Abstract

Biospeckle is a technique whose purpose is to observe and study the underlying activity of some material. It has its roots in optical physics, and its first step is an image acquisition process that produces a video sequence of the reflection of a laser. The video content can be analyzed to have an interpretation of the activity of the observed material. The literature on this subject presents several different measures for analyzing the video sequence. Three of the most popular measures are the generalized difference (GD), the weighted generalized difference (WGD), and Fujii’s method. These measures have drawbacks such as high computation time or limited visual quality of the results. In this paper, we propose (i) an alternative O(n) algorithm for the computation of the GD, (ii) an alternative measure based on the GD, (iii) an alternative measure based on the WGD, and (iv) a generalized definition of the Fujii’s method with better visual quality. We discuss the similarities between the new measures and the existent ones, showing when they are applicable. We prove the gain in time computation. The proposed measures will help researchers to gain time during their research and to be able to develop faster tools based on biospeckle application.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
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    [CrossRef]

2011

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

2010

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

2009

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

2008

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

2006

2004

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

2003

2002

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

2000

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

1993

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

1987

1985

1976

1975

J. D. Briers, “Wavelength dependence of intensity fluctuations in laser speckle patterns from biological specimens,” Opt. Commun. 13, 324–326 (1975).
[CrossRef]

Alanís, E.

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Andermann, M.

Arizaga, R.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Bio-speckle assessment of bruising in fruits,” Opt. Lasers Eng. 40, 13–24 (2003).
[CrossRef]

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

Asakura, T.

Baldwin, G.

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Bio-speckle assessment of bruising in fruits,” Opt. Lasers Eng. 40, 13–24 (2003).
[CrossRef]

Boas, D.

Bolay, H.

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Braga, R. A.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Briers, J. D.

J. D. Briers, “Wavelength dependence of intensity fluctuations in laser speckle patterns from biological specimens,” Opt. Commun. 13, 324–326 (1975).
[CrossRef]

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice Hall, 1988).

Cap, N.

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Bio-speckle assessment of bruising in fruits,” Opt. Lasers Eng. 40, 13–24 (2003).
[CrossRef]

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

Cardoso, R. R.

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Costa, A. G.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Cybulska, J.

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

da Costa, F. M.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

da Silva, W. S.

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Dale, A.

Devor, A.

Dunn, A.

Federico, A.

Frankevych, L.

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Freitas, P. L. S.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Fujii, H.

Galizzi, G. E.

Gonzalez, J. F.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Goodman, J. W.

J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66, 1145 (1976).
[CrossRef]

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

J. W. Goodman, Laser Speckle and Related Phenomena, 2nd ed. (Springer Verlag, 1984).

Ikawa, H.

Jakobsson, A.

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

Kaufmann, G. H.

Konstankiewicz, K.

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Limia, M. F.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

Lucía, I. P.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Menezes, F. S.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Moskowicz, M.

Murialdo, S. E.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Nilsson, G.

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

Nobre, C. M. B.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Nohira, K.

Núñez, A. M.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

Ohura, T.

Pajuelo, M.

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Bio-speckle assessment of bruising in fruits,” Opt. Lasers Eng. 40, 13–24 (2003).
[CrossRef]

Rabal, H.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Bio-speckle assessment of bruising in fruits,” Opt. Lasers Eng. 40, 13–24 (2003).
[CrossRef]

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Rabal, H. J.

H. J. Rabal, Dynamic Laser Speckle and Applications (CRC Press, 2008), pp. 115–136.

Rabelo, G. F.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Ranachowski, Z.

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Romero, G.

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Sáfadi, T.

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

Saúde, A. V.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

Sendra, G. H.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Shintomi, Y.

