Georges Rasigni

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.

Characterization of layered synthetic microstructure by transmission electron microscopy and diffraction

Transmission electron diffraction patterns related to the cross section of layered synthetic microstructures (LSMs) are obtained. By depositing the multilayers onto (111) orientation silicon single-crystal substrates, it is possible to obtain on the same plate both the LSM diffraction pattern and a calibrated one and thus to measure the LSM mean period accurately. Results concerning tungsten-carbon LSMs are presented.

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.

Optical constants of lithium deposits as determined from the Kramers-Kronig analysis

Optical constants of Li have been determined between 0 and 10.7 eV, using Kramers-Kronig analysis of the reflectance data. The dielectric constant ∊ = ∊1 + i∊2 and the optical conductivity are deduced and compared with theoretical calculations. The plasma energy as determined from the condition ∊1(ω) = 0 is near 6.73 eV and the energy loss function peaks at 6.90 eV. The effective mass m* deduced from the analysis of ∊1 in terms of a nearly-free-electron model is found equal to 1.80m. The optical conductivity exhibits important differences from the theoretical calculations. These discrepancies have been attributed to properties of the metal surfaces measured, particularly roughness and granularity.

Method for characterizing masses in digital mammograms

A method for characterizing tumoral masses in mammograms is described. It is based on two significant features of breast cancer, namely the degree of spiculation and the presence of fuzzy areas in the boundary of the tumor. The quantization of these features is performed by means of polar and pseudopolar representations of the neighborhood of the tumor to take advantage of its symmetry . The degree of spiculation is deduced from a shape parameter that characterizes the irregularity of the boundary after enhancing divergent structures. The radial component of the gradient on the boundary provides a measurement of fuzzy appearance. In the next step, the identification of malignant and benign tumors is achieved with a two-level hierarchical classification using a Bayesian classifier. A set of 19 masses are processed and results are presented and discussed.

Optical properties of aggregated lithium deposits

Reflectance and transmittance of aggregated lithium deposits, prepared under static and dynamic ultrahigh vacuum, have been studied at normal incidence in the spectral range 1–6 eV. The structure of these deposits was determined in situ using a carbon film replication technique. It is shown that the optical conductivity exhibits peaks in the visible and infrared ranges, which are due to plasma resonance of the conduction electrons. In the uv range, the conductivity rises due to interband transitions. The particle size histograms show that deposits are made up of axially symmetrical ellipsoids. It follows that Maxwell-Garnett theory is inappropriate to describe the optical properties of granular lithium deposits. A generalized Maxwell-Garnett theory for ellipsoidal particles, which takes the interactions between particles into account, is used. Good agreement between experiment and theory is obtained.

Statistical parameters for rough surfaces of thin films of CaF(2) and Ag/CaF(2).

Statistical parameters, rms roughness delta and autocovariance length sigma, are determined both for rough surfaces of CaF(2) deposits and for surfaces of silver films deposited on these CaF(2) underlayers. The dependence of delta and sigma on the CaF(2) film thickness d is investigated. It is shown that the silver films do not replicate well the CaF(2) underlayers. A review of the relationships between delta, sigma and d when seeking control of the roughness of a silver film by controlling d is proposed. It is also shown that CaF(2) is a good underlayer compared with LiF.

Fabry-Perot etalons for x-rays: Construction and characterization

Abstract A solid Fabry-Perot etalon (FPE) for X-rays has been constructed using sputtering technique. This FPE is made up of two layered synthetic microstructures (LSMs) separated by a carbon spacer. Each LSM consists of fifteen pairs of tungsten/ carbon having a mean period d = 27 A and deposited onto (111) orientation silicon single crystal substrate. The carbon spacer thickness is 470 A. The FPE has been characterized by new processes, namely electron microscopy and transmission electron diffraction pattern. The results obtained are in good agreement with those provided by reflectivity measurements using Cu K α (1.5418 A) radiation. Another FPE made of two different LSMs has been constructed. The effect of such an asymmetry is investigated.

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