This PDF file contains the front matter associated with SPIE Proceedings Volume 7790, including the Title Page, Copyright information, Table of Contents, and the Conference Committee listing.

JWST optical component in-process optical testing and cryogenic requirement compliance certification, verification & validation is probably the most difficult metrology job of our generation in astronomical optics. But, the challenge has been met: by the hard work of dozens of optical metrologists; the development and qualification of multiple custom test setups; and several new inventions, including 4D PhaseCam and Leica Absolute Distance Meter. This paper summarizes the metrology tools, test setups and processes used to characterize the JWST optical components.

The James Webb Space Telescope (JWST) Optical Telescope Element (OTE) consists of a 6.6 m clear aperture, allreflective, three-mirror anastigmat. The 18-segment primary mirror (PM) presents unique and challenging assembly, integration, alignment and testing requirements. A full aperture center of curvature optical test is performed in cryogenic vacuum conditions at the integrated observatory level to verify PM performance requirements. The Center of Curvature Optical Assembly (CoCOA), designed and being built by ITT satisfies the requirements for this test. The CoCOA contains a multi wave interferometer, patented reflective null lens, actuation for alignment, full in situ calibration capability, coarse and fine alignment sensing systems, as well as a system for monitoring changes in the PM to CoCOA distance. Two wave front calibration tests are utilized to verify the low and Mid/High spatial frequencies, overcoming the limitations of the standard null/hologram configuration in its ability to resolve mid and high spatial frequencies. This paper will introduce the systems level architecture and optical test layout for the CoCOA.

The Fine Guidance Sensor (FGS) is part of the instrument module for the James Webb Space Telescope (JWST). The FGS operates at 37 K and provides feedback to correct motion blur caused by relative motion within the observatory - an issue during long exposures. It also provides a tunable camera for science observations. The FGS powered optics comprises three, Three Mirror Assembly (TMA) - style reflective systems - one with finite conjugates and the remaining two are an infinite/finite conjugate pair. This paper addresses the issues of providing traceable interferometric wave-front error measurements when the test optics are in a cryogenic vacuum chamber. To meet space and time limits, we restrict attention to the finite conjugate device for the purposes of this publication.

Frequency sweeping interferometry (FSI) is a technique where absolute distance measurements are made without ambiguity, by using synthetic wavelengths resulting from a frequency sweep. In FSI, the measurement uncertainty increases with the distance, as consequence of the propagation of the uncertainty in the synthetic wavelength measurement. For long ranges, this component of the uncertainty budget is one of the major drawbacks of the technique. To overcome this problem, we introduced the concept of the dual FSI mode, where the measurement process for longer ranges is reduced to the close range case, by limiting the Optical Path Diference in the interferometer. This was achieved by increasing the reference arm with a long reference fiber, and using a second ancillary interferometer to calibrate continuously the fiber length and compensate temperature variations. In the context of the ESA PROBA3 space mission (coronagraph and demonstration of metrology for free-flying formation), we implemented a FSI sensor composed of a mode-hop free frequency sweep external cavity diode laser, a high finesse Fabry-Perot interferometer (to measure accurately the frequency sweep range) and a dual measurement system. This dual FSI concept, presented in San Diego in 2008, was now implemented and fully tested in view of the PROBA3 mission. Accuracies smaller than 32 μm for a measurement range from 51 m to 61 m were achieved using a reference fiber with 71 m, maintaining the reduced complexity inherent to FSI technique, a mandatory condition for space applications. Implementation issues and performance results are also discussed in this paper.

Phase-shifting Fizeau interferometry on spherical surfaces is impaired by phase-shift errors increasing with the numerical aperture, unless a custom optical set-up or wavelength shifting is used. This poses a problem especially for larger numerical apertures, and requires good error tolerance of the phase-shift method used; but it also constitutes a useful testing facility for phase-shift formulae, because a vast range of phase-shift intervals can be tested in a single measurement. In this paper I show how the "characteristic polynomials" method can be used to generate a phase-shifting method for the actual numerical aperture, and analyse residual cyclical phase errors by comparing a phase map from an interferogram with a few fringes to a phase mpa from a nulled fringe. Unrelated to the phase-shift miscalibration, thirdharmonic error fringes are found. These can be dealt with by changing the nominal phase shift from 90°/step to 60°/step and re-tailoring the evaluation formula for third-harmonic rejection. The residual error has the same frequency as the phase-shift signal itself, and can be removed by averaging measurements. Some interesting features of the characteristic polynomials for the averaged formulae emerge, which also shed some light on the mechanism that generates cyclical phase errors.

