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A self-homodyne laser communication system based on orthogonally polarized binary phase shift keying is demonstrated. The working principles of this method and the structure of a transceiver are described using theoretical calculations. Moreover, the signal-to-noise ratio, sensitivity, and bit error rate are analyzed for the amplifier-noise-limited case. The reported experiment validates the feasibility of the proposed method and demonstrates its advantageous sensitivity as a self-homodyne communication system.

A pair of orthogonal tilting prisms has been explored in our previous work to perform the orientation and position tracking function with tracking accuracy better than submicroradian order. Crucial to the function implementation, however, is the real-time nonlinear control of the tilting angles of double prisms for tracking a given target trajectory. In previous papers [Proc. SPIE5892, 1-5 (2005).PSISDG0277-786X; Appl. Opt.45, 8063 (2006).PSISDG0277-786X; Proc. SPIE6709, 41 (2007).PSISDG0277-786X; Appl. Opt.51, 356 (2011).10.1364/AO.51.000356APOPAI1559-128X; Appl. Opt.53, 3712 (2014).10.1364/AO.53.003712APOPAI1559-128X], a new driving method by a cam-based mechanism, which can transfer the control problem to the design of corresponding cam configuration, is investigated. The design process of a cam-based mechanism is explained from the mapping relation between the tilting angles of a prism and the configuration curve of a corresponding cam. Based on the designed cam-based mechanism, a tracking error less than 0.375% is depicted between the tracking trajectory and the original one. Moreover, the dynamic characteristic of the tracking mechanism is discussed in detail as well as the impacts of different tilting speeds on the tracking trajectory. The proposed tracking mechanism of a tilting double-prism scanner can create a new avenue for passively tracking a given target.

A principle scheme of a lensless optical processor for synthetic-aperture imaging ladar (SAIL) is proposed. The collected data from SAIL is initially digitally added with a quadratic phase in the range direction. These data are then uploaded on a liquid crystal spatial light modulator to modulate the incident light. The target image is obtained through two-dimensional (2D) free-space Fresnel diffraction. The imaging process is mathematically analyzed using a 2D data-collection equation of strip-mode side-looking SAIL. The design equation, imaging resolutions, and target-image compression ratios are presented. Based on this principle scheme, we construct an experimental optical SAIL processor and present the imaging result of data obtained from one SAIL demonstrator. The optical processor is found to exhibit the flexible property of digital processing, as well as the fast processing capability of optical means, because this optical processor is a lensless system.

A two-dimensional (2D) Fourier transform algorithm for the image reconstruction of synthetic-aperture imaging ladar (SAIL) collected data is suggested. This algorithm consists of quadratic phase compensation in azimuth direction and 2D fast Fourier transform. Based on this algorithm and the parallel 2D Fourier transform capability of spherical lens, an optical principle scheme that processes the SAIL data is proposed. The basic principle, design equations, and necessary analysis are presented. To verify this principle scheme, an experimental optical SAIL processor setup is constructed. The imaging results of SAIL data obtained by our SAIL demonstrator are presented. The optical processor is compact, lightweight, and consumes low power. This optical processor can also provide inherent parallel and speed-of-light computing capability, and thus has potential applications in on-board and satellite-borne SAIL systems.

Recent developments in optical communication systems have presented an emerging need for scanning and tracking dynamic targets with high accuracy. Unfortunately, conventional scanners have difficulty supplying either sufficient vision information or high scanning resolution because of the fixed optical parameters and optomechanical structure. This paper introduces a novel cascaded double-prism scanner that combines the two scanning modes of rotating and titling motions into a nested device. The analysis results show that both the vertical field angle range and the horizontal field range of the coarse scanning are no less than ±10°, with the scanning accuracy superior to 50 μrad, while the vertical field angle range and the horizontal field range of the fine scanning are, respectively, no less than 2500 μrad and 1200 μrad, with the scanning accuracy superior to 1 μrad. The scanning method not only meets the requirements of collaboratively steering the beam deviation in a large range with high accuracy but also can obtain a variety of scanning modes and trajectories, which has important engineering significance for the solution of steering a fine beam to track and position a dynamical target.

