Abstract

This paper reports the development of a simple dynamic microscopic model to describe the main features of the phenomenon known as dynamic speckle, or biospeckle. Biospeckle is an interference pattern formed when a biological surface is illuminated with coherent light. The dynamic characteristics of biospeckle have been investigated as possible tools for assessing the quality of biological products. Our model, despite its simplicity, was able to reproduce qualitatively the main features of biospeckle. We were able to correlate variations in a microscopic parameter associated with movement of the particles comprising the organic surface with changes in a macroscopic parameter that measures the change rate of a dynamic interference pattern. We showed that this correlation occurs only within a limited range of parameter microscope values. We also showed how our model was able to describe nonuniform surfaces composed of more than one type of particles.

© 2013 Optical Society of America

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References

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  1. E. Hecht, Optics (Addison-Wesley, 2002).
  2. R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
    [CrossRef]
  3. J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
    [CrossRef]
  4. R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
    [CrossRef]
  5. R. Arizaga, M. Trivi, and H. Rabal, “Speckle time evolution characterization by the co-occurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
    [CrossRef]
  6. A. Oulamara, G. Tribillon, and J. Duvernoy, “Biological-activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
    [CrossRef]
  7. Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
    [CrossRef]
  8. J. M. Silva and J. A. S. Lima, “Four approaches to the Brownian motion,” Rev. Bras. Ens. Fís. 29, 25–35 (2007).
  9. C. M. B. Nobre, R. A. Braga, A. G. Costa, R. R. Cardoso, W. S. da Silva, and T. Safadi, “Biospeckle laser spectral analysis under inertia moment, entropy, and cross-spectrum methods,” Opt. Commun. 282, 2236–2242 (2009).
    [CrossRef]

2009

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

2007

J. M. Silva and J. A. S. Lima, “Four approaches to the Brownian motion,” Rev. Bras. Ens. Fís. 29, 25–35 (2007).

2005

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

2003

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

2001

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
[CrossRef]

1999

R. Arizaga, M. Trivi, and H. Rabal, “Speckle time evolution characterization by the co-occurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

1997

Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
[CrossRef]

1989

A. Oulamara, G. Tribillon, and J. Duvernoy, “Biological-activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Amalvy, J. I.

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
[CrossRef]

Arizaga, R.

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
[CrossRef]

R. Arizaga, M. Trivi, and H. Rabal, “Speckle time evolution characterization by the co-occurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

Borem, F. M.

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

Braga, R. A.

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

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

Cardoso, R. R.

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

Costa, A. G.

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

da Silva, W. S.

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

Dal Fabbro, I. M.

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

Duvernoy, J.

A. Oulamara, G. Tribillon, and J. Duvernoy, “Biological-activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Granato, L. R.

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 2002).

Lasquibar, C. A.

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
[CrossRef]

Lima, J. A. S.

J. M. Silva and J. A. S. Lima, “Four approaches to the Brownian motion,” Rev. Bras. Ens. Fís. 29, 25–35 (2007).

Machado, J. C.

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

Nobre, C. M. B.

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

Oulamara, A.

A. Oulamara, G. Tribillon, and J. Duvernoy, “Biological-activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Rabal, H.

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
[CrossRef]

R. Arizaga, M. Trivi, and H. Rabal, “Speckle time evolution characterization by the co-occurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

Rabal, H. J.

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

Rabelo, G.

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

Safadi, T.

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

Santos, E. F.

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

Schmidt, R. J.

Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
[CrossRef]

Silva, J. M.

J. M. Silva and J. A. S. Lima, “Four approaches to the Brownian motion,” Rev. Bras. Ens. Fís. 29, 25–35 (2007).

Tribillon, G.

A. Oulamara, G. Tribillon, and J. Duvernoy, “Biological-activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Trivi, M.

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
[CrossRef]

R. Arizaga, M. Trivi, and H. Rabal, “Speckle time evolution characterization by the co-occurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

Wang, J. L.

Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
[CrossRef]

Williams, F. W.

Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
[CrossRef]

Wu, X. P.

Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
[CrossRef]

Zhao, Y.

Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
[CrossRef]

Biosystems Eng.

R. A. Braga, I. M. Dal Fabbro, F. M. Borem, G. Rabelo, R. Arizaga, H. J. Rabal, and M. Trivi, “Assessment of seed viability by laser speckle techniques,” Biosystems Eng. 86, 287–294 (2003).
[CrossRef]

R. A. Braga, G. Rabelo, L. R. Granato, E. F. Santos, J. C. Machado, R. Arizaga, H. J. Rabal, and M. Trivi, “Detection of fungi in beans by the laser biospeckle technique,” Biosystems Eng. 91, 465–469 (2005).
[CrossRef]

J. Mod. Opt.

A. Oulamara, G. Tribillon, and J. Duvernoy, “Biological-activity measurement on botanical specimen surfaces using a temporal decorrelation effect of laser speckle,” J. Mod. Opt. 36, 165–179 (1989).
[CrossRef]

Opt. Commun.

