Joseph W. Goodman

Some fundamental properties of speckle

A speckle pattern formed in polarized monochromatic light may be regarded as resulting from a classical random walk in the complex plane. The resulting irradiance fluctuations obey negative exponential statistics, with ratio of standard deviation to mean (i.e., contrast) of unity. Reduction of this contrast, or smoothing of the speckle, requires diversity in polarization, space, frequency, or time. Addition of M uncorrelated speckle patterns on an intensity basis can reduce the contrast by 1/√M. However, addition of speckle patterns on a complex amplitude basis provides no reduction of contrast. The distribution of scale sizes in a speckle pattern (i.e., the Wiener spectrum) is investigated from a physical point of view.

Statistical Properties of Laser Speckle Patterns

Since speckle plays an important role in many physical phenomena, it is essential to fully understand its statistical properties. Starting from the basic idea of a random walk in the complex plane, we derive the first-order statistics of the complex amplitude, intensity and phase of speckle. Sums of speckle patterns are also considered, the addition being either on an amplitude or on an intensity basis, with partially polarized speckle being a special case. Next we consider the sum of a speckle pattern and a coherent background, deriving the first-order probability density functions of intensity and phase. Attention is then turned to second-order statistics. The autocorrelation function and power spectral density are derived, both for a free-space propagation geometry and for an imaging geometry. In some cases the recorded speckle pattern may be spatially integrated or blurred, and accordingly consideration is given to the statistics of such patterns. Finally, the relationship between detailed surface structure and the resulting speckle pattern is explored, with emphasis on the effects of the surface autocorrelation function and the effects of finite surface roughness.

Optical interconnections for VLSI systems

The combination of decreasing feature sizes and increasing chip sizes is leading to a communication crisis in the area of VLSI circuits and systems. It is anticipated that the speeds of MOS circuits will soon be limited by interconnection delays, rather than gate delays. This paper investigates the possibility of applying optical and electrooptical technologies to such interconnection problems. The origins of the communication crisis are discussed. Those aspects of electrooptic technology that are applicable to the generation, routing, and detection of light at the level of chips and boards are reviewed. Algorithmic implications of interconnections are discussed, with emphasis on the definition of a hierarchy of interconnection problems from the signal-processing area having an increasing level of complexity. One potential application of optical interconnections is to the problem of clock distribution, for which a single signal must be routed to many parts of a chip or board. More complex is the problem of supplying data interconnections via optical technology. Areas in need of future research are identified.

DIGITAL IMAGE FORMATION FROM ELECTRONICALLY DETECTED HOLOGRAMS

In high precision holographic imagery of weak objects of small angular subtense, electronic detection and digital image formation have distinct advantages. Experiments with a vidicon detector and a PDP‐6 computer have yielded reconstructed images of good quality with computation times of five minutes.

A mathematical analysis of the DCT coefficient distributions for images

Over the past two decades, there have been various studies on the distributions of the DCT coefficients for images. However, they have concentrated only on fitting the empirical data from some standard pictures with a variety of well-known statistical distributions, and then comparing their goodness of fit. The Laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data. Yet, to the best of our knowledge, there has been no mathematical justification as to what gives rise to this distribution. We offer a rigorous mathematical analysis using a doubly stochastic model of the images, which not only provides the theoretical explanations necessary, but also leads to insights about various other observations from the literature. This model also allows us to investigate how certain changes in the image statistics could affect the DCT coefficient distributions.

Fiber-optic lattice signal processing

We discuss the implementation of fiber-optic lattice structures incorporating single-mode fibers and directional couplers. These fiber structures can be used to perform various high-speed time-domain and frequency-domain functions such as matrix operations and frequency filtering. In this paper we mainly consider systems in which the signals (optical intensities) and coupling coefficients are nonnegative quantities; these systems fit well in the theory of positive systems. We use this theory to conclude, for example, that for such systems the pole of the system transfer function with the largest magnitude is simple and positive-valued (in the Z-plane), and that the magnitude of the frequency response can nowhere exceed its value at the origin. We also discuss the effects of various noise phenomena on the performance of fiber-optic signal processors, particularly considering the effects of laser source phase fluctuations. Experimental results are presented showing that the dynamic range of the fiber systems, discussed in this paper, is limited, not by the laser source intensity noise or shot noise, but by the laser phase-induced intensity noise. Mathematical analyses of lattice structures as well as additional applications are also presented.

Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms

An incoherent optical data-processing method is described, which has the potential for performing discrete Fourier transforms of short length at rates far exceeding those afforded by both special-purpose digital hardware and representative coherent optical processors.

Some effects of target-induced scintillation on optical radar performance

The statistical performance of pulsed optical radars that use energy detection is considered. While the signal photoelectron statistics produced by a return from a specular target are Poisson, those produced by a return from a rough target are shown to be negative binomial. Radar performance is shown to depend on the number of spatial correlation cells of energy density observed by the receiving aperture, with performance generally deteriorating as the number of observed cells decreases. The physical factors influencing the number of observed correlation cells for the cases of partial and total interception of the transmitted beam are examined.

Neural networks for computation: number representations and programming complexity.

Methods for using neural networks for computation are considered. The success of such networks in finding good solutions to complex problems is found to be dependent on the number representation schemes used. Redundant schemes are found to offer advantages in terms of convergence. Neural networks are applied to the combinatorial optimization problem known as the Hitchcock problem and signal processing problems, such as matrix inversion and Fourier transformation. The concept of programming complexity is introduced. It is shown that for some computational problems, the programming complexity may be so great as to limit the utility of neural networks, while for others the investment of computation in programming the network is justified. Simulations of neural networks using a digital computer are presented.

Laser-induced local heating of multilayers

For a multilayer structure illuminated by a laser beam, absorption of optical energy in the absorptive layers and the diffusion of the resultant heat throughout the structure are studied. Analytical and numerical procedures for this study are described, and, as a specific example, the profiles of temperature distribution during recording on a magnetooptical disk are presented. The technique is also expected to be of value for studies of thermal marking and laser annealing.