Contiguous perfect coded aperture patterns with high throughput

Kevin Byard

doi:10.1364/AO.439798

Applied Optics
Vol. 61,
Issue 5,
pp. 1112-1124
(2022)
•https://doi.org/10.1364/AO.439798

Contiguous perfect coded aperture patterns with high throughput

Kevin Byard

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Kevin Byard, "Contiguous perfect coded aperture patterns with high throughput," Appl. Opt. 61, 1112-1124 (2022)

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Abstract

A method is described that mosaics linear uniformly redundant arrays and modified uniformly redundant arrays onto a square lattice to create coded aperture patterns of approximately 50% throughput that are contiguous, whereby every opaque element in the aperture is joined to at least one other opaque element. Parameters required to create these perfect high-throughput contiguous apertures for all coded aperture unit pattern orders of up to 300 elements are presented. The apertures presented increase significantly the number of known contiguous apertures in dimensions forbidden to the known patterns and that have the same imaging quality as uniformly redundant arrays and modified uniformly redundant arrays while having imaging quality superior to other known self-supporting apertures. The effect of supporting the weaker areas of these contiguous apertures is investigated. Contiguous apertures are of interest for coded aperture systems that require extra rigidity or use active collimation.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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$v$	$r$	$s$	$c$	$A_{c} / π$	$P_{c} / %$
5	2	0	2	2.5	63.7
13	5	2	3	6.5	63.7
17	4	6	0	8.5	63.7
29	12	9	9	14.5	63.7
37	6	18	14	18.5	63.7
41	6	13	15	18.5	70.5
53	23	4	15	26.5	63.7
61	9	7	20	26.5	73.3
73	32	34	27	32.5	71.5
89	20	12	32	42.5	66.7
97	10	27	43	42.5	72.6
101	12	45	42	44.5	72.2
109	40	9	47	44.5	78.0
113	26	6	43	48.5	74.2
137	13	32	61	56.5	77.2
149	32	70	63	62.5	75.9
157	72	42	73	68.5	73.0
173	53	82	82	72.5	76.0
181	39	23	70	74.5	77.3
193	36	96	87	78.5	78.3
197	86	51	85	86.5	72.5
229	27	14	107	92.5	78.8
233	15	0	106	98.5	75.3
241	45	49	112	98.5	77.9
257	80	53	111	102.5	79.8
269	63	109	117	112.5	76.1
277	29	104	126	116.5	75.7
281	74	103	134	120.5	74.2
293	46	9	135	116.5	80.1

$v$	$r$	$s$	$c$	$A_{r}$	$P_{r} / %$	$A_{x y}$	$P_{x y} / %$
5	2	0	2	8	62.5	9	55.6
13	5	2	3	18	72.2	25	52
17	5	2	4	24	70.8
29	4	1	8	35	82.9	35	82.9
37	4	12	11	45	82.2	45	82.2
41	6	13	15	49	83.7	49	83.7
53	23	4	15	67.6	78.4	81	65.4
61	11	18	29	72	84.7
73	8	18	20	81	90.1	81	90.1
89	40	40	34	108.8	81.8
97	15	20	36	112	86.6
101	38	6	37	117	86.3	117	86.3
109	11	43	42	121	90.1	121	90.1
113	15	0	56	128	88.3
137	11	34	50	165	83.0	165	83.0
149	27	0	66	165	90.3	165	90.3
157	12	78	67	169	92.9	169	92.9
173	80	21	90	200	86.5
181	13	89	66	195	92.8	195	92.8
193	12	46	72	221	87.3	221	87.3
197	91	22	82	221	89.1	221	89.1
229	10	29	109	262.7	87.2	247	92.7
233	11	23	98	267.2	87.2
241	12	53	100	273	88.3	273	88.3
257	47	0	124	291	88.3
269	49	26	121	305	88.2
277	12	25	118	299	92.6	299	92.6
281	38	66	125	319.8	87.9
293	14	125	130	315	93.0	315	93.0

$v$	$r$	$s$	$c$	$A_{x y}$	$P_{x y} / %$
17	4	6	0	25	68.0
61	10	27	18	77	79.2
89	41	36	40	117	76.1
97	8	13	45	117	82.9
113	25	29	43	135	83.7
173	10	39	77	209	82.8
233	15	0	106	285	81.8
257	11	7	98	299	86.0
269	128	3	114	315	85.4
281	13	3	130	315	89.2

