Local denoising of digital speckle pattern interferometry fringes by multiplicative correlation and weighted smoothing splines

Alejandro Federico; Guillermo H. Kaufmann

doi:10.1364/AO.44.002728

Applied Optics
Vol. 44,
Issue 14,
pp. 2728-2735
(2005)
•https://doi.org/10.1364/AO.44.002728

Local denoising of digital speckle pattern interferometry fringes by multiplicative correlation and weighted smoothing splines

Alejandro Federico and Guillermo H. Kaufmann

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Alejandro Federico and Guillermo H. Kaufmann, "Local denoising of digital speckle pattern interferometry fringes by multiplicative correlation and weighted smoothing splines," Appl. Opt. 44, 2728-2735 (2005)

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Abstract

We evaluate the use of smoothing splines with a weighted roughness measure for local denoising of the correlation fringes produced in digital speckle pattern interferometry. In particular, we also evaluate the performance of the multiplicative correlation operation between two speckle patterns that is proposed as an alternative procedure to generate the correlation fringes. It is shown that the application of a normalization algorithm to the smoothed correlation fringes reduces the excessive bias generated in the previous filtering stage. The evaluation is carried out by use of computer-simulated fringes that are generated for different average speckle sizes and intensities of the reference beam, including decorrelation effects. A comparison with filtering methods based on the continuous wavelet transform is also presented. Finally, the performance of the smoothing method in processing experimental data is illustrated.

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Correlation Operation	α	Q

		Without Decorrelation		With Decorrelation

		1 Pixel	2 Pixels	1 Pixel	2 Pixels
Multiplicative correlation (−I_i^HI_f^H)	1	6.30 × 10⁻²	7.49 × 10⁻⁴	1.27 × 10⁻²	1.29 × 10⁻⁴
	2	10.56 × 10⁻²	0.52 × 10⁻²	4.19 × 10⁻²	3.96 × 10⁻⁴
	3	10.69 × 10⁻²	1.53 × 10⁻²	6.45 × 10⁻²	1.74 × 10⁻⁴
	4	11.58 × 10⁻²	3.67 × 10⁻²	7.02 × 10⁻²	0.26 × 10⁻²
Subtraction correlation [(I_i − I_f)²]	1	3.03 × 10⁻²	6.52 × 10⁻⁴	4.62 × 10⁻⁵	−2.46 × 10⁻⁴
	2	4.58 × 10⁻²	0.32 × 10⁻²	0.11 × 10⁻²	1.35 × 10⁻⁷
	3	4.10 × 10⁻²	0.75 × 10⁻²	0.27 × 10⁻²	1.40 × 10⁻⁴
	4	4.43 × 10⁻²	1.34 × 10⁻²	0.43 × 10⁻²	3.10 × 10⁻⁴
Addition correlation [−(I_i + I_f)²]	1	1.75 × 10⁻²	−0.12 × 10⁻²	0.27 × 10⁻²	1.15 × 10⁻⁴
	2	2.46 × 10⁻²	−3.00 × 10⁻⁴	0.80 × 10⁻²	−4.57 × 10⁻⁵
	3	1.99 × 10⁻²	0.25 × 10⁻²	1.00 × 10⁻²	−9.30 × 10⁻⁵
	4	1.66 × 10⁻²	0.78 × 10⁻²	1.01 × 10⁻²	2.04 × 10⁻⁴

