Spatial Poincaré Plots as Descriptors of Speckle Pattern Second-Order Statistics

Anindya Majumdar
Department of Biomedical Engineering, Michigan Technological University, Houghton, USA

Sean J. Kirkpatrick (Login required)
Department of Biomedical Engineering, Michigan Technological University, Houghton, USA

Paper #3231 received 12 Jul 2017; revised manuscript received 19 Sep 2017; accepted for publication 19 Sep 2017; published online 30 Sep 2017.

DOI: 10.18287/JBPE17.03.030501


It is demonstrated herein that the use of spatial Poincaré plots provides an efficient means to describe short and long-range correlations in the spatial structure of the measured intensity distribution of scattered coherent fields. The intensity distribution over a row of pixels in single frames of speckle fields with varying speckle sizes was considered. Statistical descriptors from the spatial Poincaré plots for these intensity data with variable lags were used to estimate the short and long-term variations in the measured intensities, and from these descriptors, the minimum speckle size in the speckle patterns was estimated. This approach yielded similar results for speckle size estimates as the more standard method of calculating the power spectral density of the intensity pattern and simultaneously provided information on the relative contributions of short-term and long-term variations in the measured intensity to the spatial structure of the scattered fields.


coherence optics; statistical optics; speckle; Fourier optics; signal processing; speckle imaging

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1. J. C. Dainty (Ed.), Laser Speckle and Related Phenomena, 2nd edition, Springer Verlag (1984).

2. X. Zhao, and G. Zhao, “Surface roughness measurement using spatial-average analysis of objective speckle pattern in specular direction,” Optics and Lasers in Engineering 47(11), 1307-1316 (2009). Crossref

3. R. Jones, and C. Wykes, Holographic and Speckle Metrology, 2nd edition, Cambridge University Press (1989).

4. A. F. Fercher, and J. D. Briers, “Flow visualization by means of single-exposure speckle photography,” Optics Communications 37(5), 326-330 (1981). Crossref

5. Y. Aizu, and T. Asakura, “Coherent optical techniques for diagnostics of retinal blood flow,” Journal of Biomedical Optics 4(1), 61-75 (1999). Crossref

6. P. Li, S. Ni, L. Zhang, S. Zeng, and Q. Luo, “Imaging cerebral blood flow through the intact rat skull with temporal laser speckle imaging,” Optics Letters 31(12), 1824-1826 (2006). Crossref

7. J. C. Ramirez-San-Juan, R. Ramos-Garcia, I. Guizar-Iturbide, G. Martinez-Niconoff, and B. Choi, “Impact of velocity distribution assumptions on simplified laser speckle imaging equation,” Optics Express 16(5), 3197-3203 (2008). Crossref

8. K. Khaksari, and S. J. Kirkpatrick, “Laser speckle contrast imaging is sensitive to advective flux,” Journal of Biomedical Optics 21(7), 076001 (2016). Crossref

9. J. W. Goodman (Ed.), Speckle Phenomena in Optics: Theory and Applications, Roberts & Company, Englewood, CO (2007). ISBN 0-9747077-9-1.

10. S. J. Kirkpatrick, D. D. Duncan, and E. M. Wells-Gray, “Detrimental effects of speckle-pixel matching in laser speckle contrast imaging,” Optics Letters 33(24), 2886-2888 (2008). Crossref

11. K. Khaksari, and S. J. Kirkpatrick, “Combined effects of scattering and absorption on laser speckle contrast imaging,” Journal of Biomedical Optics 21(7), 076002 (2016). Crossref

12. M. Brennan, M. Palaniswami, and P. Kamen, “Distortion properties of the interval spectrum of IPFM generated heartbeats for heart rate variability analysis,” IEEE Transactions on Biomedical Engineering 48(11), 1251-1264 (2001). Crossref

13. D. D. Duncan, and S. J. Kirkpatrick, “The copula a tool for simulating speckle dynamics,” Journal of the Optical Society of America A 25(1), 231-237 (2008). Crossref

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