Thomas Dresel

Three-dimensional sensing of rough surfaces by coherence radar

We introduce a three-dimensional sensor designed primarily for rough objects that supplies an accuracy that is limited only by the roughness of the object surface. This differs from conventional optical systems in which the depth accuracy is limited by the aperture. Consequently, our sensor supplies high accuracy with a small aperture, i.e., we can probe narrow crevices and holes. The sensor is based on a Michelson interferometer, with the rough object surface serving as one mirror. The small coherence length of the light source is used. While scanning the object in depth, one can detect the local occurrence of interference within the speckles emerging from the object. We call this method coherence radar.

Design and fabrication of computer-generated beam-shaping holograms

For the design of computer-generated holograms reconstructing certain intensity patterns with phase freedom, we use an object-oriented approach. The given intensity pattern is decomposed into elementary objects for which appropriate phase-only hologram functions can be constructed. The total hologram function is found by the subsequent superposition of its constituents, with a relative amplitude and phase weighting for each of them. Thus, the degrees of freedom are dramatically reduced compared with those of sampling approaches. The design algorithm allows us to compensate on the one hand for the intensity and phase distribution of the impinging laser beam and on the other hand for the shape of the hologram aperture. We report on the computer-aided design of such holograms, as well as their fabrication through the use of laser lithography and reactive ion etching. Optical reconstructions are shown.

Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption

Computer-generated phase-only holograms can be used for laser beam shaping, i.e., for focusing a given aperture with intensity and phase distributions into a pregiven intensity pattern in their focal planes. A numerical approach based on iterative finite-element mesh adaption permits the design of appropriate phase functions for the task of focusing into two-dimensional reconstruction patterns. Both the hologram aperture and the reconstruction pattern are covered by mesh mappings. An iterative procedure delivers meshes with intensities equally distributed over the constituting elements. This design algorithm adds new elementary focuser functions to what we call object-oriented hologram design. Some design examples are discussed.

Some considerations of reduction of reference phase error in phase-stepping interferometry

Positioning errors and miscalibrations of the phase-stepping device in a phase-stepping interferometer lead to systematic errors proportional to twice the measured phase distribution. We discuss the historical development of various error-compensating phase-shift algorithms from a unified mathematical point of view. Furthermore, we demonstrate experimentally that systematic errors can also be removed a posteriori. A Twyman-Green-type microlens test interferometer was used for the experiments.

Interferometric testing of plane and cylindrical workpieces with computer-generated holograms

Increasing demands for accuracy and speed in manufacturing and international standards of quality control require faster and more precise measurement techniques. Surface inspection and shape control of technical workpieces is commonly done by tactile profilometers. A faster alternative to this mechanical tool can be realized interferometrically. Grazing incidence of laser light onto the technical surface reduces speckle noise significantly. In our setup computer-generated holograms (CGHs) are used both as references for the technical surfaces to be tested and as beamsplitter or recombining element. Each class of workpieces requires specific CGHs, e.g., phase gratings for plane surfaces or diffractive axicons for cylindrical and conical surfaces. An ideally shaped workpiece will result in a zero fringe field. Deviations from the ideal shape will be indicated by interference fringes and fringe distortions. The sensitivity of the interferometer can be adapted to technical needs. The surface deviations of the workpiece are superimposed by adjustment aberrations which can be described mathematically with sufficient accuracy and eliminated by a least squares fit. This measurement technique is demonstrated with workpieces of different shape.

Testing of rod objects by grazing incidence interferometry: theory

Interferometry at grazing incidence allows one to perform macroscopic shape tests of rough surfaces with submicrometer precision. The highest measurement accuracy is achieved with a null test: the object wave front is adapted to the ideal surface under test through the use of diffractive optical elements. Deviations between the ideal and the real surface shape result in characteristic phase distributions at the interferometer output. Rod objects with rather arbitrary cross-section profiles are especially suitable for this type of measurement. The design of appropriate test wave fronts can be carried out by means of geometrical considerations. Expressions describing aberrations that are due to misalignments of the work piece can easily be derived. Misalignment aberrations and genuine surface deviations are separated by least-squares fitting.

Testing of rod objects by grazing-incidence interferometry: experiment

A grazing-incidence interferometer for the testing of technical surfaces for macroscopic surface deviations is described. Computer-generated holograms serve as beam splitters and references for the workpieces tested. The sensitivity of the interferometer depends on the period of the computer-generated holograms. The method is demonstrated at a rod object of convex profile. Using phase-stepping techniques, the grazing-incidence interferometer provides fast measurements of the entire mantle surface of the test sample with submicrometer precision.

Axicon-type test interferometer for cylindrical surfaces: systematic error assessment

The principle and the alignment aberration functions are described for an axicon-type test interferometer for measuring cylindrical mantle surfaces. Additionally, we show that the derived systematic alignment functions fulfill for reasonably small misalignments the requirements for measurements in the range of approximately 1/100 of a fringe. We verify this with optical path-length calculations, using ray tracing.

Empirical strategy for detection and removal of misalignment aberrations in interferometry

Abstract Misalignments of the object under test relative to the instruments coordinate system play an important role in interferometrical form metrology. Degrees of freedom, coordinate systems, object symmetries, calibration methods, mathematical models, and misalignment terms are closely interrelated. Especially in low-symmetry applications like the testing of aspheres, specific models have to be elaborated and implemented. An alternative, flexible and universal way to carry out misalignment removal is to use an empirical strategy: For every degree of freedom the affiliated misalignment term is measured through the use of phase shifting interferometry. The terms obtained during these measurements are then used to fit a set of misalignment coefficients to the data of the actual measurement. The method is discussed in detail and, as a proof of concept, is demonstrated experimentally by the example of the testing of high aperture micro spheres.

Form assessment of hollow cylindrical specimens

Grazing-incidence interferometry that makes use of diffractive axicons for the measurement of cylindrical mantle surfaces has already been reported. However, measurement of concave rod structures poses a severe problem because these structures are subject to spurious fringes caused by parasitic diffraction orders of the diffractive axicons. By breaking the symmetry of the interferometric setup it is possible to obtain unique interferograms of the inner mantle surfaces of hollow cylinders as cages for roller bearings or other workpieces produced on lathe machines that have a suitable surface finish. Special design issues for the computer-generated holograms and the interferometric setup are discussed, and test examples are given.