$v$	$r$	$s$	$c$	$A_{c} / π$	$P_{c} / %$
11	3	3	3	6.5	53.9
19	4	13	5	8.5	71.2
31	7	5	11	14.5	68.1
43	9	11	16	22.5	60.8
47	13	34	15	22.5	66.5
59	25	25	18	26.5	70.9
67	19	38	25	32.5	65.6
71	16	56	30	32.5	69.5
79	30	44	34	36.5	68.9
83	15	62	40	36.5	72.4
103	16	81	45	48.5	67.6
107	41	26	51	48.5	70.2
127	12	75	59	54.5	74.2
131	40	48	58	56.5	73.8
139	30	8	63	58.5	75.6
151	12	92	67	62.5	76.9
163	50	158	73	68.5	75.7
167	36	9	81	72.5	73.3
179	41	19	83	74.5	76.5
191	14	94	94	78.5	77.4
199	17	44	92	84.5	75.0
211	87	151	111	92.5	72.6
223	18	95	123	96.5	73.6
227	27	23	98	98.5	73.4
239	19	221	109	102.5	74.2
251	53	119	117	110.5	72.3
263	82	25	130	110.5	75.8
271	80	179	127	112.5	76.7
283	89	79	121	120.5	74.8

$v$	$r$	$s$	$c$	$A_{r}$	$P_{r} / %$	$A_{x y}$	$P_{x y} / %$
11	3	3	3	15	73.3	15	73.3
19	4	13	5	25	76	25	76.0
31	7	5	11	40	77.5
43	6	32	14	49	87.8	49	87.8
47	13	34	15	60	78.3
59	17	57	27	63	93.7	63	93.7
67	6	45	19	77	87.0	77	87.0
71	7	2	32	88.7	80.0
79	30	44	34	96.6	81.8
83	9	52	37	99	83.8	99	83.8
103	8	40	49	117	88.0	117	88.0
107	7	23	44	131.1	81.6	135	79.3
127	15	86	56	144	88.2
131	8	128	63	153	85.6	153	85.6
139	11	43	52	165	84.2	165	84.2
151	55	67	59	165	91.5	165	91.5
163	59	55	67	194.0	84.0
167	11	42	83	197.7	84.5
179	40	129	80	208	86.1
191	20	18	95	220	86.8
199	57	128	91	235	84.7
211	10	87	90	231	91.3	231	91.3
223	13	97	105	259.9	85.8	285	78.2
227	105	79	106	267	85.0	323	70.3
239	15	255	104	238	100.4	255	93.7
251	12	38	117	273	91.9	273	91.9
263	10	114	121	300.0	87.7	351	74.9
271	42	41	127	311.8	86.9
283	44	4	142	336.0	84.2

$v$	$r$	$s$	$c$	$A_{x y}$	$P_{x y} / %$
31	4	12	12	45	68.9
47	7	5	17	63	74.6
71	16	56	30	99	71.7
79	8	47	34	99	79.8
127	8	36	62	153	83.0
163	15	53	77	195	83.6
167	59	75	81	221	75.6
179	14	11	87	225	79.6
191	15	76	79	255	74.9
199	83	165	101	247	80.6
271	95	65	123	357	75.9
283	75	4	129	399	70.9

Aperture Type	${S N R}_{i j}^{c M} / {S N R}_{i j}^{O}$
GS3	1.90
IC ( $n = 4$ )	1.50
IC ( $n = 8$ )	2.60
IC ( $n = 16$ )	4.02
M-M	2.27
rec-MURA	1.01

	Figure 9(a)			Figure 9(b)
$x$	Peak	Variance	SNR	Peak	Variance	SNR
0	146	0	$\infty$	146	0	$\infty$
0.1	145.3	0.01	1673.0	145.3	0.01	1771.3
0.2	143.3	0.12	412.4	143.2	0.11	436.4
0.25	141.8	0.29	261.1	141.6	0.26	276.2
0.3	139.9	0.61	178.9	139.7	0.54	189.2
0.4	135.1	1.93	97.2	134.8	1.72	102.7
0.5	129.0	4.72	59.4	128.5	4.21	62.7

Abstract

Data availability

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Figures (11)

Tables (8)

Equations (11)

Applied Optics