Optimal recording wavelength for maximum diffraction efficiency of thermal fixing in LiNbO(3):Fe crystal is investigated. Holographic gratings are recorded using three typical recording wavelengths including 488, 514, and 633 nm. Optimal switching from recording to thermal fixing is taken into consideration. The fixed holograms are developed by an original recording setup. Diffraction efficiencies of recording and thermal fixing are measured by a two-wave coupling technique. The theoretical and experimental results are analyzed and compared. With a blue beam, the nonvolatile hologram with maximum fixing efficiency is achieved. This work can obtain high persistent diffraction of the nonvolatile holographic storage in LiNbO(3):Fe crystals.

The three-dimensional coupled wave theory is extended to systematically investigate the diffraction properties of finite-sized anisotropic volume holographic gratings (VHGs) under ultrashort pulsed beam (UPB) readout. The effects of the grating geometrical size and the polarizations of the recording and readout beams on the diffraction properties are presented, in particular under the influence of grating material dispersion. The wavelength selectivity of the finite-sized VHG is analyzed. The wavelength selectivity determines the intensity distributions of the transmitted and diffracted pulsed beams along the output face of the VHG. The distortion and widening of the diffracted pulsed beams are different for different points on the output face, as is numerically shown for a VHG recorded in a LiNbO3 crystal. The beam quality is analyzed, and the variations of the total diffraction efficiency are shown in relation to the geometrical size of the grating and the temporal width of the readout UPB. In addition, the diffraction properties of the finite-sized and one-dimensional VHG for pulsed and continuous-wave readout are compared. The study shows the potential application of VHGs in controlling spatial and temporal features of UPBs simultaneously.

Ce3+ and B2O3 are introduced into erbium-doped Bi2O3-SiO2 glass to enhance the luminescence emission and optic spectra characters of Er3+. The energy transfer from Er3+ to Ce3+ will obviously be improved with the phonon energy increasing by the addition of B2O3. Here, the nonradiative rate, the lifetime of the 4I11/2→4I13/2 transition, and the emission intensity and bandwidth of the 1.5 μm luminescence with the 4I13/2→4I15/2 transition of Er3+ are discussed in detail. The results show that the optical parameters of Er3+ in this bismuth-borate-silicate glass are nearly as good as that in tellurite glass, and the physical properties are similar to those in silicate glass. With the Judd-Ofelt and nonradiative theory analyses, the multiphonon decay and phonon-assisted energy-transfer (PAT) rates are calculated for the Er3+/Ce3+ codoped glasses. For the PAT process, an optimum value of the glass phonon energy is obtained after B2O3 is introduced into the Er3+/Ce3+ codoped bismuth-silicate glasses, and it much improves the energy-transfer rate between Er3+4I11/2→4I13/2 and Ce3+2F5/2→2F7/2, although there is an energy mismatch.

Vectorial Kukhtarev equations modified for nonvolatile holographic recording in doubly doped crystals are analyzed, in which the bulk photovoltaic effect and external electrical field are both considered. On the basis of the small modulation approximation, both the analytic solution to space-charge field with time in recording phase and the steady-state solution in readout phase are deduced. Because bulk photovoltaic current is determined by polarized state of incident light, and refractive index change depends on not only the modulus of space-charge field but also its direction, the optimum design parameters for maximizing space-charge field are different from those for maximizing refractive index change. Therefore a trade-off exists between them. Based on the vectorial analyses of band transport model for nonvolatile holographic recording in doubly doped crystals, an optimal recording direction is given for maximizing refractive index change in doubly doped LiNbO3 :Fe:Mn crystals.

The influence of the recording conditions, including the widths of the recording beams, the width ratio of the recording beams, and the recording angles, on the properties of crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals is studied. A theoretical model that combines the band transport model with two-dimensional coupled-wave theory is proposed. The numerical calculations of the space-charge field, the intensity profiles of the diffracted beam, and the diffraction efficiency are presented.

