Numerical methods of generating rough edges, surfaces, and volumes for subsequent
simulations are commonly employed, but result in data with a variance that is
downward biased from the desired value. Thus, it is highly desirable to quantify
and to minimize this bias. Here, the degree of bias is determined through
analytical derivations and numerical simulations as a function of the
correlation length and the roughness exponent of several model power spectral
density functions. The bias can be minimized by proper choice of grid size for a
fixed number of data points, and this optimum grid size scales as the
correlation length. The common approach of using a fixed grid size for such
simulations leads to varying amounts of bias, which can easily be confounded
with the physical effects being investigated.
© 2013 Optical Society of America
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