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

The automatic, non contact measurement of objects in industrial applications is one of the most important 
applications of the optical 3-D shape measurement methods A well established 3-D shape measurement technique 
is triangulation with structured light In this paper, it will outline on two important aspects of this technique: 
pattern-codification strategy and calibration procedure, in order to obtain a high accuracy reconstruction

Tridimensional reconstruction using structured light systems

The two-dimensional phase unwrapping problem (PHUP) has been solved with discrete Fourier transforms (FTs) and many other techniques traditionally. Nevertheless, a formal way of solving the continuous Poisson equation for the PHUP, with the use of continuous FT and based on distribution theory, has not been reported yet, to our knowledge. The well-known specific solution of this equation is given in general by a convolution of a continuous Laplacian estimate with a particular Green function, whose FT does not exist mathematically. However, an alternative Green function called the Yukawa potential, with a guaranteed Fourier spectrum, can be considered for solving an approximated Poisson equation, inducing a standard procedure of a FT-based unwrapping algorithm. Thus, the general steps for this approach are described in this work by considering some reconstructions with synthetic and real data.

Two-dimensional phase unwrapping based on Fourier transforms and the Yukawa potential spectrum.

There are several algorithms to solve the shape from shading problem. Most of these algorithms rely on basic assumptions about the surface reflective properties, camera projection and location, and the light source distribution. In this paper, we implemented an algorithm based on a Wiener filter to obtain surface estimation from a single image. We tested the algorithm with images generated synthetically and also employing images from a real object. We were able to obtain the shape of objects with different geometries.

Ricardo Legarda-Saenz

Papers

Tridimensional reconstruction using structured light systems

Two-dimensional phase unwrapping based on Fourier transforms and the Yukawa potential spectrum.

A Wiener filter approach to shape from shading

Parallel algorithm for wrapped phase denoising

Surface contouring of vibrating objects using quadrature transform