This PDF file contains the front matter associated with SPIE Proceedings Volume 8493, including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.

A Doppler Asymmetric Spatial Heterodyne (DASH) interferometer is a device that is suited to making line-of-sight measurements of thermospheric wind speeds from either ground- or space-based platforms. However, DASH interferometer characteristics are sensitive to temperature changes. These instrument changes can be tracked with calibration sources and subsequently corrected during data analysis. Even though these thermal effects can be corrected, a quantitative understanding of the physics driving them is important for future instrument designs. A previous study of the thermal behavior of a monolithic DASH system [Harlander et al, Opt. Express, 2010] measured a thermal response that was not consistent with a simplified model. It was suggested that this discrepancy was a result of the rotation of various optical components caused by the thermoelastic distortion of the monolithic interferometer elements which were cemented together yet had different coefficients of thermal expansion. This distortion effect was not included in the simplified model. In this study we assemble an interferometer with separate optical components which are allowed to expand independently with changes in temperature and therefore eliminates any distortion due to stresses induced by different coefficients of thermal expansion. Thus, by measuring the thermally induced change to the interference pattern generated by this interferometer, we may characterize the thermal behavior of the system and verify whether all the relevant physics is included in the simplified model. We find that the thermal drift measured by the experimental interferometer closely matches that predicted by the model. This important result will help in the material selection and overall design of future monolithic interferometers.

In digital holography an object wave is numerically reconstructed from a recorded hologram. Using this technique it is possible to detect the position and size of particles in a 3D domain. In this work, particular focus is placed on quantification of particles with non-spherical morphologies. The in-line configuration is chosen due to the simplicity of the optical setup and minimal distortions of in-plane morphologies. However, this geometry is also characterized by a large depth-of-focus and high uncertainty in the detected depth. To quantify these uncertainties, this work begins with the definition of a non-dimensional model of hologram recording and reconstruction applied to single spherical and nonspherical particles. Typical CCD noise sources are included. Application of this model to two particle detection methods reveals the relevant merits and limitations of each particle detection method. From the lessons learned, a new hybrid particle detection method is proposed. Simulations indicate the hybrid method significantly improves upon the accuracy of the measured depth and particle morphologies. Furthermore, the proposed method automatically determines the optimum threshold for each particle, and, therefore, requires minimal user inputs. Finally, initial experimental results for spherical particles confirm the accuracy of the proposed hybrid method.

Optical sub-wavelength structures allow to code space-varying complex transmittance functions that induce both amplitude and phase variations on a given wavefront at the micrometer scale. This paves the way to the miniaturization of optical devices based on the spatial coding of the complex transmittance. We describe here a dedicated setup in the infrared range (3-14,um) for the spatial and spectral characterization of such components. The setup combines (i) a quadri-wave lateral shearing interferometer, which enables a two dimensional measurement of phase and amplitude, and (ii) a Fourier Transform Infrared Interferometer for spectral resolution. We present both theoretical simulations and experimental results of the characterization of subwavelength gratings.

An optical, full-field measurement technique called Digital Gradient Sensing (DGS) has been developed for measuring angular deflections of light rays propagating through transparent planar solids subjected to non-uniform stresses. The technique is based on the elasto-optic effect exhibited by transparent materials due to an imposed stress field that cause light rays to deflect. The working principle of the method and the governing equations are presented. DGS relies on 2D Digital Image Correlation (DIC) approach to quantify the angular deflections, which can then be related to spatial gradients of stresses under plane stress conditions. The feasibility of this method to study material failure/damage is demonstrated on transparent planar sheets of PMMA subjected to both quasi-static and dynamic lineload acting on an edge. In the latter case, ultra high-speed digital photography (200,000 frames/sec) is used to perform time-resolved measurements. The quasi-static measurements are successfully compared with those for a line-load acting on a half-space in regions where plane stress conditions prevail. The dynamic measurements, prior to material failure, are also successfully compared with finite element computations.

Both optical vortices and polarization vortices (vectorial vortices) are known to have attracted great interest in the field of optics. Although there have been some proposals concerning axially symmetrical polarizers, also referred to as radial polarizers, axially symmetrical wave plates (AS-WPs) have not previously been proposed. Particularly, the AS-WP has strongly dependence on both the wavelength and the temperature. Moreover, the structure of AS-WPs inherently introduce spatial dispersion. As a solution to these problems, we have proposed an achromatic axially symmetrical wave plate (AAS-WP) based on Fresnel reflection that does not introduce spatial dispersion. In this paper, we show the principle of generation, the optical properties of the optical element, and the generation method of the vortex spectrum for changing the polarization order, a well-known characteristic in singularity optics Moreover, in this paper, we also describe a generation technique for a high-order optical vortex based on geometric phase and the interferometric observation of the topological effect of the proposed AAS-WP.