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

Opt. Laser Technol.

R. Arizaga, M. Trivi, and H. Rabal, “Speckle time evolution characterization by the co-occurrence matrix analysis,” Opt. Laser Technol. 31, 163–169 (1999).
[CrossRef]

Opt. Lasers Eng.

Y. Zhao, J. L. Wang, X. P. Wu, F. W. Williams, and R. J. Schmidt, “Point-wise and whole-field laser speckle intensity fluctuation measurements applied to botanical specimens,” Opt. Lasers Eng. 28, 443–456 (1997).
[CrossRef]

Prog. Org. Coat.

J. I. Amalvy, C. A. Lasquibar, R. Arizaga, H. Rabal, and M. Trivi, “Application of dynamic speckle interferometry to the drying of coatings,” Prog. Org. Coat. 42, 89–99 (2001).
[CrossRef]

Rev. Bras. Ens. Fís.

J. M. Silva and J. A. S. Lima, “Four approaches to the Brownian motion,” Rev. Bras. Ens. Fís. 29, 25–35 (2007).

Other

E. Hecht, Optics (Addison-Wesley, 2002).

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Figures (26)

Fig. 1.
Fig. 1.

Schematic representation of the various contributions of N point scatterers for the formation of an interference pattern at an arbitrary point A on the screen.

Fig. 2.
Fig. 2.

Half-maximal-width (HMW).

Fig. 3.
Fig. 3.

Time series intensity variation module ( δ I ) generated by N = 2000 point scatterers after P = 50 steps with λ ¯ = ( 50 / 12 ) ( 1 × 10 4 ) m for 50,000 units of time in a screen.

Fig. 4.
Fig. 4.

Autocorrelation of the time series of Fig. 3 for the first 600 and 15,000 units of time.

Fig. 5.
Fig. 5.

Histogram of the time series of intensity variances module δ I n .

Fig. 6.
Fig. 6.

HMW as a function of step size, and the values of HMW obtained from the distribution of the modules of the variations of intensity generated by N = 2000 scatterers, after P = 50 steps, for 50,000 units of time.

Fig. 7.
Fig. 7.

HMW as a function of step size, and the values of the HMW obtained from the distribution of the modules of variations in the intensity generated by N = 20 , 200, and 2000 scatterers after P = 50 steps for 50,000 units of time.

Fig. 8.
Fig. 8.

HMW depending on the position of the CCD (pixel), and the values of HMW obtained from the distribution of the modules of the variations of intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 2 × 10 7 ) m for 50,000 units of time.

Fig. 9.
Fig. 9.

HMW depending on the position of the CCD (pixel), and the values of HMW obtained from the distribution of the modules of the variations of intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 8 × 10 6 ) m for 50,000 units of time.

Fig. 10.
Fig. 10.

HMW depending on the position of the CCD (pixel), and the values of HMW obtained from the distribution of the modules of the variations of intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 1 × 10 4 ) m for 50,000 units of time.

Fig. 11.
Fig. 11.

HMW depending on the position of the CCD (pixel), and the values of HMW obtained from the distribution of the modules of the variations of intensity generated by N = 2000 scatterers, after P = 50 steps with size λ ¯ = { ( 50 / 12 ) ( 2 × 10 7 ) , ( 50 / 12 ) ( 8 × 10 6 ) , ( 50 / 12 ) ( 1 × 10 4 ) } m for 50,000 units of time.

Fig. 12.
Fig. 12.

Comparison of HMW and IM, with the values of the HMW obtained from the distribution of intensity variations produced by N = 2000 scatterers and IM values from the magnitudes of variations in the intensity generated by N = 2000 scatterers after P = 50 steps of size λ ¯ = 1 × 10 4 for 50,000 units of time.

Fig. 13.
Fig. 13.

Illustration of the configuration of positions of the scatterers with respect to the CCD.

Fig. 14.
Fig. 14.

HMW as a function of step size, with the values of HMW obtained from the distribution of magnitudes of variations in the intensity generated by N = 2000 scatterers, after P = 50 steps for 50,000 units of time. The scatterers were divided into two equal groups and placed in separate regions.

Fig. 15.
Fig. 15.

