A new seven-sample algorithm has been developed which is particularly useful for phase evaluation in systems with non-sinusoidal periodic waveforms. The algorithm performs well in systems with significant amounts of second, third, fourth, and sixth harmonic content and in the presence of phase shift errors. The algorithm is characterized by an equi-spaced symmetrical sampling pattern in which the end samples are one full period apart. Principal features of the algorithm in terms of the Fourier theory of phase-shifting are presented. Performance of the seven-sample algorithm is outlined and compared with several conventional algorithms.

Phase shifting microscopy is a technique that has been successfully developed for performing surface metrology on optical and microelectronic materials. It has proved particularly well adapted to applications in which the samples are nearly flat, or in which the features are smaller than (lambda) /4 in height, giving angstrom vertical resolution. Because of the problems in phase unwrapping due to the cyclic nature of fringes, and the limited depth of field in high magnification work, it is not yet practically suited to shape measurement of semiconductor components where step height may be many microns. To overcome this problem we have developed a new technique, called Peak Fringe Stepping Microscopy (PFSM), which has a depth of field and a working height range of 15 micrometers , and up to 4 nm vertical resolution. A whole 3-D image can be built up or critical measurements at specific points can be made. The technique is based on white light interferometry combined with precise height stepping of the sample and image processing. Some examples of shape measurement are given in the analysis of various electro-optical and microelectronic structures.

In the Twyman-Green type interferometer the absolute height of a sample can be measured using a broad-band light source. The reference mirror is scanned along the optical axis to detect the point that the optical path difference is zero. We can obtain a three dimensional contour map without restricting 2(pi) phase unwrap. We constructed an interferometric system using a white-light as a light source and measured a step of 20 micrometers .

This paper describes an automated measuring system using reversal two-step phase algorithm. An automated analysis package has been developed for phase-stepped fringe fields. Factors limiting the measuring accuracy and reliability are discussed. This system has been applied to the measurements of thermal deformation, in-plan deformation, resonant vibration amplitude measuring, and nondestructive testing of carbon fiber honeycomb structure.

Using highly coherent laser sources in interferometry often leads to speckles in the interferograms. These speckles constitute a noise on the fringe phase and, hence, lead to a reduction of wavefront measurement precision. They arise from the light scattered by random imperfections of the optical surfaces. A new technique was developed at Carl Zeiss to reduce the effects of speckles in the laser interferometer DIRECT 100 by a virtual reduction of the spatial coherence regarding the speckle contrast. In the technique presented here the direction of the illuminating light beam in the interferometer is modulated while averaging wavefronts (not intensities) with the real-time wavefront averaging capability of DIRECT 100, resulting in a virtually larger extent of the light source. The fringe contrast is independent of this beam modulation, whereas the speckle contrast in the accumulated wavefront is determined by the virtual extent of the light source. Thus, speckle effects not only from the imaging part of the optical train but also from the illuminating part are reduced.

Electro-optic holography (EOH) generates a large array of three-dimensional values (displacement at each x, y location) as its final output. In the past, a number of techniques have been employed to display the displacement data ranging from topographic maps and enhanced versions of the holograms themselves, through fringe skeletonizing, to wire frame surface plots. This paper discusses the application of 3-D shaded rendering techniques to holographic displacement data. Both modeling the object and rendering the model are covered. The resultant shaded images show the displacements of the surface clearly and the software allows the user complete control over the orientation of the view and the characteristics of the light sources. Results are shown for a number of modes of vibrating rectangular plates.

A new technique for measuring spatially dense vibration amplitude and phase using stepped optical phase dual reference double exposure or real time computer aided holometry (CAH) methods along with phase stepping of a strobed laser beam has been developed. The technique is called `stepped strobe phase' and is analogous to the `stepped optical phase' technique. The theory and experimental results are presented.

Quantitative results concerning TV-holography and shearography associated with endoscopy are presented here. In both cases, a cw argon laser has been used. Moreover, shearography experiments have been performed with the help of a pulsed YAG laser working at 25 Hz.