The absorption characteristic of lithium niobate crystals doped with chromium and copper (Cr and Cu) is investigated. We find that there are two apparent absorption bands for LiNbO3:Cr:Cu crystal doped with 0.14 wt.% Cr2O3 and 0.011 wt.% CuO; one is around 480 nm, and the other is around 660 nm. With a decrease in the doping composition of Cr and an increase in the doping composition of Cu, no apparent absorption band in the shorter wavelength range exists. The higher the doping level of Cr, the larger the absorbance around 660 nm. Although a 633 nm red light is located in the absorption band around 660 nm, the absorption at 633 nm does not help the photorefractive process; i.e., unlike other doubly doped crystals, for example, LiNbO3:Fe:Mn crystal, a nonvolatile holographic recording can be realized by a 633 nm red light as the recording light and a 390 nm UV light as the sensitizing light. For LiNbO3:Cr:Cu crystals, by changing the recording light from a 633 nm red light to a 514 nm green light, sensitizing with a 390 nm UV light and a 488 nm blue light, respectively, a nonvolatile holographic recording can be realized. Doping the appropriate Cr (for example, N-Cr = 2.795 X 10(25)m(-3) and N-Cr/N-Cu = 1) benefits the improvement of holographic recording properties. (c) 2005 Optical Society of America.

We report the formulation of an ABCD matrix for reflection and refraction of Gaussian light beams at the surface of a parabola of revolution that separate media of different refractive indices based on optical phase matching. The equations for the spot sizes and wave-front radii of the beams are also obtained by using the ABCD matrix. With these matrices, we can more conveniently design and evaluate some special optical systems, including these kinds of elements. (c) 2005 Optical Society of America

We analyze mutual alignment errors due to wave-front aberrations. To solve the central obscured problem, we introduce modified Zernike polynomials, which are a set of complete orthogonal polynomials. It is found that different aberrations have different effects on mutual alignment errors. Some aberrations influence only the line of sight, while some aberrations influence both the line of sight and the intensity distributions.

Electrochromic phenomena accompanying the ferroelectric domain inversion in congruent RuO2-doped z-cut LiNbO3 crystals at room temperature are observed in experiments. During the electric poling process, the electrochromism accompanies the ferroelectric domain inversion simultaneously in the same poled area. The electrochromism is completely reversible when the domain is inverted from the reverse direction. The influences of electric field and annealing conditions on domain inversion and electrochromism are also discussed. We propose the reasonable assumption that charge redistribution within the crystal structure caused by domain inversion is the source for electrochemically oxidation and reduction of Ru ion to produce the electrochromic effect.

The superresolution technique is well known for its ability to compress the central diffraction spot to a size that is smaller than the Airy diffraction spot. The radial birefringent filter, which consists of two parallel polarizers and a rotationally symmetric birefringent element, is introduced into the superresolution technology, and the pupil function of it is deduced. It is shown that such a filter can be adapted either for transverse superresolution or for axial superresolution simply by changing the angle between either of the two polarizers and the radial birefringent element. At the same time the superresolution parameters are discussed. The filter is relatively simple in construction as it requires no phase changes, and low-cost replication is possible.

A Jamin double-shearing interferometer with three changeable schemes is proposed for the measurement of diffraction-limited laser wave front. A concept of detectable wave-front height is thus defined, and on this basis the limits of detectable wave-front height from the suggested schemes of interferometer are analyzed. The design is detailed, the simulation for wave aberrations is given, and the experiment is demonstrated. One of the major features of this interferometer is that it is capable of visually testing a diffraction-limited wave front immediately by the fringes with the matched accuracy and minimum detectable wave-front height on the order of 0.1lambda.

A circular Dammann grating that can produce circular equal intensities at various orders in the far field is described. A set of parameters such as order, circular number, uniformity, and diffraction efficiency has been defined to describe the novel diffractive phase elements. Numerical solutions of binary-phase (0, pi) circular Dammann gratings are given. The results of experiments with a four-order circular Dammann grating made by a lithographic technique are presented. This novel diffractive optical element should be highly interesting in a wide variety of practical applications.

