Eugene L. Church

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.

Optimal estimation of finish parameters

This paper discusses basic issues involved in the estimation of surface spectra from laboratory measurements, the development of physically-based spectral models, and the estimation of finish parameters and their associated errors.

Long Trace Profile Measurements On Cylindrical Aspheres

A new long-trace optical profiling instrument is now in operation at Brookhaven National Laboratory measuring surface figure and macro-roughness on large optical components, principally long cylindrical mirrors for use in synchrotron radiation beam lines. The non-contact measurement technique is based upon a pencil-beam interferometer system. The optical head is mounted on a linear air bearing slide and has a free travel range of nearly one meter. We are able to sample surface spatial periods between 1 mm (the laser beam diameter) and 1 m. The input slope data is converted to surface height by a Fourier filtering technique which distributes the random noise error contributions evenly over the entire trace length. A number of optical components have been measured with the instrument. Results are presented for fused silica cylinders 900 mm and 600 mm in length and for a fused silica toroid and several electroless nickel-plated paraboloids.

Comments On The Correlation Length

Surface finish has vertical and transverse attributes. In optics the first is characterized by the root-mean-square roughness, and it is natural to seek an analogous length parameter, or correlation length, to characterize its transverse properties. This paper evaluates various candidates for this purpose by examining their robustness to the finite-bandwidth effects inherent in all real measurement processes. The critical consideration is the magnitude of the correlation length with respect to the range of surface wavelengths in-cluded in the measurement: When the length parameters of the surface fall outside the measurement bandwidth it is possible to get totally spurious values for the measured parameters, and when they fall inside the band-width, the measured and true values can still differ by significant factors. This sensitivity of the correlation function to bandwidth effects arises from the fact that the measurement process modifies it by convolution; in contrast to the finish power spectrum, where the modifications involve simple multiplication. The present results argue against the use of length parameters derived from the measured correlation function as precise measures of the transverse character of surface finish, although they may still be useful for compar-ative and diagnostic purposes. The most precise characterization of the combined vertical and transverse properties of surface finish are given in terms of its power spectral density.

Role Of Surface Topography In X-Ray Scattering

This paper discusses the relationship between x-ray mirror scattering and surface topography using vector electromagnetic scattering theory. The results relate the angular distribution of the scattered intensity to various surface-finish parameters which can, in principle, be determined independently; for example, by x-ray scattering in other geometries, visible-light scattering, or stylus measurements. The key role of spatial band-width limits in such parameters is emphasized. General results are described and illustrated by a discussion of the scattering from isotropically rough surfaces, measured in both a point-detector and in a line-detector geometry. Recent experimental results are then interpreted in terms of the surface-tension model of surface roughness, which predicts a hyperbolic scattering in the line-detector geometry. The present results are offered as a subject for further experimental investigation, a mechanism for predicting the scattering from a given surface, and as a rationale for specifying surface finish in terms of system performance.

Surface Topography Measurements Over The 1 Meter To 10 Micrometer Spatial Period Bandwidth

A recently-developed long-trace surface profiling instrument (LTP) is now in operation in our laboratory measuring surface profiles on grazing incidence aspheres and also conventional optical surfaces. The LTP characterizes surface height profiles in a non-contact manner over spatial periods ranging from 1 meter (the maximum scan length) to 2 mm (the Nyquist period for 1 mm sampling period) and complements the range of our WYKO NCP-1000 2.5X surface roughness profiler (5 mm to 9.8 pm). Using these two instruments, we can fully characterize both figure and finish of an optical surface in the same way that we normally characterize surface finish, e.g., by means of the power spectral density function in the spatial frequency domain. A great deal of information about the distribution of figure errors over various spatial frequency ranges is available from this data, which is useful for process control and predicting performance at the desired wavelength and incidence angle. In addition, the LTP is able to measure the absolute radius of curvature on long-radius optics with high precision and accuracy. Angular errors in the optical head are measured in real time by an electronic autocollimator as the head traverses the linear air bearing slide. Measurements of kilometer radius optics can be made very quickly and the data analyzed in a format that is very easy to understand.

Figure and finish of grazing-incidence mirrors☆

Abstract Great improvement has been made in the past several years in the quality of optical components used in synchrotron-radiation (SR) beam lines. Most of this progress has been the result of vastly improved metrology techniques and instrumentation permitting rapid and accurate measurement of the surface finish and figure on grazing-incidence optics. A significant theoretical effort has linked the actual performance of components used at X-ray wavelengths to their topological properties as measured by surface-profiling instruments. Next-generation advanced light sources will require optical components and systems to have sub-arcsec surface figure tolerances. We will explore the consequences of these requirements in terms of manufacturing tolerances to see if the present manufacturing state-of-the-art is capable of producing the required surfaces. It is now possible to routinely measure figure and finish on meter-long optical surfaces in our laboratory with a long trace profiler of our own design and with a commercial microinterferometer profiler. Our instrumentation allows us to analyze surface profile data in terms of the power spectral density function over the range of spatial periods that are of relevance to X-ray mirror performance: 1 m to 5 μm. We have been able to recognize several classes of problems in the manufacture of grazing-incidence optics from the results of our measurements. In some cases we have been able to provide feedback to the manufacturer, who has then been able to modify and improve his process. Results from our analyses of mirror figure and finish measurements will be presented and their impact on the design of high-resolution soft-X ray SR systems will be discussed.

The Precision Measurement And Characterization Of Surface Finish

This paper presents a rationale for the precision measurement and characterization of surface finish using Fourier techniques. It offers a precise definition of figure and finish errors in the frequency domain and discusses particular finish statistics of importance for optical surfaces: the finish power spectral density and the mean-square finish error. Problems involved in estimating these quantities from practical measurements are discussed and illustrated. The need for an expanded data base of spectral shapes is emphasized.

Subsurface And Volume Scattering From Smooth Surfaces

This paper discusses expressions for the BRDF of a weakly inhomogeneous half space and contrasts them with the analogous results for topographic scattering.