Surface-relief, holographic transmission gratings are generated in positive photoresist with excellent performance characteristics. High intrinsic grating efficiencies of 99% are obtained using an inherently fringe-stable holographic interferometer, which is maximally insensitive to incident pointing errors, to create high aspect ratio nonsinusoidal grooves. Uniform exposures are achieved over apertures of 100 mm in diameter using scanning techniques. Repeatable results are achieved by maintaining pre-exposure and post-exposure processing along with the various exposure parameters.

This paper presents a hybrid holography-tomographic technique whereby surface displacement around an area inaccessible by direct optical exposure is measured holographically and the displacement in the obstructed area is calculated by a tomographic technique.

A non-contact (i.e., optical) technique is required to measure the deformation of a free oil surface under the influence of a localized thermal load. This deformation is caused by surface tension driven thermal convective flow inside the fluid, and can be as large as 250 micrometers. Therefore, conventional interferometry is not possible. Instead, a Ronchi technique is proposed for contour mapping the oil surface. This paper presents a two channel Ronchi instrument, and some preliminary results from the analysis of two aspheric surfaces, a diamond machined metal surface and the free oil surface.

We present two new devices that contain a lateral shear-plate interferometer, held in a mount that can be rotated about the centerline of the incident laser beam. This configuration ensures constant shear while allowing the shear orientation to be varied. One of these new systems relays the sheared image to a fixed video, 35 mm film, or other camera. With the proper camera, it can record the wavefront quality of optical systems of almost any wavelength. The other system holds a large, 150-mm-diameter shear plate in a light-weight structure that can be set on any of several surfaces. This instrument will shear a 100 mm dia. beam horizontally, vertically, and at +/- 45 degree(s). These tools allow quick and easy measurement of the defocus, and third order spherical aberration, coma, and astigmatism in a system without computerized data reduction. The accuracy is about a quarter of a wave.

A novel piston sensing concept is described for measuring piston over the +/- 0.5 wave range. The image of a white light point source is optically processed using a half-wave phase plate to enhance the presence of piston in the incident wavefront. The resultant point spread function is recorded on a CCD camera and analyzed using a simple intensity balance algorithm. Theoretical derivation and experimental results are provided, with emphasis on piston values below 0.25 waves. Piston values are measured to +/- 1/200 wave accuracy or better with a repeatability on the order of +/- 1/1000 wave.

The Fabry-Perot interferometer for ultraprecise measurement of the thermal coefficient of very low expansion, including its working principle and the construction of its practical system, is described in detail in this paper. The measurement principle is given by the frequency filter character of F-P resonator, and the acoustic frequency shifter is used to modulate the frequency of the laser beam. This F-P interferometer system can be used to measure the thermal coefficients of very low expansion as low as 10^-9 with high accuracy.

Stroboscopic heterodyne holographic interferometry, and computational methods were used to study vibrations of submillimeter size cantilever beams. The holographic method described performs phase measurements on an image which has been magnified up to 20 X. With the ability to measure vibration amplitudes with an accuracy of 1/1000 of one fringe, an effective measurement was made every 50 microns along the surface of the object. Both analytical and finite element method solutions were obtained and comparison to experimental results showed good correlation.

This paper presents a novel method combining digital moire technique and rotatable single wedge plate interference technique for collimation testing. Theoretical analyses and experiment results are given.

This paper reports the moire technique by means of electronic XOR logic for obtaining 3-D object contour moire fringes in real time. The main advantage of this method is removal of carrier frequency noise. In this method, the rotation of equiorder surfaces is obtained by changing the period of projection grating. Also, the slope contour fringes are obtained by moving the object in lateral. The projection system is used by means of a self-imaging Talbot effect. The details of equations and the experimental results are presented.