A theoretical explanation of nonvolatile holographic recording in LiNbO3:Fe:Mn crystals is given based on jointly solving the two-center material equations and the coupled-wave equations. The nonuniformity of the dynamics of the photorefractive grating can be effectively described and analyzed by using this method. The time–space evolution, including the space-charge field, the diffraction efficiency, the light modulation depth, the phases of the space-charge field and the interference field, as well as the relative spatial phase shift between them, is studied for both oxidized and reduced crystals. The optimal conditions for material prescriptions and oxidation–reduction processing are discussed in detail. The bending isophase of the fringe pattern and the redistributed intensities of the two-coupled beams inside the crystal are presented. The theoretical results can confirm and predict experimental results. Some new effects are also discovered, such as: The fixed diffraction efficiency can exceed the saturation diffraction efficiency for strongly recorded gratings; the energy transfer direction between two-coupled beams can be reversed with crystal thickness; and the holographic readout in reduced crystal is always accompanied by fast phase changes, which results in the slow deterioration of the recorded holograms as a result of the production of homogeneous distributions of electrons.

A uniform formulation for the self-imaging of gratings with any kind of partially coherent illumination is developed in terms of the cross mutual spectral density of the partial coherence theory. The formulation includes the time diffractive intensity distribution and the averaged diffractive intensity distribution at self-imaging distances and can be applied to both continuous and temporal illuminations with any kind of spectra. It is found that the averaged intensity distribution is related only to the intensity spectrum of illumination. The continuous polychromatic illumination and the ultrashort laser pulses with or without frequency chirp are then studied by a numerical stimulation. It is shown that the ultrashort laser pulse and the continuous polychromatic illuminations have similar averaged self-image distributions. Thus the Talbot effect may help in the study of the temporal and spectral characteristics of ultrashort laser pulses. An experiment with an LED is given, as well.

Previous pulse-width measurement methods for ultrashort laser pulses have broadly employed nonlinear effects; thus any of these previous methods may experience problems relating to nonlinear effects. Here we present a new pulse-width measuring method based on the linear selfdiffraction effect. Because the Talbot effect of a grating with ultrashort laser pulse illumination is different from that with continuous laser illumination, we are able to use this difference to obtain information about the pulse width. Three new techniques - the intensity integral technique, the intensity comparing ratio technique, and the two-dimensional structure technique - are introduced to make this method applicable. The method benefits from the simple structure of the Talbot effect and offers the possibility to extend the measurement of infrared and x-ray waves, for which currently used nonlinear methods do not work.

We have studied theoretically the inherent mechanisms of nonvolatile holographic storage in doubly doped LiNbO3 crystals. The photochromic effect of doubly doped LiNbO3 crystals is discussed, and the criterion for this effect is obtained through the photochromism-bleach factor a = S(21)gamma(1)/S(11)gamma(2) that we define. The two-center recording and fixing processes are analytically discussed with extended Kukhtarev equations, and analytical expressions for recorded and fixed steady-state space-charge fields as well as temporal behavior during the fixing process are obtained. The effects of microphysical quantities, the macrophotochromic effect on fixing efficiency, and recorded and fixed steady-state space-charge fields, are discussed analytically and numerically. (C) 2002 Optical Society of America.

A hexagonal array not only is a nature-preferred pattern but also is widely used in optoelectronical materials and devices. We report a simple method of hexagonal array illumination based on the Talbot effect that has a theoretical efficiency of 100%. An experimental efficiency of 90.6% with a binary phase (0, pi) hexagonal grating is given. This method should be highly interesting for applications of hexagonal array illumination in optical devices as well as in other hexagonal cells.

