Design and analysis of a diffractive optical filter for use in an optoelectronic error-diffusion neural network

Barry L. Shoop; Thomas D. Wagner; Joseph N. Mait; Gregory R. Kilby; Eugene K. Ressler

doi:10.1364/AO.38.003077

Applied Optics
Vol. 38,
Issue 14,
pp. 3077-3088
(1999)
•https://doi.org/10.1364/AO.38.003077

Design and analysis of a diffractive optical filter for use in an optoelectronic error-diffusion neural network

Barry L. Shoop, Thomas D. Wagner, Joseph N. Mait, Gregory R. Kilby, and Eugene K. Ressler

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Barry L. Shoop, Thomas D. Wagner, Joseph N. Mait, Gregory R. Kilby, and Eugene K. Ressler, "Design and analysis of a diffractive optical filter for use in an optoelectronic error-diffusion neural network," Appl. Opt. 38, 3077-3088 (1999)

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Abstract

The design, fabrication, experimental characterization, and system-performance analysis of a diffractive optical implementation of an error-diffusion filter for use in digital image halftoning is reported. A diffractive optical filter was fabricated as an eight-level phase element that diffuses the quantization error nonuniformly in both the weighting and the spatial dimensions, according to a prescribed algorithm. Ten identical diffractive elements were fabricated on ten different wafers and subsequently characterized experimentally. A detailed error analysis including both fabrication and instrumentation errors was carried out to quantify the performance of the fabrication process as well as the expected system performance of the filters. Halftone system performance was evaluated by use of the experimental filter’s performance and both quantitative and qualitative performance metrics. The results of this analysis demonstrate that multiple identical copies of a diffractive optical filter can be produced with sufficient accuracy that no loss in the halftoning system performance results.

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Equations (18)

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w _x,y	x Coefficients

y Coefficients	x = -3	x = -2	x = -1	x = 0	x = 1	x = 2	x = 3
y = -3	0.0003	0.0019	0.0051	0.0068	0.0051	0.0019	0.0003
y = -3	0.0003	0.0019	0.0051	0.0068	0.0051	0.0019	0.0003
y = -2	0.0019	0.0103	0.0248	0.0328	0.0248	0.0103	0.0019
y = -1	0.0051	0.0248	0.0583	0.0766	0.0583	0.0248	0.0051
y = 0	0.0068	0.0328	0.0766	0.0000	0.0766	0.0328	0.0068
y = 1	0.0051	0.0248	0.0583	0.0766	0.0583	0.0248	0.0051
y = 2	0.0019	0.0103	0.0248	0.0328	0.0248	0.0103	0.0019
y = 3	0.0003	0.0019	0.0051	0.0068	0.0051	0.0019	0.0003

Θ_ub (x, y)	x Values
y Values	x = -3	x = -2	x = -1	x = 0	x = 1	x = 2	x = 3
y = -3	1.2566	0.2038	-0.1017	-2.9513	-0.1017	0.2038	1.2566
y = -2	1.1104	0.5581	-0.7317	-2.7790	-0.7317	0.5581	1.1104
y = -1	0.6649	-0.2590	-1.8587	2.5672	-1.8587	-0.2590	0.6649
y = 0	-2.9513	-2.7790	2.5672	0.0000	2.5672	-2.7790	-2.9513
y = 1	0.6649	-0.2590	-1.8587	2.5672	-1.8587	-0.2590	0.6649
y = 2	1.1104	0.5581	-0.7317	-2.7790	-0.7317	0.5581	1.1104
y = 3	1.2566	0.2038	-0.1017	-2.9513	-0.1017	0.2038	1.2566

\|p(x, y)\|²	x Values
y Values	x = -3	x = -2	x = -1	x = 0	x = 1	x = 2	x = 3
y = -3	0.0003	0.0016	0.0046	0.0062	0.0046	0.0016	0.0003
y = -2	0.0016	0.0093	0.0235	0.0307	0.0235	0.0093	0.0016
y = -1	0.0046	0.0234	0.0541	0.0698	0.0541	0.0234	0.0046
y = 0	0.0062	0.0305	0.0699	0.0000	0.0699	0.0305	0.0062
y = 1	0.0046	0.0234	0.0541	0.0698	0.0541	0.0234	0.0046
y = 2	0.0016	0.0093	0.0235	0.0307	0.0235	0.0093	0.0016
y = 3	0.0003	0.0016	0.0046	0.0062	0.0046	0.0016	0.0003

\|p(x, y)\|²	x Values
y Values	x = -3	x = -2	x = -1	x = 0	x = 1	x = 2	x = 3
y = -3	0.0003	0.0016	0.0046	0.0063	0.0046	0.0016	0.0003
y = -2	0.0016	0.0094	0.0234	0.0308	0.0234	0.0094	0.0016
y = -1	0.0046	0.0234	0.0541	0.0698	0.0541	0.0234	0.0046
y = 0	0.0063	0.0306	0.0699	0.0001	0.0699	0.0306	0.0063
y = 1	0.0046	0.0234	0.0541	0.0698	0.0541	0.0234	0.0046
y = 2	0.0016	0.0094	0.0234	0.0308	0.0234	0.0094	0.0016
y = 3	0.0003	0.0016	0.0046	0.0063	0.0046	0.0016	0.0003

\|p(x, y)\|²	x Values
y Values	x = -3	x = -2	x = -1	x = 0	x = 1	x = 2	x = 3
y = -3	0.0004	0.0017	0.0051	0.0071	0.0052	0.0018	0.0004
y = -2	0.0018	0.0104	0.0251	0.0339	0.0256	0.0105	0.0017
y = -1	0.0050	0.0247	0.0597	0.0744	0.0594	0.0254	0.0052
y = 0	0.0069	0.0327	0.0739	0.0008	0.0755	0.0335	0.0071
y = 1	0.0049	0.0245	0.0599	0.0751	0.0593	0.0252	0.0053
y = 2	0.0018	0.0103	0.0250	0.0337	0.0253	0.0113	0.0018
y = 3	0.0004	0.0018	0.0052	0.0071	0.0052	0.0017	0.0003

Abstract

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Applied Optics