Zernike phase-contrast is a well known and a often used method for the visualization of phase-structures. Because it applies a fixed phase-shift between the zero'th order and the scattered field, quantitative phase-measurements are only possible for small phase-shifts but not for arbitrary ones. The basic idea of the presented generalization of the method is to use polarization-optical pupil-filters for a separation of the zero'th from the higher orders in combination with phase-shifting polarization interferometry: In the simplest version, a drilled half-wave retarder is used in connection with linearly polarized illumination. This pupil-filter rotates the polarization of the scattered field by (pi) /2 while the dc-term is unaffected because it traverses the hole. The transmitted field is analyzed by phase-shifting polarization-interferometry: Using a liquid-crystal phase shifter (LCPS), both components can be phase-shifted relative to each other; they interfere at a subsequent analyzer. By means of a signal-evaluation according to phase-shifting interferometry, the complex amplitude of the scattered field can be determined relative to the dc-term enabling a computation of the complete field's phase. The method works for general complex objects. The applications we consider are in the field of microstructure inspection.

In this presentation, I present a novel phase-shifting interferometer/ellipsometer. The uniqueness arises from the fact that this study is the consolidation of four distinct ideas drawn from the field of optics and the field of statistics. A conventional four-step phase-shifting interferometer is modified to allow for both TE and TM polarized measurements. Maximum-likelihood estimation theory is then used to extract the three parameters of interest, namely the real and imaginary components of the complex index of refraction and the surface profile. Finally, Cramer-Rao lower bounds serve as a quantitative means of assessing the particular system design at the task of estimating the three parameters in question. I will demonstrate the feasibility of the proposed technique with a Mach-Zehnder prototype, and show how three system parameters, namely the incident amplitude and the relationship between the TE and TM polarized light in terms of amplitude and phase, affect the performance. I also show how quantization of the measured irradiance affects the performance.

Young's fringes pattern in speckle photography is a distribution modulated by the diffraction halo. The halo, among other effects, limits countable number of fringes for the analysis. The fringes in the outer boundaries of the halo are buried in noise due to their diminishing maximum modulated intensity. We introduce here the application of histogram equalization to maximize countable number of fringes. We find that the usually decreasing halo intensity becomes uniform by the procedure. Consequently the fringe contrast throughout the pattern becomes practically constant rather than diminishing as we move to higher orders in the halo. Results with experimental patterns are described to establish the usefulness of the procedure.

Bragg Gratings are waveguides, typically single-mode optical fibers, into which a periodic refractive index modulation has been imprinted by a patterned UV exposure. Fiber Bragg Gratings separate telecom frequency bands or compensate for optical dispersion in long-haul fiber networks, and also serve as strain sensors for civil engineering or geophysical studies and oil, gas or mining exploitation. A Bragg Grating writer is an interferometer for generating the UV exposure pattern. It is one of the unusual cases where an interferometer is a production tool, rather than a metrology instrument. In this paper, we review the most common Bragg Grating writing geometry and propose an opto-mechanical structure having minimal adjustment and very high mechanical stability.

This paper describes the development of an optical method of phase measurement and further three-dimensional surface reconstruction using colored structured light. The paper investigates a new method for improving the measurement of three-dimensional shapes by using color information of the measured scene as an additional parameter. The general problems of the most widely used algorithms (phase shifting profilometry and Fourier fringe analysis) are that phase maps produced by these methods are wrapped, in some cases the acquired fringe pattern does not fill the field of view, there may be spatially isolated areas and there is often invalid and/or noisy data. This paper aims to demonstrate a new method for three- dimensional surface reconstruction using colored fringe patterns. The proposed technique uses colored fringe patterns, which are projected at different angles onto the measured scene. Shortcomings, which arise using standard methods, can be overcome using a color multichannel Fourier fringe technique.

Because the wavelength of a laser diode (LD) has the temperature-sensitivity, in conventional LD interferometers, a temperature control is required to stabilize the wavelength in long-term measurements. We propose a self-mixing laser diode interferometer that has two coaxial measurement arms. Two interference signals are used for the measurement of displacement and wavelength stabilization in our system. As the wavelength is not stabilized thermostatically, but by adjusting current feedback, compensation is simple and response-time minimal. The feedback controls for displacement measurement and wavelength stabilization were implemented on a time-sharing basis. The devise we propose enables us to conduct long-term measurements of microscopic levels of displacement.

