A Gaussian transition of an optical speckle field studied by the minimal spanning tree method

O. Vasseur; I. BergoÃ«nd; X. Orlik

doi:10.2971/jeos.2010.10052

Journal of the European Optical Society - Rapid publications, Vol 5 (2010)

A Gaussian transition of an optical speckle field studied by the minimal spanning tree method

O. Vasseur, I. BergoÃ«nd, X. Orlik

Abstract

We propose to study the Gaussian transition of an optical speckle field using the Minimal Spanning Tree method. We perform an analysis of the spatial intensity distribution and show that the maxima of intensity evolve from a cluster distribution in the strongly non Gaussian regime, to a gradient distribution around the transition and then approach the random distribution area when we tend to the Gaussian regime. In the generated minimal spanning trees, we observe that the standard deviation of the edges length exhibits a maximum around the Gaussian transition when about 4 correlation cells of the surface roughness are illuminated.

Full Text: PDF

Citation Details

Cite this article

References

J. W. Goodman, Speckle phenomena in optics, theory and applications (Roberts and Company, Colorado, 2006).

H. Fujii, "Contrast variation of non-Gaussian speckle" Opt. Act. 27, 409-418 (1980).

M. Deka, S. P. Almeida, and H. Fujii, "Root-mean-square difference between the intensities of non-Gaussian speckle at two different wavelengths" J. Opt. Soc. Am. 71, 155-163 (1981).

I. Bergoënd, X. Orlik, and E. Lacot, "Study of a circular Gaussian transition in an optical speckle field" J. Europ. Opt. Soc. Rap. Public. 3, 08028 (2008).

H. Kadano, T. Asakura, and N. Takai, "Roughness and correlation length determination of rough-surface objects using speckle contrast" Appl. Phys. B 44, 167-173 (1987).

H. Kadano, T. Asakura, and N. Takai, "Roughness and correlation length measurements of rough-surface objects using the speckle contrast in the diffraction field" Optik 80, 115-120 (1988).

C. Cheng, C. Liu, N. Zhang, T. Jia, R. Li, and Z. Xu, "Absolute measurement of roughness and lateral-correlation length of random surfaces by use of the simplified model of image-speckle contrast" Appl. Opt. 41, 4148 (2002).

C. Zhan, "Graph-theoretical methods for detecting and describing gestalt clusters" IEEE T. Comput. C-20, 68-86 (1971).

R. Grella, "Fresnel propagation and diffraction and paraxial wave equation" J. Opt. 13, 367-374 (1982).

A. K. Fung, and M. F. Chen, "Numerical simulation of scattering from simple and composite random surfaces" J. Opt. Soc. Am. A 2, 2274-2284 (1985).

J. Beardwood, J. Halton, and J. Hammersley, "The shortest path through many points" P. Camb. Philos. Soc. 55, 299-327 (1959).

R. Hoffman, and A. Jain, "A test of randomness based on the minimal spanning tree" Pattern Recogn. Lett. 1, 175-180 (1983).

C. Dussert, G. Rasigni, M. Rasigni, and J. Palmari, "Minimal spanning tree: A new approach for studying order and disorder" Phys. Rev. B 34, 3528-3531 (1986).

F. Wallet, and C. Dussert, "Comparison of spatial point patterns and processes characterization methods" Europhys. Lett. 42, 493- 498 (1998).