F. Varnier

Autocovariance functions for polished optical surfaces

Autocovariance functions (ACF’s) G(x) for polished optical surfaces of CaF2, MgF2, and LiF are deduced from surface profiles determined by using microdensitometer analysis of micrographs of surface-shadowed carbon replicas. The different estimators allowing the ACF computation from its standard definition are reviewed, and their values are compared. ACF’s are also computed by using the fast-Fourier-transform algorithm. Results of both computations are in good agreement. It is shown that initial portions of ACF’s have a reasonable Gaussian form. The rms roughness height δ and the autocovariance length σ are deduced for each surface. The ACF’s of the surface slopes Gs′(x) are also computed, and it is shown that results obtained are consistent with results deduced from ACF’s for surface profiles. In particular, the standard relation between the second derivative of G(x) and Gs′(x) is reasonably verified. Finally, the exponential ACF model is discussed, and it is shown that this model would not be suitable to describe the initial portions of the ACF’s for the polished optical surfaces that we have studied.

Study of surface roughness for thin films of CaF2 deposited on glass substrates

Abstract The dependence of the surface roughness of CaF 2 thin films on the film thickness d is determined by a technique using microdensitometer analysis of electron micrographs of surface replicas. The rms surface roughness δ and the autocovariance length σ have been found to depend linearly on d in the range 250 d

Spectral-density function of the surface roughness for polished optical surfaces

The spectral density functions g(k) of the surface roughness for polished optical surfaces of CaF2, MgF2, and LiF are computed from autocovariance functions, which in turn have been determined from surface profiles obtained by using a microdensitometer analysis of electron micrographs of shadowed surface replicas. The fast-Fourier-transform algorithm and a smoothing procedure have been used to determine the g(k) estimates. It is shown that g(k) is not a Gaussian function throughout, as is usually assumed. Spectral density functions gS′(k) of the surface slopes are also computed, and it is shown that results obtained are consistent with those deduced from g(k). Limitations of our method at low spatial frequency are discussed. An analytical model for g(k) is investigated that should be useful in performing theoretical calculations on scattering problems.

Study of the surface roughness for thin films of LiF and Ag/LiF

The results of a systematic study of the roughness of LiF deposits and of Ag upon these LiF underlayers are provided. The rms roughness σ and the autocovariance length σ of various LiF and Ag/LiF films are determined. The dependence of δ and σ on the film thickness is carefully investigated. It is shown that LiF is a poor underlayer compared with CaF 2 and that silver films reliably replicate the LiF surfaces.

Influence of some parameters on the surface profile restored from microdensitometer analysis of electron micrographs of surface replicas.

From the micrograph density of a shadowed carbon replica of a surface it is possible, by using a microdensitometer analysis, to rebuild line by line the profile of that surface. After summarizing the different stages necessary for such a reconstruction, we study the influence on the restored profiles of the various parameters that are encountered during the various steps of experiment and computation. It is shown that the most important parameters are the shadow-casting angle, microdensitometer scanning aperture, and filtering characteristics. Other parameters such as magnification micrograph, microdensitometer scanning speed, and microdensitometer noise play a minor role. The best way to choose and fit the appropriate value of the various parameters is discussed.

Height and slope distributions for surfaces of rough metallic deposits.

This paper deals with the accurate determination of height and slope distributions for surfaces of rough metallic deposits (magnesium, copper, silver, and gold). These distributions are computed using a microdensitometer analysis of electron micrographs of surface replicas. It is shown that most of the surfaces examined have reasonable Gaussian height and slope distributions. Apart from magnesium surfaces, the rms roughnesses determined from these distributions agree (within the accuracy range of their measurements) with rms roughnesses deduced from the autocovariance functions computed previously. Within the framework of scalar scattering theory, some emphasis is laid on the value of slopes to draw certain conclusions about the validity of the assumptions under which the scalar scattering theory is derived.

Microdensitometer analysis of electron micrographs of shadowed surface replicas: A powerful method in surface structure characterization

Abstract From the micrograph density of a shadowed carbon replica of a surface it is possible by using a microdensitometer analysis to rebuild line by line the profile of that surface. The different stages necessary for such a reconstruction are summarized. Various reconstructions connected with metallic, optical, dielectric and biological surfaces are presented. Those restored profiles are used to estimate the moments (particularly the second one named the autocovariance function) that summarize statistical information on the various characteristic lengths describing the surface.

Roughness spectrum for surfaces of silver deposits

Abstract The roughness spectrum g ( k ) (or spectral density function) for surfaces of silver deposits is deduced from surface profiles determined by using microdensitometer analysis of micrographs of surface shadowed carbon replicas. We used a process based on the computation of autocovariance function (ACF) via the fast Fourier transform (FFT) algorithm. Results are compared with those provided by attenuated total reflexion (ATR) method. It is shown that the g ( k ) function is not perfectly gaussian as it is usually assumed.

Surface Topography Restitution From Electron Micrographs Of Extended Surface Replicas In Situ

An original image processing procedure that reconstructs the surface topography of a heavy metal-shadowed replica from a digitized micrograph is presented. The theory of this method is established and its limits are discussed. The usefulness and validity of the median filtering algorithm used in the data reduction are shown. The entire procedure has been implemented in a small 16 bit minicomputer. The method has been used to study the rough surfaces of copper, silver, magnesium and gold deposits by autocovariance functions of surface profiles. The results show that good reconstructions of extended surface replicas are obtained. Several new methods of improving the reconstruction process have been tested and are briefly presented. Under good experimental conditions the lateral resolution was 50 A for an overall field size of 40.000 A. This shows that our method may have important applications besides the study of alterable metallic surfaces.