With the development of high-resolution CCD cameras, digital holography was made possible and has been used in laser metrology¹. A reference wave interferes with the object wave and an amplitude hologram is formed and digitally recorded on the high-resolution camera CCD. The object intensity and phase information is numerically reconstructed. In this work a different approach is introduced. A digital complex hologram of the object wave is determined without an explicit reference wave. In order to do that, a shearing device is introduced in front of the CCD of a high-resolution camera. A phase shifting device is also used to change the relative phase between each shearing pair. Twelve different images are acquired: (a) four 90 degree(s) phase-shifted images without shearing, (b) four with shearing in the x direction and (c) four with shearing in the y direction. Those images are combined and three phase difference maps are calculated: (a) the phase difference between the two wave fronts without shearing, (b) the phase difference between two neighbor pixels in the x direction and (c) the phase difference between two neighbor pixels in the y direction. To compute the complex hologram, the amplitude and phase values for each pixel must be determined. An initial arbitrary phase value is assigned to a seed point of the image. The phase values of the next neighbor pixels are propagated using the available three phase difference maps and an appropriate algorithm. The digital complex hologram is used to reconstruct the object wave. The intensity and phase patterns are numerically computed in the object plane in a way similar to conventional digital holography. This work presents the mathematical models to compute the digital complex hologram and its numerical reconstruction. In addition, a very early application of digital complex holography to record and reconstruct a point source is presented.

Resolution and speckle size in the reconstructed wavefields of digital holography depend on the aperture defined by the size of the CCD-array. Here we introduce the concept of synthesizing a larger aperture by recording simultaneously the same scene by at least two CCD-arrays. It is shown that an improvement in resolution can be obtained which corresponds to a virtual aperture of the size defined by the distance between the two CCDs. This is shown by a comparison of the point spread functions of systems with one and with two apertures. Open problems are stated and future prospects are presented.

Sensitivity, accuracy, and precision characteristics in quantitative optical metrology techniques, and specifically in optoelectronic holography based on fiber optics and high-spatial and high-digital resolution cameras, are discussed in this paper. It is shown that sensitivity, accuracy, and precision dependent on both, the effective determination of optical phase and the effective characterization of the illumination-observation conditions. Sensitivity, accuracy, and precision are investigated with the aid of National Institute of Standards and Technology (NIST) traceable gages, demonstrating the applicability of quantitative optical metrology techniques to satisfy constantly increasing needs for the study and development of emerging technologies.

In the paper a new approach to quasi real-time phase reconstruction of digitally recorded holograms is presented. A new, low cost and fast measurement system based on digital holographic interferometry is described. Examples of experimental results representing deformations of an object under thermal load are shown.

White-light interferometry is a powerful tool for high resolution measurements on rough surfaces. The technology can be used for roughness measurements on technical surfaces with sub-micrometers tolerances. However, in automotive industry the surface of interest may be located inside a small drilling. In this case the surface properties cannot be measured by conventional white-light interferometry. For this purpose we introduce the concept of white-light interferometry via an endoscope. The setup uses a Michelson-Interferometer and the endoscope is placed into the object arm. The endoscope produces several intermediate images of the object within the object arm. In order to approximately gain a Linnik-setup we insert a second endoscope into the reference arm. We investigate different concepts in order to perform a depth scan: A scan of the reference mirror, a scan of the object and a new intermediate image scan. By using this intermediate image scan, the measuring range in depth is not limited by the aperture of the endoscope and each point of the object is measured with the maximum lateral resolution. Feasibility experiments have been performed in our laboratory. First measurement results are presented and benefits and limitations of white-light interferometry via an endoscope are discussed.

White light interferometer (WLI) has become a common tool for measuring surfaces with large height range and/or roughness. Typically, the object is scanned through focus, thus varying the optical path difference (OPD) between the object and reference beams. The rate of the OPD change affects the quality and accuracy of the surface measurement. For high quality measurements a scanning device is often enhanced by a closed loop feedback while the scanning speed is assumed to be known and constant. In this paper we describe a white light interferometer that yields excellent results without requiring a high-end scanner. These results are achieved by embedding an additional interferometer with a long coherence length source that provides an interferometric reference signal that is used to monitor the motion of the scanner during each measurement in real time. The information about the scanner motion is then used in a WLI algorithm. This yields significant improvements in both the accuracy and repeatability of topography measurements.