In recent years, there has been an ever-growing interest in exploring novel, highly efficient optical materials to develop compact and effective optical components. The design and fabrication of high-performance optics require nondestructive metrology techniques to inspect the samples. We have investigated the capability of optical coherence tomography (OCT) to nondestructively characterize layered polymeric materials. Using a swept-source OCT system with a wavelength range of 1.25 - 1.41 μm, we achieved micron-scale three-dimensional visualization of the interior structures and details of the layered polymers. The 3D OCT imaging also enabled accurate identification of the locations of defects within the samples. Based on the imaging data, nondestructive metrology of the thickness of each observed layer was accomplished and the obtained layer thickness profiles over depth offered valuable feedback to the manufacturing process. Our results correlated well with light microscope observance, however caused no surface damage in comparison. In this paper we present the technique of nondestructive metrology enabled by OCT and discuss the experimental results on typical layered polymeric samples.

We present the use of sub-micron resolution optical coherence tomography (SMR SD-OCT) in volumetric characterization of ink- jet printed color filters, aimed for electronic paper display (EPD). The device used in the study is based on supercontinuum light source, Michelson interferometer centered at 600 nm and employs 400-800 nm spectral region. Spectra are acquired at a continuous rate of 140,000 per second. Color filter array of 143 μm x 141 μm sized and 6 rtm deep ink pools was studied. The volumetric OCT reconstruction was done using the experimental SMR SD-OCT device and a commercial SD-OCT imaging system. The ink layer in the pools was estimated to be 2μm thin. The optical profilometer was used for reference measurements.

A novel method for the wavelength-scanning interferometry is developed by use of the channeled spectroscopic polarization state generator (CSPSG), consisting of a polarizer and two high-order birefringent retarders, and the polarimetric common-path cyclical interferometer. This method has a feature that it is almost immune to the vibrational perturbations because the unbalanced path differences are introduced by the high-order birefringent retarders in the CSPSG. In addition, the fluctuation of the CSPSG due to the temperature change can be compensated in parallel to the phase distribution measurement of the sample, based on the self-calibration technique.

Imaging and measurement of the surface profile of an object with high resolution has become essential in both of biological research and industry application. Many samples under investigation such as cultured cells are usually immersed in liquid. Although the techniques such as scanning electron microscope and atomic force microscope can provide imaging or measurement of the surface profile with nanometer resolution, it is difficult for them to image an immersed object with their typical types. Recently, we have proposed and demonstrated a new technique based on composite interferometer which can perform imaging and measurement of the surface profile of an object with accuracy in the axial direction within 5 nm through a self-phase-compensation mechanism. In this research, an optical system based on the concept of combination of optical coherence microscopy (OCM) and composite interferometer was built for imaging of biological tissue immersed in water with axial accuracy at nanometer scale. In the system, a Ti:sapphire laser with center wavelength at 800 nm and spectral width of 140 nm was used as the light source. The composite interferometer comprises two Michelson interferometers sharing common light source, reference arm and photodetector. One of the two interferometers served as a typical OCM system and the other was used to measure the phase shift in the reference arm in each axial scan with the sample being a fixed reflection mirror. The system was used to image the surface profiles of various immersed biological samples with accuracy at nanometer scale through the self-phasecompensation mechanism.

Non-contact, 3D optical interferometric profilers provide detailed topography measurements of super-smooth surfaces such as hard disk substrates and super-polished optics. However, the contribution of the interferometer system to the measurement can be significant for surfaces with an RMS roughness of one Angstrom and below. Special care must be taken to minimize random noise as well as to remove the systematic instrument error from the measured data. While the random noise can be addressed by low-noise design and averaging of measurements, the systematic instrument error is more difficult to eliminate. In this paper an interferometer configuration is presented that eliminates the mid to higher spatial frequencies from the reference beam. This configuration is called a virtual-reference interferometer, since there is no physical surface in focus conjugate to the test surface. This provides very smooth systematic instrument errors with essentially no contribution in the mid to high spatial frequencies of surface waviness and roughness. The virtual-reference interferometer has a midsize measurement area of 20x20 mm, is fully compensated for white light, extended source illumination, and enables data acquisition for both phase shifting and coherence scanning modes. Current performance data show a residual systematic tool waviness error of < 0.2 Angstrom RMS, with potential for improvement. Efficient stitching of subaperture measurements accommodates high resolution roughness and waviness maps of test surfaces up to 150 mm x100 mm.