Holographic interferometry promises highly accurate and precise measurement of displacement or deformation. Modern fringe evaluation systems allow determination of the relative fringe order down to less than one percent, and are expected to have the same accuracy in the evaluated dislocation and deformation field. However, one should recognize that accuracy starts with the optimization of the set-up and ends with it. A method to optimize the set-up for holographic interferometric measurements and to predict the sensitivity for the different displacements is reported. The method is developed from the holo-diagram by a quantification of the change of the light way. This leads to functions which describe the sensitivity of the set-up for displacements in the different directions. These functions are called the geometric functions. The values of the geometric functions at a given point are identical with the components of the sensitivity vector. The potential to optimize set-ups by means of these functions is shown by an example.

Because in interferometry the phase is the primary quantity to be measured the main interest during the last ten years was focused on the development of high precision phase reconstruction techniques. Although the measurement of the other quantities to be measured, as for instance the 3 coordinates of the object points, can be reduced to a phase measurement from the practical point of view three strongly connected tasks have to be solved for the measurement of vector displacement fields: interferometer design, data acquisition, and data evaluation. This paper deals with the discussion of the theoretical background of these three procedures concerning the topical state of the art and tries to derive some general rules as well as some problems remaining to be solved for the investigation of extended specimens.

Theoretical performances of stationary Fourier spectrometers without mechanical scanning are compared with the performance of a scanning Fourier spectrometer. In spectrometers employing amplitude-splitting interferometers the reduction of fringe visibility, due to the extended source, can be avoided resulting in high optical throughput. In a wave-front-splitting interferometer the fringe contrast depends on the size of the source. However, the wave-front-splitting double-mirror spectrometer avoids the use of a beam splitter and forms an instrument especially suited for the detection of broad band radiation. Noise characteristics, spectral response, and resolving power of the double-mirror spectrometer are theoretically considered and measured. Due to the charge coupled device based detection the sensor characteristics affect the performance of stationary spectrometers. By background subtraction the effect of detection non-uniformity can be radically reduced increasing the signal-to-noise ratio and resolution of the spectrometer. The maximum resolving power reached in measuring the spectra of two lasers was 1600.The stationary spectrometer is applicable to a wide range of measurements ranging from recording temporally variant wide-band radiation to monitoring the wavelength of lasers.

This paper describes the methods of extracting shock wavefront deleting fringes from the interferograms of transient flow field and registering time series shock wavefront on a single image. These methods have been used to extract and register time-series shock wavefront from the interferograms of explosive flow field and muzzle flow field and to calculate the propagation velocity of the shock wavefront.

In this paper an algorithm of rapid fringe thinning is presented. It consists of fringe smoothing and skeleton extracting. The pulsed noise and `barr' in the fringes can be restrained effectively and the `hole' in the fringes can be padded. Some applications of the method to interferograms of explosive flow field and hypersonic shock tunnel flow field are also presented.

We present a modified scheme of an optical heterodyne interferometric microscope. Reference signal is taken from a low-frequency generator rather than a photodiode to improve stability. Slit aperture is introduced to increase the detected signal. Frequencies of acoustic waves applied to the Bragg cell are adjusted to improve spatial resolution.

Spatial and temporal phase-measurement interferometry techniques are affected by a number of sources of error. This paper focuses on the influence of major error sources on the results of phase calculations using the most popular algorithms. These error sources include phase-shifter miscalibration for N-frame temporal methods and its equivalent of the wrong carrier frequency in N-point spatial techniques and detector nonlinearities. Other errors considered are detector nonlinearities and leakage in the Fourier-transform method. Computer simulations in one dimension with straight, equally spaced fringes reveal the character and magnitude of these errors.

Recently, measurements with slope sensitive optical tests, such as shearing interferometry, Shack-Hartmann test, or Ronchi test, have become of great interest. The primary outcome of these measurements are the slope or difference data of the wavefront under test. Therefore, a numerical reconstruction procedure is necessary to integrate these difference data in order to obtain the desired wavefront map. This paper describes a numerically efficient reconstruction technique for orthogonal difference data as they are obtained, e.g., in lateral shearing interferometers. The reconstruction process consists of two steps. The integration is carried out as a filtering operation in the spatial frequency domain. Since it requires two full rectangular arrays of valid x- and y-difference data, an additional step is necessary to accommodate for general pupil shapes, e.g., circular pupil with central obscuration. This additional step consists of synthetically generating difference data at the previously invalid data points. The reconstruction is unbiased and has a very slow error propagation, i.e., the variance of the noise on the reconstructed wavefronts is approximately equal to the variance of the difference noise.

