Diffractive optical element design with memory-matrix-based identification methodology

Dhawat E. Pansatiankul; Alexander A. Sawchuk

doi:10.1364/AO.39.005921

Applied Optics
Vol. 39,
Issue 32,
pp. 5921-5928
(2000)
•https://doi.org/10.1364/AO.39.005921

Diffractive optical element design with memory-matrix-based identification methodology

Dhawat E. Pansatiankul and Alexander A. Sawchuk

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Dhawat E. Pansatiankul and Alexander A. Sawchuk, "Diffractive optical element design with memory-matrix-based identification methodology," Appl. Opt. 39, 5921-5928 (2000)

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Abstract

We present a new technique for the design of diffractive optical elements (DOE’s) that is based on previous nonlinear least squares (NLS) and phase-shifting quantization methods [Appl. Opt. 36, 7297–7306 (1997)]. The technique uses a memory-matrix-based identification (MMBI) optimization procedure. We compare results from the MMBI method with those from iterative Fourier transform and NLS methods. In comparison, the MMBI DOE designs produce better-quality reconstructions for DOE’s with eight or more fabrication phase levels and generally have a higher signal-to-noise ratio and better uniformity.

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Method	Phase Levels	Nonuniformity (%)	Window Efficiency (%)	Grating Efficiency (%)	SNR (dB)	Quality Factor	Number of Initial Guesses	Objective Efficiency (%)
MMBI	4	1.86	81.14	76.18	10.50	82.48	600	100
	8	0.75	91.68	88.01	15.30	85.65	600	100
	16	0.57	93.90	91.12	17.34	86.52	600	97
	32	0.28	94.35	91.87	17.90	86.91	600	97
	64	0.15	94.53	92.14	17.68	87.01	600	97
	CPa	0.04	94.61	92.25	18.00	87.15	600	97
IFT	4	1.85	82.10	77.31	9.16	82.46	600	100
	8	1.00	91.80	88.42	15.09	85.50	600	100
	16	0.74	94.05	91.84	15.66	86.26	600	100
	32	0.25	94.54	92.64	15.45	86.69	600	100
	64	0.42	94.65	92.83	15.52	86.61	600	100
	CP	0.43	94.70	92.92	15.58	86.62	600	100
NLS	4	4.71	81.15	76.46	10.93	80.55	20	100
	8	2.11	91.80	88.39	14.26	84.58	20	100
	16	1.07	93.89	91.13	17.36	86.16	20	97
	32	0.51	94.44	92.08	17.66	86.74	20	97
	64	0.33	94.60	92.27	17.87	86.93	20	97
	CP	0.18	94.66	92.32	17.98	87.05	20	97

Method	Phase Levels	Nonuniformity (%)	Window Efficiency (%)	Grating Efficiency (%)	SNR (dB)	Quality Factor	Number of Initial Guesses	Objective Efficiency (%)
MMBI	4	1.03	86.69	57.90	11.49	80.61	600	100
	8	1.74	93.94	63.78	16.77	81.69	600	100
	16	0.73	94.49	64.55	16.64	82.51	600	98
	32	0.38	95.32	65.11	18.94	83.17	600	98
	64	0.27	95.31	65.23	18.47	83.19	600	97
	CP	0.01	95.17	65.12	18.25	83.33	600	96
IFT	4	0.58	89.38	58.56	11.22	80.98	600	100
	8	4.75	96.89	66.49	16.09	79.84	600	100
	16	1.83	93.29	64.29	11.13	80.90	600	100
	32	1.42	96.85	65.92	15.22	82.00	600	100
	64	0.38	96.90	66.00	14.98	82.72	600	100
	CP	0.32	97.17	66.07	16.42	82.98	600	100
NLS	4	7.54	87.78	59.00	9.13	75.77	20	100
	8	4.75	96.89	66.49	16.09	79.84	20	100
	16	1.99	88.35	59.35	6.20	79.37	20	98
	32	0.35	95.55	65.20	18.16	83.09	20	98
	64	0.88	95.34	65.17	18.70	82.78	20	97
	CP	0.16	95.20	65.13	18.08	83.20	20	96