The structure function (SF) represents the average height difference squared as a function of separation. The linear SF has been used in astronomy and captures data of all spatial frequencies. However, it does not capture anisotropy on the surface. The one-quadrant area SF has been introduced to represent surface roughness information, but it is inadequate when surfaces are rotationally varying, as is frequently the case for optical surfaces. The recently introduced twoquadrant representation of the area SF can be calculated for any aperture shape, for all spatial content and isotropies. This paper describes the physical interpretation of the two-quadrant area SF and the comparison to area power spectral density (PSD) and area autocorrelation function (ACF) for a range of optical surfaces.

Aspheric surfaces are often measured using interferometers with null correctors. The null corrector creates a wavefront that matches the surface under test, but also introduces imaging aberrations, such as mapping distortion and field curvature. These imaging aberrations cause high frequency features in the surface under test to be filtered out and create artifacts at edges. We provide a concise methodology for analyzing these effects using field curvatures, and showing how they couple with diffraction as represented by the Talbot effect and Fresnel edge diffraction.

While the use of Zernike polynomials to represent simulated or measured data on a grid of points is common, the accuracy of the coefficients can be limited by the non-orthogonality of the functions over the pixelated domains. The Zernike polynomials are defined to be analytically orthogonal over a circular domain, but this breaks down for discrete data. A simple correction is presented that uses a weighted scalar product to determine coefficients. This method preserves the meaning of the Zernike polynomials and allows efficient calculations using an inner product. The algorithm for defining the weighting function is provided, and simulations are included that demonstrate nearly an order of magnitude improvement in accuracy when the new weighted scalar product is used.

We describe a method for measuring the deflection due to gravity (sag) of horizontally mounted reference flats of phase shifting interferometers. The planarity of a test flat can be measured sag-free while supporting it iso-statically on a suitable visco-elastic polymer foam. A sag map is obtained when the sag-free flatness error is subtracted from the flatness error of the same flat held at its edge.

Traceability of interferometric form measurements requires characterization of the reference wavefront. We investigate absolute tests for spherical surfaces where the form errors of both reference and test surface are estimated by minimizing the difference in measurements obtained at various positions and orientations of the test surface. This approach yields an estimate for the test surface errors without changing experimental settings, such as cavity length, that may affect the apparent reference errors. The method requires at least one translation of the test surface in the field of view and one rotation. Additional measurements provide redundancies to improve and characterize measurement uncertainties. The errors of the reference and test surface are estimated with pixel-level spatial resolution without assuming an underlying error model, such as a representation based on Zernike polynomials. The estimation algorithm consists of an iterative sequence of stitching steps, with the role of reference and test surface reversed for each step. Measurement uncertainties are evaluated using Monte-Carlo procedures and analysis of residual errors for experiments with redundant measurements. Key sources of measurement uncertainty are spatially correlated measurement errors resulting from errors in test surface location, image distortion, and environmental effects. Experimental results are presented comparing the method to a random ball test.

Current commercial height profile measuring instruments, e.g. the confocal microscope and, the white light interferometer, are widely used in both research institutes and industry. The systematic error of such instruments can be the same order of magnitude as features on the surface to be measured, if care is not taken with calibration. Instrument error in most cases depends on the surface slope. Thus, calibration of the instrument is important. The random ball test, proposed by Parks et al, is a self calibration technique for transmission sphere calibration in phase shift interferometry. The idea is, by measuring a collection of random patches on the surface of a sphere and then averaging the results, the contributions from the ball go to zero leaving only the systematic biases due to the instrument. This paper shows it can also be used to calibrate slope-dependent errors in profilometers such as the scanning white light interferometer (SWLI). This will be demonstrated with both simulation and experimental results. For example, with a commercial SWLI measurement with a 20X objective, our random ball test indicates that the height error can be as large as 250 nm at a slope value of 2.9 degrees when using the envelope peak algorithm for analysis. Similarly, with a confocal microscope measurement using a 50X objective, the height error can be as large as 800 nm at a slope value of 12.1 degrees. These slope-dependent errors can be used to compensate future sloped-surface measurements.

