New family of binary arrays for coded aperture imaging

Stephen R. Gottesman; E. E. Fenimore

doi:10.1364/AO.28.004344

Applied Optics
Vol. 28,
Issue 20,
pp. 4344-4352
(1989)
•https://doi.org/10.1364/AO.28.004344

New family of binary arrays for coded aperture imaging

Stephen R. Gottesman and E. E. Fenimore

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Stephen R. Gottesman and E. E. Fenimore, "New family of binary arrays for coded aperture imaging," Appl. Opt. 28, 4344-4352 (1989)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

We introduce a new family of binary arrays for use in coded aperture imaging which are predicted to have properties and sensitivity (SNR) equal to that of the uniformly redundant array (URA). The new arrays, called MURAs (modified URAs), have decoding coefficients all of which are unimodular, resulting in a reconstructed image with noise terms completely independent of image–source structure. Although the new arrays are derived from quadratic residues, they do not belong to the cyclic difference set or set of pseudonoise sequences and consequently are constructible in configurations forbidden to those designs, thus providing the user with a wider selection of aperture patterns to match his particular needs. With the addition of MURAs to the family of binary arrays, all prime numbers can now be used for making optimal coded apertures, increasing the number of available square patterns by more than a factor of 3.

Full Article | PDF Article

More Like This

Contiguous perfect coded aperture patterns with high throughput

Kevin Byard
Appl. Opt. 61(5) 1112-1124 (2022)

Time-resolved and energy-resolved coded aperture images with URA tagging

E. E. Fenimore
Appl. Opt. 26(14) 2760-2769 (1987)

Complementary lattice arrays for coded aperture imaging

Jie Ding, Mohammad Noshad, and Vahid Tarokh
J. Opt. Soc. Am. A 33(5) 863-881 (2016)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (5)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (36)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Length	Sequence
05	01001
13	01011	00001	101
17	01101	00011	00010	11
29	01001	11101	00010	01000	10111	1001
37	01011	00101	11100	01000	01000	11110	10011	01
41	01101	10011	10000	01010	11010	10000	01110	01101	1
53	01001	01101	11010	11100	00001	10011	00000	01110	10111
	01101	001
61	01011	10001	00111	11001	10100	10100	00001	01001	01100
	11111	00100	01110	1
73	01111	01011	00100	01011	00011	10100	00100	11110	01000
	01011	10001	10100	01001	10101	111
89	01101	10011	11000	01110	11100	10000	00101	01001	10101
	10101	10010	10100	00001	00111	01110	00011	11001	1011

Dimension (P, q)	q − p = 0 (MURA)	q − p=2 (URA)	m-seq (URA)
3,3	X
5,3		X	X
5,5	X
7,5		X
7,7	X
9,7			X
11,11	X
13,11		X
13,13	X
17,15			X
17,17	X
19,17		X
19,19	X
23,23	X
29,29	X
31,29		X
31,31	X
33,31			X
37,37	X
41,41	X
43,41		X
43,43	X
47,47	X
53,53	X
59,59	X
61,59		X
61,61	X
65,63			X
67,67	X
71,71	X
73,71		X
73,73	X
79,79	X
83,83	X
89,89	X
97,97	X

Length	Sequence
05	01001
13	01011	00001	101
17	01101	00011	00010	11
29	01001	11101	00010	01000	10111	1001
37	01011	00101	11100	01000	01000	11110	10011	01
41	01101	10011	10000	01010	11010	10000	01110	01101	1
53	01001	01101	11010	11100	00001	10011	00000	01110	10111
	01101	001
61	01011	10001	00111	11001	10100	10100	00001	01001	01100
	11111	00100	01110	1
73	01111	01011	00100	01011	00011	10100	00100	11110	01000
	01011	10001	10100	01001	10101	111
89	01101	10011	11000	01110	11100	10000	00101	01001	10101
	10101	10010	10100	00001	00111	01110	00011	11001	1011

Dimension (P, q)	q − p = 0 (MURA)	q − p=2 (URA)	m-seq (URA)
3,3	X
5,3		X	X
5,5	X
7,5		X
7,7	X
9,7			X
11,11	X
13,11		X
13,13	X
17,15			X
17,17	X
19,17		X
19,19	X
23,23	X
29,29	X
31,29		X
31,31	X
33,31			X
37,37	X
41,41	X
43,41		X
43,43	X
47,47	X
53,53	X
59,59	X
61,59		X
61,61	X
65,63			X
67,67	X
71,71	X
73,71		X
73,73	X
79,79	X
83,83	X
89,89	X
97,97	X

Hexagonal Rank	Number of Elements	URA	MURA
1	7	X	-
2	19	X	–
3	37	–	X
4	61	–	X
5	91	–	–
6	127	X	–
7	169	–	–
8	217	–	–
9	271	X	–
10	331	X	–
11	397	–	X
12	469	–	–
13	547	X	–
14	631	X	–
15	721	–	–
16	817	–	–
17	919	X	–
18	1027	–	–
19	1141	–	–
20	1261	–	–
21	1387	–	–
22	1519	–	–
23	1657	–	X
24	1801	–	X
25	1951	X	–

Abstract

Cited By

Figures (5)

Tables (3)

Equations (36)

Applied Optics