Charles D. Hendrix

Phase-only filters with maximally sharp correlation peaks

A performance measure called the peak-to-correlation energy is used to characterize the sharpness of correlation outputs. This measure is then used to determine the phase-only filter with maximally sharp correlation peaks.

Multicriteria optimal binary amplitude phase-only filters

Filters with binary amplitude (i.e., 0 and 1) that provide optimal trade-offs among three important criteria (i.e., noise robustness, correlation-peak sharpness, and Horner efficiency) are presented. A method for optimizing the discrimination capabilities is also presented.

Tradeoffs in the design of correlation filters

Designing filters for use with optical correlators is really an exercise in trading one performance measure against another. In this critical review, we present several different situations where such a tradeoff is carried out. An informed understanding of this law of nature is important in making sure that our goals in optical pattern recognition are realistic.

Choice of threshold line angle for binary phase-only filters

The choice of threshold line angle (TLA) is an important issue in designing Binary Phase-Only Filters (BPOFs). In this paper, we derive expressions that explicitly relate the TLA to correlation peak intensity. We also show some examples that illustrate the effect of choosing the wrong TLA.

Design and testing of three-level optimal correlation filters

Previously, we have designed 3-level filters(suitable for implementation on magneto-optic spatial light modulators) to maximize the output signal-to-noise ratio (SNR) and to separately maximize peak-to-correlation energy (PCE) that measures the correlation peak sharpness. In practice, we want the correlation peaks to be sharp (i.e., large PCE) as well as noise-tolerant (i.e., large SNR). In this paper, we present a new method to optimally combine these two desirable properties into a single optimization procedure. Similar methods to trade off SNR versus peak efficiency and PCE versus peak efficiency will be presented. Both simulation and experimental results will be included.

Design and evaluation of three-level composite filters obtained by optimizing a compromise average performance measure

Correlation filters with three transmittance levels ( +1 , 0, and -1) are of interest in optical pattern recognition because they can be implemented on available spatial light modulators and because the zero level allows us to include a region of support (ROS). The ROS can provide additional control over the filters noise tolerance and peak sharpness. A new algorithm based on optimizing a compromise average performance measure (CAPM) is proposed for designing three-level composite filters. The performance of this algorithm is compared to other three-level composite filter designs using a common image database and using figures of merit such as the Fisher ratio, error rate, and light efficiency. It is shown that the CAPM algorithm yields better results.

Comparative evaluation of binary phase-only synthetic discriminant function filters

Because of their suitability to two-level spatial light modulators, binary phase-only synthetic discriminant function (BPOSDF) filters are of much interest in optical pattern recognition. In this paper, we will compare three BPOSDF filter design methods using a common database. The three methods are Relaxation Algorithm, Successive Forcing Algorithm and a Phase Grating Approach recently introduced by us. The figures of merit used for this comparison include: Fisher Ratio, Recognition Rate, and Light Efficiency.

Iterative algorithm for designing binary phase-only composite filters

Use of the Magneto-Optic Spatial Light Modulator (MOSLM) in the filter plane of optical correlators is attractive because it is capable of high frame rates. This has led to the design of several different types of Binary Phase-Only Filters (BPOFs) and Ternary Filters matched to a single reference. To further increase the throughput of an optical correlator employing the MOSLM, attempts at designing Binary Phase-Only Composite Filters have been made. In this paper, we introduce a new iterative technique to design such Composite Filters in which we simultaneously maximize the peak sharpness and minimize the deviation of the actual correlation peak intensities from their desired values.

Phase-only filters that best approximate the classical matched filters' outputs

Much research effort has been directed to designing phase-only and binary phase-only filters that maximize the signal-to-noise ratio (i.e., the noise tolerance) or the peak-to-correlation energy (i.e., the correlation peak sharpness). In this paper, we propose a filter design algorithm for phase-only filters that produce correlation outputs that approximate classical matched filter outputs in a minimum mean squared error sense. Simulation results are presented to illustrate the use of the design algorithm.