Bozenko F. Oreb

Real-time holographic interferometry: a microcomputer system for the measurement of vector displacements

A system is described which uses a diode array TV camera to view the real-time fringes and digital electronics to measure and store the irradiance levels at a 100 × 100 array of points. A microcomputer calculates the phase at each point from the irradiance values obtained from three successive scans of the array made with the phase of the reference beam shifted in steps of 120° by means of a mirror mounted on a piezoelectric translator. The optical system permits four holograms to be recorded in quick succession, using a photothermoplastic camera, with the object illuminated from four different directions. Phase data from these holograms are processed in a microcomputer to determine the components of the vector displacement at each of these points; these figures can then be transferred to a fast computer for further processing to evaluate the stress distribution.

Stitching interferometric measurement data for inspection of large optical components

An algorithm for stitching together a set of individual phase measurements into a unified larger phase map is presented. The set of individual phase maps results from scanning a component over the interferometer aperture and acquiring a measurement at each position. The algorithm is based on an iterative approach, where singular value decomposition is used to solve the rigid body movement problem between the different phase maps. The algorithm has been tested in numerical experiments and has been successfully applied to real data.

300-mm-aperture phase-shifting Fizeau interferometer

A 300-mm-aperture digital phase-shifting Fizeau interferometer (LADI) has been developed in house for precision metrology of optical components fabricated by the Optical Workshop at CSIRO Division of Telecommunications and Industrial Physics. This paper describes the optical and mechanical configuration of the instrument as well as its calibration and performance characteristics. Recent measurements on 250-mm-diam uncoated optical surfaces have consistently shown shortterm repeatability of 0.3 nm rms from measurement to measurement and allowed absolute characterization of these surfaces to an accuracy of a few nanometers.

PROFILOMETRY BY PHASE-SHIFTED TALBOT IMAGES

We introduce a profilometry sensor that combines phase shifting with a Talbot self-image of a sinusoidal grating as the illumination part of the sensor. Contrast of the Talbot diffraction pattern produced with a sinusoidal grating in a diverging beam is theoretically discussed and verified experimentally. The mathematical relationship that is used to convert the phase measured with this sensor to the corresponding relief of an object is derived in the Appendix. A ceramic former used in the production of lenses was profiled with this sensor, and measurement results are presented.

Simultaneous measurement of three orthogonal components of displacement by electronic speckle-pattern interferometry and the Fourier transform method

The measurement of three-dimensional displacement by electronic speckle-pattern interferometry with three object beams and one reference beam is presented. Multiple interference fringes corresponding to different sensitivity vectors are recorded in a single interferogram and separated by means of the Fourier transform method to give three components of displacement. The relationship between the ratio of the speckle size to the pixel size of a TV camera and the measurement error is investigated experimentally and compared with the research of others. The optimum condition leading to a minimum measurement error occurs when the speckle size is approximately equal to the pixel size. With this condition satisfied, the measurement error varies from 1.5% to 6.0%.

Testing aspherics using two-wavelength holography: use of digital electronic techniques.

Two-wavelength holography has been shown to be quite useful for testing aspheric surfaces since it can produce interferograms with a wide range of sensitivities. However, TWH has the drawback that the accuracy attainable from measurements on photographs of the fringes is limited. It is shown how this limitation can be overcome by using digital electronic techniques to evaluate the phase distribution in the interference pattern.

Calibration of a 300-mm-aperture phase-shifting Fizeau interferometer

A 300-mm-aperture digital phase-shifting Fizeau interferometer has been developed in-house for precision metrology of optical components fabricated by the optical workshop at Telecommunications and Industrial Physics, Commonwealth Scientific and Industrial Research Organization. We describe the procedures used in the calibration of the instrument. A reference data file representing the deviations from flatness of the reference surface is generated, measurement uncertainty estimated, and aberrations in the instrument assessed. Measurements on 250-mm-diameter uncoated optical surfaces have consistently shown short-term repeatability of 0.3-nm rms from measurement to measurement and allowed for absolute characterization of these surfaces to within a few nanometers.

Power spectral density analysis of optical substrates for gravitational-wave interferometry

The power spectral density of surface-relief variations on polished optical surfaces across microscopic through to macroscopic spatial scales is calculated from measurements on substrates that are being produced for the Laser Interferometer Gravitational-Wave Observatory (LIGO). These spectra give a guide to the scattering properties of the surface, which in turn critically influence the performance of LIGO. Measurements obtained by use of a full-aperture interferometer and an interference microscope with two different objectives are combined to produce one-dimensional power spectral density representations of the surfaces across spatial frequencies ranging from 0.1 to 8000 cm(-1). These measurements from different instruments are in good agreement with an analytic power spectrum that varies as nu(-1.5), where nu is the spatial frequency. Some anomalies in the power spectral density spectra can be related to aspects of the polishing process.

Stroboscopic holographic interferometry: measurements of vector components of a vibration

The interpretation of time-averaged holographic fringes recorded with a vibrating object presents problems when the direction of the motion is not known or when points on the object are moving in two or three dimensions. Measurements on additional holograms with properly chosen directions of the sensitivity vector are then required to evaluate the vibration amplitude. However, reduction of the data, even along a single line, is laborious and subject to errors. This paper describes a computerized system which uses stroboscopic illumination in conjunction with digital phase-shifting techniques to evaluate the magnitude and direction of the surface displacements at a uniformly spaced array of points covering the vibrating object. These values are used along with data on the shape of the object to calculate the in-plane and out-of-plane components of the vibration at these points. The operation of the system is illustrated with some results obtained with a compressor blade from a jet engine. Measurements of the surface displacements at different epochs of the vibration cycle permit a detailed analysis of complex vibrations.

Tunable phase-extraction formulae for simultaneous shape measurement of multiple surfaces with wavelength-shifting interferometry

The interferometric surface measurement of single or stacked parallel plates presents considerable technical difficulties due to multiple-beam interference. To apply phase-shifting methods, it is necessary to use a pathlength-dependent technique such as wavelength scanning, which separates interference signals from various surfaces in frequency space. The detection window for frequency analysis has to be optimized for maximum tolerance against frequency detuning due to material dispersion and scanning nonlinearities, as well as for suppression of noise from other frequencies. We introduce a new class of phase-shifting algorithms that fulfill these requirements and allow continuous tuning of phase detection to any frequency of interest. We show results for a four-surface stack of nearparallel plates, measured in a Fizeau interferometer.