https://doi.org/10.1140/epjd/e2005-00210-x
The accuracy of Kirchhoff's approximation in describing the far field speckles produced by random self-affine fractal surfaces
1
Department of Physics, Shandong Normal University, Jinan, Shandong
250014, P.R. China
2
Optical Physics Laboratory, Institute of Physics and Center for
Condensed Matter Physics, Chinese Academy of Sciences, Beijing 100080, P.R. China
3
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of
Sciences, P.O. Box 800-211, Shanghai, P.R. China
Corresponding author: a chxqr@aphy.iphy.ac.cn
Received:
26
November
2004
Revised:
30
April
2005
Published online:
2
August
2005
Based on the rigorous formulation of integral equations for the propagations
of light waves at the medium interface, we carry out the numerical solutions
of the random light field scattered from self-affine fractal surface
samples. The light intensities produced by the same surface samples are also
calculated in Kirchhoff's approximation, and their comparisons with the
corresponding rigorous results show directly the degree of the accuracy of
the approximation. It is indicated that Kirchhoff's approximation is of good
accuracy for random surfaces with small roughness value w and large
roughness exponent 
. For random surfaces with larger w and
smaller , the approximation results in considerable errors, and
detailed calculations show that the inaccuracy comes from the simplification
that the transmitted light field is proportional to the incident field and
from the neglect of light field derivative at the interface.
PACS: 42.25.Fx – Diffraction and scattering / 42.30.Ms – Speckle and moire patterns
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
