In the process of surface recovery using interferometric methods, a mixture of artifacts, noise, and errors affect the phase map stage of the process. Based on a methodology called data dependent systems (DDS), a stochastic approach is developed which discerns the phase signal from noisy data points and uses it to reconstruct a clean phase map. Such a phase map is then easily converted to a height distribution. Stepwise, the procedure first identifies the presence of discontinuities, then applies an adaptive thresholding criteria to return an outlier free set of residuals, and finally uses them to reconstruct a clean phase map. The methodology is robust and can handle very complex phase maps. It reduces reliance on complicated and expensive experimental setups and replaces them with relatively inexpensive but reliable computation. Phase unwrapping is shown to be accomplished in a natural way, but the method also provides other benefits such as diagnostic identification of surface defects and other trouble spots.

We propose a sinusoidal phase-modulating Fizeau interferometer using self-pumped conjugate wave for surface profile measurements. The interferometer is self-referencing and free from the effects of the axial movements of object surfaces. The characteristics of the interferometer are made clear through the surface measurement of a diamond-turned aluminum disk. For large-size objects, the size of the plate glass can be much smaller than that of the object. The small-size plate glass provides the accurate sinusoidal phase modulation easily. We also propose the method of absolute measurement to eliminate the undesirable phase distribution caused by aberration of the lenses. It is shown through the surface profile measurements of a mirror that the interferometer and the method of absolute measurement are useful for large- size objects.

A technique is proposed to measure x-ray projection optics. Simultaneous linear equations are derived from the wavefront distortions to obtain form errors of optical surfaces discretely. Simulations proved that the arithmetic operation errors are small enough to achieve nanometer level accuracy. This technique is effective to test aspheric reflectors, as well as the reflector misalignments. It also is able to be applied to adaptive optics compensating for thermal deformation effects or drifts on the exposure system.

In this communication the issue of the micro-inspection of the relief structure of surfaces in the industrial world is discussed. Microtopographic inspection of surfaces, especially rough ones, by non-contact optical means is gaining more and more interest. New approaches to well-established methods like triangulation, both area and discreet, are being tried to meet the new requirements. We present a comparative study of three triangulation based dimensional inspection methods: moire that combines interferometry and triangulation, contrived lightning, and discreet active triangulation that in recent years regained interest by its versatility. New approaches are presented with emphasis to a new active, discreet, triangulation based system recently developed.

Optical heterodyne carriers have been generated by mixing the stimulated Brillouin scattered light generated from optical fiber ring resonators. The first technique mixes the SBS generated from two separate resonators to produce a carrier in the 200 - 400 MHz region. For this system a temperature coefficient of the carrier frequency of approximately 5 MHzK^-1 was obtained. The second technique mixes the two SBS signals produced from the orthogonal polarization eigenmodes of a ring resonator constructed from high birefringence fiber. A carrier frequency of 11.68 MHz was obtained with a temperature coefficient of 6.7 kHz K^-1.

A new technique for distributed fiber-optic sensors with polarization mode coupling is presented. The technique includes wavelength scanning and optical path compensation, allowing the user to choose the sensitive part at different positions along the fiber. A new digital processing procedure with birefringence dispersion data taken into account makes it possible to measure the coupling distribution along the sensitive part at more than 300 points simultaneously with a spatial resolution of 0.3 cm.

The problems of image transmission via distorting media have been discussed in literature and different methods have been suggested to solve these problems which include phase conjugation by four-wave mixing. Image by phase conjugation requires it to pass twice through the distortion. It is a major disadvantage in the practical field where the picture information is to be transmitted from one place to the other. In this paper we present our results of image transmission in transmission and reflection geometries. We have demonstrated the abilities of performing optical processing using two-wave and four-waving mixing of one- way phase conjugation with ferroelectric crystal BaTiO₃.

Optical metrology was developed to sense the wavefront of a mosaic optical system to correctly position and bend an active optical element. The optical system being examined is a telescope, with a segmented primary mirror, tested in auto-collimation. Located in the focal plane are two interferometers, a simultaneous phase shifting interferometer which measures the system wavefront and a lateral shearing interferometer which measures piston. The resultant wavefront and piston data are passed to a master computer which computes the forces and vectors necessary to position and bend the active element. This paper describes these interferometers, their evolution, requirements, calibration, and data evaluation techniques employed. Results from actual system testing are presented.