A new scheme for synthesizing three-dimensional longitudinal spatial coherence function is proposed. By manipulating the irradiance of an extended quasi-monochromatic spatially incoherent source with a spatial light modulator, we generated a special optical field that exhibits high coherence selectively for the specified location along the optical axis of propagation and for the specified inclination between the two mirrors in the interferometer. The feasibility of the proposed principle is demonstrated by measuring a step height made by standard gauge blocks. The proposed scheme permits one to perform phase shift without recourse to mechanical movement. The quantitative experimental proof of the principle is presented.

White light phase shifting interferometric (WLPSI) techniques allow high precision shape measurement thanks to a combination of phase detection of the interference fringes and detection of the position of the fringe envelope. The WLPSI technique gives excellent results as long as ideal scanning and system aberration-free conditions exist. Ideal conditions rarely exist, however, and errors creep into measurements from a number of error sources. Scanner errors affect the measured phase of the object surface, and the finite size of the optical system and its aberrations cause a variation in the offset between the phase and coherence peak across the field of view of the system. This variation in turn causes unwanted 2π jumps in the phase portion of the measurement. This paper shows ways to overcome these challenges. We propose a real-time solution to correcting scanning position influence on measurement in WLPSI algorithm. In addition, we present adaptive phase shifting algorithms that avoid these jumps. Our overall technique is simple, very fast and yields highly precise and accurate results.

White-light scanning interferometry uses a wide-band spectrum light source and observes the short coherent variation of interferometric intensity obtained while moving either the test surface or the reference surface along the optical axis of the interferometric optics. When one employs the scanning interferometry for gauging the step height between two separate surface points that are made of different materials, a significant amount of measurement error occurs due to the phase change on reflection. The phase change varies with wavelength and materials, so its effects on resulting interferograms are not easy to be precisely identified. In this paper, we present a practical method for compensating for the measurement error caused by the phase change on reflection in step height gauging. The method takes a first-order approximation to the wavelength-dependent nonlinear behavior of the phase change and then determines its precise value from the phase information of the Fourier-transformed intensity data in the spatial frequency domain. The method can be realized simply by performing two additional quasi-monochromatic phase-shifting interferometric measurements, or more conveniently by adopting a special form of light source that has two spectral peaks. Experimental results prove that the propose compensation method is capable of reducing the measurement error to an accuracy of +/- 2 nm.

New digital demodulation algorithm for white-light interferometric sensors with signal processing in spectral domain is presented. The algorithm uses phase calculation from an interferometric pattern in the acquired spectrum from the sensor to evaluate the optical path difference. Suggested demodulation method provides high accuracy with uncertainty close to theoretical limit imposed by system noise. For a fiber-optic sensor with birefringent fiber and a CCD spectrometer for signal acquisition, the algorithm demonstrated the random error of the optical path difference estimate about 0.18 nm.

The presented paper reports on a conceptual design of a High Precision Optical Metrology (HPOM) system for SMART-2 with the emphasis of establishing and controlling the distance between the satellites. SMART-2 serves as a pre-cursor technology mission for DARWIN where critical technologies will be demonstrated. An overview about the DARWIN and SMART-2 mission and requirements is given. The HPOM system must take over from the Radio Frequency (RF) system at an inferometer arm difference of some cm and must establish and control an arm difference of smaller than 5nm at a 3dB bandwidth of 100Hz. A cascaded metrology system has been developed using different optical metrology methods such as time of flight, dual-wavelength and white light interferometry within one system to meet the ambitious requirement.

Digital Speckle Radiography (DSR) is a measurement technique which uses flash X-rays combined with the computer analysis used in digital speckle photography. The technique has proven to be particularly powerful in the study of internal deformation fields, in both 2- and 3-dimensions, in high-speed events such as ballistic and explosive studies. In this paper, we present details of a new stereoscopic DSR apparatus. A new approach to the pre-processing of digitized radiographs prior to the displacement analysis results in a significant improvement in accuracy. An accurate determination of the scaling factor between the sample and the radiograph is demonstrated, and corrections for the Gaussian intensity profile of the X-ray beam included.