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Trivi, M.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

H. Rabal, N. Cap, M. Trivi, R. Arizaga, A. Federico, G. E. Galizzi, and G. H. Kaufmann, “Speckle activity images based on the spatial variance of the phase,” Appl. Opt. 45, 8733–8738 (2006).
[CrossRef]

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Bio-speckle assessment of bruising in fruits,” Opt. Lasers Eng. 40, 13–24 (2003).
[CrossRef]

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

Wårdell, K.

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

Yamamoto, Y.

Zdunek, A.

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Acta Agrophysica

A. Zdunek, L. Frankevych, K. Konstankiewicz, and Z. Ranachowski, “Comparison of puncture test, acoustic emission and spatial-temporal speckle correlation technique as methods for apple quality evaluation,” Acta Agrophysica 11, 303–315 (2008).

Appl. Opt.

IEEE Trans. Biomed. Eng.

K. Wårdell, A. Jakobsson, and G. Nilsson, “Laser Doppler perfusion imaging by dynamic light scattering,” IEEE Trans. Biomed. Eng. 40, 309–316 (1993).
[CrossRef]

IEEE Trans. Image Process.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Trans. Image Process. 13, 600–612 (2004).
[CrossRef]

J. Biomed. Opt.

S. E. Murialdo, G. H. Sendra, I. P. Lucía, R. Arizaga, J. F. Gonzalez, H. Rabal, and M. Trivi, “Analysis of bacterial chemotactic response using dynamic laser speckle,” J. Biomed. Opt. 14, 064015 (2009).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

J. D. Briers, “Wavelength dependence of intensity fluctuations in laser speckle patterns from biological specimens,” Opt. Commun. 13, 324–326 (1975).
[CrossRef]

C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Sáfadi, “Biospeckle laser spectral analysis under inertia moment, entropy and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
[CrossRef]

R. A. Braga, C. M. B. Nobre, A. G. Costa, T. Sáfadi, and F. M. da Costa, “Evaluation of activity through dynamic laser speckle using the absolute value of the differences,” Opt. Commun. 284, 646–650 (2011).
[CrossRef]

Opt. Eng.

R. Arizaga, N. Cap, H. Rabal, and M. Trivi, “Display of the local activity using dynamical speckle patterns,” Opt. Eng. 41, 287–294 (2002).
[CrossRef]

G. Romero, E. Alanís, and H. Rabal, “Statistics of the dynamic speckle produced by a rotating diffuser and its application to the assessment of paint drying,” Opt. Eng. 39, 1652–1658 (2000).
[CrossRef]

Opt. Lasers Eng.

M. Pajuelo, G. Baldwin, H. Rabal, N. Cap, R. Arizaga, and M. Trivi, “Bio-speckle assessment of bruising in fruits,” Opt. Lasers Eng. 40, 13–24 (2003).
[CrossRef]

Opt. Lett.

Sensors

A. Zdunek and J. Cybulska, “Relation of biospeckle activity with quality attributes of apples,” Sensors 11, 6317–6327 (2011).
[CrossRef]

Signal Process.

A. M. Núñez, M. F. Limia, M. Trivi, H. Rabal, and R. Arizaga, “Characterization of a paint drying process through granulometric analysis of speckle dynamic patterns,” Signal Process. 90, 1623–1630 (2010).
[CrossRef]

Other

H. J. Rabal, Dynamic Laser Speckle and Applications (CRC Press, 2008), pp. 115–136.

A. V. Saúde, F. S. Menezes, P. L. S. Freitas, G. F. Rabelo, and R. A. Braga, “On generalized differences for biospeckle image analysis,” in Conference on Graphics, Patterns and Images (SIBGRAPI), 2010 23rd SIBGRAPI (2010), pp. 209–215.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 2nd ed. (Prentice Hall, 2002).

E. O. Brigham, The Fast Fourier Transform and Its Applications (Prentice Hall, 1988).

J. W. Goodman, Laser Speckle and Related Phenomena, 2nd ed. (Springer Verlag, 1984).

H. J. Rabal and R. A. Braga, eds., Dynamic Laser Speckle and Applications (CRC Press, 2008).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

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