A real-time method for heterodyne speckle pattern interferometry using the correlation image sensor (CIS) is proposed. The CIS demodulates the interference phase of heterodyned speckle pattern waves from a singleframe set of temporal correlation images between the beat signal of incident light and three-phase sinusoidal reference signals at each pixel at an ordinary video frame rate. The proposed method does not suffer loss of spatial resolution or decrease in signal-to-noise ratio that would happen for a high-speed image sensor. In-plane and out-of-plane deformation measurement systems are developed with a 200 × 200-pixel CIS camera. The experimental results obtained on these systems show good linearity of the change in speckle interference phase to the voltage applied to a piezoelectric actuator that moves the object.

Phase-shifting algorithms are methods used for recovering the modulating phase of an interferogram sequence obtained by Phase Stepping Interferometry (PSI) techniques. Typically, the number of interferograms in a PSI sequence is from 3 to around 9 interferograms, although we can find algorithms that works with more than 9 interferograms. In this paper, we are going to show the analysis and design of phase-shifting algorithms from the point of view of the linear systems paradigm from digital signal processing. We will show how this paradigm describes in a general fashion the phase-shifting algorithm systems, and how we can easily design tunable phase-shifting algorithms using this simple scheme.

The method of excess fractions has a long history in metrology. More recently excess fractions has been exploited to resolve the fringe order ambiguity in interferometric metrology with varying degrees of success. There are a variety of reports detailing the performance of excess fractions, for example, using 4 wavelengths an unambiguous measurement range of 2.4 mm was achieved with a phase noise of 1/900th of a fringe. In an independent report a 4 wavelength interferometer gave an unambiguous measurement range of 17 mm with a phase noise of 1/200th of a fringe. It has been found that the unambiguous range of an excess fractions multi-wavelength interferometer depends on the wavelengths used within the system. A theoretical model is reported in this paper that can be used in a predictive way to determine the unambiguous measurement range based on three wavelength dependent parameters. The excess fractions model is consistent with beat wavelength techniques but offers many alternative sets of wavelengths to achieve, for a given phase noise, a particular unambiguous measurement range with a given reliability.

A uni-axial measurement of three dimensional surface profiles by a liquid crystal digital shifter is proposed using a telecentric optical system. Height information is captured by measuring the contrast in the projected pattern. A shadow less measurement of the object's area is archived by using a uni-axial system. The magnification of the object image captured by a CCD camera is made constant by changing the focus distance. The liquid crystal digital shifter is a powerful tool to make arbitrary intensity and frequency distribution. Surface profiles of mechanical parts were measured to demonstrate this method.

This paper presents a technique that reaches 3-D shape measurement speed beyond the digital-light-processing (DLP) projector's projection speed. For this technique, a "solid-state" binary structured pattern is generated with each micromirror pixel always being at one status (ON or OFF). By this means, any time segment of projection can represent the whole signal, thus the exposure time can be shorter than the projection time. A sinusoidal fringe pattern is generated by properly defocusing a binary one, and the Fourier method can be adopted for 3-D shape measurement. We have successfully reached 2000 Hz 3-D shape measurement speed with good measurement quality. Because the fringe pattern is generated digitally, this proposed technique provides an alternative flexible approach for high-speed applications.

A compact LED illumination based shape measurement system of glossy surfaces is presented. The system is based on Phase Measuring Deflectometry (PMD). In this system the sinusoidal fringe pattern is formed using photographic 35 mm film frame which is illuminated from behind using LED and diffuser. Beam splitter is used to combine x- and y-direction fringe patterns, which are needed by PMD. Phase shifting is generated manually using translational stages and micrometer actuators. Compared to digital fringes displayed on the screen, our LED based setup can provide higher power, completely diffuse light and produce smoother sinusoidal fringes with continuous intensity distribution. LED usage enables also pulsed illumination to freeze sample movement. The resolution of the method is submicron level. Due to the compact size this setup is promising in the small scale measurement field.

Phase-based 3-D fringe projection imaging systems have been widely studied because of the advantages of fullfield, high accuracy, fast acquisition and automatic processing. The calibration of phase-based 3-D systems is an important procedure, which builds up the relationship between the obtained absolute phase map and the depth information. In this paper, a fast and flexible calibration method for phase-based 3-D imaging systems is presented based on an uneven fringe projection method. The relationship between the measured phase and the object's depth is linear and independent of pixel position, so it is possible to calibrate the 3-D imaging system by using discrete markers (with known separation) on a white plate. Projecting uneven fringe pattern sets onto the plate can calculate the absolute phase of each marker. At the same time, the depth of the markers can be obtained by general camera calibration methods. Therefore, the linear relationship between the measured phase and the depth can be determined. The proposed method was applied to calibrate an existing phase-based 3-D imaging system which utilizes the uneven fringe projection technique. The entire calibration procedure does not require accurate movement of a reference plane within the measurement volume. The calibrated system was evaluated by measuring an accurately positioned white plate. Experimental results show that the proposed calibration method can easily build up an accurate relationship between the absolute phase and the depth information.

