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In the optical quality measuring process of an optical system, including diamond-turning components, the use of a laser light source can produce an undesirable speckle effect in a Shack--Hartmann (SH) CCD sensor. This speckle noise can deteriorate the precision and accuracy of the wavefront sensor measurement. Here we present a SH centroid detection method founded on computer-based techniques and capable of measurement in the presence of strong speckle noise. The method extends the dynamic range imaging capabilities of the SH sensor through the use of a set of different CCD integration times. The resultant extended range spot map is normalized to accurately obtain the spot centroids. The proposed method has been applied to measure the optical quality of the main optical system (MOS) of the mid-infrared instrument telescope smulator. The wavefront at the exit of this optical system is affected by speckle noise when it is illuminated by a laser source and by air turbulence because it has a long back focal length (3017 mm). Using the proposed technique, the MOS wavefront error was measured and satisfactory results were obtained. [c] 2010 Optical Society of America OCIS codes: 120.3940, 100.5070, 120.4630, 120.6085.

Liquid crystal variable retarders (LCVRs) are starting to be widely used in optical systems because of their capacity to provide a controlled variable optical retardance between two orthogonal components of incident polarized light or to introduce a known phase shifting (PS) between coherent waves, both by means of an applied voltage. Typically, the retardance or PS introduced by an LCVR is not homogeneous across the aperture. On the one hand, the LCVR glass substrates present a global bend that causes an overall variation of the retardance or PS. On the other hand, in the manufacturing process of an LCVR, there sometimes appears a set of micro-air bubbles that causes local retardance or PS inhomogeneities. In this work, we present an interferometric technique based on a Mach-Zehnder interferometer that is insensitive to vibrations and capable of inspecting and characterizing the LCVR's retardance or PS inhomogeneities. The feasibility of the proposed method is demonstrated in the experimental results, where the LCVR retardance is measured with an error of about 0.2 rad. The thickness of possible micro-air bubbles is obtained with a resolution of about 50 nm. [c] 2010 Optical Society of America OCIS codes: 120.3180, 230.3720, 120.4630.

It is well known that spatial phase shifting interferometry (SPSI) may be used to demodulate two-dimensional (2D) spatial-carrier interferograms. In these cases the application of SPSI is straightforward because the modulating phase is a monotonic increasing function of space. However, this is not true when we apply SPSI to demodulate a single-image interferogram containing closed fringes. This is because using these algorithms, one would obtain a wrongly demodulated monotonic phase all over the 2D space. We present a technique to overcome this drawback and to allow any SPSI algorithm to be used as a single-image fringe pattern demodulator containing closed fringes. We make use of the 2D spatial orientation direction of the fringes to steer (orient) the one-dimensional SPSI algorithm in order to correctly demodulate the nonmonotonic 2D phase all over the interferogram. OCIS codes: 050.5080, 100.5070, 120.5050, 120.3180.

Active triangulation measurement systems with a rigid geometric configuration are inappropriate for scanning large objects with low measuring tolerances. The reason is that the ratio between the depth recovery error and the lateral extension is a constant that depends on the geometric setup. As a consequence, measuring large areas with low depth recovery error requires the use of multiresolution techniques. We propose a multiresolution technique based on a camera-projector system previously calibrated. The method consists of changing the camera or projector's parameters in order to increase the system depth sensitivity. A subpixel retroprojection error in the self-calibration process and a decrease of approximately one order of magnitude in the depth recovery error can be achieved using the proposed method. OCIS codes: 000.3119, 110.0110, 120.0120, 120.4640, 150.0150.

In many fringe pattern processing applications the local phase has to be obtained from a sinusoidal irradiance signal with unknown local frequency. This process is called asynchronous phase demodulation. Existing algorithms for asynchronous phase detection, or asynchronous algorithms, have been designed to yield no algebraic error in the recovered value of the phase for any signal frequency. However, each asynchronous algorithm has a characteristic frequency response curve. Existing asynchronous algorithms present a range of frequencies with low response, reaching zero for particular values of the signal frequency. For real noisy signals, low response implies a low signal-to-noise ratio in the recovered phase and therefore unreliable results. We present a new Fourier-based methodology for designing asynchronous algorithms with any user-defined frequency response curve and known limit of algebraic error. We show how asynchronous algorithms designed with this method can have better properties for real conditions of noise and signal frequency variation. OCIS codes: 100.0100, 100.2650, 100.6890, 120.5050.