The application of phase-stepping to photoelasticimetry is presented. Photoelasticimetry is a widespread method for strain analysis. It provides information about the tensorial strain field of the structure or sample under test. An actual challenge is to complete the automation of photoelastic data processing. The phase-stepping method is easily adaptable to the isoclinic fringe pattern, as a simple rotation of the analyzer makes the isoclinic fringes move across the field of examination. The processing of phase-stepped isoclinic fringe patterns provides a whole-field map of the principal directions of the strain tensor. From this map, a very simple algorithm allows us to draw the isostatic lines. Different results concerning classical mechanical configurations are presented: tensile test of a specimen with a hole and diametrical compression of a ring. For the last example, a comparison is made with the analytical results.

India is planning to build a large Optical/Infrared Telescope of 4 to 5 M in size. This telescope will adopt most of the features of the New Technology Telescope including active and adoptive optics corrections for achieving improved image quality. Keeping this in view a prototype active optics system for a 27 inch thin mirror is being developed at Indian Institute of Astrophysics. A new digital polarization shearing interferometer will be used for wavefront sensing. The paper describes in detail the procedure for wavefront sensing and the approach for the active correction.

A new method for automatic and fast self-detection of the main indexes of radial grating is proposed and achieved, based on digital sampling and digital processing. High-multiple digital subdivision and improvement of the quality of the signal lead to high detection precision.

Abstract not available.

This paper describes a system based upon electronic speckle pattern interferometry (ESPI) for the measurement of in-plane radial strains on rotating specimens. Repeatable fringe patterns are obtained over a wide range of rotational speeds, and analyzed using the Fourier transform method. Radial strain data, extracted from the unwrapped phase fields, is compared with an established theory, and demonstrates a good agreement.

Double pulse holographic interferometry (DPHI) ideally completes standard accelerometrical techniques used for dynamic analysis but has some limitations. We present in this paper the development of a new original method based on DPHI allowing the measurement of the 3-D displacement vectors field with multi-pulse recordings. The method is based on three illuminating beams and one viewing direction and multi-pulse recording is achieved by fast deflection of reference beams. Accuracy is discussed and validated in experimental dynamic conditions through the analysis of vibration modes of a sinusoidally excited cylinder.

Addition fringes are obtained in real time from electronic speckle pattern interferometry (ESPI) using a twin-pulsed laser, when two pulses are fired during a single frame of a CCD camera. This enables object deformations to be studied under very harsh environmental conditions. However, the fringe patterns have poor visibility, because optical noise is reinforced. Automatic phase extraction from addition fringes has not previously been achieved: low-pass filtering to suppress random speckle noise also eliminates the fringes due to their low visibility. A phase-stepping algorithm that calculates phase from ESPI addition fringes without the need for a pre-processing filter is presented in this paper. This has enabled phase to be extracted from ESPI addition fringes for the first time. The algorithm is demonstrated with theoretical and experimental ESPI fringe patterns.

Originally developed as a method to assist in the assessment of optical components, the phase shifting technique has recently seen application to many other types of interferometers, including holographic, speckle, and moire systems for strain analysis. In these applications, close control of the phase shifts may be impossible due to the effect of mechanical vibrations, and this presents difficulties when extracting the phase, since the reference phase shifts are generally assumed to be known. Several approaches to the problem of determining the reference phase shifts in a perturbing environment are critically evaluated using computer simulations. The precision and accuracy of these methods are demonstrated through a practical solid mechanics example. It was found that the reference phase shifts can be determined with sufficient accuracy using all of the methods considered, and that the ultimate precision of the system was limited by additional factors -- particularly grating noise.

The application of phase-stepping to moire is presented. An analysis of the precision attainable with this technique shows that a resolution comparable to that of strain gauges is possible. We present preliminary experimental results from computer aided processing of phase-shifted moire fringe patterns (software FRANGYNE developed in our laboratory). Although this software is not specific, only results from in-plane moire are presented. Our moire setup consists of a CCD camera whose sensor acts as the reference grid. The phase shift is obtained by translating the camera perpendicular to the optical axis. The experimental results concern isotropic and anisotropic materials, and show the potential interest of such a technique in the field of experimental mechanics.

In a moire deflectometric phase object measuring system the contrast of the moire fringes formed by the first grating (G₁) image and the second grating (G₂) degrates and it causes some measurement errors in the system because of the diffraction effect of G₁. This paper analyzes and measures the contrast degradation of the image of G₁ directly. The complex amplitude, intensity, and contrast expressions of the G₁ images with varied distance to the grating are also formulated and it is concluded that the determinative factors affecting the contrast of the grating image, in other words, the moire deflectometric fringes, are the black-white ratio of grating and the distance between the image and the grating.

