Spectral and parameter estimation problems arising in the metrology of high performance mirror surfaces

The accurate characterization of mirror surfaces requires the estimation of two-dimensional distribution functions and power spectra from trend-contaminated profile measurements. The rationale behind this, and our measurement and processing procedures, are described. The distinction between profile and area spectra is indicated, and since measurements often suggest inverse-power-law forms, a discussion of classical and fractal models of processes leading to these forms is included.