A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Recent progresses on real-time 3D shape measurement using digital fringe projection techniques

System calibration, which usually involves complicated and time-consuming procedures, is crucial for any 3-D shape measurement system. In this work, a novel systematic method is proposed for accurate and quick calibration of a 3-D shape measurement system we developed based on a structured light technique. The key concept is to enable the projector to "capture" images like a camera, thus making the calibration of a projector the same as that of a camera. With this new concept, the calibration of structured light systems becomes essentially the same as the calibration of traditional stereovision systems, which is well estab- lished. The calibration method is fast, robust, and accurate. It signifi- cantly simplifies the calibration and recalibration procedures of struc- tured light systems. This work describes the principle of the proposed method and presents some experimental results that demonstrate its performance. © 2006 Society of Photo-Optical Instrumentation Engineers.

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Novel method for structured light system calibration

two–dimensional phase unwrapping. theory, algorithms, and two dimensional phase unwrapping theory algorithms and two dimensional phase unwrapping theory algorithms and two-dimensional phase unwrapping using neural networks two-dimensional phase unwrapping: theory, algorithms, and (size 43,32mb) link download two dimensional phase phase unwrapping: project liverpool john moores university pixel-wise absolute phase unwrapping using geometric 2d phase unwrapping on fpgas and gpus phase unwrapping producing bright bands if phase unwrapping and affine transformations using cuda phase unwrapping on reconfigurable hardware ll.mit absolute three-dimensional shape measurement using coded fast twodimensional simultaneous phase unwrapping and low unwrapping differential x-ray phase-contrast images connections between transport of intensity equation and space geodesy seminar sio 239 scripps institution of experiment of phase unwrapping algorithm in interferometric reference documents esa 3d shape measurement technique for multiple rapidly moving phase unwrapping for large sar interferograms: statistical superfast phaseshifting method for 3-d shape measurement space geodesy seminar sio 239 scripps institution of off-axis quantitative phase imaging processing using cuda angular phase unwrapping of optically thick objects with a a comparison of phase unwrapping techniques in synthetic noise robust linear dynamic system for phase unwrapping fast phase processing in off-axis holography by cuda cat d2 dozer manual fiores fourier analysis of rgb fringe-projection profilometry and dynamic quantitative phase imaging for biological objects twowavelength quantitative phase unwrapping of dynamic comparison of phase unwrapping algorithms applied to feminist theory crime and social justice theoretical conscience volume 4 dr-caloriez henry and the paper route cafebr chapter 3 what is money mishkin cafebr

Two Dimensional Phase Unwrapping Theory Algorithms And Software

A procedure is proposed to calibrate a generic structured light system, consisting of one camera and one projector. The proposed pro- cedure is based on defining a unique coordinate system for both devices in the structured light system, and thus, a rigidity constraint is introduced into the transformation process. This constraint is used to derivate a simple function for the simultaneous estimation of the parameters, result- ing in parameters that are more reliable. The performance of the pro- posed procedure is shown on examples of the calibration of two different structured light systems. © 2004 Society of Photo-Optical Instrumentation Engi- neers. (DOI: 10.1117/1.1635373)

Accurate procedure for the calibration of a structured light system

In order to overcome the limitations of the sequential phase-shifting fringe pattern profilometry for dynamic measurements, a color-channel-based approach is presented. The proposed technique consists of projecting and acquiring a colored image formed by three sinusoidal phase-shifted patterns. Therefore, by using the conventional three-step phase-shifting algorithm, only one color image is required for phase retrieval each time. However, the use of colored fringe patterns leads to a major problem, the color crosstalk, which introduces phase errors when conventional phase-shifting algorithms with fixed phase-shift values are utilized to retrieve the phase. To overcome the crosstalk issue, we propose the use of a generalized phase-shifting algorithm with arbitrary phase-shift values. The simulations and experimental results show that the proposed algorithm can significantly reduce the influence of the color crosstalk.

Color-fringe pattern profilometry using a generalized phase-shifting algorithm.

One of the powerful approaches to demodulate a single fringe pattern is the regularized phase tracking (RPT) technique. Here, a new improvement in the RPT technique is presented. This new improvement consists in the addition of one term that models the fringe-pattern modulation. With this new term, the RPT technique can be used for the demodulation of nonnormalized fringe patterns. The performance of the improved RPT technique is shown on examples of various fringe patterns.

Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns.

A new framework for phase recovery from a single fringe pattern with closed fringes is proposed. Our algorithm constructs an unwrapped phase from previously computed phases with a simple open-fringe-analysis algorithm, twice applied for analyzing horizontal and vertical oriented fringes, respectively. That reduces the closed-fringe-analysis problem to that of choosing the better phase between the two oriented computed phases and then of estimating the local sign. By propagating the phase sign [and a tilewise constant (DC) term] by regions [here named tiles] instead of a pixelwise phase propagation, our analysis of closed-fringe patterns becomes more robust and faster. Additionally, we propose a multigrid refinement for improving the final computed phase.

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Fast phase recovery from a single closed-fringe pattern

A quadratic cost functional for computing an estimate of a wave front from multiple directional derivatives is presented. This functional is robust to noise and is specially suited for moire deflectometry, Ronchi testing, and lateral shearing interferometry.

Ricardo Legarda-Saenz

Papers

Accurate procedure for the calibration of a structured light system

Color-fringe pattern profilometry using a generalized phase-shifting algorithm.

Improvement of the regularized phase tracking technique for the processing of nonnormalized fringe patterns.

Fast phase recovery from a single closed-fringe pattern

Robust wave-front estimation from multiple directional derivatives.