The phase shifting technique, used almost universally across those disciplines in metrology that use fringe analysis, is a powerful method to reconstruct the phase of a periodic signal from very few irradiance samples of a moving fringe pattern. Its known weaknesses, such as susceptibility to incorrect slope or shape of the phase-shift function, or harmonics in the periodic signal, have been treated quite comprehensively by signal-analysis techniques, in particular the characteristic polynomial (CP) theory (Surrel, Appl. Opt 35, 51-60, 1996). I show how to deal with one of the few problems for which the CP theory does not give a direct solution: how do we remove a fundamental-frequency phase error from the result? A straightforward way is found by a variation on standard averaging techniques. The improvement of phase maps is clearly evident in experimental results with 90° nominal phase shift per step, and suggests that the original signal does not always need to be known in detail: it is sufficient to observe the error fringes and tweak the phase-shift formula according to the rules given here. Application of the CP theory to the findings leads to some general conclusions: (i) the averaging can be generalised for any desired behaviour and any phase shift; (ii) to remove a certain harmonic from the phase result, it must be bracketed by CP zeroes at the harmonics above and below it.

Error estimation method of phase detection in phase shift method is proposed. Phase detection algorithms extract phase of fringes from several interferograms that are acquired during phase shifting. The Fourier domain expression of phase detection algorithms show frequency response for sine and cosine components, and it shows behavior of detected phase in the case if phase shifting error exists. However, these two response functions do not directly show frequency response of phase detection itself. On the contrary, newly proposed frequency response function directly shows frequency response of phase detection. And it clearly shows the behavior of phase detection algorithm when phase tuning error exists. The proposed method is inspired by the Bode plot. It is easy to assume that magnitude plot also can be defined in addition to the phase plot. The magnitude plot can be used for prediction of the sensitivity to the signal and noise. And the phase plot can be used for error estimation of phase detection in the presence of phase tuning error. After some investigations, it was found that there is good agreement between the developed frequency response function and calculated error value. Therefore, it can be used as an error estimation method for phase detection algorithm. A window function modifies specifications of phase detection algorithm. Comparisons of several numbers of window functions on phase detection method were demonstrated using proposed method. Additionally, we discuss window function, which makes phase detection algorithm insensitive to phase detuning.

In this work, we develop a regularization technique to demodulate a phase-shifting interferogram sequence with arbitrary inter-frame phase shifts. With this method, we can recover the modulating phase and inter-frame phase shifts in the same process. As all phase-shifting algorithms, the assumption is that the wavefront under test does not change over time, but the introduction of phase-shifts can vary in a nonconstant way. A notable characteristic of this demodulation method is that not only can it recover the modulating phase, but it is also capable of filtering-out large amounts of corrupting noise. We will show numerical experimental results and comparisons with another already published method to see the performance of the demodulation technique developed herein.

The S-transform, a time frequency representation proposed in 1996 by R.G. Stockwell, can be conceptually thought of either as a variable window short-time Fourier transform or a phase corrected Wavelet transform. Whose window size verifies with the frequency and here both the local amplitude and local phase spectrum of a time varying signal can be simultaneously estimated. As a reversible time-frequency analysis tool, it is well suited to analyzing of non-stationary signals and has many desirable characteristics. Distinct from the wavelet transformation, averaging the local S spectra over the direction of time can correctly form the Fourier transform spectra of the signal. Therefore S transform have direct relationship with the Fourier transform. In recent years, the S-transform has been introduced in three-dimensional optical measurement based on a fringe projection technique and attracted many researchers to work on the field. In this paper, for verifying the advantages of S transform, we compare the reconstruction of S transform, including S transform ridge method and S transform filtering method, with that of other methods, such as Fourier transform method, wavelet transform method for eliminating phase errors caused by the existences of both nonlinear factor and noise. In addition, we have a discussion and make a comparison on these methods by means of computer simulations appearing robust within different white Gaussian noise levels. It shows that S-transform profilometry based on the filtering way is helpful to the enhancement of measurement accuracy, which is verified by experiments for its better reconstruction results.

Sinusoidal wavelength-scanning (SWS) interferometry is unique in that a time-varying interference signal contains phase-modulation amplitude Zb due to the SWS besides a conventional phase α. Propagation time and wavefront of the light wave diffusely reflected from a metal surface can be detected from the amplitude Zb and the phase α, respectively. A concave shape with the depth of about a few hundreds microns is measured with an error less than a few microns by using only the amplitude Zb of the detected interference signal.