Method	Phase Levels	Nonuniformity (%)	Window Efficiency (%)	Grating Efficiency (%)	SNR (dB)	Quality Factor	Number of Initial Guesses	Objective Efficiency (%)
MMBI	4	5.68	77.21	53.17	10.35	76.45	600	100
	8	1.12	87.71	62.29	11.85	81.22	600	99
	16	0.78	89.89	63.81	13.60	81.93	600	100
	32	0.50	91.31	65.34	13.31	82.31	600	99
	64	0.31	91.44	65.30	14.20	82.56	600	98
	CP	0.14	91.41	65.19	14.89	82.77	600	97
IFT	4	5.14	78.85	53.95	10.90	77.02	600	100
	8	1.48	88.05	62.39	12.81	81.12	600	100
	16	1.23	90.72	65.00	11.94	81.54	600	100
	32	1.36	91.23	65.58	11.13	81.41	600	100
	64	1.60	90.96	65.18	12.10	81.32	600	100
	CP	1.67	92.04	65.64	13.41	81.53	600	100
NLS	4	5.63	73.28	49.69	9.30	75.83	20	100
	8	2.41	88.77	62.42	12.78	80.45	20	99
	16	3.20	91.25	65.35	12.95	80.33	20	100
	32	0.82	91.59	65.58	13.19	82.10	20	99
	64	0.93	91.95	65.84	12.82	82.00	20	98
	CP	1.86	91.81	65.50	14.55	81.53	20	97

Method	Phase Levels	Nonuniformity (%)	Window Efficiency (%)	Grating Efficiency (%)	SNR (dB)	Quality Factor	Number of Initial Guesses	Objective Efficiency (%)
MMBI	4	1.86	81.14	76.18	10.50	82.48	600	100
	8	0.75	91.68	88.01	15.30	85.65	600	100
	16	0.57	93.90	91.12	17.34	86.52	600	97
	32	0.28	94.35	91.87	17.90	86.91	600	97
	64	0.15	94.53	92.14	17.68	87.01	600	97
	CPa	0.04	94.61	92.25	18.00	87.15	600	97
IFT	4	1.85	82.10	77.31	9.16	82.46	600	100
	8	1.00	91.80	88.42	15.09	85.50	600	100
	16	0.74	94.05	91.84	15.66	86.26	600	100
	32	0.25	94.54	92.64	15.45	86.69	600	100
	64	0.42	94.65	92.83	15.52	86.61	600	100
	CP	0.43	94.70	92.92	15.58	86.62	600	100
NLS	4	4.71	81.15	76.46	10.93	80.55	20	100
	8	2.11	91.80	88.39	14.26	84.58	20	100
	16	1.07	93.89	91.13	17.36	86.16	20	97
	32	0.51	94.44	92.08	17.66	86.74	20	97
	64	0.33	94.60	92.27	17.87	86.93	20	97
	CP	0.18	94.66	92.32	17.98	87.05	20	97

Method	Phase Levels	Nonuniformity (%)	Window Efficiency (%)	Grating Efficiency (%)	SNR (dB)	Quality Factor	Number of Initial Guesses	Objective Efficiency (%)
MMBI	4	1.03	86.69	57.90	11.49	80.61	600	100
	8	1.74	93.94	63.78	16.77	81.69	600	100
	16	0.73	94.49	64.55	16.64	82.51	600	98
	32	0.38	95.32	65.11	18.94	83.17	600	98
	64	0.27	95.31	65.23	18.47	83.19	600	97
	CP	0.01	95.17	65.12	18.25	83.33	600	96
IFT	4	0.58	89.38	58.56	11.22	80.98	600	100
	8	4.75	96.89	66.49	16.09	79.84	600	100
	16	1.83	93.29	64.29	11.13	80.90	600	100
	32	1.42	96.85	65.92	15.22	82.00	600	100
	64	0.38	96.90	66.00	14.98	82.72	600	100
	CP	0.32	97.17	66.07	16.42	82.98	600	100
NLS	4	7.54	87.78	59.00	9.13	75.77	20	100
	8	4.75	96.89	66.49	16.09	79.84	20	100
	16	1.99	88.35	59.35	6.20	79.37	20	98
	32	0.35	95.55	65.20	18.16	83.09	20	98
	64	0.88	95.34	65.17	18.70	82.78	20	97
	CP	0.16	95.20	65.13	18.08	83.20	20	96

Abstract

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Equations (16)

Applied Optics