HMW as a function of step size, and the values of the HMW obtained from the distribution of magnitudes of variations in the intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps for 50,000 units of time. The scatterers were divided into two equal groups and placed in separate regions.

Fig. 16.
Fig. 16.

HMW as a function of the position on the CCD (pixel), with values obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 2 × 10 7 ) m for 50,000 units of time. The scatterers were divided into two homogeneous groups and placed in separate regions.

Fig. 17.
Fig. 17.

HMW as a function of the position on the CCD (pixel), with values obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 8 × 10 6 ) m for 50,000 units of time. The scatterers were divided into two homogeneous groups and placed in separate regions.

Fig. 18.
Fig. 18.

HMW as a function of the position on the CCD (pixel), with values obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 1 × 10 4 ) m for 50,000 units of time. The scatterers were divided into two homogeneous groups and placed in separate regions.

Fig. 19.
Fig. 19.

HMW as a function of the position on the CCD (pixel), with values obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 2000 scatterers, after P = 50 steps of sizes λ ¯ = { ( 50 / 12 ) ( 2 × 10 7 ) , ( 50 / 12 ) ( 8 × 10 6 ) , ( 50 / 12 ) ( 1 × 10 4 ) } m in 50,000 units of time. The scatterers were divided into two homogeneous groups and placed in separate regions.

Fig. 20.
Fig. 20.

HMW as a function of the position on the CCD (pixel). Values were obtained from the distribution of magnitudes of variations in the intensity generated by N = 2000 scatterers, after P = 50 steps, with reference to the center of the CCD. Curve 1, λ ¯ = ( 50 / 12 ) ( 2 × 10 6 ) m (left) and λ ¯ = ( 50 / 12 ) ( 3 × 10 5 ) m (right). Curve 2, λ ¯ = ( 50 / 12 ) ( 3 × 10 5 ) m (left) and λ ¯ = ( 50 / 12 ) ( 2 × 10 6 ) m (right). The scatterers were divided into two homogeneous groups and placed in separate regions.

Fig. 21.
Fig. 21.

HMW as a function of the position on the CCD (pixel), with values obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 2 × 10 6 ) m (right of the center of the CCD) and λ ¯ = ( 50 / 12 ) ( 3 × 10 5 ) m (left of the center of the CCD) for 50,000 units of time. The scatterers were divided into two homogeneous groups and placed in separate regions.

Fig. 22.
Fig. 22.

HMW as a function of the position on the CCD (pixel), with values obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 3 × 10 5 ) m (right of the center of the CCD) and λ ¯ = ( 50 / 12 ) ( 2 × 10 6 ) m (left of the center of the CCD) for 50,000 units of time. The scatterers were divided into two homogeneous groups and placed in separate regions.

Fig. 23.
Fig. 23.

HMW as a function of the position on the CCD (pixel), with values obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 2000 scatterers, after P = 50 steps of size λ ¯ = ( 50 / 12 ) ( 2 × 10 6 ) and λ ¯ = ( 50 / 12 ) ( 3 × 10 5 ) m for 50,000 units of time, and with the step sizes randomly assigned to each source. The scatterers were positioned randomly.

Fig. 24.
Fig. 24.

HMW as function of position on the CCD (pixel), the values has been obtained from the HMW distribution of magnitudes of variations in the intensity generated by N = 20 , 200, and 2000 scatterers, after P = 50 steps size λ ¯ = ( 50 / 12 ) ( 2 × 10 6 ) and λ ¯ = ( 50 / 12 ) ( 3 × 10 5 ) m for 50,000 units of time, and the step sizes randomly assigned to each source. The scatterers were positioned randomly.

Fig. 25.
Fig. 25.

HMW as a function of STS images of a sample coin covered with concealer. Each image of STS was calculated on a discrete time and sequence. Each image of STS collected 10,240 pieces of information related to the intensities of a pixel group with the same behavior. This information was derived from the union of pixels in the range of 240–260 that generated a series of data. In this time series the HMW value was calculated.

Fig. 26.
Fig. 26.

HMW images as a function of the STS parasites of sheep samples with different concentrations of parasites. Each image of STS was calculated on a discrete time and sequence. Each STS image collected 20,951 pieces of information of a group of pixels with the same behavior. This information was derived from the union of the pixels in the range from 230 to 270; by generating a series, the HMW values were calculated.

Equations (2)

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r⃗ s ( p τ ) = x s ( p τ ) ι ^ + y s ( p τ ) j ^ ,
x s ( p τ ) = x s ( ( p 1 ) τ ) + Γ , y s ( p τ ) = y s ( ( p 1 ) τ ) + Γ ,

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