A new fringe analysis for shadow moiré new fringe analysis for shadow moiré using a SEM is proposed in order to perform a high resolution 3-D shape measurement. Two sheets of shadow moiré fringe images are grabbed by shifting the grating using PZT. One sheet of deformed shadow of grating image which does not include any original grid image is reconstructed from two shadow moiré fringe images by using the new method. In experiments, a sphere that is a bearing ball(diameter:700μm) was measured by the method. The standard deviation of the difference between the measured result and the ideal shape as the sphere was 95nm. From the results, it was confirmed that the proposed method had not only a high measuring accuracy but also a spatial high-resolution power(330nm). using a SEM is proposed in order to perform a high resolution 3-D shape measurement. Two sheets of shadow moiré fringe images are grabbed by shifting the grating using PZT. One sheet of deformed shadow of grating image which does not include any original grid image is reconstructed from two shadow moiré fringe images by using the new method. In experiments, a sphere that is a bearing ball(diameter:700μm) was measured by the method. The standard deviation of the difference between the measured result and the ideal shape as the sphere was 95nm. From the results, it was confirmed that the proposed method had not only a high measuring accuracy but also a spatial high-resolution power(330nm).

The calibration of reference surfaces becomes important in interferometry whenever the tolerances for the tested component are comparable to the imperfections of the reference surface itself. To achieve measurement accuracy better than the reference surface, its errors must be characterised and subtracted from the measurement result. We propose a rapid and simple technique utilising a flat mirror in the focus of the converging test wavefront and a partial occlusion of the test beam, to implement a double-pass self-calibration of the reference surface. Stitching together three or more measurements, with the beam stop appropriately rotated, yields the full-aperture calibration data. The method cannot detect point-antisymmetric errors, but common errors in reference spheres, such as spherical aberration and astigmatism, are point-symmetric and should still be adequately captured. For calibrating spherical surfaces in Fizeau interferometry, a ball of good sphericity can be measured against the reference surface in a number of random orientations. This averages out the errors of the ball and converges toward the stationary error in the reference sphere. Depending on the quality of the ball and the desired uncertainty, the number of orientations required can be large (50-100), which is laborious and time-consuming. We compare the performance of the new technique with the ball-averaging method and the so-called "cat's eye" method to assess the practical trade-offs involved.

The concept of lateral scanning white-light interferometer (LSWLI) has been introduced nearly a decade ago [1] as an alternative to the conventional white-light (WL) interferometers [2-14], capable of improved speed and image stitching. The general principle of this type of measurement is shown in Figure 1. A conventional white light interferometer is equipped with an XYZ stage which can perform an accurate lateral (XY) translation. The interferometer objective is tilted with respect to this stage such that the zero optical path difference (OPD) makes an angle α with respect to the direction of the translation. By convention, the tilt angle will be measured from the direction of the translation. For the case when this angle is different than zero, an object placed on the stage will present a specific fringe pattern whose density is dictated by the magnitude of the angle. In Figure 2, a linear fringe pattern obtained from a flat surface is shown. As the profiled object is translated at a constant speed, the CCD will record interference frames at a constant rate. Figure 3 shows how different pixels of the object (marked by up or down pointing arrows) will be recorded in consecutive frames during the object translation. In the case when the CCD frame rate and the stage speed are properly correlated, a given point of the object will be translated by exactly one pixel from one CCD frame to the other. The correlogram of each object point can thus be recovered by taking a "diagonal section" through the stack of recorded frames (Figure 4). Because during the scan the optical path difference of each point of the sample changes continuously, the LSWLI correlogram looks similar with its counterpart obtained by using WL interferometers. As mentioned before, the LSWLI measurements allow for a continuous data acquisition process, eliminating thus the need for a cumbersome stitching procedure that must be done for large samples when measured by using a standard WL interferometer. It also allows for a faster data acquisition and, in principle, it is possible for very large samples to be measured during a single pass.

