Chris L. Koliopoulos

Fourier description of digital phase-measuring interferometry

A general description of phase measurement by digital heterodyne techniques is presented in which the heterodyning is explained as a filtering process in the frequency domain. Examples of commonly used algorithms are given. Special emphasis is given to the analysis of systematic errors. Gaussian error propagation is used to derive equations for the random phase errors of common algorithms.

Modal estimation of a wave front from difference measurements using the discrete Fourier transform

It is shown that a wave front, or in general any scalar two-dimensional function, can be reconstructed from its discrete differences by a simple multiplicative filtering operation in the spatial-frequency domain by using complex exponentials as basis functions in a modal expansion. Various difference-sampling geometries are analyzed. The difference data are assumed to be corrupted by random, additive noise of zero mean. The derived algorithms yield unbiased reconstructions for finite data arrays. The error propagation from the noise on the difference data to the reconstructed wave fronts is minimal in a least-squares sense. The spatial distribution of the reconstruction error over the array and the dependence of the mean reconstruction error on the array size are determined. The algorithms are computationally efficient, noniterative, and suitable for large arrays since the required number of mathematical operations for a reconstruction is approximately proportional to the number of data points if fast-Fourier-transform algorithms are employed.

An Optical Profilometer for Surface Characterization of Magnetic Media

Conventional surface-characterization techniques either are not sophisticated enough to provide complete surface-topographical data or cannot be employed because of the relatively low hardness of magnetic media. An optical profilometer has been developed which provides a noncontact method of obtaining surface characteristics from a magnetic medium. The system consists of a standard Leitz reflection microscope, a Mirau interferometer controlled by a piezoelectric transducer, a linear array of photodiode detectors, and a microcomputer. The combination yields a system that measures the optical-height variations of surfaces to a high degree of precision. This height variation is processed by a computer to provide surface-topographical statistical parameters, which are useful to predict tribological and magnetic performances of the head-media interface. Sample data of magnetic media (tape, floppy disk, and rigid disk) are presented. Presented at the 38th Annual Meeting in Houston, Texas, April 24–28, 1983

Time integrating acoustooptic correlator

This paper describes an acoustooptic technique for achieving signal correlation with a time-bandwidth product of 10(6)-10(8), using existing devices. One signal is used to intensity modulate a light beam that illuminates an acoustic cell. The other signal appears in the cell as a traveling wave and is Schlieren imaged onto a detector array. The detected image intensity is integrated in time, achieving the desired correlation function. Since the correlation integration is performed in time rather than space, the time-bandwidth limitations of earlier acoustooptic correlators are greatly reduced. Experimental procedures for implementation of this technique are discussed and results shown.

Development of a Three-Dimensional Noncontact Digital Optical Profiler

A noncontact three-dimensional optical profiler for measuring surface roughness is described. The system consists of a reflection microscope, Mirau interferometer with a reference surface mounted on a piezoelectric transducer, CID detector array, frame grabber, and micro-computer. Interferometric phase-shifting techniques are used to obtain surface height information. The height measurements areprocessed by a computer to obtain topographical statistical parameters, which are useful in predicting tribological and magnetic performances of the head-media interface in magnetic storage systems. Sample data are presented for magnetic media (tape, floppy disk, and rigid disk), a magnetic head, a silicon wafer, and a glass slide.

Infrared point-diffraction interferometer

A point-diffraction interferometer (PDI) for use in the infrared is discussed. It is shown that the PDI is simple and easy to use and also yields fringes of constant optical path difference similar to those obtained with a Twyman–Green interferometer. The fabrication of the PDI is described, and typical results obtained using the interferometer at a wavelength of 10.6 μm are shown.

Radial grating lateral shear heterodyne interferometer

A variable lateral shear heterodyne interferometer has been developed that is capable, for example, of measuring the high-bandwidth wave fronts in adaptive optical systems. The interferometer is used with a radial Ronchi grating and operates with a variety of spatially and temporally coherent light sources such as whitelight extended sources. The interferometer has been operated successfully in a real-time atmospheric compensation adaptive optical system.

Moiré topography, sampling theory, and charged-coupled devices.

Projection-type moiré contouring can be done without a reference grid by undersampling projected cosine fringes with a charged-coupled-device detector array to eliminate entirely the unwanted sum, shadow, and grid terms of classical moiré methods as well as the spurious moiré fringes that are due to higher harmonics. The technique produces a high-visibility sampled version of the moiré difference contour fringes. Higher-order aliasing can provide increased sensitivity when the same detector array is used. The sampling conditions are formulated as a moiré extension to the Whittaker-Shannon sampling theorem.

Wavefront Reconstruction from Noisy Slope or Difference Data Using the Discrete Fourier Transform

A general algorithm is presented for reconstructing a two-dimensional wavefront optical path difference (OPD) map from noisy slope or difference measurements by means of a least squares fit using complex exponentials. This form of modal estimation can be described as a filtering operation in the spatial frequency domain. Thus fast Fourier transform (FFT) algorithms can be used for rapid reconstruction. The reconstruction is unbiased also in the case of finite data arrays. The error propagation from the noisy measurement data to the integrated wavefront is minimal in a least squares sense. It is believed that this reconstruction algorithm can be implemented in an adaptive optical system by using commercially available array processor hardware, thus reducing the total system cost and the need for specialized hardware.

Measurement of the thermal diffusivity of nonlinear anisotropic crystals using optical interferometry

We describe a simple common-path self-referencing interferometric method requiring no auxiliary optical elements which accurately and directly measures the thermal diffusivity of anisotropic crystals in nonsteadystate conditions. We determine the thermal diffusivity of a lithium niobate crystal as a function of temperature ranging from room temperature up to 500 degrees C.