Fringe-pattern analysis using a 2-D Fourier transform (original) (raw)
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Fourier fringe processing by use of an interpolated Fourier-transform technique
Recently a powerful Fourier transform technique was introduced that was able to extract the phase from only one image. However, because the method is based on the two-dimensional Fourier transform, it inherently suffers from leakage effects. A novel procedure is proposed that does not exhibit this distortion. The procedure uses localized information and estimates both the unknown frequencies and the phases of the fringe pattern (using an interpolated fast Fourier transform method). This allows us to demodulate the fringe pattern without any distortion. The proposed technique is validated on both computer simulations and the profile measurements of a tube.
Fourier Fringe Analysis with Improved Spatial Resolution
Applied Optics, 2003
The spatial resolution of the phase image derived from the interferogram by Fourier fringe analysis is limited by the necessity to isolate a first order in the Fourier plane. By use of the two complementary outputs of the interferometer, it is possible to eliminate the zero order and thus to improve the spatial resolution by a factor of approximately 2. The theory of this improvement is presented and confirmed experimentally.
Fourier fringe processing using a regressive Fouriertransform technique
Optics and Lasers in Engineering, 2005
Since the introduction of a fourier fringe algorithm by Takeda, it has been possible to determine the phase of a particular light source impinging on an object from one sole image. This has lead to applications in many whole field optical measurement techniques such as ESPI, holography, profilometry and so on. However the basic processing technique, in casu the 2D-fourier transform, is object to a major drawback. Because this technique supposes periodicity in a fringe image, so-called leakage effects occur. This gives rise to non-negligible errors, which can be resolved by using a regressive fourier transformation technique. In the method introduced in this article, the fringe signal is represented by a model using sines and cosines where the frequency is not fixed (which is the case for classical FFT-techniques). The coefficients of those sines and cosines together with the frequency components are then estimated locally by means of a frequency domain system identification technique. This allows the fringe pattern to be unwrapped without any distortion. This method will be applied in particular to Fourier transform profilometry (determines object geometry using shifts of projected fringes) although it can be used in any of the techniques mentioned above. Moreover, it will be shown that the proposed method can deal with other distortions that occur in practice such as over-modulation and varying fringe visibility. The proposed technique will be validated on both simulations and on a profile measurement of a pipe section.
Three-dimensional Fourier Fringe Analysis
Optics and Lasers in Engineering, 2008
Over the years two-dimensional Fourier Fringe Analysis (2D-FFA) has demonstrated both its capability and its relative robustness in analysing fringe patterns within a short time-frame from static objects. Nowadays, there is an increasing demand to measure dynamic objects. Today 2D-FFA is seen as a fast and flexible method of processing fringe patterns for dynamic objects. But it is still inherently a 2D approach, i.e. it deals with three-dimensional data (video sequences) on an individual 2D frame-by-frame basis. In this paper, a novel three-dimensional Fourier Fringe Analysis (3D-FFA) algorithm is proposed to demodulate fringe pattern sequences taken from dynamic objects. This technique processes the stack of fringe patterns as a single 3D volume, not as a set of individual 2D frames that are each processed in isolation. The proposed algorithm has been evaluated on both computer simulated and real dynamic objects. Results show that the proposed technique is able to demodulate fringe pattern volumes successfully.
Optics & Laser Technology, 1998
In this paper we describe a technique based on two-dimensional fast Fourier fringe pattern analysis for the automated evaluation of the inclination angle of parallel fringe patterns. Analysis of noise-free theoretical parallel fringe patterns is presented and numerical results of the angle evaluation error using this algorithm are discussed. We also demonstrate an application of the method to the measurement of the inclination angle of experimental parallel fringe patterns. #
Optics Communications, 2006
The spatial resolution of the phase map in the Fourier transform fringe analysis method is determined by the size of the filter's window in frequency domain. This article reports a straightforward technique to improve the method's resolution by a factor of nearly two. The technique requires capturing a second image with a fringe pattern orthogonal to the first one, therefore using the information from both patterns to eliminate the central component in frequency space. The resulting spectrum supports double sized filter windows for removal of the carrier frequency without leaking into adjacent orders. The overall spatial resolution of the method is thus increased. In the following, the Fourier fringe analysis method is briefly reviewed, the new technique is described and analyzed and the experimental results are shown and discussed.
Two-Dimensional Frequency Estimation for Fringe Analysis by Phase Gradient Detection
SICE Trans. on Industrial Application, 2009
A new frequency estimation technique is proposed, which enables us to estimate two-dimensional frequencies of interferometric fringes with high accuracy and low computational cost. It is accomplished by phase gradient detection, where phases are calculated by a local model fitting algorithm for carrier pattern analysis. The algorithms used and experimental results are presented.
Optics Communications, 2017
A compact simplified algorithm for digital detection of the amplitude and phase of the interferometric signal delivered by a two-wave interferometer with sinusoidal phase modulation is presented. The algorithm consists of simple mathematical combinations of four frames obtained by integration by a camera of the time-varying intensity in an interference pattern during the four successive quarters of the modulation period. The algorithm is invariant by circular permutation of the four image frames. Any set of four consecutive frames can be used for the calculations, which simplifies the practical implementation of the method. A numerical simulation has been carried out to evaluate the efficiency of the algorithm for fringe envelope extraction in low-coherence interferometry. A theoretical analysis of the effect of noise in phase map calculation is conducted. A comparison with the conventional sinusoidal phase-shifting algorithm is made.
Robust fringe pattern analysis method for transient phenomena
Optics and Lasers in Engineering, 2018
We propose a method for analysing a sequence of noisy interferograms with closed fringes acquired at a high-speed frame rate. Our method is appropriate for analysing ESPI sequences of transient phenomena such as deformations caused by vibrations. Firstly, we compute a differential phase between frames using a procedure based on a Gabor filter bank. We then refine this initial phase with a regularised quadratic cost function that keeps the consistency of the restored phase with the fringe patterns. In addition, we also present the robust version of our phase refining method. This prevents the introduction of phase deformations by the smoothing process. We demonstrate by means of numerical and real-data experiments that our method is appropriate for analysing ESPI sequences of transient phenomena.
Image processing applied to the interactive analysis of interferometric fringes
Appl Opt, 1981
A computer software system for performing interferometric fringe analysis interactively (FAI) is described. FAI is based on a general-purpose image-processing system running on a DEC PDP-11. The images contain 144 X 144 pixels with 64 gray levels. FAI permits manual definition of difficult fringe-pattern boundaries. The fringes are traced by an algorithm which makes use of the 2-1) gray-level image information. The user can interactively guide the system and correct errors. The application of the system to analyzing moire fringes defining eardrum shape is described.