Tunable lasers are used in optical metrology, but their intrinsic tuning accuracy is sometimes inadequate and an external wavemeter is then required to measure the wavelength more accurately. In this paper, we present the design of a discrete step wavemeter to measure the wavelength of the light from a tunable laser during the operation of a multi-wavelength interferometric shape measuring system. This relatively low-cost wavemeter is embedded in the metrology system and consists of a discrete set of small retroreflectors mounted at different ranges on a super-invar base, which eases alignment and allows it to be insensitive to temperature changes. During operation, interference patterns from the retroreflectors are captured by a camera for each phase shift and commanded wavelength and analyzed to determine the actual wavelength. The phase measurement uses a least square fitting algorithm. A Fourier Transform peak finding measurement technique is used for phase unwrapping. Both numerical simulation and experiments indicate improved system performance using this internal wavemeter technique.

We describe a distance-measuring interferometer based on a novel frequency-stepping laser that is tunable over 30 nm. Conventional tunable lasers provide continuous tuning over a range of wavelengths without any mode transitions. The new frequency-stepping laser was designed to maximize frequency repeatability by exploiting the mode-hopping behavior to achieve equal frequency increments. An interferometric image is collected at consecutive laser mode frequencies making it very easy to perform Fourier transforms. The modulation frequency of the interference on each pixel is directly proportional to the optical path difference between the reference and test arms of the interferometer as well as the laser mode spacing. The inherent stability of the frequency-stepping laser results in a very accurate conversion from the modulation frequency of the pixel to its OPD. A Fourier transform is performed on each pixel to determine the height difference between the reference and measurement arms independent of its neighboring pixels. Our laser mode spacing of 36 GHz results in an unambiguous measurement range of 2.1 mm. Prior knowledge about the features of the part being measured allows us to measure over 300 mm of range with 10 nm resolution. This can be combined with conventional PMI techniques to achieve sub-nanometer resolution. This technique is applicable to both rough and smooth parts making it possible to perform metrology on individual components as well as partial assemblies that require tight tolerances.

Interferometry can be extremely useful for testing optical components and optical systems as well as the metrology of many other components, such as the flatness and roughness of hard disk drive platters, the shape of magnetic recording heads and machined parts, and the deformations of diffuse surfaces. To make good use of interferometric data the data must be analyzed by a computer to determine if the surface shape is correct or not and if it is not correct what has to be done to correct it and how well the surface being evaluated will perform if it is not corrected. Until recently a major limitation of interferometry for precision metrology was the sensitivity to the environment.

The spatial frequency response of the pixelated phase mask sensor has been investigated both theoretically and experimentally. Using the small phase step approximation, it is shown that the instrument transfer function can be approximated as the product of the system optical transfer function and the spatial carrier processing filter transfer function. To achieve optimum performance it is important that the bandwidth of the optical imaging system is adequate so that the limiting factor is the detector pixel width. Actual measurements on a commercial Fizeau interferometer agree very well with the theory, and demonstrate detector limited performance. The spatial resolution of the calculated phase map is algorithm dependent; however, both the 2x2 and 3x3 convolution algorithms result in a frequency response that is significantly more than what would be obtained by a simple parsing of the image. Therefore, a 1k x 1k sensor has a spatial frequency response that is approximately equal to the detector limited resolution of a 700 x 700 array with its frequency response extending to the full Nyquist limit of the 1k x 1k array.

Aspheric surfaces are measured using standard interferometers coupled with computer generated holograms (CGHs) that compensate the aspheric wavefronts. Such systems can measure complex aspheric shapes with accuracy of a few nanometers. However, the imaging properties of the interferometer-CGH combination can provide limitations for data mapping, resolution, and accuracy. These effects are explored, with an emphasis on the diffraction effects that are unique to interferometry.

Zernike polynomials have emerged as the preferred method of characterizing as-fabricated optical surfaces. From here, over time, they have come to be used as a sparsely sampled representation of the state of alignment of assembled optical systems both during and at the conclusion of the alignment process. We show here that it is possible to develop the field dependence that analytically interconnects the coefficients of the Zernike polynomial (which has to-date been characterized only by its aperture dependence) as a more complete representation of an aligned rotationally symmetric optical system and in a paper to follow a misaligned optical system. This significant expansion to this valuable polynomial provides an important new tool for characterizing high performance optical systems throughout the optical design, fabrication, assembly, and interim and acceptance test process.

The statistical properties of the spatial derivatives of the Stokes parameters for polarization speckle are investigated theoretically and experimentally. Based on the Gaussian assumption, the six-dimensional joint probability density function (p.d.f) for the derivatives of the Stokes parameters (S₁, S₂, and S₃) are all derived analytically for the first time. Subsequently, three two-dimensional p.d.f of derivatives for each Stokes parameters and the corresponding six marginal p.d.f are also given. Based on polar-interferometry, experiments have also been conducted to demonstrate the validity of the principle.

A method for reducing the coherent noise, by a factor of two, in dynamic interferometry measurements is presented. Reducing coherent noise is particularly important in "on-machine" metrology applications where residual noise can be polished into the surface under test. Both theory and experimental measurements are discussed.