A hologram generally is formed in a photorefractive crystal by the interaction of the grating formulation that is due to the space-charge field that grows from the beam interference pattern and of the beam energy exchange that results from two-beam coupling in the grating. Analytic expressions for the grating recording formed by this interaction can be obtained only by simultaneous solution of the material equations and the coupled-wave equations. Using Moharam’s space-charge field function, we deduce both the exact steady-state analytic solution for two-beam coupling under any boundary-light modulation and constant-light excitation and the approximate analytic solutions with distance-dependent light excitation. Based on Kukhtarev’s idea of three-step calculation, the formulation of a hologram under any light modulation and excitation is further solved analytically. These steady-state analytic solutions understanding are useful in arriving at a clearer and more exact understanding of photorefractive two-beam coupling and holographic recording.

A previously suggested birefringence-customized modular optical interconnect technique is extended for lens-free relay operation. Various lens-free relay imaging models are developed. We claim that the lens-free relay system is important in simplifying an optical interconnect system whenever the imaging conditions permit. To verify the validity of various proposed concepts, we experimentally implemented some 8 x 8 optical permutation modules. High-power efficiency and low channel cross talk were experimentally observed. In general, the larger the channel spacing, the less the cross talk. A quantitative cross-talk measurement of the lens-free relay system shows that, for a fixed channel width of 0.5 mm and channel spacings of 0.5, 1, and 2 mm, a less than -20-dB cross-talk performance can be guaranteed for lens-free relay distances of 40, 280, and 430 mm, respectively.

We present a theoretical model in which the band-transport equations and the coupled-wave equations are considered to study the two thermal-fixing methods (simultaneous fixing and postfixing) in Fe:LiNbO(3). We found that, in simultaneous fixing, the existing ionic-grating affects the writing of the electronic grating by reduction of the coupling gain, and the grating envelope of the fixed-index grating is quite uniform inside the photorefractive crystal in comparison with the method of postfixing. The resulting diffraction efficiency of the fixed-volume grating is dependent mainly on the initial intensity modulation of the two writing beams. A set of experiments is also presented.

A grating-lens combination unit is developed to form a scaling self-transform function that can self-image on scale. Then an array of many such grating-lens units is used for the optical interconnection of a two-dimensional neural network, and experiments are carried out. We find that our idea is feasible, the optical interconnection system is simple, and optical adjustment is easy.

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous FRT’s and complex FRT’s are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy.

A stacked integration technique based on polarization optics is studied for implementing shuffle-based interconnection networks with three-dimensional solid-state modules. A basic building block of the proposed scheme consists of a hole-patterned half-wave retarder for birefringence customizations and a calcite slab for subsequent beam deflections. On the basis of a cascade of such building blocks the submodules of various shuffle-family permutations can be implemented. To minimize channel cross talk, we incorporated a collimating-relaying imaging system. To help design birefringence customization, we developed algebraic formulations of folded shuffle operations using separable shuffles. Proof-of-concept experimental results, as well as system design, fabrication, and integration issues, are discussed.

The mixing of two sets of mutually coherent beams, termed double two-beam mixing, is considered. At low modulation depth, combination gratings of the primaries are analyzed theoretically and show that the internal electric fields in photorefractive media also have cross components with wave vectors K1 ± K2 in addition to the primary components K1 and K2 and higher orders of 2K1 and 2K2, where K1 and K2 are wave vectors of two fringes. Each component is given in the form of an analytical solution, and the coupling behavior is studied for all relations between K1 and K2. The results show that the coupling behavior depends not only on the primary gratings but also on the combination grating K1 and K2 and the high-order grating 2K1 or 2K2. These features can be employed theoretically in phase-intensity transform and wavelength conversion.

A scheme for the readout of a hologram recorded in bacteriorhodopsin film with high diffraction efficiency and intensity is suggested and demonstrated. Two weak coherent continuous beams function as the recording beams, and a strong light pulse is used to read the real-time hologram. The width of the readout light pulse is modulated to be short compared with the erase time of the reading beam; the time space between two adjacent pulses is ensured to be longer than the time the beams take to recover the hologram, and high diffraction efficiency and intensity (~11 mW/cm(2)) can be obtained.

