J. P. Palmari

Study of surface roughness using a microdensitometer analysis of electron micrographs of surface replicas: I. Surface profiles

A new method for studying surface roughness is presented that uses a microdensitometer to analyze electron micrographs of shadowed surface replicas. First we give a preliminary description of the replication technique and the microdensitometer analysis. Then we proceed to show that the micrograph density (or transmittance) is approximately proportional to the slope of the surface elements, which enables us to determine the surface profile by integration of the microdensitometer data. Bidimensional and monodimensional median-filtering algorithms are used in the data reduction, and their validity is analyzed. With the help of a computer program that plots a perspective view of rough surfaces, we find that a close approach to the real profiles is obtained. This shows that our method may have other important applications in addition to the study of alterable metallic surfaces.

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.

Statistical parameters for random and pseudorandom rough surfaces

We confront the problem of retrieving statistical parameters from statistical functions characterizing random or pseudorandom surfaces. Some complications arise when the definition of the autocovariance length for a pseudorandom surface is considered. These complications are carefully investigated, and solutions are proposed to overcome them. In particular, a deduction of certain statistical parameters from the spectrum instead of the autocovariance function is proposed.

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.

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.

Improvement in the reconstruction of surface profile deduced from microdensitometer analysis of electron micrographs of shadowed surface replicas

The different steps leading to the determination of a surface profile deduced from microdensitometer analysis of electron micrographs of shadowed surface replicas are reviewed. It is shown that monodimensional median filtering is sometimes inadequate to remove the low-frequency noise generated by the Levy–Wiener process. A new treatment is proposed that corrects this disadvantage.

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.