The present article reports on numerical studies of phase front propagation for the Laser Interferometer Space Antenna (LISA). The main objective is to determine the sensitivity of the average phase of the metrology beam with respect to fluctuations of the pointing of the beam. For this purpose, the metrology beam is propagated numerically along the interferometric arm of the instrument. The effects of the obscurations from the secondary mirror and its supporting struts are studied in detail. Further, the effects of random wavefront distortions that occur due to imperfections of the optical elements are estimated through a series of Monte Carlo simulations. The results of this study can be used to determine design requirements for the instrument.

I measure the optical thickness of thin substrates using a transmitted wavefront test in which the object is placed inside a Fizeau cavity comprised of a reference flat and a mechanically actuated transmission flat for phase shifting interferometry (PSI). Traditionally, this test had been complicated by the unwanted secondary reflections between the object surfaces even when the object is tilted. These reflections generate errors that are increasingly difficult to suppress as the substrate thickness decreases. The new technique involves two successive PSI measurements of the optical profile separated by a discrete change in source wavelength. The change in source wavelength is calculated so as to invert the error contributions from multiple surface reflections. Thus the average of the two measurements is relatively free of these error contributions.

We propose a non-mechanical scanning Mirau-type spectral interference microscopic imaging system for the measurement of three-dimensional step-height of discontinuous objects. In this system a superluminescent diode is used as a broad- band light source, and an acousto-optic tunable filter (AOTF) as a high-resolution frequency scanning device. The interferometric system was made unbalanced by putting the reference mirror position exactly half-way between the top and bottom of the total step-height of the discontinuous object. While scanning the frequency of the broad-band light source using AOTF, the interference fringes move in opposite directions on the top and bottom of the object, respectively. A two-dimensional Fourier transform method was used for the unique determination of the sign of fringe movement over a large area of the object without any photo- detectors and fringe counters. From the detected sign of the fringe movement and phase information, the three-dimensional step-height is measured. Experimental results of the measurement of 100 μm step-height are presented. The main advantages of the proposed system are non-mechanical scanning and large measurement range without ambiguity in the sign of phase.

The state-of-the-art technique for measuring discontinuous surface profiles, e.g. diffractive optical elements (DOE) is white-light interferometry. Compared to single wavelength phase-shifting interferometry conventional white-light-interferometry is rather slow, because the number of frames to be evaluated is about ten times greater than in phase-shifting-interferometry. Therefore white-light-interferometry needs more memory capacity and computer time. Single wavelength phase-shifting interferometry cannot be used for the mentioned task since the order of the interference fringes cannot be determined. But if three wavelengths, e.g. a red, a green, and a blue one are used which preferably have no common factor it is possible to determine the interference order of the fringes or the absolute optical path difference (OPD) of the interferometer. The interference patterns are simultaneously recorded by a color CCD-camera having 3 separate chips. The OPD is calculated for each pixel from the three phase values mod 2π . The algorithms used and experimental results will be presented.

In this document, we describe twin-rainbow metrology, a non-invasive optical technique for measurement of the thicknesses of thin solid and liquid films to sub-micron accuracy. TRM allows measurement of coating thicknesses in two separate ways: first, directly, by a measurement of the difference between two scattering angles; ; and second, by the analysis of a Moire pattern found in the superposition of two sets of interference fringes. In this paper we will examine the conditions under which twin-rainbow metrology can be used, the accuracy of measurements made by it, and its potential applications.

Wavelength scanning interferometry allows the simultaneous measurement of the surface profile and the optical thickness variation of a parallel plate. However, it is necessary to evaluate the modulation frequencies of the signal and noise which depend on the optical thickness and dispersion of the test plate. New nineteen-sample, wavelength scanning algorithms allow variation in these parameters and give a measurement resolution of 1-2 nanometers rms. Measurement of a BK7 near-parallel plate of 250 mm diameter and 25 mm thickness was demonstrated in a Fizeau interferometer.

