photodeposition. Spatial frequencies of about 1500 lines/mm can be recorded with amorphous selenium, whose colloidal particle sizes range from 30 to 80 nm.
A quadratic-phase holographic lens can give a Fourier transform that is multiplied by an undesired parasitic phase, caused by the off-axis configuration. We show that it is possible to significantly reduce the parasitic phase by controlling the recording and readout geometries of the holographic lens so as to allow complete Fourier transformation. As a practical example we incorporate such a holographic lens into a conventional coherent light correlator, and show how to optimize the correlation peaks even when the illumination wavelength of the correlator differs from that used when recording the holographic lens and the filter.
A novel single multifunctional holographic optical element is incorporated into a surface measurement system. As a result the system is lightweight, compact, and simpler than conventional ones. Numerical calculation reveals that submicron resolutions are possible both in the horizontal and vertical directions. Finally, experimental results demonstrate the feasibility of the approach.
Photodeposition is an emerging new thin-film material deposition and optical image patterning technique with photographic recording characteristics. In the past, lasers and incoherent light sources were exploited for photodeposition of various materials in micropatterns. Here we report that photodeposition can also be used for recording holographic relief gratings of 2000 lines/mm and periodically modulated depths of 1 to 20 nm.
An algorithm based on circular harmonic expansion has been incorporated into a pattern recognition system
using spatially incoherent light. In this algorithm the model used for recording the necessary recognition filter is
derived from the absolute value of one of the circular harmonic components of the desired pattern so that both
rotation and shift invariances are obtained. Computer simulations reveal that the algorithm can indeed provide
adequate peak to background ratios regardless of the input rotation and lateral shift. The details of the algorithm
along with results of computer simulations are presented.
We present design methods for high efficiency computer generated diffractive optical elements that produce
multiple beams. Both binary and continous phase (kinoform) approaches are considered. Experimental results for
a specific binary grating for far-IR applications are shown.
We present a novel non-contact holographic optical profilometer, which is light weight, compact and relatively
simpler. Computer simulation results reveal that surface measurements with sub-micron resolution are possible both
in the horizontal and vertical directions.
We present a novel aspheric holographic optical element (hOE), having an extended depth of focus while
keeping high lateral resolution. The phase function of the HOE is derived, and computer simulations verify the
theoretical prediction for the optical performances.
A quadratic phase holographic lens can perform Fourier transformation on a two-dimensional input, but the
transform is multiplied by a detrimental parasitic phase that is caused by the off-axis configuration. Fortunately,
with the proper geometry, and for a limited spatial frequency, this parasitic phase can be considered as a constant,
so it need not affect the Fourier transformation. We show how to set the frequency dependence ofthe parasitic phase
in order to handle inputs with different spectrum characteristics, and how to choose the geometrical parameters of
the system in an optimal way.
A technique for obtaining a sharp output-to--input response from optically addressed spatial light modulators is
presented. In this technique, a portion of the output light is fed back into the input. By controlling the portion of
light that is fed back it is possible to change the slope and the shape of the response curve of the modulator so as
to improve the sensitivity to external inputs. Experimental results demonstrating sharp thresholding by exploiting
both positive and negative feedbacks with a liquid crystal light valve SLM are illustrated.
Recent advances in the design and recording of holographic optical elements are illustrated by means of two representative examples - focussing lens and multiple beam grating. The focussing lens design method is based on an analytic ray-tracing procedure that yields an analytic solution for the diffractive grating function. It will be elucidated by describing the recording and testing ofaspheric low 1 number focussing elements for 10. 6 microns wavelength having diffraction - limited performance over a broad range of incidence angles. The design of the multiple beam grating is based on solving a set of nonlinear equations to obtain a grating structure that can convert one incident beam into a set of specified output beams. Both the lens and the multiple grating elements are recorded with binary optics that involve computer generated plots with high resolution laser printer and plotolithographic techniques. Reflective and trismissive elements are formed by either etching reflective metal layers or GaAs substrates. 1.
Of the various holographic measuring methods, holographic interferometry has found the broadest application in
biological and medical research. It allows for non-destructive evaluation and for high resolution deformation analysis.
By combining holographic interferometry with endoscopic imaging it is possible to obtain holographic imaging inside
natural cavities of the body , thus making possible intracavitary measurements of size, shape or deformation of the
objects under study. Some applications of holographic interferometry with endoscopic imaging are reviewed in this
The Inverted Neural Network (INN) model especially designed for optical implementation is presented. This model takes into account the physical constraints imposed by conventional optical components and ensures that all the connections are positive. Thus subtraction of light intensities is not required for implementation nor are electronic computations. In the laboratory realization of the INN model a liquid crystal light valve fulfills the function of an array of neurons while an array of subholograxns serves as the interconnects. The overall network was tested with 64 neurons and four stable states. 1. INTRODTJCTION Several problems have to be solved in order to realize neural network models optically. The first problem stems from the fact that most models consist of both positive and negative interconnects. Conventional solutions to this problem usually involve electronic subtractions or dynamic threshold levels. It has been recently shown1''2 how the Hopfleld model can be modified into a model with positive values only. An all-optical realization of the modified model for 16 neurons and two stable states has also been demonstrated1 . The second problem that has to be considered is the fact that most of the optical devices that are used for realizing the neurons cannot exhibit very sharp thresholding. Although neurons with graded response have collective computational properties like those of two state neurons the memory capacity of Hopfield-type networks decreases as the slope of the neural
Noveldesigns for forming space variant holographic ifiters that perform general types ofcoordinate transformations on two dimensional pictures are presented. The designs are without any paraxial approximations and include planar and curved filter configurations. The experimental results indicate that high quality transformations can be obtained. 1.
An optical correlator using incoherent light was exploited with a composite filter comprised of a multiplicity of sub-filters to simultaneously detect the presence of a number of objects or alternatively allow rotation and scale changes of one object. We determined that for high SNR it is necessary to record the sub-filters with diffused light. Moreover for a certain geometry of the correlator the sub-ifiters diameter can be as low as 4 mm without significantly affecting the correlation performance. 1.