Intrinsically fuzzy morphological erosion and dilation are extended to a total of eight operations that have been formulated in terms of a single morphological operation--biased dilation. Based on the spatial coding of a fuzzy variable, a bidirectional projection concept is proposed. Thus, fuzzy logic operations, arithmetic operations, gray-scale dilation, and erosion for the extended intrinsically fuzzy morphological operations can be included in a unified algorithm with only biased dilation and fuzzy logic operations. To execute this image algebra approach we present a cellular two-layer processing architecture that consists of a biased dilation processor and a fuzzy logic processor. (C) 1996 Optical Society of America

Fuzzy sets in the subject space are transformed to fuzzy solid sets in an increased object space on the basis of the development of the local umbra concept. Further, a counting transform is defined for reconstructing the fuzzy sets from the fuzzy solid sets, and the dilation and erosion operators in mathematical morphology are redefined in the fuzzy solid-set space. The algebraic structures of fuzzy solid sets can lead not only to fuzzy logic but also to arithmetic operations. Thus a fuzzy solid-set image algebra of two image transforms and five set operators is defined that can formulate binary and gray-scale morphological image-processing functions consisting of dilation, erosion, intersection, union, complement, addition, subtraction, and reflection in a unified form. A cellular set-logic array architecture is suggested for executing this image algebra. The optical implementation of the architecture, based on area coding of gray-scale values, is demonstrated.

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Because of the advances made in optical technology, an extension can be made from the well-known stack filter to a new kind of gray-scale filter by using arbitrary Boolean functions instead of positive Boolean functions in the second step of a three-step process. Applications of these threshold-decomposed Boolean-based gray-scale filters in image processing include image smoothing and feature detection. A general optical implementation approach of nonlinear threshold-decomposed Boolean-based gray-scale filters is also described that utilizes area coding, gray scale correlation and lookup table thresholding techniques. Some experimental results are demonstrated.

A parallel architecture for gray-tone image processing is proposed that utilizes the concept of threshold sum-superposition into a cellular two-layer logic binary-image processor. Various processing functions constituted by gray-tone dilation, erosion, fuzzy-logic operations, and arithmetic operations are obtained. The optoelectronic implementation is illustrated.

A parallel binary image algebra with a logic operation followed by a dilation is developed in this paper. A cellular two-layer logic image processor architecture is proposed to execute such a one-operation image algebra, which consists of a parallel logic layer followed by a morphological layer. All the possible image processing functions can be written by the algebra. We construct an optoelectronic array based on optical logic operation using spatial coding techniques, optical neighborhood interconnection in a defocused system, and electronic thresholding and feedback. Any image transformation can be performed through iterative programming of the logic operations. Experimental results are also given.

An optical crossbar element that uses birefringent crystal plates and programmable half-wave plates is proposed. It is compact, cascadable, and well suited for realizing an array of switching elements employed in multistage interconnection networks. Arrays of two-input/two-output and four-input/fourputput crossbar switching elements and a Clos (4, 4, 4) network are also presented.

A modified gamma network that is based on the bar-plus-2(i) and modulo-N connection patterns is proposed. The gamma network, one class of important O (N log(2)N) interconnection networks, needs arrays of 1 × 3 or 3 × 3 switches, which makes it difficult to realize in optics. We modify the gamma network to meet the characteristics of optics by employing a bar-plus-2(i) connection pattern and a modulo N output stage. Two-by-two switches and regular interconnections are used in the network, so the network is suitable for optics. The optical implementation of the network with a birefringent crystal and an array of programmable half-wave plates is suggested, and a proof-of-principle experiment is presented. The network is a rearrangeable nonblocking network, and the nonblocking routing algorithm for an N × N network is given; (2 log(2)N - 2) switching stages [with a total of (2 log(2)N + 1/2)N - 4 log(2)N - 1 switches] can permute N input nodes to N output nodes in any order in a one-to-one manner. The network is applicable to packet synchronous optical traffic.