The spatial orientation of fringes has been demonstrated to be a key point in reliable phase demodulation from a single n-dimensional fringe pattern, regardless of the frequency spectrum of the signal. Recent publications have shown a general method for determination of the orientation factor by use of a regularized phase-tracking (RPT) algorithm. We propose a generalization of a RPT algorithm for estimation of the spatial orientation in a general n-dimensional case. The proposed algorithm makes use of a simplified cost function that remains one dimensional regardless of the dimension of the problem. This makes the calculation faster than with a standard RPT algorithm, with which it is necessary to minimize an n + 1-dimensional cost function for each point of the sample space. We have applied the method to the three-dimensional demodulation of a time-evolving fringe pattern, with good results. OCIS codes: 100.2650, 100.5070.

In recent years the availability of high-speed digital video cameras has motivated the study of electronic speckle pattern interferometry (ESPI) in the time domain. To this end a properly sampled temporal sequence of N-fringe patterns is used to analyze the temporal experiment. Samples of temporal speckle images must fulfill the Nyquist criteria over the time axis. When the transient phenomena under study are too fast, the required sampling frequency over time may not be fulfilled. In that case one needs to extend the measuring range of the algorithm used to extract the modulating phase. We analyze how to use short laser pulses or short video acquisition times with fairly long temporal separation among them to estimate the modulating phase of a dynamic ESPI experiment. The only requirement is that the modulating phase being estimated be properly sampled in the spatial domain.

The red-blue-green (RGB) calibration technique consists in constructing an a priori calibration table of the isochromatic retardation versus the triplet of RGB values obtained with a RGB CCD camera. In this way a lookup table (LUT) is built in which the entry is the corresponding RGB triplet and the output is the given retardation. This calibration (a radiometric quantity) depends on the geometric and chromatic parameters of the setup. Once the calibration is performed, the isochromatic retardation at a given point of the sample is computed as the one that minimizes the Euclidean distance between the measured RGB triplet and the triplets stored in the LUT. We present an enhanced RGB calibration algorithm for isochromatic fringe pattern demodulation. We have improved the standard demodulation algorithm used in RGB calibration by changing the Euclidean cost function to a regularized one in which the fidelity term corresponds to the Euclidean distance between RGB triplets; the regularizing term forces piecewise continuity for the isochromatic retardation. Additionally we have implemented a selective search in the RGB calibration LUT. We have tested the algorithm with simulated as well as real photoelastic data with good results.

An improved moire deflectometry phase-shifting technique is presented. A squared grating is used to multiplex the information of the deflections in two orthogonal directions in one image. This procedure avoids the need to rotate the gratings to obtain complete deflection information. However, the use of these gratings makes impossible the application of standard phase-shifting algorithms. Specifically, the problems associated with the nonsinusoidal profile of the moire fringes and the low-modulation areas produced by the square gratings are solved. A modified moire deflectometry phase-shifting method is designed to deal with these problems. In addition, a method to obtain the zero order of the prismatic effect is developed. The technique configures a complete and automatic method of mapping ray deflections. From them the refractive power maps can be derived. Experimental results obtained with a progressive-addition lens are shown.

We present a method of error analysis that can be applied for phase-measuring algorithms applied to photoelasticity. We calculate the contributions to the measurement error of the different elements of a circular polariscope as perturbations of the Jones matrices associated with each element. The Jones matrix of the real polariscope can then be calculated as a sum of the nominal matrix and a series of contributions that depend on the errors associated with each element separately. We apply this method to the analysis of phase-measuring algorithms for the determination of isoclinics and isochromatics, including comparisons with real measurements.

A histogram-based technique for robust contrast measurement is proposed. The method is based on fitting the histogram of the measured image to the histogram of a model function, and it can be used for contrast determination in fringe patterns. Simulated and experimental results are presented. [C] 2000 Optical Society of America OCIS codes: 100.0100, 100.2650, 100.2960.

We propose a robust procedure based on the regularized phase-tracking (RPT) technique to demodulate squared-grating deflectograms. The use of squared gratings, already reported, lets us multiplex the information of the deflections in two orthogonal directions in a single image, thus avoiding the necessity of rotating the gratings. The good noise-rejection characteristics of the RPT technique are improved by use of a quasi-Newton optimization algorithm and a quality-map-based algorithm for the crystal-growing process. [C] 2000 Optical Society of America OCIS codes: 120.2650, 120.4120, 100.2650, 170.4460, 100.5070, 120.5050.