We propose a simple implementation of off-axis coherence holography with a commercial projector combined with a Sagnac radial shearing interferometer. The projector functions as a device for display and incoherent illumination of a coherence hologram, which permits reconstruction of the hologram with a generic spatially-incoherent quasimonochromatic thermal light source. The Sagnac radial shearing interferometer, with its inherent stability of a common-path interferometer and controllable magnification introduced by variable shear, functions as a device for correlating optical fields to detect the 3-D coherence function that represents the object recorded in the coherence hologram. A set of phase-shifted Fourier transform holograms was displayed sequentially with the projector. The coherence function was detected by applying the phase-shift technique to the Sagnac radial shearing interferometer, and the object was reconstructed as the 3-D correlation map of the fields diffracted from the hologram. The technique can be applied for dispersion-free spatial coherence tomography and profilometry.

The paper presents concept, summary of numerical modeling and technology chain proposition for fabrication of measurement heads of integrated grating interferometer and interferometric tomograph. In both cases, the measurement head is a monolithic PMMA cuboidal block with diffraction grating integrated. The structures replace a set of bulk optical elements used in classical interferometric setups. Fabrication of the measurement heads by replication is the crucial aspect of significant reduction of proposed system manufacturing. Numerical treatment performed in geometrical and scalar-wave regime, covers investigation of external as well as internal properties of the measurement heads. Modeling was also the basis for determination of acceptable measurement head replicas quality providing beam propagation proper for both considered interferometric techniques. The technology chain proposed in the paper covers master fabrication and its replication steps leading to fabrication of truly low-cost measurement devices.

Moiré technique is a technique used for 2D and 3D imaging and surface characterization. Moiré systems may have a range of zooms to image an object at different levels of details or Moiré images may be combined (or compared) with images from other interferometers. So, it is needed to inter-relate images together in order to keep the continuity of the images at different levels of zoom or images from different types of interferometers. This paper uses image registration techniques to correlate images and find scale and translation between two images. Image registration is widely used in medical imaging and range imaging to relate two different images from a single object or scene. In this work, only interferograms from two successive levels of zooms of a Moiré system are used. Saved interferograms are correlated using one of the affine algorithms which are used in image registration and then relative scale and shift are calculated. Calculation of these parameters makes it possible to locate the position of area that the Moiré system is zoomed in, related to the area with lower zoom level. Simulation results show that this technique is applicable and successful in finding the scale and shift parameters and therefore can keep the continuity between images at different levels of zoom.

Recently rapid development of ultrahigh speed optical coherence tomography (OCT) instruments have been observed. This imaging modality enables performing cross-sectional in vivo imaging of biological samples with speeds of more than 100,000,000 axial scans per second. This progress has been achieved by the introduction of Fourier domain detection techniques to OCT instruments. High-speed imaging capabilities lifts the primary limitation of early OCT technology by giving access to in vivo 3-D volumetric reconstructions in large scales within reasonable time constraints. New perspectives for existing OCT applications has been added by creating new instrumentation including the functional imaging. The latter shows a potential to differentiate tissue pathologies via metabolic properties or functional responses.

Multiple-wavelength optical fields at a detecting plane of an interferometer are generated by a computer from the detected interference signals of a thin glass sheet. The generated optical fields are backpropagated towards the glass sheet along the optical axis. An optical field along the optical axis is reconstructed by summing the backpropagated fields over the multiple wavelengths. The amplitude and phase distributions of the reconstructed optical field provide the positions of the two surfaces of the glass sheet where peak values of the amplitude and zero or π values of the phase appear. The accuracy of the position measurement is several nanometers.

There are various methods for film thickness measurement. This paper aims at thin film measurement methods which work with wavelength-dependent sensor signals, no matter how the signal was captured. These measurement systems are called Thin Film Reflectometers (TFR). The resolution of thin film reflection measurement is limited by the spectral resolution of the detection system, the spectral wavelength range and the analyzing algorithm. Analytical theory of four different algorithms for thin film measurement is described and algorithms are compared via numerical simulations. Most of these algorithms can be found both in the literature and in different software-libraries (e.g. MATLAB, LabVIEW...) To compare different algorithms, the reflected light intensities of a thin film have been simulated for an exemplary thin glass film and a common off-the-shelf-spectrometer, a broadband visible light source and characteristic noise levels. The same data was fed for four selected algorithms in order to compare the results. To characterize algorithms in resolution, range and accuracy, the standard deviation of the output data has been computed for different spectral windows and resolutions. As a result we can provide a concise recommendation for appropriate use of the presented TFR algorithms.