This paper describes recent advances in developing an automatic background leveling algorithm for a new, novel interference microscope system and presents images and data of live biological samples. The specially designed optical system enables instantaneous 4-dimensional video measurements of dynamic motions within and among live cells without the need for contrast agents. "Label-free" measurements of biological objects in reflection using harmless light levels are possible without the need for scanning and vibration isolation. This instrument utilizes a pixelated phase mask enabling simultaneous measurement of multiple interference patterns taking advantage of the polarization properties of light enabling phase image movies in real time at video rates to track dynamic motions and volumetric changes. Optical thickness data are derived from phase images. This data is processed with an automatic background leveling routine which separates the objects from the background by thresholding the calculated gradient magnitude of the optical thickness data. Low-order Zernike surfaces are fit to the unmasked background pixels and the resulting background shape is removed. This method effectively eliminates background shape for datasets containing both large and small objects. By applying this method to many sequential frames, it results in all the frames having the same mean background value across all frames which is essential for quantitatively montoring time-dependent processes.

Multi-wavelength interferometry (MWI) has a long tradition in the field of optical metrology and is used as a solution to a number of applications. MWI phase unwrapping procedures are usually based on beat wavelength approaches, Chinese Remainder Theorem (CRT) techniques, or the method of Excess Fractions (EF). Each of these unwrapping approaches have a distinct advantage for a given application: Beat wavelength and CRT based approaches offer a direct calculation of integer fringe order, and EF offers many alternative sets of wavelengths to achieve a large unambiguous measurement range (UMR) with high reliability. Nevertheless, a drawback of Beat wavelength and CRT based approaches is that they have a limited UMR due to the available measurement wavelengths, and the alternative approach the EF is often impractical in practice, because the calculation of the integer fringe order involves a large number of computational steps. Recently, we have reported a unified theory of beat wavelength, EF and CRT approaches, which enables the derivation of phase unwrapping approaches with low computational effort, which hitherto had only been possible for CRT and beat wavelength approaches, whilst offering flexibility in choosing the measurement wavelengths for a given UMR, which had previously only been the case for EF. In this work, we briefly summarize the previous developed framework that determines the UMR and measurement reliability and derive optimization criteria that are based on parameters, which are dependent on the choice of the measurement wavelengths. The developed optimum wavelength selection strategies maximize the dynamic range of interferometer for a given value of phase noise the dynamic range of interferometer.

Here, we are going to show a 2D recursive phase unwrapping system that unwraps the phase and cleans noise in the same process. This recursive phase unwrapping system behaves as an Infinite Impulse Response (IIR) system and we will show its stability and frequency analysis in 1D. The unwrapping results shown here, are compared with the well known least squares phase unwrapping method. The recursive phase unwrapping system shown here is robust to noise and it can be used to unwrap modulus 2π phase maps following simple row by row scanning strategies.

Phase wrapping is an intermediate step ffor interferometry analysis. When phase is smooth, its unwrapping can be carried out fitting local planes with finite extension at each point of the phase gradient. We propose a method easy to implement that spends the same computation time than those techniques based on basis functions.

Deflectometric methods that are capable of providing full-field topography data for specular freeform surfaces have been around for more than a decade. They have proven successful in various fields of application, such as the measurement of progressive power eyeglasses, painted car body panels, or windshields. However, up to now deflectometry has not been considered as a viable competitor to interferometry, especially for the qualification of optical components. The reason is that, despite the unparalleled local sensitivity provided by deflectometric methods, the global height accuracy attainable with this measurement technique used to be limited to several microns over a field of 100 mm. Moreover, spurious reflections at the rear surface of transparent objects could easily mess up the measured signal completely. Due to new calibration and evaluation procedures, this situation has changed lately. We will give a comparative assessment of the strengths and – now partly revised – weaknesses of both measurement principles from the current perspective. By presenting recent developments and measurement examples from different applications, we will show that deflectometry is now heading to become a serious competitor to interferometry.

We present a fast and ambiguity-free method for slope measurement of reflective optical elements based on reflectometry. This novel reflectometric method applies triangulation to compute the slope based off projected patterns from an LCD screen, which are recorded by a camera. Accurate, ambiguity-free measurements can be obtained by displaying one pixel at a time on the screen and retrieving its unique image. This process is typically accelerated by scanning lines of pixels or encoding the information with phase using sinusoidal waves. Various classes of solutions exist, centroiding and phase-shifting being the most accepted, but their sensitivities vary with experimental conditions. This paper demonstrates solutions based on various parameters such as accuracy or efficiency. The results are presented in a decision matrix and merit function. Additionally, we propose a new class of solutions – Binary Square screens – in an attempt to address system limitations and compare current systems to our solutions using the decision matrix. Several test conditions are proposed along with the best suited solution.

We present a novel method to reconstruct the shape of a moving specular object from multiple camera images taken near a calibrated display with a known color-encoded pattern. The method is based on voxel carving exploiting the consistency of the cones of allowed normal vectors, or normal vector maps (NVMs). The algorithm is highly parallel, does not rely on pattern recognition and applies to surfaces of arbitrary complexity.

