Optimal realizable filters and the minimum Euclidean distance principle.

Minimizing a Euclidean distance in the complex plane optimizes a wide class of correlation metrics for filters implemented on realistic devices. The algorithm searches over no more than two real scalars (gain and phase). It unifies a variety of previous solutions for special cases (e.g., a maximum signal-to-noise ratio with colored noise and a real filter and a maximum correlation intensity with no noise and a coupled filter). It extends optimal partial information filter theory to arbitrary spatial light modulators (fully complex, coupled, discrete, finite contrast ratio, and so forth), additive input noise (white or colored), spatially nonuniform filter modulators, and additive correlation detection noise (including signaldependent noise). An appendix summarizes the algorithm as it is implemented in available computer code.

[1]  J. Loomis,et al.  Transform-ratio ternary phase-amplitude filter formulation for improved correlation discrimination. , 1988, Applied optics.

[2]  J W Goodman,et al.  Optimal binary phase-only matched filters. , 1988, Applied optics.

[3]  Z. Q. Wang,et al.  Amplitude-compensated matched filtering. , 1988, Applied optics.

[4]  B. V. Vijaya Kumar,et al.  Phase-only filters with improved signal to noise ratio. , 1989, Applied optics.

[5]  R. Juday.  Correlation with a spatial light modulator having phase and amplitude cross coupling. , 1989, Applied optics.

[6]  F. Dickey,et al.  Quad-phase correlation filters for pattern recognition. , 1989, Applied optics.

[7]  J W Goodman,et al.  Optimal maximum correlation filter for arbitrarily constrained devices. , 1989, Applied optics.

[8]  B. V. K. Vijaya Kumar,et al.  Phase-only filters with maximally sharp correlation peaks , 1990 .

[9]  Louis A. Romero,et al.  Complex ternary matched filters yielding high signal-to-noise ratios , 1990, Annual Meeting Optical Society of America.

[10]  James M. Florence,et al.  Full-complex spatial filtering with a phase mostly DMD , 1991, Optics & Photonics.

[11]  R D Juday,et al.  Optimal real correlation filters. , 1991, Applied optics.

[12]  P Refregier.  Optimal trade-off filters for noise robustness, sharpness of the correlation peak, and Horner efficiency. , 1991, Optics letters.

[13]  R. Juday,et al.  Design of phase-only, binary phase-only, and complex ternary matched filters with increased signal-to-noise ratios for colored noise. , 1991, Optics letters.

[14]  James M. Florence,et al.  Full-complex modulation with two one-parameter SLMs , 1991, Optics & Photonics.

[15]  R Eschbach,et al.  Comparison of error diffusion methods for computer-generated holograms. , 1991, Applied optics.

[16]  B. Saleh,et al.  Complex amplitude reflectance of the liquid crystal light valve. , 1991, Applied optics.

[17]  J D Downie,et al.  Effects and correction of magneto-optic spatial light modulator phase errors in an optical correlator. , 1992, Applied optics.

[18]  J L Horner,et al.  Metrics for assessing pattern-recognition performance. , 1992, Applied optics.

[19]  Leonid P. Iaroslavskii.  Is the phase-only filter and its modifications optimal in terms of the discrimination capability in pattern recognition? , 1992 .

[20]  E. Tam,et al.  Full complex modulation using liquid-crystal televisions. , 1992, Applied optics.

[21]  MEDOF - MINIMUM EUCLIDEAN DISTANCE OPTIMAL FILTER , 1994 .

[22]  Takeshi Takahashi,et al.  Phase-only matched filtering with dual liquid-crystal spatial light modulators , 1995, Optics & Photonics.