We established an interferometric sensor for optical precision measurement of distance changes. A fiber-coupled micro-optical probe with an integrated reference surface is mounted on a bending beam. A piezoelectric actuator deflects the beam. Besides focus scanning this deflection modulates the optical path length of the measuring arm of the interferometer, while the reference path remains unchanged. If the distance between optical probe and measuring object changes, characteristic phase shifts of the corresponding interference signals appear. This enables us to achieve an interferometric resolution. The problem of λ/2 ambiguity is solved by using the signal envelope resulting from confocal focus scanning.

A coherent dual fiber-comb spectrometer centered at 1.5 μm wavelengths is transferred to 3.4 μm by differencefrequency generation with a 1064 nm cw laser. It is shown that the residual linewidth between the comb teeth at 3.4 μm is resolution-limited to 200 mHz; such narrow linewidths can enable coherent dual-comb spectroscopy at high-precision and signal-to-noise ratio. We then discuss different interferometric configurations for coherent dual-comb spectroscopy. We find that a two-branch interferometric setup is appropriate to measure both the magnitude and phase spectrum of purely Doppler-broadened absorption lines. An initial measurement of methane lines in the υ₃ band P-branch with a resolution of 114 MHz is demonstrated.

We aim to develop a method for distinguishing quality of stone artifacts. A value of stone artifacts depends on the polishing quality of the surface. However, it is difficult to evaluate quantitatively and its evaluation is performed by sensibility of experts. According to a theory, experts can sense a minute difference of optical characteristic of polished stone surface. We propose a simultaneous measurement of spectral reflectivity and birefringence of polished stone surface using the polarization phase-shifting interferometer. In the polarization phase-shifting interferometry, the phase-shifter gives a phase difference between perpendicular polarized beams. This phase difference can be considered the optical retardation. When the linearly polarized beam passes though a sample which has birefringence, the initial phase of interferogram is shifted. Thus, retardations in each wavelength can be calculated by Fourier analyzing a interferogram. First, we constructed a coaxial illumination type optical system for verification experiments. As a result, we confirmed the reflected light from surface is stronger than light from inner. Therefore, it cannot measure inner reflected light which has valuable optical characteristics. Based on these results, we improved the illumination method of optical system to oblique illumination. Finally, we can obtain the 2-dimentional spectral reflectivity and birefringence characteristics.

We developed a simple and accurate method for measuring the refractive indices of transparent plates by analyzing the transmitted fringe pattern as a function of angle of incidence. By using two different wavelengths, we resolved the 2π- ambiguity inherent to the phase measurement involving a thick medium, leading to independent determination of the absolute index of refraction and the thickness with a relative uncertainty smaller than 10^-5 for a 1 mm-thick fused silica plate. The accuracy of our method was confirmed with a standard reference material.

Optical interferometry techniques were used for the first time to measure the surface resistivity/conductivity of carbon steel samples in blank seawater and in seawater with different concentrations of a corrosion inhibitor, without any physical contact. The measurement of the surface resistivity/conductivity of carbon steel samples was carried out in blank seawater and in seawater with a concentration range of 5-20ppm of RA-41 corrosion inhibitor, at room temperature. In this investigation, the real-time holographic interferometric was carried out to measure the thickness of anodic dissolved layer or the total thickness, U_total, of formed oxide layer of carbon steel samples during the alternating current (AC) impedance of the samples in blank seawater and in 5-20 ppm RA-41 inhibited seawater, respectively. In other words, the surface resistivity/conductivity of carbon steel samples was determined simultaneously by holographic interferometry, an electromagnetic method, and by the Electrochemical Impedance (E.I) spectroscopy, an electronic method. In addition, a mathematical model was derived in order to correlate between the AC impedance (resistance) and to the surface (orthogonal) displacement of the surface of the samples in solutions. In other words, a proportionality constant (surface resistivity (ρ) or surface conductivity(σ)=1/[surface resistivity (ρ)] between the determined AC impedance (by EIS technique) and the orthogonal displacement (by the optical interferometry techniques) was obtained. Consequently the values ρ and σ of the carbon steel samples in solutions were obtained. Also, the value of ρ from other source were used for comparison sake with the calculated values of this investigation. This study revealed that the thickness of the anodic dissolved layer of the carbon steel sample has been removed from the surface of the sample, in the blank seawater. Therefore, the corresponding value of the resistivity to such layer remained the same as the value of the resistivity of the carbon steel sample in air, around 1x10^-5 Ohms-cm. On the contrary, the measured values of the resistivity of the carbon steel samples were 2.4x10⁶ Ohms-cm, 2.2x10⁷ Ohms-cm, and 1.1x10⁸ Ohms-cm in 5ppm,10ppm, and 20ppm RA-41 inhibited seawater solutions, respectively. Furthermore, the determined value range of the ρ of the formed oxide layers, 2.4x10⁶ Ohms-cm to 1.1x10⁸ Ohms-cm, is found in a reasonable agreement with the one found in literature for the Fe Oxide-hydroxides, i.e., Goethite(α-FeOOH) and for the Lepidocrocite (γ-FeOOH), 1x10⁹ Ohms-cm. The ρ value of the Goethite(α-FeOOH) and of the Lepidocrocite (γ-FeOOH), 1x10⁹ Ohms-cm, was found slightly higher than the ρ value range of the formed oxide layer of the present study. This because the former value was determined by a DC method rather than by an electromagnetic method,i.e., holographic interferometry, with applications of EIS, i.e., AC method. As a result, erroneous measurements were recorded due to the introduction of heat to Fe oxide-hydroxides. This led to higher value of the resistivity of the Goethite(α-FeOOH) and for the Lepidocrocite (γ-FeOOH)), 1x10⁹ Ohms-cm, compared to the determined value range of the resistivity of the formed oxide layers, 2.4x10⁶ Ohms-cm to 1.1x10⁸ Ohms-cm.