This paper describes the statistical distribution of metrological fields and the phase measurement method in quasi-heterodyne reference-beam ESPI under limited detector resolution. The effects of resolution, electronic noise, intensity saturation, and the quantization error on the phase measurement are discussed. The limitation of non-linearity of the detector to the phase extraction is also investigated.

Abstract not available.

Fringe analysis has progressed from classical fringe-following techniques to modern phase- shifting interferometry (PSI). Recent efforts have extended PSI to more difficult situations, including transient, complex wave fronts. This paper discusses the pros and cons of various PSI techniques and shows examples of the capabilities of spatial phase-shifting interferometry.

One approach for obtaining a surface representation is to fit Zernike polynomials (in a least squares sense) to discrete data points in the full aperture. The mathematics for this have been described using both matrix and vector notation. Additionally, vector notation has been used to describe how to obtain a surface representation from orthogonal (x, y) slope data. The result of that paper was a matrix operator for linearly combining the first eight Zernike polynomial coefficients fit to x- and y-slope data to produce a Zernike polynomial surface representation. This paper extends that process by presenting a systematic approach for obtaining the linear relationship between slope and surface using the first 49 Zernike polynomials.

This paper describes the application of digital Fourier transform to phase encoded intensity distribution. Attention is drawn to a method of extracting quantitative information automatically from the interferometric fringe data. To achieve this a set of carrier fringes has been added to interferometric fringe data. This has made it possible to form a phase map using a FFT (Fast Fourier Transform) algorithm. A Minimum Spanning Tree (MST) phase unwrapping strategy has been used to create a contiguous map of the whole fringe field. Finally, the measurement parameter related to the fringe field has been calculated from one single image. Experimental results are given for the burner flames, a compressible flow, and photoelastic fringe data.

We describe a holographic deformation measurement system which uses FFT and carrier fringe method. Since all processes are fully automatic and we use a real time holographic interferometer, continuous deformation could be measured in real time.

This paper describes a simple and effective phase unwrapping technique that prevents the propagation of errors introduced at some locations on a surface from being included in or propagating to all subsequent calculations for the remaining area of the surface. Unlike conventional phase unwrapping methods that use only the principal phase value, the proposed technique utilizes the modulation information about the fringe pattern to divide the principal phase map into regions, performs mathematical morphology operations to generate a labeled unwrapping sequence mask, and carries out multi-stage phase unwrapping procedures.

Modern interferometric measurements have evolved beyond simple interference fringe tracing to automatic phase measurement over large data array sizes. Through the use of video digitizers and inexpensive PC computers, phase shifting interferometry has become fairly commonplace, with various commercially available instruments on the marketplace. As data arrays grow in size, the number of calculations increases to where the PC computers are stretched for performance. Real time manipulation and display of results are beyond the capabilities of even workstation class computers. In response to the desire to rapidly manipulate large data sets from interferometric measurements, special electronics were developed to operate in conjunction with a high performance interferometer to aid in the testing of large optics.

This paper deals with the investigation of 3D-shape measurement techniques with respect to the calibration of the optical setup. It is shown that the accuracy of the measuring results depends on a high degree from the used geometric model and the calibration procedure. Rough approximations as generally used in practice will result in non neglectable systematic distortions of the measured 3D-coordinates. The relevance and practical ability of these theoretical investigations for optical shape measurement are demonstrated on an example of the fringe projection technique. The derived method can be used for other optical 3D- techniques too.

The measurement of focal length of lens with a three-grating system is proposed. High- precision measurement of focal length is achieved with the new system.

The accuracy of multi-aperture overlap-scanning technique (MAOST) is about (lambda) /50 with the new way to estimate the accuracy established in this paper. Two main factors to influence the accuracy, that is the connection mode and the overlap coefficient, are analyzed.

This paper describes the analysis of holographic interferograms of turbulent flowfields, obtained from hypersonic shock tunnel evaluation tests of cooled, aero-optic window designs. Three different fringe analysis techniques -- phase shifting, spatial Fourier transform, and fringe tracking -- are compared and contrasted.

