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Based on the coherent superposition principle of direct-transmited light with the Gaussian speckle field, and also with the Kirchhoff approximation, the speckle in the deep Fresnel diffraction region is investigated. Expressions of speckle field in the deep Fresnel diffraction region, and the probability density of intensity, and contrast are obtained. In the deep Fresnel diffraction region of different scattering distance the variation of speckles is simulated with the height distribution data of random scattering surface measured by atomic force microscopy, and the curves of these two statistic functions are drawn. Combining the theory with the simulation, characteristics of these two statistic functions, the effect of the fraction of the direct transmit light intensity as well as their variations with the scattering distance are discussed.
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Keywords:
- deep Fresnel diffraction region /
- speckle /
- probability density /
- contrast
[1] Goodman J W 2000 Statistical Optics (New York: Wiley) p347
[2] Dainty J C 1984 Laser Speckle and Related Phenomena (Berlin: Spring-Verlag) p18, p29
[3] Dixon P K, Durian D J 2003 Phys. Rev. Lett. 90 184302
[4] Williams G, Pfeifer M, Vartanyants I, Robinson I 2003 Phys. Rev. Lett. 90 175501
[5] Pierce M S, Moore R G, Sorensen L B, Kevan S D, Hellwig O, Fullerton E E, Kortright J B 2003 Phys. Rev. Lett. 90 175502
[6] Zhang N Y Teng S Y, Song H S, Liu G Y, Cheng C F 2009 Chin. Phys. Lett. 26 034209
[7] Cerbino R 2007 Phys. Rev. A 75 053815
[8] Gatti A, Magatti D, Ferri F 2008 Phys. Rev. A 78 063806
[9] Teng S Y, Cheng C F, Liu M, Gui W L, Xu Z Z 2005 Chin. Phys. 14 1990
[10] Brogilio D, Vailati A, Giglio M 2002 Appl. Phys. Lett. 81 4109
[11] Cheng C F 2004 Europhys. Lett. 65 73
[12] Ogilvy J A 1991 Theory of wave scattering from random rough surfaces (California: Adam Hilger) p117
[13] Song H S, Liu M, Liu G Y, Xu Z W, Teng S Y, Cheng C F 2010 Chin. Phys. B 19 124202
[14] Goodman J W 2006 Speckle Phenomena in Optics (Greenwood: Roberts and Company) p31
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[1] Goodman J W 2000 Statistical Optics (New York: Wiley) p347
[2] Dainty J C 1984 Laser Speckle and Related Phenomena (Berlin: Spring-Verlag) p18, p29
[3] Dixon P K, Durian D J 2003 Phys. Rev. Lett. 90 184302
[4] Williams G, Pfeifer M, Vartanyants I, Robinson I 2003 Phys. Rev. Lett. 90 175501
[5] Pierce M S, Moore R G, Sorensen L B, Kevan S D, Hellwig O, Fullerton E E, Kortright J B 2003 Phys. Rev. Lett. 90 175502
[6] Zhang N Y Teng S Y, Song H S, Liu G Y, Cheng C F 2009 Chin. Phys. Lett. 26 034209
[7] Cerbino R 2007 Phys. Rev. A 75 053815
[8] Gatti A, Magatti D, Ferri F 2008 Phys. Rev. A 78 063806
[9] Teng S Y, Cheng C F, Liu M, Gui W L, Xu Z Z 2005 Chin. Phys. 14 1990
[10] Brogilio D, Vailati A, Giglio M 2002 Appl. Phys. Lett. 81 4109
[11] Cheng C F 2004 Europhys. Lett. 65 73
[12] Ogilvy J A 1991 Theory of wave scattering from random rough surfaces (California: Adam Hilger) p117
[13] Song H S, Liu M, Liu G Y, Xu Z W, Teng S Y, Cheng C F 2010 Chin. Phys. B 19 124202
[14] Goodman J W 2006 Speckle Phenomena in Optics (Greenwood: Roberts and Company) p31
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