Optimal synthesis of three-dimensional complex amplitude distributions.

The synthesis of three-dimensional (3-D) light distributions is important for many applications. For example, in scanning applications it is preferable that the scanning beam preserve its characteristics over a large distance to yield elongated scanning range. It is evident that any 3-D light distribution must satisfy the wave equation or, in second-order approximation, the Fresnel diffraction formula. Thus many desirable 3-D light distributions may not be realizable. We propose a single optical element (OE) that synthesizes a physical beam within a certain 3-D region. The OE provides the optimal physical beam in comparison with a desired one in the sense of minimal mean-square error.

Joint transform correlator for optical temporal signals.

Correlation is considered to be a fundamental operation in the field of signal processing. The fact that this operation can be implemented optically in a relatively simple manner is an important advantage of utilizing optical systems for signal processing. The VanderLugt 4-f system and the joint transform correlator (JTC) are the two most popular configurations for performing a spatial correlation operation optically. So far the JTC architecture has been used for performing correlation between two images, which are illuminated by a quasi-monochromatic light source. We propose a generalization of the JTC that performs a correlation between two temporal optical signals.

Synthesis of spatial coherence.

The mutual intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We propose to use the mutual intensity as a carrier of information to avoid speckle noise in coherent illumination systems and to permit the use of complex functions that are prohibited spatially incoherent sources. To do this we require methods for encoding the information as a coherence function. An optical system for synthesizing a beam with a given mutual intensity function is proposed. The optical system permits the synthesis of any desired mutual intensity function. The illumination is supplied by a quasi-monochromatic, spatially incoherent source. Experimental results demonstrate the performance of this system for several cases.

Modified morphological correlation based on bit-map representations.

Pattern recognition with high discrimination can be achieved with a morphological correlator. A modification of this correlator is carried out by use of a binary slicing process instead of linear thresholding. Although the obtained correlation result is not identical to the conventional morphological correlation, it requires fewer calculations and provides even higher discrimination. Two optical experimental implementations of this modified morphological correlator as well as some experimental results are shown.

Synthesis of hybrid spatial coherence.

Spatial coherence plays a major role in characterizing quasi-monochromatic, partially coherent, optical signals. Here a fairly simple system for synthesizing special cases of spatial coherence is proposed. The special cases, called hybrid, include the case of total coherence in the x direction and, simultaneously, total incoherence in the y direction. The optical setup is based on a quasi-monochromatic, spatially coherent light source, such as a laser, and a simple moving optical element.

Iterative algorithm for determining optimal beam profiles in a three-dimensional space.

A new, to our knowledge, iterative algorithm for achieving optimization of beam profiles in a three-dimensional volume is presented. The algorithm is based on examining the region of interest at discrete plane locations perpendicular to the propagation direction. At each such plane an intensity constraint is imposed within a well-defined transverse spatial region of interest, whereas the phase inside that region as well as the complex amplitude outside the region is left unchanged from the previous iteration. Once the optimal solution is found, the mask that generates the desired distribution can be readily implemented with a planar diffractive optical element such as a computer-generated hologram. Several computer simulations verified the utility of the proposed approach.

Display of spatial coherence.

The mutual-intensity function plays a major role in characterizing quasi-monochromatic, partially coherent optical signals. We demonstrate an optical system for displaying the mutual intensity of a one-dimensional input beam. The experimental system is based on the fact that the mutual intensity of a signal can be expressed as the ensemble averaging of a cross-correlation operation between two related optical signals. The setup consists of a Sagnac interferometer followed by an optoelectronic joint transform correlator. Experimental results demonstrate the capabilities of the mutual-intensity analyzer.

Proposal for optical implementation of the wigner distribution function.

The Wigner distribution function (WDF) offers comprehensive insight into a signal, for it employs both space (or time) and frequency simultaneously. Whenever optical signals are involved, the importance of the WDF is significantly higher because of the diffraction (or dispersion) behavior of optical signals. Novel optical implementations of the WDF and of the inverse Wigner transform are proposed. Both implementations are based on bulk optics elements incorporating joint transform correlator architecture. A similar implementation is derived for the ambiguity function, which is related to the WDF through Fourier transformation.

Optical implementation of the continuous wavelet transform.

A simple optical implementation for the one-dimensional wavelet transform (WT) is proposed. In contrast with previous WT optical implementations, the obtained WT is continuous along both axes (dilation and shift). An optical implementation to the inverse WT is proposed as well. Thus an optical continuous WT processor can be implemented.

Optoelectronic implementation of the triple correlation.

The auto triple correlation has several fundamental advantages over the ordinary autocorrelation of second order. We present an optoelectronic processor for the computation of the auto triple correlation.

Optical transfer function design by use of a phase-only coherent transfer function.

The design of a desired optical transfer function (OTF) is a common optical problem that has many possible applications. A well-known application for the OTF design is beam shaping for incoherent illumination. However, other applications, such as optical signal processing, can also be addressed with these systems. We derive a mathematical expression for an optimal phase-only filter that, when attached to an imaging lens, provides an optimal approximation in the sense of the minimal mean square error to the desired OTF function. Because of the fact that a phase-only filter is used, high efficiency is achieved.

Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms.

Diffractive optical elements able to generate zero-order (on-axis) distributions with phase as well as amplitude distributions are described. The proposed elements are surface relief plates, i.e., phase-only elements, that are based on the concept of computer-generated masks followed by common etching processes. The encoding method assumes fixed spatial partitioning of the cell and a phase-only value allocated to each subelement. The reconstructed amplitude and phase distributions contain imperfections (noise) resulting from the encoding process. Methods of error reduction and improvements are provided.

High-efficiency arbitrary array generator.

Implementation of a beam-shaping system, whereby an arbitrary array of spots is generated, is proposed. The suggested beam-shaping generator, which is based on the Gerchberg-Saxton algorithm, contains two phase-only filters and thus yields a very-high-power throughput. The flexibility of the suggested approach is demonstrated with some computer simulations.