In this paper, we recall some basic concepts and the vocabulary of metrology. We propose some terms which today are not present in the terminology recommended by ISO. We address also the data post-processing, in particular spatial smoothing that usually decreases a lot the spatial resolution. We recommend to separate in the analysis what we call the phase sensor and the phase-to-measurand mapping. In some cases, the larger part of the uncertainty comes from the parameters which are present in this mapping.

In combination with phase shifting techniques electronic speckle pattern interferometry (ESPI) is a versatile tool in the field of deformation measurements. However, in applications outside the laboratory, it suffers from the influence of external disturbances, especially mechanical vibrations and temperature fluctuations. These effects result in global phase fluctuations that are constant over the field of measurement, but vary in time. Phase fluctuations of this kind can be compensated by an active phase stabilization system. In previous papers we introduced a DSP-controlled digital phase stabilization system on the basis of a synthetic heterodyne technique which needs no additional optical components in the ESPI set-up and stabilizes the phase at one point of the field of measurement. In this paper we will report on further improvements of the system. The functionality of further components has been integrated in the DSP, making the handling of the system and the variation of parameters of the control system even simpler. Furthermore, a high speed CMOS-camera with high full well capacity is used in the set-up instead of a CCD-camera and the system is operated with unresolved speckles. This CMOS-camera makes not only the tracking of fast deformation processes and the observation of objects with strongly varying brightness possible, but it can simultaneously generate the input signal for the control system. Finally, the control signal can be analyzed in order to get further information about object movements, especially rigid body motions and the sign of an object deformation itself.

Reliable real-time surface inspection of extended surfaces with high resolution is needed in several industrial applications. With respect to an efficient application to extended technical components such as aircraft or automotive parts, the inspection system has to perform a robust measurement with a ratio of less then 10^-6 between depth resolution and lateral extension. This ratio is at least one order beyond the solutions that are offered by existing technologies. The concept of scaled topometry consists of arranging different optical measurement techniques with overlapping ranges of resolution systematically in order to receive characteristic surface information with the required accuracy. In such a surface inspection system, an active algorithm combines measurements on several scales of resolution and distinguishes between local fault indicating structures with different extensions and global geometric properties. The first part of this active algorithm finds indications of critical surface areas in the data of every measurement and separates them into different categories. The second part analyses the detected structures in the data with respect to their resolution and decides whether a further local measurement with a higher resolution has to be performed. The third part positions the sensors and starts the refined measurements. The fourth part finally integrates the measured local data set into the overall data mesh. We have constructed a laboratory setup capable of measuring surfaces with extensions up to 1500mm x 1000mm x 500mm (in x-, y- and z-direction respectively). Using this measurement system we will be able to separate the fault indicating structures on the surface from the global shape and to classify the detected structures according to their extensions and characteristic shapes simultaneously. The level of fault detection probability will be applicable by input parameter control.

The measurement of dynamic displacements using speckle interferometry and temporal phase unwrapping allows the evaluation of displacement fields without the propagation of spatial unwrapping errors. In this work we present a novel temporal phase-shifting (TPS) method that searches for the peak of the windowed Fourier transform of the modulated intensity signal and evaluates the phase at that frequency instead of at the carrier frequency. The performance of this TPS method is compared with that of standard algorithms by using numerical simulations. The unwrapping success rate and the spatial rms phase error are evaluated, and experimental results that show the performance of this new approach are finally presented.

A digital phase locked loop (DPLL) algorithm has been applied successfully to demodulate continuous fringe patterns. An attempt was made by Ochoa et al. to extend the DPLL algorithm to demodulate non-continuous fringe patterns. Their algorithm depends on masking the invalid regions in a fringe pattern and exclude them from processing using the DPLL algorithm. Ochoa et al. have employed the standard deviation algorithm to mask the invalid regions and detect the regions with valid information. The algorithm failed in masking noisy invalid areas and detecting valid regions with low modulation indices. In this paper, a different method is used successfully in the masking of the invalid regions, detecting the valid areas and the method is applied to demodulate non-continuous fringe patterns using the DPLL algorithm.