The scan results of optical 3D measurements at translucent objects deviate from the real objects surface. This error is caused by the fact that light is scattered in the objects volume and is not exclusively reflected at its surface. A few approaches were made to separate the surface reflected light from the volume scattered. For smooth objects the surface reflected light is dominantly concentrated in specular direction and could only be observed from a point in this direction. Thus the separation either leads to measurement results only creating data for near specular directions or provides data from not well separated areas. To ensure the flexibility and precision of optical 3D measurement systems for translucent materials it is necessary to enhance the understanding of the error forming process. For this purpose a technique for simulating the 3D measurement at translucent objects is presented. A simple error model is shortly outlined and extended to an efficient simulation environment based upon ordinary raytracing methods. In comparison the results of a Monte-Carlo simulation are presented. Only a few material and object parameters are needed for the raytracing simulation approach. The attempt of in-system collection of these material and object specific parameters is illustrated. The main concept of developing an error-compensation method based on the simulation environment and the collected parameters is described. The complete procedure is using both, the surface reflected and the volume scattered light for further processing.

We propose a new application of broad band lasers for digital holography. The aim is to capture the shape of objects by a single hologram using multiple wavelengths. Our approach is to separate the reference wave spectrally by a grating while the object wave remains unaffected. This leads to many lamellar holograms in one hologram. As consequence different restrictions like aperture and wavelength dependency of the reconstruction algorithm have to be taken into account. In experiments we have successfully demonstrate that lamellar holograms can be generated, reconstructed and that all necessary steps for shape measurement are accomplishable.

We simultaneously capture holograms using multiple wavelengths with a single camera using off-axis holography. Our prototype uses two tunable lasers and the references or local oscillators are configured so that the reconstructed complex signal field at each wavelength fills different quadrants. The technique can be adapted for various applications and could be especially beneficial for 3D reconstruction of moving objects and high resolution imaging.

In 1948, Gabor proposed a lens-less in-line holographic microscope where the recorded hologram is a result of interference of both reference wave and the wave diffracted from the object. In this work, an analysis of the hologram formation and sampling issues are presented using the local-spatial frequency distribution at the camera plane. Techniques are presented that enable the reconstruction of the complex object wave at the camera plane from a series of defocused images. It is suggested to use the band-limited angular spectrum method for the back-propagation of the field components, so that an accurate and quantitative estimate of the object-wave at the object plane is obtained. The reconstruction procedure does not rely on the paraxial approximation and is therefore applicable to the case of high NA beams.

The authors develop a special configuration of a digital speckle pattern interferometer using a custom diffractive optical element. The resulting interferometer is sensitive only to the in-plane radial displacement component. The area of interest is double illuminated by light diffracted from a special diffractive optical element in such a way that the interference fringe is not wavelength dependent. The authors present in this paper different strategies for improving image quality of the fringe patterns exploring wavelength and coherence properties. The results of the different approaches are presented and compared.

Often, the 3-D raw data coming from an optical profilometer contains spiky noises and irregular grid, which make it difficult to analyze and difficult to store because of the enormously large size. This paper is to address these two issues for an optical profilometer by substantially reducing the spiky noise of the 3-D raw data from an optical profilometer, and by rapidly re-sampling the raw data into regular grids at any pixel size and any orientation with advanced computer graphics tools. Experimental results will be presented to demonstrate the effectiveness of the proposed approach.

In real-time phase measurement profilometry (PMP) systems, finding point correspondence between phase-maps of cameras or camera and projector is the key technology for 3D reconstruction. A novel method based on trifocal tensor constrain, which can be directly implemented on wrapped phase-map and speed up by parallel computing technology, is present. But fringe number, images noise and system non-linear response will lead to false correspondence. The influence of these factors is deeply analyzed, and a feasible way is proposed to reject error candidate points. Finally, this method indicated a satisfactory performance in the experiment.

Our recent study found that it is very difficult to use the binary defocusing technique to completely suppress the 3rd-order harmonics, and thus it is challenging to achieve high-quality three-dimensional (3-D) measurement with the Fourier transformation method. This paper presents a novel approach to effectively eliminate the 3rd order harmonics by modulating the binary structured patterns in both x and y directions. Both simulation and experimental results will be presented to verify the performance of the proposed technique.

