Absolute phase map recovery of two fringe patterns with flexible selection of fringe wavelengths

Jiale Long; Jiangtao Xi; Ming Zhu; Wenqing Cheng; Rui Cheng; Zhongwei Li; Yusheng Shi

doi:10.1364/AO.53.001794

Applied Optics
Vol. 53,
Issue 9,
pp. 1794-1801
(2014)
•https://doi.org/10.1364/AO.53.001794

Absolute phase map recovery of two fringe patterns with flexible selection of fringe wavelengths

Jiale Long, Jiangtao Xi, Ming Zhu, Wenqing Cheng, Rui Cheng, Zhongwei Li, and Yusheng Shi

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Jiale Long, Jiangtao Xi, Ming Zhu, Wenqing Cheng, Rui Cheng, Zhongwei Li, and Yusheng Shi, "Absolute phase map recovery of two fringe patterns with flexible selection of fringe wavelengths," Appl. Opt. 53, 1794-1801 (2014)

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Abstract

A novel approach is proposed to unwrap the phase maps of two fringe patterns in fringe pattern projection-based profilometry. In contrast to existing techniques, where spatial frequencies (i.e., the number of fringes on a pattern) of the two fringe patterns must be integers and coprime, the proposed method is applicable for any two fringe patterns with different fringe wavelengths (i.e., the number of pixels in a fringe) and thus provides more flexibility in the use of fringe patterns. Moreover, compared to the existing techniques, the proposed method is simpler in its implementation and has better antierror capability. Theoretical analysis and experiment results are presented to confirm the effectiveness of the proposed method.

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$m_{1} (y)$	$m_{2} (y)$	$m_{2} (y) λ_{2} - m_{1} (y) λ_{1}$
2	0	$- 46$
4	1	$- 45$
6	2	$- 44$
8	3	$- 43$
10	4	$- 42$
12	5	$- 41$
14	6	$- 40$
16	7	$- 39$
18	8	$- 38$
20	9	$- 37$
22	10	$- 36$
24	11	$- 35$
26	12	$- 34$
28	13	$- 33$
30	14	$- 32$
32	15	$- 31$
1	0	$- 23$
3	1	$- 22$
5	2	$- 21$
7	3	$- 20$
9	4	$- 19$
11	5	$- 18$
13	6	$- 17$
15	7	$- 16$
17	8	$- 15$
19	9	$- 14$
21	10	$- 13$
23	11	$- 12$
25	12	$- 11$
27	13	$- 10$
29	14	$- 9$
31	15	$- 8$
33	16	$- 7$
0	0	0
2	1	1
4	2	2
6	3	3
8	4	4
10	5	5
12	6	6
14	7	7
16	8	8
18	9	9
20	10	10
22	11	11
24	12	12
26	13	13
28	14	14
30	15	15
32	16	16

$m_{1} (y)$	$m_{2} (y)$	$m_{2} (y) λ_{2} - m_{1} (y) λ_{1}$
13	6	$- 76$
11	5	$- 72$
9	4	$- 68$
7	3	$- 64$
5	2	$- 60$
3	1	$- 56$
1	0	$- 52$
14	7	$- 28$
12	6	$- 24$
10	5	$- 20$
8	4	$- 16$
6	3	$- 12$
4	2	$- 8$
2	1	$- 4$
0	0	0
13	7	24
11	6	28
9	5	32
7	4	36
5	3	40
3	2	44
1	1	48

$m_{1} (y)$	$m_{2} (y)$	$m_{2} (y) λ_{2} - m_{1} (y) λ_{1}$
2	0	$- 46$
4	1	$- 45$
6	2	$- 44$
8	3	$- 43$
10	4	$- 42$
12	5	$- 41$
14	6	$- 40$
16	7	$- 39$
18	8	$- 38$
20	9	$- 37$
22	10	$- 36$
24	11	$- 35$
26	12	$- 34$
28	13	$- 33$
30	14	$- 32$
32	15	$- 31$
1	0	$- 23$
3	1	$- 22$
5	2	$- 21$
7	3	$- 20$
9	4	$- 19$
11	5	$- 18$
13	6	$- 17$
15	7	$- 16$
17	8	$- 15$
19	9	$- 14$
21	10	$- 13$
23	11	$- 12$
25	12	$- 11$
27	13	$- 10$
29	14	$- 9$
31	15	$- 8$
33	16	$- 7$
0	0	0
2	1	1
4	2	2
6	3	3
8	4	4
10	5	5
12	6	6
14	7	7
16	8	8
18	9	9
20	10	10
22	11	11
24	12	12
26	13	13
28	14	14
30	15	15
32	16	16

$m_{1} (y)$	$m_{2} (y)$	$m_{2} (y) λ_{2} - m_{1} (y) λ_{1}$
13	6	$- 76$
11	5	$- 72$
9	4	$- 68$
7	3	$- 64$
5	2	$- 60$
3	1	$- 56$
1	0	$- 52$
14	7	$- 28$
12	6	$- 24$
10	5	$- 20$
8	4	$- 16$
6	3	$- 12$
4	2	$- 8$
2	1	$- 4$
0	0	0
13	7	24
11	6	28
9	5	32
7	4	36
5	3	40
3	2	44
1	1	48

Abstract

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Tables (2)

Equations (25)

Applied Optics