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Journals >Chinese Optics Letters >Volume 19 >Issue 4 >Page 041404 > Article

Chinese Optics Letters
Vol. 19, Issue 4, 041404 (2021)

Speckle characteristics of simulated deep Fresnel region under shadowing effect

Zengshun Jiang, Xingqi An, Yuqin Zhang, Xuan Liu, Xifeng Qin, Yanjie Zhao, Huilin Wang, Guiyuan Liu, and Hongsheng Song^*

Author Affiliations

School of Science, Shandong Jianzhu University, Jinan 250101, China

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DOI: 10.3788/COL202119.041404 Cite this Article Set citation alerts

Zengshun Jiang, Xingqi An, Yuqin Zhang, Xuan Liu, Xifeng Qin, Yanjie Zhao, Huilin Wang, Guiyuan Liu, Hongsheng Song. Speckle characteristics of simulated deep Fresnel region under shadowing effect[J]. Chinese Optics Letters, 2021, 19(4): 041404 Copy Citation Text

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Abstract

After the three-dimensional self-affine fractal random surface simulation, we use the optical scattering theory to calculate the deep Fresnel region speckle (DFRS) under consideration of the more strict shadowing effect. The evolution of DFRS with the scattering distance and the intensity probability distribution are studied. It is found that the morphology of the scatterer has an antisymmetric relationship with the intensity distribution of DFRS, and the effect of micro-lenses on the scattering surface causes the intensity probability distribution of DFRS to deviate from the Gaussian speckle in the high light intensity area.

Keywords

deep Fresnel region shadowing effect simulation speckle

h_{c} (x_{0}, y_{0}) = h_{r} (x_{0}, y_{0}) + j h_{i} (x_{0}, y_{0}) = \sqrt{2} \iint_{- \infty}^{+ \infty} p (x_{01}, y_{01}) η (x_{01}, y_{01}) \exp [- j 2 π (x x_{0} + y_{01} y_{0})] d x_{01} d y_{01},

(1)

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p (x_{01}, y_{01}) = {[P (x_{01}, y_{01})]}^{1 / 2},

(2)

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P (x_{01}, y_{01}) = \iint_{- \infty}^{+ \infty} ω^{2} \exp {- {[(x_{0} + y_{0}) / ξ]}^{2 α}} \exp [j 2 π (x_{01} x_{0} + y_{01} y_{0})] d x_{0} d y_{0},

(3)

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U (x, y) = \frac{1}{4 π} \iint [G \frac{\partial U_{0} (x_{0}, y_{0})}{\partial n} - U_{0} (x_{0}, y_{0}) \frac{\partial G}{\partial n}] d S_{0},

(4)

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U_{0} (x_{0}, y_{0}) = \exp [j k (m - 1) h (x_{0}, y_{0})],

(5)

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G = \frac{\exp (j k r)}{r},

(6)

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r = {{(x - x_{0})}^{2} + {(y - y_{0})}^{2} + [z' - h {(x_{0}, y_{0})}^{2}]}^{1 / 2},

(7)

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\frac{\partial}{\partial n} = (n \times \nabla) = \frac{1}{γ} [- \frac{\partial h (x_{0}, y_{0})}{\partial x_{0}} \frac{\partial}{\partial x_{0}} - \frac{\partial h (x_{0}, y_{0})}{\partial y_{0}} \frac{\partial}{\partial y_{0}} + \frac{\partial}{\partial z}],

(8)

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γ = {1 + {[\frac{\partial h (x_{0}, y_{0})}{\partial x_{0}}]}^{2} + {[\frac{\partial h (x_{0}, y_{0})}{\partial y_{0}}]}^{2}}^{1 / 2},

(9)

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U (x, y) = \frac{1}{4 π} \iint d S_{0} [G \frac{\partial U_{0} (x_{0}, y_{0})}{\partial n} - U_{0} (x_{0}, y_{0}) \frac{\partial G}{\partial n}] = \frac{1}{4 π} \iint d S_{0} \exp {j k [(m - 1) h (x_{0}, y_{0}) + r]} [\frac{j k (m - 1) γ}{r} - (j k - \frac{1}{r}) \frac{χ}{r^{2}}],

(10)

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χ = h (x_{0}, y_{0}) - z' - (x_{0} - x) \frac{\partial h (x_{0}, y_{0})}{\partial x_{0}} - (y_{0} - y) \frac{\partial h (x_{0}, y_{0})}{\partial y_{0}} .

(11)

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P_{I} (I) = \frac{1}{< I >} \exp (- \frac{I}{< I >}),

(12)

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P (I) = \exp (- \frac{I}{< I >}) .

(13)

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References (16)

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Zengshun Jiang, Xingqi An, Yuqin Zhang, Xuan Liu, Xifeng Qin, Yanjie Zhao, Huilin Wang, Guiyuan Liu, Hongsheng Song. Speckle characteristics of simulated deep Fresnel region under shadowing effect[J]. Chinese Optics Letters, 2021, 19(4): 041404

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