A two-path adaptive phase-shifting interferometry, which is insensitive to the disturbance of constant term of phase perturbations induced by environmental vibration and air turbulence, is proposed. The beam sent from the source is divided into two parts by polarization beam splitter and the two parts enter a phase-shifting interference system, and then a two-path adaptive phase-shifting interference system is formed. The beam intensity of the one path is modulated in high frequency with an acousto-optic modulator, and phase lock-in as well as the closed loop control techniques is used in this path. Thus, the wobble of interference fringes can be compensated, and sequentially the fringes will be locked at arbitrarily chosen phase for phase-shifting testing. Meantime, surface profile of an optical element is measured in another path with five-step phase-shifting interferometry algorithm. Comparing with other similar techniques, here the depth of signal modulation is not limited by the optical path difference and the contrast of the fringe used to evaluate the surface profile is not reduced, hence a high signal-to-noise ratio can be obtained. In order to verify the feasibility of this interferometry, a two-path adaptive phase-shifting interference system is set up and the experiments of phase-locking and surface profile testing have been carried out. After phase-locking being realized, the residual wobble amplitude of optical phase difference is 2.65°RMS. Comparing with ZYGO interferometer, the result of surface profile testing is the same but the measurement repeatability is better.

Pixelated phase-mask (PPM) interferometers have become an industry standard for instantaneous phase-shifting interferometry. In commercially available PPM interferometers, an array with 2x2 unit-cells is used, which codify up-to 4 phase-steps within a single PPM interferogram. Recently we have shown that such 2x2 unit-cell arrays allows a harmonic rejection as good as the 4-step leastsquares phase-shifting algorithm (LS-PSA); this harmonics rejection is relatively-low and may not be enough to correctly demodulate some severely intensity distorted fringe patterns. In previous works we have proposed a new PPM with a 3x3 unit-cell to improve the harmonics rejection of the 2x2 array. With this new 3x3 unit-cell one is able to reject as many harmonics as with a 9-step LS-PSA¹⁰. In this paper we are extending the analysis of MxN unit-cell synchronous demodulation of PPM. The new results allow us to answer some important open questions about the method: for a given configuration, which harmonics cannot be rejected and why? Why, prior to low-pass filtering, we observe multiple copies of the interferogram’s spectrum and what does this imply? We believe these preliminary results are important contributions towards a formulation of a general theory MxN unit-cell pixelated carrier interferometry.

We have developed an interferometer for gauge block calibration based on phase shifting evaluation. The measurement process can provide flatness, parallelism and longitude. The employed wavelengths need to be corrected according to the refractive index of the air the light beams passes through. In our case, this correction is obtained indirectly using readings of temperature, pressure and relative humidity taken by high resolution sensors. To preserve stability, the interferometer is encapsulated in a chamber with active temperature control. The design, measurement principle, calibration, stability and reproducibility are analyzed. Since one of our goals is to employ robust and cheap diode lasers as light sources, this paper describes also the system we are developing to carry out a red diode laser stabilization using a mode locking technique. The instruments and assembly employed to avoid the Doppler effect in the gas cells, which limit wavelength resolution, are described as well. Several experimental tests have been carried out that show the great susceptibility of this assembly to changes in environmental conditions, which affect the iodine cell's absorption spectrum.

In this paper we shows the results obtained to fabricate and implement Mach-Zehnder interferometers of conventional fiber optic using Long Period Fiber Gratings (LPFG´s) which were developed by electric arc technique. We obtains this type of interferometer when we fabricated two LPFG’s in series or in cascade with the same characteristics such as number of discharges and the same period, placing them in cascade separated by a distance which three times the length of the LPFG. The application which was given at interferometer fabricated was as a liquids sensor, volume sensor of liquids and micro-displacement sensor. The sensors of liquids and liquids volumes were placed in a container in which the interferometer is fixed so that results of measurements are only by incorporating each of the liquid and not by some external movement. The sensed fluids were: water, alcohol and solution (water with sugar). Final length of the interferometer is between 4 to 6 cm. We analyze the results obtained to when a section the Mach-Zehnder interferometer is displaced in of the order of microns. The variations observed in transmission spectra obtained from each of the sensors mentioned, show changes in the amplitude and the attenuation peak of the interferometer was displaced.

The knowledge of the flow structure of fluids is essential in many industrial sectors as it determines the quality and success of processes like welding, cutting or material treatment. The employed fluid flow plays a fundamental role and in all cases to understand the complex pressure and shock waves patterns becomes necessary. The only way to absolutely ensure that the theoretical behavior predicted by numerical simulations fits with the real gas flow behavior is the experimental check. For such application, the optical techniques are very well suited resources due to their non invasive features. Schlieren, shadowgraph and interferometry are the typical techniques used for the study of the mass flow in fluids. In this work, we present the qualitative results obtained from a conventional interferometric technique combined with a new numerical approach used for analyzing the inner structure of supersonic flows provided by nozzles with Laval profile used in industrial oxy-fuel cutting processes. The extraction of the optical phase from the fringe patterns is performed through a Differential Fourier Transform Evaluation. We show that with further numerical processing we can obtain a complete qualitative description of the flow field including the first and second optical phase derivatives (Gradient and Lapacian phase maps).