One-dimensional perfect-shuffle networks are extended to two-dimensional perfect-shuffle networks, and this extension is analyzed by means of the finite-state model. The routing algorithm presented is based on quaternary numbers for 4 × 4 switches, and its extension to k × k switches is briefly discussed. In order to take full advantage of the three-dimensional interconnection capability and two-dimensional space-bandwidth product of free-space optics, we map one-dimensional perfect-shuffle networks into two-dimensional perfect-shuffle networks, with both having 4 × 4 switching elements. Finally we compare the permutation capability of two-dimensional perfect-shuffle networks with one-dimensional perfect-shuffle networks.

The optical logic-operated moiré is a new method to extract a specific moiré pattern. It has the capabilities of eliminating original carrier frequencies, increasing the contrast, and narrowing the fringes. We introduce its applications in moiré topography and deflectometry and also present the experimental results.

Based on the cross-spectral density function in coherence theory, we describe the Lau effect of a skew-periodic object. First we derive the intensity of the Lau image of a general plane object, then we derive the intensity of the Lau image of a skew-periodic object and the Lau imaging conditions, and finally we explain the Lau effect of a skew-periodic object and the experimental results.

A birefringence phenomenon is used to construct Boolean logic gates that output three logic functions. Logic gate modules are proposed that consist of Bi12SiO20 opto-optical birefringence switches, LiNbO3 electro-optical half-wave plates, and calcite plates. The gate can be driven by optical inputs and can also be electrically programmed for different logic operations. An array-packed solid-state module is described.

A cyclic matrix representation for complex numbers is proposed for sequential multiplication of complex matrices. The related optical implementation is discussed.

An optical parallel architecture is suggested to implement a basic programmable cellular logic array for image processing. Interconnection of the neighboring cells is achieved by using an optical correlator. The required parallel logic gates are executed with spatial coding and electronic thresholding methods. Another optical correlator is used to spatially code the outputs from the 2-bit decoder array of shadowgrams. The optical method for the directional interconnection is also discussed. An image processing example is simulated and verified experimentally.

A joint Talbot effect with two separated and crossed gratings of substructures is proposed. The mutual coupling in the joint self-imaging leads to a mechanism for the formation of the new moire patterns. The conditions are studied for generating the logic-operated moire fringes. Both theoretical analyses and experiments are given.

The authors have demonstrated the principle of a novel optical multichannel-scale range-tunable Fourier-transforming system. The experimental results show good agreement with the theoretical analysis.

Both the Talbot and the Lau effects of Ronchi and binary phase gratings on an incident wavefront of arbitrary wavefront are discussed. General and analytic solutions are obtained in terms of the Fresnel diffraction theory. Numerical simulations and supporting verification for Gaussian beams are demonstrated. It is found that the distortion of the self-image is closely linked to that of the far field distribution in a two-grating system, and both depend on the Talbot distance and the beam wavefront. Some interesting phenomena are explored such as light modulation and phase compensation. Possible applications are accordingly suggested.

Based on optical correlation in a defocused system with two masks, strong phase variations can be contour mapped. Typical systems are analyzed mathematically by virtue of the backward impulse response suggested here. Three general parameters are defined to characterize performances. The condition of invariant correlation is discussed, and the process of contour mapping is investigated in detail. It is found that the configurations are the same as for quasi-interferometers with coded correlation filtering but treated from different viewpoints. Combining the analyses in the space domain with the explanations in the spatial frequency domain, a simple way is provided to synthesize any new type of quasi-interferometer. In addition, the necessary requirements for construction are introduced, and further examples are given.

An optoelectronic implementation based on optical neighborhood operations and electronic nonlinear feedback is proposed to perform morphological image processing such as erosion, dilation, opening, closing, and edge detection. Results of a numerical simulation are given and experimentally verified.

We study the diffraction effect of gratings under partially coherent illumination generated by a source slit. Various fringe distributions from Lau fringes to the Talbot self-image can be observed by continuous adjustment of the slit width. An expression for describing the effect is derived in terms of an ambiguity function, which is a joint correlation among the functions of the source slit and the two gratings. It is concluded that the profile of the fringe pattern changes not only as the degree of spatial coherence is varied but also as one of the gratings is shifted in a lateral direction. The experimental results are in good agreement with the theoretical intensity distributions.