Method	α	Q

		Without Decorrelation		With Decorrelation

		1 Pixel	2 Pixels	1 Pixel	2 Pixels
Smoothing spline	1	64.22 ×10⁻²	1.38 × 10⁻²	40.39 × 10⁻²	–2.51 × 10⁻²
	2	79.75 × 10⁻²	7.98 × 10⁻²	68.09 × 10⁻²	–0.87 × 10⁻²
	3	79.77 × 10⁻²	21.43 × 10⁻²	71.67 × 10⁻²	2.97 × 10⁻²
	4	79.60 × 10⁻²	45.88 × 10⁻²	72.90 × 10⁻²	6.62 × 10⁻²
Wavelet shrinkage	1	51.62 × 10⁻²	0.60 × 10⁻²	24.50 × 10⁻²	–0.49 × 10⁻²
	2	67.34 × 10⁻²	3.77 × 10⁻²	49.21 × 10⁻²	–0.33 × 10⁻²
	3	68.39 × 10⁻²	12.63 × 10⁻²	55.36 × 10⁻²	0.31 × 10⁻²
	4	68.71 × 10⁻²	27.30 × 10⁻²	57.42 × 10⁻²	2.87 ×10⁻²

Correlation Operation	α	Q

		Without Decorrelation		With Decorrelation

		1 Pixel	2 Pixels	1 Pixel	2 Pixels
Multiplicative correlation (−I_i^HI_f^H)	1	6.30 × 10⁻²	7.49 × 10⁻⁴	1.27 × 10⁻²	1.29 × 10⁻⁴
	2	10.56 × 10⁻²	0.52 × 10⁻²	4.19 × 10⁻²	3.96 × 10⁻⁴
	3	10.69 × 10⁻²	1.53 × 10⁻²	6.45 × 10⁻²	1.74 × 10⁻⁴
	4	11.58 × 10⁻²	3.67 × 10⁻²	7.02 × 10⁻²	0.26 × 10⁻²
Subtraction correlation [(I_i − I_f)²]	1	3.03 × 10⁻²	6.52 × 10⁻⁴	4.62 × 10⁻⁵	−2.46 × 10⁻⁴
	2	4.58 × 10⁻²	0.32 × 10⁻²	0.11 × 10⁻²	1.35 × 10⁻⁷
	3	4.10 × 10⁻²	0.75 × 10⁻²	0.27 × 10⁻²	1.40 × 10⁻⁴
	4	4.43 × 10⁻²	1.34 × 10⁻²	0.43 × 10⁻²	3.10 × 10⁻⁴
Addition correlation [−(I_i + I_f)²]	1	1.75 × 10⁻²	−0.12 × 10⁻²	0.27 × 10⁻²	1.15 × 10⁻⁴
	2	2.46 × 10⁻²	−3.00 × 10⁻⁴	0.80 × 10⁻²	−4.57 × 10⁻⁵
	3	1.99 × 10⁻²	0.25 × 10⁻²	1.00 × 10⁻²	−9.30 × 10⁻⁵
	4	1.66 × 10⁻²	0.78 × 10⁻²	1.01 × 10⁻²	2.04 × 10⁻⁴

Method	α	Q

		Without Decorrelation		With Decorrelation

		1 Pixel	2 Pixels	1 Pixel	2 Pixels
Smoothing spline	1	64.22 ×10⁻²	1.38 × 10⁻²	40.39 × 10⁻²	–2.51 × 10⁻²
	2	79.75 × 10⁻²	7.98 × 10⁻²	68.09 × 10⁻²	–0.87 × 10⁻²
	3	79.77 × 10⁻²	21.43 × 10⁻²	71.67 × 10⁻²	2.97 × 10⁻²
	4	79.60 × 10⁻²	45.88 × 10⁻²	72.90 × 10⁻²	6.62 × 10⁻²
Wavelet shrinkage	1	51.62 × 10⁻²	0.60 × 10⁻²	24.50 × 10⁻²	–0.49 × 10⁻²
	2	67.34 × 10⁻²	3.77 × 10⁻²	49.21 × 10⁻²	–0.33 × 10⁻²
	3	68.39 × 10⁻²	12.63 × 10⁻²	55.36 × 10⁻²	0.31 × 10⁻²
	4	68.71 × 10⁻²	27.30 × 10⁻²	57.42 × 10⁻²	2.87 ×10⁻²

Abstract

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Tables (2)

Equations (15)

Applied Optics