Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy

M. Sjödahl; L. R. Benckert

doi:10.1364/AO.32.002278

Applied Optics
Vol. 32,
Issue 13,
pp. 2278-2284
(1993)
•https://doi.org/10.1364/AO.32.002278

Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy

M. Sjödahl and L. R. Benckert

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M. Sjödahl and L. R. Benckert, "Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy," Appl. Opt. 32, 2278-2284 (1993)

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Abstract

Replacing photographic recording by electronic processing has some obvious advantages. An algorithm used for electronic speckle pattern photography is presented, and the reliability and accuracy is analyzed by using computer-generated speckle patterns. The algorithm is based on a two-dimensional discrete cross correlation between subimages from different images. Subpixel accuracy is obtained by a Fourier series expansion of the discrete correlation surface. The accuracy of the algorithm was found to vary in proportion to σ/n(1 − δ)², where σ is the speckle size, n is the subimage size, and δ is the amount of decorrelation, with negligible systematic errors. For typical values the uncertainty in the displacement is approximately 0.05 pixels. The uncertainty is found to increase with increased displacement gradients.

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Dataset	k_x	k_y	n	σ	I_max/I_t	δ
1	7.5	7.5	32	2.4	7.8	0
2	7.5	7.5	16	2.4	7.8	0
3	7.5	7.5	32	2.4	7.8	0.25
4	7.5	7.5	32	4.8	7.8	0
5	7.5	7.5	32	2.4	20	0
6	7.5	7.5	32	2.4	7.8	0.5
7	0.5	0.5	32	2.4	7.8	0
8	0.5	0.5	16	2.4	7.8	0
9	7.5	7.5	32	7.2	7.8	0
10	7.5	7.5	64	2.4	7.8	0
	ɛ_x

11	0.05	0	16	2.4	7.8	0
12	0.05	0	32	2.4	7.8	0

Dataset	Success Rate (%)	$\bar{k_{x}}$	$\bar{k_{y}}$		s		s_l	S_u
1	100	7.496	7.497		0.049		0.045	0.052
2	73	7.498	7.496		0.103		0.098	0.108
3	98	7.500	7.497		0.081		0.076	0.085
4	92	7.490	7.490		0.122		0.114	0.130
5	100	7.493	7.494		0.047		0.044	0.050
6	45	7.524	7.513		0.195		0.185	0.204
7	100	0.497	0.495		0.046		0.043	0.050
8	80	0.498	0.495		0.101		0.096	0.105
9	77	7.494	7.485		0.176		0.166	0.185
10	100	7.490	7.488		0.017		0.015	0.019
		$\bar{Δ k_{x}}$	s_x	s_lx	s_ux	$\bar{k_{y}}$	s_y	s_ly	s_uy

11	82	−0.002	0.154	0.146	0.160	0.001	0.071	0.068	0.074
12	100	−0.005	0.154	0.143	0.165	0.000	0.047	0.045	0.049

Dataset	k_x	k_y	n	σ	I_max/I_t	δ
1	7.5	7.5	32	2.4	7.8	0
2	7.5	7.5	16	2.4	7.8	0
3	7.5	7.5	32	2.4	7.8	0.25
4	7.5	7.5	32	4.8	7.8	0
5	7.5	7.5	32	2.4	20	0
6	7.5	7.5	32	2.4	7.8	0.5
7	0.5	0.5	32	2.4	7.8	0
8	0.5	0.5	16	2.4	7.8	0
9	7.5	7.5	32	7.2	7.8	0
10	7.5	7.5	64	2.4	7.8	0
	ɛ_x

11	0.05	0	16	2.4	7.8	0
12	0.05	0	32	2.4	7.8	0

Dataset	Success Rate (%)	$\bar{k_{x}}$	$\bar{k_{y}}$		s		s_l	S_u
1	100	7.496	7.497		0.049		0.045	0.052
2	73	7.498	7.496		0.103		0.098	0.108
3	98	7.500	7.497		0.081		0.076	0.085
4	92	7.490	7.490		0.122		0.114	0.130
5	100	7.493	7.494		0.047		0.044	0.050
6	45	7.524	7.513		0.195		0.185	0.204
7	100	0.497	0.495		0.046		0.043	0.050
8	80	0.498	0.495		0.101		0.096	0.105
9	77	7.494	7.485		0.176		0.166	0.185
10	100	7.490	7.488		0.017		0.015	0.019
		$\bar{Δ k_{x}}$	s_x	s_lx	s_ux	$\bar{k_{y}}$	s_y	s_ly	s_uy

11	82	−0.002	0.154	0.146	0.160	0.001	0.071	0.068	0.074
12	100	−0.005	0.154	0.143	0.165	0.000	0.047	0.045	0.049

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Applied Optics