John F. Walkup

Ambiguity function display: an improved coherent processor

A coherent optical processor for displaying a signals ambiguity function is described. The required time delay is realized by 45 degrees rotations of two identical input transparencies and the Doppler shift by a 1-D Fourier transformation. The entire ambiguity function is displayed in the output (Doppler shift-time delay) plane. Examples of the optically computed ambiguity function for single and double pulse signals are shown to be in excellent agreement with theory. Advantages of this approach over other schemes and possible extension to real time processing are also discussed.

Multiplex holography with chirp-modulated binary phase-coded reference-beam masks.

Certain binary codes developed for spread-spectrum communication applications can be used to construct families of pseudorandom diffuser masks suitable for multiplex holography. Binary codes are used so that fabrication of the diffuser masks can be relatively straightforward. A simple technique is described for chirp-modulating the binary diffuser masks to achieve the advantage of polyphase masks, i.e., improved correlation properties, without having to construct them. Numerical comparisons of the correlation properties of optimal binary codes with and without chirp-modulation are presented.

Limitations of fringe-parameter estimation at low light levels*

Fundamental limitations of estimating the amplitudes and phases of interference fringes at low light levels are determined by the finite number of photoevents registered in the measurement. By modeling the receiver as a spatial array of photon-counting detectors, results are obtained that permit specification of the minimum number of photoevents required for estimation of fringe parameters to a given accuracy. Both a discrete Fourier-transform estimator and an optimum joint maximum-likelihood estimator are considered. In addition, the Cramer–Rao statistical error bounds are derived, specifying the limiting performance of all unbiased estimators in terms of the collected light flux. The performance of the spatial sampling receiver is compared with that of an alternate technique for fringe-parameter estimation that uses a barred grid and temporal sampling of a moving fringe.

2-D Optical Multistage Interconnection Networks

This paper discusses the need for 2-D multistage optical interconnection networks in parallel computing systems and demonstrates the benefits obtained from a 2-D multi-stage perfect shuffle network.

Holographic representations of space-variant systems using phase-coded reference beams

A new holographic implementation of a sampling technique permits, in principle, a straightforward representation of 2-D space-variant optical systems. The set of sample transfer functions required for the representation is recorded on a single holographic plate by utilizing phase coded reference beams. Because this approach does not depend on volume effects in the recording medium in an essential way, the holograms can be produced digitally, as well as optically. Basic concepts and preliminary experimental investigations related to this approach are presented and discussed.

Image compression in signal-dependent noise.

The performance of an image compression scheme is affected by the presence of noise, and the achievable compression may be reduced significantly. We investigated the effects of specific signal-dependent-noise (SDN) sources, such as film-grain and speckle noise, on image compression, using JPEG (Joint Photographic Experts Group) standard image compression. For the improvement of compression ratios noisy images are preprocessed for noise suppression before compression is applied. Two approaches are employed for noise suppression. In one approach an estimator designed specifically for the SDN model is used. In an alternate approach, the noise is first transformed into signal-independent noise (SIN) and then an estimator designed for SIN is employed. The performances of these two schemes are compared. The compression results achieved for noiseless, noisy, and restored images are also presented.

Optimal estimation in signal-dependent noise

Optimal estimators are derived for a class of signal-dependent noise processes. Such processes are of interest in optics because phenomena, such as film grain noise, are often modeled in this manner. This paper demonstrates that when one ignores the presence of signal-dependent noise and instead assumes only signal-independent noise models, the resulting estimators may pay a severe penalty in performance. This “mismatch” problem is explored, with the results of Monte Carlo simulations of the performances of both optimum and mismatched estimators being presented. The Cramer-Rao lower bounds on the mean-square estimation errors for unbiased estimators are evaluated and compared with the lower bounds derived for the signal-independent noise case. Overall, the results indicate that improved performance will, in most cases, offset the increased complexity inherent in estimators designed for the signal-dependent noise model.

Space-variant processing of 1-D signals

Two general schemes for 1-D space-variant processing are proposed. The direct output display scheme gives the space-variant system output along a line in the processors output plane. The output spectrum display scheme directly computes the space-variant systems output spectrum. Both of these schemes utilize a 1-D input and a line spread function mask. Example applications and experimental results are also presented.

Estimation in signal-dependent film-grain noise

Optimal estimators are derived for a signal-dependent film-grain noise model, and the effect of signal-dependence on the estimatorss structures is investigated. Due to the mathematical complexity of these optimal estimators, various suboptimal estimators are proposed. Computer simulations are then presented which compare the optimal and suboptimal estimators with regard to mean square estimation error, sensitivity to signal-dependence, and robustness with respect to the a priori signal probability density function.

A sampling theorem for space-variant systems

A sampling theorem applicable to that class of linear systems characterized by sufficiently slowly varying line-spread functions is developed. For band-limited inputs such systems can be exactly characterized with knowledge of the sampled system line-spread function and the corresponding sampled input. The desired sampling rate is shown to be determined by both the system and the input. The corresponding output is shown to be band limited. A discrete matrix representation of the specific system class is also presented. Applications to digital processing and coherent space-variant system representation are suggested.