The detectors based on non-steady-state photo-electromotive force (p-EMF) effect, induced in a photoconductor by an oscillating light pattern, have been proposed recently for localization of self-images generated by a periodical object in real time and without any image processing. Here, we present the detailed theoretical analysis of the p- EMF effect induced by an arbitrary 1-D periodical light pattern. Analytical expression for p-EMF current density in a case of light distribution containing only odd harmonics is derived. In order to illustrate our results, axial dependence of the photo-EMF signal induced by patterns generated in near field by the diffraction on a binary grating was simulated numerically. Our results demonstrated, that the optimum regime for the localization of selfimages using the p-EMF based detector is when the fundamental spatial harmonic of the light pattern is smaller than the inverse of the diffusion length of the charge carriers, being the p-EMF current proportional to the sum of the squares of the spatial harmonics visibilities.

There is large aperture and diffraction-limited laser beam in the space laser applications such as laser communication. Laser wavefront can be measured by shearing interferometer or Shark-Hartmann sensor etc. Large-Optics shearing interferometer based on Mach-Zehnder plate structure has been manufactured to differentially analyze the laser wavefront from two parts of aperture-divided fringes. One of six optical plates of the interferometer is divided to the up part and the down. The precision of measurement is higher than the full aperture design. It is suitable for the diameter below 290mm with the changeable shear amount from 1mm to 150mm. There are two sets of collimators used for the parallel of the plates. Another single-mode 635nm laser collimator which is measured through double-shearing plate before is serving as a standard wavefront of 150mm diameter. One path of the interference is changed with precise adjustment unit in several microns that the interference may be happened between equal optical path reflection and the other. It can be used for widely tunable laser and other laser system which has short coherent length. The apparatus and the experiments are explained in detail in this paper. Many systems of different quality and diameter and coherent length are measured by the large-optics shearing interferometer. The experimental wavefront results are fitted to Zernike polynomial and the Zernike coefficients are derived.

We propose a new point diffraction interferometer using a polarizer with a pinholed for qualitative optical analysis. Diffraction from a polarizer with a pinholed makes reference and measurement waves. Interference fringe between diffracted-undiffracted measurement wave and undiffracted-diffracted reference wave is stabilized by common-path configuration. We examined the pinhole size and divergence angle of the diffracted wave for test optics with various numerical aperture. Optical parts comprising the interferometer can be assembled into a small monolithic component and embedded into an imaging target for easy alignment. Optical systems evaluating imaging performances such as modulation transfer function would benefit in aligning target objects.

In this paper we show the results as well as the description of the followed process to calculate the electromagnetic field scattered by optical surface elements, where the optical surface is not considered as a flat surface that follows a shape, but as a rough one, roughness that in general may be regarded as random. We use the profile of a parabolic mirror to calculate the scattered electromagnetic field, this mirror can be used in the design and construction of a reflector telescope. We calculate the effect caused by the roughness on the performance of this optical elements, the calculation is done within the Rayleigh approximation. In another work presented in this meeting we show a comparison of the results obtained numerically using different roughness parameters and calculate its effect on the wavefront.

Visibility of interference fringes, as known, is defined by the ratio of intensities of measuring and reference waves. In interferometric measurements, intensity of measuring wave depends on reflection coefficient of an object under test. The difference between the intensities of reference and measuring waves causes visibility decrease of interference fringes. In the present paper, a possibility of controlling the fringe visibility by introducing two reference waves with mutual phase shift between them is considered for the cases of monochromatic and broadband light sources.

