Klaus Leonhardt

Microshape and rough-surface analysis by fringe projection

A fringe-projection system for microscopic applications, fringe-projecting microscopy, is developed and analyzed. Projection of the grating and imaging of the fringe system, modulated by the surface, are accomplished by the same high-aperture objective. The spectrum of the grating is spatially filtered and projected into the aperture with a lateral shift, which leads to a telecentric projection under oblique incidence and telecentric imaging. Topographies of specularly as well as diffusely reflecting surfaces can be obtained. The measurement of highly rough surfaces is described together with preprocessing steps. The resulting intensity distribution of the fringes is analyzed. Formulas for vertical and lateral resolution, measuring range, and dynamic range, based on noise considerations, are presented and verified by topographies of technical surfaces.

Topometry for locally changing materials.

Three-dimensional topometry is supplemented with ellipsometric measurements on the same pixel raster for calculation of the phase of the reflected waves and correction of the height fields. Lateral resolution is <1mum . The ellipsometric angles are determined by phase shifting and contrast evaluation. Three-dimensional fields of the ellipsometric angles, the real and the imaginary parts of the refractive index, and the corrected topography of the heights are presented.

Micro-Ellipso-Height-Profilometry

A new instrumental concept for surface measurement is described. In Micro-Ellipso-Height-Profilometry three independent profiles h(x), ψ(x) and Δ(x) of a surface are measured from one diffraction limited scanning spot. The basic equations for the extraction of these three quantities are derived and first results are discussed.

Interferometry for Ellipso-Height-Topometry – Part 1: Coherence scanning on the base of spacial coherence

Summary A modified Linnik and a Mirau interferometer are introduced which can be used for Ellipso-Height-Topometry. With these, a set of topographies can be measured, where the measured height H(x, y), the ellipsometric angles Φ(x, y), Δ(x, y) and the degree of polarization P(x, y) all refer to the same pixels of the raster. This coherent set of topographies can be used to calculate topographies of further quantities, e. g. the complex refractive index N(x, y) = n(x, y) – k(x, y) i of bulk surfaces or parameters of thin films, even for discontinuous structures. Material maps which indicate the presence of specific materials and show their exact location in the frame can be generated. In part I, these interferometric configurations are described and results are presented. It is shown that for oblique incidence, which is obligatory for an ellipsometric detection, the envelope of the interferogram or correlogram can be narrowed for improved z-scan (vertical) discrimination, even in the case of the height detection. By a theoretical analysis, we prove that this is an effect of conventional spatial coherence as a function of the width of the source and can be utilized without any source modulation or source shaping even for small spectral bandwidth of the radiation. This is verified for tungsten incandescent lamps, and for LEDs. In part II algorithms for ellipsometric measurements, calibration procedures and first complete topography sets are presented.

Optical Methods Of Measuring Rough Surfaces

The statistical parameters of surfaces to be measured for industrial applications vary over several orders of magnitude. Surfaces with large slopes or edges are particularly difficult to be recorded. Some measuring methods developed in our laboratory are compared and the range of applications are discussed. For polished and fine ground glass and metal surfaces a heterodyne profilometer with a vertical resolution of 0.5 nm, lateral resolution of 0.6 μm, and large scanning length is discussed. The interferometer can be changed from single- to double-pass operation by rotation of a quarter-wave-plate. For rougher surfaces a profilometer of the photometric-balance type with resolution Rq < 4 nm and dynamic range of 20 μm and an interference microscope with automated fringe evaluation is described. An integral white light roughness sensor covers the roughness range 0.04µm to 10µm and measures independently mean roughness and autocorrelation width.

Ellipso-Height Topometry, EHT: extended topometry of surfaces with locally changing materials

Summary The principle of the new Ellipso-Height Topometry and the basic relations for measurement and calibration are shown in detail. First topography sets are presented and discussed: topography of the height, of the ellipsometric angles Ψ and Δ, of the real and imaginary part of the complex refractive index, of the corrected heights, of the local thickness, and material maps. Results for two different samples are presented: a photolithographic object with microstructures of silicon and SiO2 and a rough surface of a cylinder bore of a automobile engine, demonstrating the use for industrial application.

Optical topometry of surfaces with locally changing materials, layers, and contaminations. Part 1: Topographic methods, based on two-beam interferometry

Abstract Conventional topometry, applied to surfaces with locally changing materials can result in significant errors in the measured heights. A new theoretical approach is developed for the case of two-beam interferometry. Applied to some surface structures—gold on glass, oil on steel and SiO2 on Si—important effects of contrast and phase variations are brought to attention. They are explained by a new theory using the complex contrast. Ways for surface correction procedures are outlined.

Intensity and polarization of interference systems of a two-beam interferometer

Abstract Expressions are developed for the intensity, azimuth, ellipticity, and the degree of polarization as functions of the path difference, the optical parameters of the elements, and the partial polarization state of the light entering the instrument. The expressions are available in closed form and illustrate clearly the interaction of light with the instrument and may, in the future, lead to a theory encompassing all polarization and intensity effects.

Determination of average roughness and profile autocorrelation width of metallic surfaces with a white light sensor

A new procedure to determine simultaneously a horizontal descriptor of the surface - the autocorrelation width - and the most important vertical descriptor - the root-mean-square roughness - is presented. It is based on the inversion of an analytic contrast formula. After a short introduction to white light random phase contrast measurement we describe the elimination process and show first experimental verifications.

Anwendung der Vektoriellen Kohärenztheorie zur Herleitung Grundlegender Ausdrücke für die Interferometerberechnung

Aus der Formulierung der Koharenzmatrix der zur Interferenz uberlagerten Teilstrahlenbundel eines Zweistrahlinterferometers, die unterschiedliche Polarisation erleiden und unterschiedliche Intensitaten aufweisen, wird eine Herleitung der fur die Berechnung und Analyse wichtigen skalaren Grose s, dem komplexen Kontrast, entwickelt. Fur die Praxis der Interferometerdurchrechnung wird die Koharenzmatrix im Ausdruck fur s durch eine modifizierte Form des Jonesvektors ersetzt, wobei fur teilpolarisiertes Licht nur noch der Polarisationsgrad zusatzlich in die Formel eingeht. Vollstandig polarisiertes Licht und unpolarisiertes Licht ergeben sich dann als Sonderfalle mit entsprechend einfacheren Ausdrucken. Der Zusammenhang mit der mittleren Intensitat, der Modulation und der Streifenversetzung fur einen oder mehrere Ausgange eines Interferometers wird anhand einer Darstellung in der komplexen Zahlenebene, dem s -Diagramm diskutiert.