The mathematical properties of the arctangent function are investigated, revealing the mechanism of error propagation in digital phase-shifting applications. The analysis gives a systematic approach to the assessment of errors and, as such, provides a valuable tool for understanding the propagation of errors in any phase-shifting algorithm.

Ronchi interferometry is an optical testing technique similar to shearing interferometry. A coherent wavefront is interfered with a sheared form of itself by placing a periodic grating at, or near, the focus of an optical system. The resultant interference pattern contains information about the wavefront's slope in a direction perpendicular to the grating structure. The wavefront can be reconstructed from two orthogonal slope data sets via the process of sampling, ordering, and fitting. This paper develops a linear-algebra vector notation model of the interferogram sampling and fitting process.

We have developed a highly sensitive method for measuring thermal expansion, mechanical strain, and creep rates. We use the well known technique of observing laser speckle with a pair of linear array cameras, but employ a novel data processing approach that provides estimates of the time rate of in-plane strain. Our approach is appropriate for assessing very small strain rates in hostile environments. It provides simultaneous global estimates of the strain at both small and large gauge sizes. This may be of importance in studying materials with different short- and long-range orders. General advantages of our technique are compact design, modest resolution requirements, insensitivity to surface microstructure changes (as seen with oxidation), and insensitivity to zero mean noise processes such as turbulence and vibration. We detail the results of a number of experiments and of a simulation of vibration. These tests are intended to demonstrate the performance advantages of the transform method of processing speckle strain gauge data.

The review of the advantages and disadvantages of analytical phase measurement methods of automatic fringe pattern analysis is given. The pros and cons for their applications due to the complexity of an interferogram, the accuracies required, and the type of a quantity measured are considered. The architecture of the system which enables the proper choice between Fourier transform method, temporal and spatial phase-shifting methods is described. The error considerations for these errors are given. The philosophy of the expert system which should apply the various image processing and phase-measuring possibilities in the most efficient way is presented.

Inhomogeneity measurements of the continuous and slow deviation of the refractive index were automatized. The software package based on the phase stepping method was applied for fringe pattern analysis. It includes three methods of inhomogeneity measurements which can be applied depending on the type of the interferometer or the sample.

The application of fringe analysis has enhanced the application of all optical analysis techniques to industry. Emphasis has traditionally been placed upon such issues as the accuracy of the algorithm used, the number of frames required and the speed of processing. However, the practical use of such techniques at Rover has resulted in a more pragmatic view of this technology and the opinion that other issues dominate its successful use in industry. This paper presents these views by relating experience of applying fringe analysis to TV Holography, Moire, and Photoelastic systems.

This paper investigates the effect of partial speckle decorrelation due to the transverse component of the object displacement on the phase measurement using statistical optical theory. The theoretical values of statistical phase errors are derived under the in-plane and out-of-plane displacement sensitive arrangement when using the phase subtracting method. The selection of the optimum system parameters is also discussed. The theoretical and experimental results show that this phase extracting method is sensitive to speckled and additive noise.

It has been shown experimentally in this work that the phase difference in two points in the developed speckle-field has a non-uniform probability density with maxima for values of O and (pi) rad. Such a phenomenon is most typical if the source (scatterer) is (delta) -correlated and the intensity distribution on its surface is described by the even function of the coordinates. A theoretical example is given in this work.

The three-wave lateral shearing interferometer is an interferometer specially designed for optical testing. It determines three non-collinear phase gradients from one single fringe pattern. From these quantities, two orthogonal derivatives and the measurement error are estimated, allowing the reconstruction of the aberrated wavefront. This new interferometer has several benefits; among them that its sensitivity and dynamics can be easily adjusted to the analyzed aberrations.