Roland Schreiner

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.

Absolute testing of the reference surface of a Fizeau interferometer through even/odd decompositions

Absolute testing of spherical surfaces is a technological necessity because of increased accuracy requirements. In a Fizeau setup, the main part of the interferometer deviations thereby comes from the reference surface. We demonstrate the validity of an absolute testing procedure for the reference surface that has been proposed earlier. The procedure relies on the decomposition of the surface deviations into odd and even parts and could be used in partially coherent illumination. The odd deviations are obtained from a basic and a 180 degree-rotated position of an auxiliary sphere, and the even deviations can be measured with the help of a cats eye position in double pass using an opaque half screen in the interferometer aperture.

Interferometric shape measurement of rough surfaces at grazing incidence

Interferometric shape measurements of technical objects are hampered by stochastic phase variations in the micro region caused by the surface roughness of the test object. Without special precautions, low-contrast interference patterns or even totally stochastic fringe patterns may be observed. However, illuminating the surface under test at grazing incidence reduces the phase variations because it increases the effective wavelength by a factor of 1/cos β, where β is the angle of incidence. Here, an interferometer for testing plane objects is described where the test wavefront is provided by means of diffractive optical elements (DOEs). A pair of identical DOEs is used to do the necessary beam splitting and beam shaping. The resulting fringes, showing the surface deviations of the test object from the ideal plane, are evaluated by means of phase-shifting interferometry. Serial measurements on different rough surfaces were made to find out the limits of grazing-incidence interferometry when technical objects are measured. To do this, different incidence angles have been realized by choosing a suitable set of diffractive elements. The contrast of the interference fringes has been taken as the evaluation criterion for the measurability of the shape of the rough surfaces within the grazing incidence interferometer.

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.

Grazing-incidence test for cylindrical microlenses with high numerical aperture

Cylinder symmetry of test objects allows grazing incidence tests. Here we propose the use of two diffractive optical elements (DOEs) instead of a single DOE in perpendicular incidence. The splitting of the optical function of the DOEs allows low spatial frequencies in the diffractive elements. In fact, the diffractive structures are curves parallel to the meridian of the cylinder lens. Here an interferometric test is described where identical DOEs serve as beamsplitter and combiner. The undiffracted wavefront serves as reference. Phase shifting evaluations are possible by axial translations of one of the DOEs. The effective wavelength can be chosen within wide limits. Actually, we used a pitch of 5?m, which is identical to the effective wavelength of the test. A surface deviation of 2.5?m corresponds to a fringe distance. The interferometric test enables rms values of better than 20 nm for any aspheric geometry of the meridian curve, even with lenses having numerical apertures up to 0.9.

Compensation for anamorphotic distortion in grazing-incidence interferometry testing planar specimens

One important feature of grazing-incidence interferometry is the anamorphotic distortion or the fore-shortened view of the interference pattern along the optical axis caused by the geometry of theinterferometer. To compensate for the consequential lower resolution along the optical axis, a setup was built in which the object plane is imaged onto a rectifying grating, ensuring sharp mapping of the whole specimen onto the detector. A volume hologram and a diffraction grating serve as rectifying elements and are applied to measure various types of planar objects such as mirrors and structured plastic samples. Accuracy, image sharpness, and residual distortion for both cases are discussed.

Interferometric testing of technical surfaces with computer-generated holograms

Increasing demands for accuracy 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 are used both as references for the technical surfaces to be tested and as beam splitter or recombing element. Each class of workpieces requires specific computer generate holograms, 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 square fit. We will demonstrate this measurement technique with workpieces of different shape.