Abstract

The question is examined as to whether the spectrum of the far field produced on scattering of a polychromatic plane wave on a spatially random object can be the same in every direction of scattering. It is shown that within the accuracy of the first Born approximation a sufficiency condition for this to be so is that the two-point correlation function of the dielectric susceptibility of the scatterer obey a certain scaling law. It is further shown that if, in addition, the isotropic far-zone spectrum is the same as the spectrum of the incident field, the second moment of the dielectric susceptibility of the scatterer must have the form of a 1/f noise, well known in the theory of fractals.

© 1997 Optical Society of America

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