Effective suppression of speckle noise content in interferometric data images can help in improving accuracy and resolution of the results obtained with interferometric optical metrology techniques. In this paper, novel speckle noise reduction algorithms based on the discrete wavelet transformation are presented. The algorithms proceed by: (a) estimating the noise level contained in the interferograms of interest, (b) selecting wavelet families, (c) applying the wavelet transformation using the selected families, (d) wavelet thresholding, and (e) applying the inverse wavelet transformation, producing denoised interferograms. The algorithms are applied to the different stages of the processing procedures utilized for generation of quantitative speckle correlation interferometry data of fiber-optic based opto-electronic holography (FOBOEH) techniques, allowing identification of optimal processing conditions. It is shown that wavelet algorithms are effective for speckle noise reduction while preserving image features otherwise faded with other algorithms.

The Fourier transform method has become a popular technique to retrieve the phase map encoded by Digital Speckle Pattern Interferometry (DSPI) fringes. When closed fringes need to be analyzed, carrier fringes must be introduced in the pattern to eliminate the sign ambiguity that appears in the phase distribution. Recently, a method based on the application of the continuous wavelet transform (CWT) has been reported to evaluate phase maps in SPI. The CWT method does not produce ambiguities in the phase sign even when carrier fringes are not introduced in the interferometer. In the present paper the performance of the CWT phase-extraction method is evaluated using computer-simulated fringes, approach that allows knowing precisely the phase map contained in the pattern. It is shown that only DSPI fringes that verify the stationary phase approximation and its analytic asymptotic limit can be processed with this method. The influence of the filtering process to smooth the DSPI fringes and of the method used to extend the fringe pattern edges is also analyzed. Additional drawbacks that emerge when this method is applied are finally discussed.

We present a novel procedure of phase recovery from undersampled phase-shifted interferograms. First, we use synthetic interferograms to calculate the wrapped phase differences along two orthogonal directions. Second, we unwrap them to recover the true Laplacian of the phase. The final step is to integrate the unwrapped phase differences to give the searched phase. This method may be used with either path independent or path dependent phase unwrapping algorithms. The technique overcomes the sensitivity to noise of previous algorithms when low pass filtering techniques are applied during the calculation of the phase differences and least square methods are employed in the final step of phase integration.

In many practical applications of speckle interferometry, the commonly known phase unwrapping approaches cannot cope with the stability and performance requirements of industrial environments. The use of low-cost optical components even increases the high noise levels of non-laboratory surroundings. Therefore, two fast window based techniques have been developed, which are then combined by a hybrid algorithm to obtain optimum performance and stability. The first method is a polynomial approximation method on the complex phasor image. A fast update technique on overlapping data windows is used for those areas in an interferogram with fringe densities less than one fringe per window. In areas with higher fringe densities, a second FFT-based approach is used to perform local phase unwrapping. For each data window, the FFT is computed and the gradient of the underlying phase function is given by the peak position. This method is slower than the polynomial approach, but it proves stable with all fringe densities. Any noise not exceeding the fringe information in the frequency domain will not alter the result of the gradient computation. The algorithm has been tested with different types of industrial interferograms. Compared to pixel-based methods it proves in general more stable and faster. Especially images with high fringe densities but low level of detail can be handled very efficiently since the window size and step width can be adjusted accordingly. The hybrid method is therefore suitable in an industrial environment, where quick response and a wide measurement range is needed.

Reliable in-line and in-situ measurement of structure of highly polished surfaces remains a major challenge for the modern industry. Evaluation of the wavefront of a scanning laser beam reflected from a surface allows one to establish a direct correlation between the statistics of the optical signal and the surface roughness. Phase structuring of the laser beam greatly increases the height sensitivity down to the nanometer level. High sampling rate allows one to collect a very large number of sampled data and provide a complete analysis of the surface structure rather than a single parameter such as the rms roughness.

The low-pass characteristic of the optical imaging limits severely a quantitative measurement of structure-sizes below the optical wavelength and leads to measurement errors. On the other hand, small structures show different optical characteristics for different polarizations. A fact that corresponds to the form-birefringence of microstructures. It is described for zero-order gratings by polarization dependent dielectric constants in the effective medium theory. The birefringence can be measured accurately by use of polarization interferometry where two orthogonal polarizations interfere so that their phase-difference can be determined. To that end an electro-optic modulator is inserted into the optical path of a polarization microscope to provide the well-defined phase steps for an evaluation according to phase-shifting interferometry. From the phase difference we can conclude on the optical path-difference for both polarizations and from this - using the structure thickness - on the birefringence. Waveguide-models are applied for image interpretation. For an estimation of the width of the structure we compare polarization-interferometrical measurements with rigorous numerical simulations.