A universal strategy for evaluation of ESPI (Electronic Speckle Pattern Interferometer)-phase images is proposed. Starting points of the strategy are the phase-shifted sets of the speckle- pattern of two object states. Special algorithms for calculating the modulo 2(pi) phase-image (so called `saw-tooth-image') and filtering to reduce the speckle noise and mask out areas of bad intensity modulation and of local discontinuities are described. A new area based algorithm works automatically. Regional discontinuities in the saw-tooth-images don't cause errors in the results of the true phase data. All of the proposed algorithms are implemented and tested in the hardware independent (UNIX, C, X-Windows, OSF-MOTIV) program system PISA.

This paper presents an interesting algorithm, suitable for substantial noise reduction in images with 2(pi) phase jumps. It first applies a cosine transform to the phase map associated with the corresponding fringe pattern then filters (low pass) the resulting images and computes phase again from both images. Since the cosine transform is invariant to a 2(pi) phase jumps the low pass filtering does not distort the measuring signal in such regions.

The feasibility of using diffraction pattern analysis for the quality assessment of small components, with a specific application aimed at electronic components, is discussed. An electro-optical system for the capture of reflected diffraction patterns is presented. Preliminary simulation results for simple faults have been obtained and are used to illustrate the described feature vector and neural network classifier.

A new method of unwrapping two-dimensional periodically discontinuous phase data is developed in this paper and results from application of the method to electro-optically generated phase data are presented. The method, whose foundations lie in the minimization of the energy of the surface determined by the unwrapped data, fits planar surface patches to previously processed data, then uses the best fit plane's parameters to estimate the value of the pixel under consideration. At each pixel, a new value composed of the sum of the original value and an integral multiple of the magnitude of the phase discontinuity is assigned. Processing proceeds along an expanding wavefront originating from a seed point chosen as the reference for the measurement. The facet based fringe number selection method has been found to be highly reliable even for incomplete, noisy data.

An interferogram obtained from a laser interferometer under industrial circumstance usually has a low and unconstant S/N rate, which makes it difficult to analyze the fringe pattern with enough accuracy by using fringe skeleton and fit method, making a low fidelity of a reconstructed wavefront unavoidable. The Gaussian threshold technique (GTT) for digital fringe processing was developed at our lab recently, by which we have processed many interferograms which were either generated by computer simulation or taken from a Fizeau laser interferometer with severe coherence noise, varying background intensity, and contrast. In this paper, the mathematic mode of Gaussian threshold and its algorithm are described. Rigorous estimation of the wavefronts reconstructed from interferograms with poor quality processed by GTT is also presented, the results show that the reconstruction error is less than (delta) /70, and its repeatability is much better than (lambda) /200.

Phase shifting interferometry (PSI) is a highly efficient and accurate phase measuring method. The accuracy of PSI is most seriously impaired by calibration error and nonlinearity in the phase shifter. This paper presents a new algorithm, the overlapping averaging 4-frame (OAF) algorithm, which can reduce the phase error due to phase shifter errors. The relationship between the accuracy of OAF algorithm and phase shifter errors is given. From this relationship, it is verified that the OAF algorithm can reduce the phase error due to phase shifter errors. The computer simulation providing the magnitude of a calibration error and nonlinearity in the phase shifter are shown for a number of different phase-measurement algorithms. From the analysis, the result is obtained that the OAF algorithm is more highly accurate than other phase-measurement algorithms.

We describe the use of a self-stabilized setup for time-average holographic interferometry recording of a vibrating surface in a perturbated environment. The hologram is recorded with the 632.8 nm wavelength of an He-Ne laser on a Bi₁₂TiO₂₀ crystal. The performance of the setup is discussed and experimentally evaluated.

This paper describes a large-aperture high-accuracy phase-shifting digital flat interferometer which is a combination of optic, mechanics, electricity, and algorithm. The aperture size is 250 mm and liquid surface is used as an absolute flat to eliminate systemic error. The accuracy is better than (lambda) /50 ((lambda) is Hz-Ne laser wavelength) (peak-to-valley value). The tested aperture can be enlarged to 500 mm. This interferometer will be used as our country optical flat standard instrument. This paper describes the optical interferometer, phase shifter, and calibration of precision.

Pulsed laser is transmitted by optical fibers, the polarity is changed into random distribution and the coherence is decreased somewhat. But when used in holographic interferometry, optical fibers have substantial advantages, having no influence on formation and clarity of coherent fringes. Two kinds of optical fiber speckle holographic interferometry systems are often used. The first kind employs an optical bundle to form object and reference beams, respectively. The clarity of the formed hologram decreases somewhat, but there is no effect on the contrast and clarity of holographic interferometry fringe. On the basis of the above system, the other makes use of a multimode optical fiber bundle for transmitting the image of an object, and applying lens imaging on the plate. Used in double exposure holographic interferometry the system forms holographic speckle interferometry, the subsequently reconstructed coherent pattern is similar to Young's fringe.