A data fitting model is proposed to estimate phases from its cosine and sine. The a priori assumption is that the phases to be reconstructed should be expressed by polynomials. The cosine and sine of the phases are obtained from interferograms with high fringe density by generalized phase-shifting techniques The proposed method is employed for phase reconstrution by line integration of the phase gradient or any other phase-unwrapping technique and the fit is achieved by a least-squares minimization.

Success of optical measurement methods such as interferometry, holography and fringe projection methods mainly depends on the availability of robust phase recovery (PR) algorithms. In presence of some problems such as strong noise, abrupt phase changes, low fringe contrast and discontinuities, it’s necessary to introduce a highly reliable algorithm to overcome them. As for the experimental phase map from holographic interferometry of China coin’s micro-surface, some typical PR algorithms including the proposed (weighted) DCT (Discrete Cosine Transform) are studied to try to recover the satisfactory continuous phase. The experimental phase map (13921040 pixels) exhibits the local surface characteristic of one China coin. It features excessive noise and many bad data points. It’s very difficult to achieve the continuous phase by the general algorithms. So some robust algorithms are studied to solve this problem. These algorithms include the quality map guided method (QG), (weighted) least square method (LS or WLS), mask cut method (MC) and (weight) DCT method (DCT or WDCT). According to the tested results, the fastest algorithm is the LS method, and it only needs about 10s. The clearest pattern profile results from the DCT and WDCT algorithms that need about 30s and 31s in the consuming time, respectively. However, it’s very hard to clearly and completely reflect the smooth top of imprinted letters for all the above algorithms. This could be due to the excessively much noise, the limited resolutions of CCD setup, and so on.

In the present work digital holographic interferograms obtained by digital Fourier transform holography are used to analyze fracture propagation. Digital holography is a non-contact optical technique that consists in recording digitally a hologram with a CCD sensor as holographic media. The image reconstruction of the object is obtained numerically. Holographic interferograms are obtained by superposition of two holograms of object, being the first one in its initial state and the second one after some modification produced in this object. Basically, the main purpose is to use interferograms for investigating mixed-mode I/II fracture. Tests on cracked specimen under combined loading are performed.

When defining surface irregularities more often than not it is useful to represent these as slope errors rather than surface errors. However, surface error specifications are more commonly used even though they do not accurately represent performance but simply physical characteristics. An example of slope measurement technique and specification is a method developed by the University of Arizona called SCOTS (Software Configurable Optical Test System) which has showed to be accurate, while very fast and easy to setup. It directly measures the transverse ray aberration/slope of an optical system using transmission deflectometry.

While tin-doped indium oxide (ITO) has been extensively applied in flexible electronics, the problem of the residual stress has many obstacles to overcome. This study investigated the residual stress of flexible electronics by the double beam shadow moiré interferometer, and focused on the precision improvement with phase shifting interferometry (PSI). According to the out-of-plane displacement equation, the theoretical error depends on the grating pitch and the angle between incident light and CCD. The angle error could be reduced to 0.03% by the angle shift of 10° as a result of the double beam interferometer was a symmetrical system. But the experimental error of the double beam moiré interferometer still reached to 2.2% by the noise of the vibration and interferograms. In order to improve the measurement precision, PSI was introduced to the double shadow moiré interferometer. Wavefront phase was reconstructed by the five interferograms with the Hariharan algorithm. The measurement results of standard cylinder indicating the error could be reduced from 2.2% to less than 1% with PSI. The deformation of flexible electronic could be reconstructed fast and calculated the residual stress with the Stoney correction formula. This shadow moiré interferometer with PSI could improve the precision of residual stress for flexible electronics.

In the present letter low frequency moiré fringe patterns are used as secure numerical code generator. These moiré patterns are experimentally obtained by the superposition of two sinusoidal gratings with slightly different pitches. The Bi₁₂TiO₂₀ photorefractive crystal sample is used as holographic medium An optical numerical base was defined with patterns representing 0,1 and -1 digits like bits. Then, the complete set of these optical bits are combined to form bytes, where a numerical sequence is represented. The results show that the proposed numerical code could be used as standard numerical identification in robotic vision or in transmition of security numerical keys.