Surface feature evaluation with resolution beyond the classical diffraction limit can be achieved by a combined space--frequency representation of the scattered field. This was demonstrated in a measuring procedure where the surface was consecutively illuminated by a collection of focused beams and the diffracted data was measured in the far field. Mathematically, if the focused beam has a Gaussian profile, the optical system implements a Gabor transform. Other transformations, such as wavelet transforms can be obtained by properly structuring the illuminating beam. This work presents an approach where structured beams at several wavelengths are used. This additional information gathered by this procedure allows an increased resolution and the reduction of ambiguities that may occur in the analysis of single wavelength measurements.

We present a novel method of dark field optical microscopy for linewidth measurements on microstructures on photo masks and wafers. This method is based on alternating grazing incidence illumination of the specimen, where the angle of incidence of the illumination is perpendicular to the edges or grooves of the specimen. The main advantage of this method is the improved resolving power due to the suppression of the proximity effect and to the high pass characteristic of the optical imaging. Linewidth measurements on different structures are compared with results obtained with conventional dark field and bright field optical microscopy. The experimental results are in good agreement with theoretical simulations based on rigorous diffraction theory. The suppression of the proximity effect is strongly depending on the polarization of the illuminating light. The quality of the edge localization is affected by the optical constants of the material, the structure (e.g. single line or periodical structure, corner rounding,...) And on the illumination wavelength. The best results are obtained for single lines and metallic structures.

We present theoretical and experimental studies of the reflected field in the vicinity of sub λ structures. Rigorous numerical calculations and measurements were performed to get high-precision information of certain object parameters which go beyond the limits of classical microscopy. We show that the polarization of the illumination plays a key role for the field distribution, which is reflected from the examined objects. Furthermore, we present a simplified model, which is able to qualitatively predict the behavior of the phase singularities correctly.

The detection and classification of faults is a major task for optical nondestructive testing in industrial quality control. Interferometric fringes, obtained by real-time optical measurement methods, contain a large amount of image data with information about possible defect features. This mass of data must be reduced for further evaluation. One possible way is the filtering of these images applying the adaptive wavelet transform. The wavelet transform has been proved to be a capable tool in the detection of structures with definite spatial resolution. In this paper it is shown the extraction and classification of disturbances in interferometric fringe patterns, the application of several wavelet functions with different parameters for the detection of faults, and the combination of wavelet filters for fault classification. Furthermore the implementation of complex valued wavelet filters and correlation filters is shown. We will present an algorithm to classify interferometric fringe patterns. In order to achieve real-time processing a hybrid opto-electronic system with a digital image processing and an optical correlation module is favored. The calculated wavelet filters are implemented into the optical correlator system that is based on liquid-crystal spatial light modulators. So, all discussed items were verified experimentally in the optical setup.

Correlative stitching is on the fact that the same area has the same information. This testing thought is meaningful in extending spatial measurement ranges, keeping high resolutions, high precision and low cost. So in order to test large-scale optical workpiece, people are designing large-scale interferometer, at the same time, they are also designing stitching interferometer. The keys to realize stitching measurement are to obtain high precision wavefront of each sub-aperture and apply appropriate stitching algorithm. There are many techniques to test sub-apertures, among which phase-shifting technique has high precision, and is applied widely. How to reduce its system error is a central problem. The paper will utilize difference of two testing results to remove the system error. How to reduce the accumulative error is a key problem in stitching. The paper will apply the stitching algorithm in Descartes coordinates presented by M. Otsubo and K. Okada to realize the connecting of sub-apertures. And the paper presents a method to deal with the main random errors in sub-aperture testing. Finally, the paper does some tests.

Light emanating from the polished end of a single-mode fiber forms into a near-perfect spherical wave within a finite solid angle, which can readily be explained by diffraction theory. Utilizing the useful phenomenon, we in this paper present a fiber optic diffraction interferometer that has specially been devised for testing spherical mirrors. The interferometer adopts three optical fibers; one is for generating spherical reference wave, another is for illuminating the mirror under test and the other is for calibrating the interferometer. A special assembly of sliding prism driven by a PZT actuator provides necessary phase shifts with a high immunity to environmental disturbances. In conclusion, the proposed fiber optic diffraction interferometer enables us to achieve a measurement accuracy of an order of magnitude better than conventional testing schemes using the Fizeau interferometers of which measurement accuracy is ultimately limited by the reference surface to (lambda) /50, where λ is the wavelength of the source.