A novel one-shot in-line digital holography based two-dimensional Hilbert demodulation is proposed. By weakening the object wave compared with the reference wave and applying natural logarithmized operation on the in-line digital hologram, the real part of object wave can be well extracted. Then utilizing two-dimensional Hilbert transform to digitally realize π / 2 phase-shift makes it possible to reconstruct the object wave front from single-exposure in-line digital hologram. Preliminary experimental results are presented to demonstrate the proposed method. This technique can be used for real time imaging and monitoring moving objects.

The lensless Fourier transform digital holography has been widely employed in microscopic imaging. It enables quantitative phase analysis for both reflection and transmission objects. The phase image is obtained in the numerical reconstruction procedure. The in-focus reconstruction distance could be determined according to the extremum of the autofocusing criterion function, which is commonly applied in finding the in-focus amplitude image of the object. Then the reconstruction distance for the phase image is considered to be equal to the one for the amplitude image. When the object is a pure phase sample, such as the living cell, the minimum value of the autofocusing criterion function should be found to determine the in-focus reconstruction distance. However, in the experiment, the in-focus amplitude image is often not an ideal uniform bright field, so this method will result in some deviation. In this contribution, two derivatives-based criterion functions are applied to the phase image directly to accomplish the in-focus phase contrast imaging, which is more intuitive and precise. In our experiments, the set-up of the lensless Fourier transform digital holography is established firstly. Then the living cervical carcinoma cells are detected. The phase aberration is corrected by two-step algorithm. The final autofocusing results verify the algorithm proposed in this paper.

We present the experimental study of a new method that uses an adaptive photodetector based on the nonsteady- state photoelectromotive force (photo-EMF) effect for measuring the visibility of the Talbot patterns generated by a Ronchi grating. It was demonstrated that the photo-EMF based detector could be used for efficient localization of planes with minimal and maximal visibility in real time, with high spatial resolution and without any signal processing. The possibility for localization of self-images in turbid media was also investigated. Finally, the performance of our method was compared against conventionally used method based on analysis of images obtained by CCD camera.

A phase retrieval algorithm which only needs to measure the intensity distribution at two positions was used to reconstruct laser wavefront. It was further applied in high power laser. Results were obtained from the phase retrieval algorithm in the visible band, and the effects of measurement error on the phase retrieval process have been simulated. This algorithm is not sensitive to measurement error, but sensitive to the relative distribution of light intensity.

This paper presents a real-time 3-D, or 4-D, shape measurement technique that can reach the speed limit of a digital fringe projection system without significantly increasing the system cost. Instead of generating sinusoidal fringe patterns by a computer directly, they are produced by defocusing binary structured patterns. By this means, with a relatively inexpensive camera, the 3-D shape measurement system can double the previously maximum achievable speed, and reaches the refreshing rate of a digital-light-processing (DLP) projector: 120 Hz.

A new coding method is proposed for measuring the three-dimensional (3D) shape of spatially isolated objects . Based on Gray Code and sinusoidal stripe, this coded fringe pattern whose RGB components comprise the multiplications of three different frames in Gray Code and sinusoidal stripes, appears to be digital color coded sinusoidal fringes. The digital color coded sinusoidal fringe pattern is created by software on a computer and then projected to the tested object's surface by a projector, and the image of the object is captured by a camera positioned at an angle different from that of the projector, then the image is processed, color Gray Codes are used to obtain the phase order and sinusoidal stripes are used to get the wrapped phase, then the wrapped phase can be unwrapped and the 3D surface information can be retrieved. With only one image, 3D shape of the isolated objects can be exactly reconstructed, thus the speed is limited only by the frame rate of camera. The principle of this technique is described and an actual measurement is presented, the result of the reconstructed shapes proves the correctness and feasibility of this new coding method.

This paper proposes a fast 3D shape measurement method based on two orthogonal gratings projection. Two orthogonal gratings through a beam splitter are vertically projected on an object surface, and the tested object is placed between the imaging planes of the two gratings. Then the image of the object surface modulated by the orthogonal gratings can be obtained by a CCD camera from the same direction. The image is processed by the Fourier transform and spatial frequency domain direction filtering and reverse Fourier transform. Using the modulation distributions of two grating patterns, we can reconstruct the 3D shape of the tested object. In the measurement process, only need to capture one fringe pattern, so it is faster than the previous modulation measurement profilometry, and has also the advantages of vertical measurement without shadow problem. The method provides a possibility to be developed as a new real time pseudocolor encoding system for 3D shape.