Improvements in the accuracy and the repeatability of long trace profiler measurements.

Modifications of the long trace profiler at the Advanced Photon Source at Argonne National Laboratory have significantly improved its accuracy and repeatability for measuring the figure of large flat and long-radius mirrors. Use of a Dove prism in the reference beam path corrects phasing problems between mechanical errors and thermally induced system errors. A single reference correction now completely removes both of these error signals from the measured surface profile. The addition of a precision air conditioner keeps the temperature in the metrology enclosure constant to within +/-0.1 degrees C over a 24-h period and has significantly improved the stability and the repeatability of the measurements. Long-radius surface curvatures can now be measured absolutely with a high degree of confidence. These improved capabilities are illustrated with a series of measurements of a 500-mm-long mirror with a 5-km radius of curvature. The standard deviation in the average of ten slope profile scans is 0.3 microrad, and the corresponding standard deviation in the height error is 4.6 nm.

Specification of surface figure and finish in terms of system performance.

We describe methods of predicting the degradation of the performance of a simple imaging system in terms of the statistics of the shape errors of the focusing element and, conversely, of specifying those statistics in terms of requirements on image quality. Results are illustrated for normal-incidence, x-ray mirrors with figure errors plus conventional and/or fractal finish errors. It is emphasized that the imaging properties of a surface with fractal errors are well behaved even though fractal-power spectra diverge at low spatial frequencies.

Fractal surface finish.

Surface finish measurements are usually fitted to models of the finish correlation function which are parametrized in terms of root-mean-square roughnesses, delta, and correlation lengths, l. Highly finished optical surfaces, however, are frequently better described by fractal models, which involve inverse power-law spectra and are parametrized by spectral strengths, K(n), and spectral indices, n. Analyzing measurements of fractal surfaces in terms of sigma and l gives results which are not intrinsic surface parameters but which depend on the bandwidth parameters of the measurement process used. This paper derives expressions for these pseudoparameters and discusses the errors involved in using them for the characterization and specification of surface finish.

Residual surface roughness of diamond-turned optics.

The residual surface roughness of diamond-turned optics is expected to contain significant periodic components. The optical properties of such surfaces are explored as a special case of Rayleigh-Rice vector scattering theory applied to periodic roughness with vertical amplitudes much smaller than the wavelength of light. Expressions are given for the interpretation of differential-scatter, total-integrated-scatter, reflectometry, and ellipsometric measurements in the limit of a highly conducting. surface. In general, such measurements give varying degrees of information about the two-dimensional power spectral density of the surface roughness within the nominal range from the wavelength of light to the diameter of the probing beam spot. Such information may be useful for the practical characterization of mirror surfaces.