One of the ever-increasing demands on the performances of heterodyne interferometers is to improve the measurements resolution, of which current state-of-the-art reaches the region of sub-nanometers. So far, the demand has been met by increasing the clock speed that drives the electronics involved for the phase measurement of the Doppler shift, but its further advance is being hampered by the technological limit of modern electronics. To cope with the problem, in this investigation, we propose a new scheme of phase- measuring electronics that reduces the measurement resolution without further increase in clock speed. Our scheme adopts a super-heterodyne technique that lowers the original beat frequency to a level of 1 MHz by mixing it with a stable reference signal generated from a special phase-locked-loop. The technique enables us to measure the phase of Doppler shift with a resolution of 1.25 nanometer at a sampling rate of 1 MHz. To avoid the undesirable decrease in the maximum measurable speed caused by the lowered beat frequency, a special technique of frequency up/down counting is combined to perform required phase- unwrapping simply by using programmable digital gates without 2π ambiguities up to the maximum velocity guaranteed by the original beat frequency.

Laser Doppler Anemometry (LDA) is a most advanced velocity measurement technique in the field of fluid mechanics, combustion, hydraulics, chemical engineering, meteorology, biomedicine engineering and industrial manufactory for its non-contact, high response, and real-time velocity measurement. In LDA technique, optical signal processing is very important and very complex due to complicated flowing properties of fluid. LDA system includes optical section and signal processing section. In conventional LDA system, these two sections are separated and perform their own functions individually. Because optical section has no active control to measured signal, only mechanically indicates the variation of measured signal, the signal processing section was designed complex and costly. The existed signal-processing methods have different problems which limited the application and in turn increasing the difficulty of signal processing to detect the complex fluid. This paper describes and analyzes a new technique, C/T technique which combined optical section and signal processing section together, made the output signal simpler and solved the problems occurred in tradition methods. On the basis of analysis of C/T method, system construction is described.

The supersmooth surface roughness measurement is becoming more and more important with the development of the processing technique. This paper studies an on-line measurement system of the supersmooth surface roughness using optical heterodyne method. The simple structure and strong practicability of this system are researched. The experimental results show that this system has the feature of the good stability and high measured accuracy.

This paper presents a new method that exploits the interference and polarization properties of light to monitor, in real time, the rapid thermal elongation of near-field optical probes. The typically flat (nanometer in size) morphology of the probe apex serves as one mirror of a Fabry-Perot type cavity; a flat semitransparent metal coated surface constitutes the other mirror. The optical-interferometry set-up permits distance acquisition with a high frequency bandwidth (compared to other methods based on electronic feedback) while control of the light polarization allows an increase of the signal to noise ratio of the measurements.

Temporal phase shifting interferometers require a stable environment during the data acquisition, so that well controlled phase steps can be introduced between successively acquired interferograms. In contrast, single-frame interferometers need to acquire only one interferogram to provide a phase map with very good precision at high spatial resolution. Thus these interferometers are well suited for the interferometric testing of large optics with long radius of curvature for which vibration isolation is difficult, e.g. testing astronomical telescope mirrors in a test tower, or testing space optics inside a cryogenic vacuum chamber. This paper describes the Instantaneous Phase Interferometer (IPI) by ADE Phase Shift, together with measurement results at NASA. The IPI consists of a polarization Twyman-Green interferometer operating at 632.8nm, with single-frame phase acquisition based on a spatial carrier technique. The spatial carrier fringes are generated by introducing large amount of tilt between the test beam and the reference beam. The phase information of the optical surface under test is encoded in the straightness of the interference fringes, which can be detected in a single frame with spatial sampling of 1000x1000 pixels. Measurements taken at the NASA Marshall Space Flight Center in support of the characterization of developmental optics for the Next Generation Space Telescope are presented. Such tests consist of a mirror placed inside a cryogenic vacuum chamber, with the IPI placed outside the test chamber without any additional vibration isolation.