This paper introduces the general development on dynamic rotation rate test, discusses the advantages and the disadvantages of measuring methods in use and the problems which need solving in an actual dynamic rotation rate test-non-contact dynamic rotation rate test with a double-frequency laser. The operating principle is introduced, the practicability in theory, the measurement accuracy index in reserve, and the precision are analyzed in this paper.

The method of measuring rotating angle with double-frequency laser and wedge-plate interference based on the principle of equal-thickness interference is discussed in this paper. It makes good use of the features of good standing-interference and high sensitivity of double- frequency laser and turns the variation of rotating angle into the variation of interference fringes, so it makes measuring rotating angle with higher precision possible. It not only can determine the rotating direction automatically but also has the features of continuously measuring within 360 degree(s) and the unvarious precision of measuring angle at a higher rotating rate. It has regular theoretical and applied value.

This paper discusses the development of a new technique (including theory, method, and equipment, etc.) for testing larger optical flat only by means of a smaller interferometer. It is an overlapping subaperture interference testing (OSIT) technique. The author has established a mathematics model for OSIT to retrieve the surface of the full aperture. The theoretical accuracy of the retrieved surface of the full aperture reached (lambda) /200 (p-v). The relationship between the accuracy of the retrieved wavefront of full aperture and errors (such as system error of interferometer or position error of subapertures, etc.) has been investigated. A computer program was established to simulate the real procedure from testing surface data of subaperture to retrieved wavefront of full aperture.

An automatic technique to process Ronchigrams is presented. The phase shifting error introduced by a phase shifter is reduced using overlapping averaging four-frame algorithm. A standard plano-convex lens is tested to verify the accuracy of this technique.

This essay deals with the characteristics of scattered light on metal surface under the irradiation of dynamic speckles in theory. According to the relationship between the second order moment of the integrate intensity of scattered light in far field and the parameters of surface roughness R_q and S_m, a split system capable of generating dynamic speckles is presented which is made up of ground-glass and a BS mirror. This system causes the coherent plane wave coming from a He-Ne Laser to produce dynamic speckles and then irradiate the metal surface through which the scattered optical field was received by 1-D-CCD which is divided into two signal areas and then form two experiment conditions. Finally, based on the two received contrasting signals, the value of R_q and S_m is determined both individually and at the same time.

A new optical head for an electronic speckle pattern interferometer (ESPI) has been designed. The special design is that of a diffuser and a mirror instead of all optical elements and mechanisms of the existing optical head. Another special design is that of a double frequency grating adopted as a shearing element. The new optical head can be operated as a double beam speckle interferometry and shearography. It is light in weight and has very good anti- disturbance function. The experiments are successful when they are combined with an image processing card and software.

By combining the carrier method and electronic speckle shearography, the electronic speckle carrier shearography is realized with a PC-based image processing system. The carrier method is introduced for the unambiguous determination of the deformation fringe order and sign, as well as, for the fringe compensation. The object displacement is automatically generated with A sequence of image processing algorithm. This technique can be applied to both out-plane deformation and the deformation gradient measurement. Its successful application to the rigidity evaluation of the valve of the diesel engine is also presented.

This paper presents a general and meaningful description to the mechanism of quasi- heterodyne ESPI with smooth or speckled reference beam using statistical optical theory. The statistical distribution of metrological fields is derived. The limitations of transverse component of the object displacement to the fringe contrast and valid signal value of phase detection are discussed.

The effect of phase shifting error in phase shifting interferometry is investigated. A new algorithm for eliminating the effect is presented. The computer simulation and experiment results show that the phase shifting offset should be (pi) when two-set-bucket error compensating method is used, and this method has gotten better results than the original four bucket algorithm.

The main sources of noise that lead to speckle phase distortion and decorrelation are identified and methods to overcome these are suggested. An automated continuous reference updating technique is shown to be able to avoid speckle decorrelation induced by object drift or low frequency vibrations. A second improvement using the introduction of phase shift, and the addition of surface information during every image acquisition, is demonstrated to insure fringe pattern stability even in the presence of relatively high frequency noise due to thermal currents or air flow. Furthermore, phase modulation is used to reduce the speckle effect by removing the speckle phase term. The application of these techniques to the task of nondestructive detection of structural defects in aluminum plates is demonstrated in a very noisy environment.