Phase retrieval errors in standard Fourier fringe analysis of digitally sampled model interferograms (original) (raw)

Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms

Optics and Lasers in Engineering, 2007

In order to measure the radial displacements of facets on surface of a growing spherical Cu 2-δ Se crystal with sub-nanometer resolution, we have investigated the reliability and accuracy of standard method of Fourier analysis of fringes obtained applying digital laser interferometry method. Guided by the realistic experimental parameters (density and orientation of fringes), starting from 2-dimensional model interferograms and using unconventional custom designed Gaussian filtering window and unwrapping procedure of the retrieved phase, we have demonstrated that for considerable portion of parameter space the non-negligible inherent phase retrieval error is present solely due to noninteger number of fringes within the digitally recorded image (using CCD camera). Our results indicate the range of experimentally adjustable parameters for which the generated error is acceptably small. We also introduce a modification of the (last part) of the usual phase retrieval algorithm which significantly reduces the error in the case of small fringe density.

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.

Robust phase demodulation of interferograms with open or closed fringes

Journal of the Optical Society of America, 2005

Analysis of fringe patterns with partial-field and/or closed fringes is still a challenging problem that requires the development of robust methods. This paper presents a method for fringe pattern analysis with those characteristics. The method is initially introduced as a phase refinement process for computed coarse phases, as those obtained from partial-field patterns with a full-field method for open fringes analysis. Based on the phase refinement method, it is proposed a propagative scheme for phase retrieval from closed-fringe interferograms. The algorithm performance is evaluated in real data with no homogeneous illumination components and shows a superior performance thanstateoftheartmethods.

Interferometric fringe analysis using a single phase step technique

Applied Optics, 1988

The quasi-heterodyne or phase stepping method of ex tracting displacement information from optical interferograms is well established in the fields of holographic and speckle interferometry. 1-7 In its usual implementation, the phase of one of the inter ferometer beams is stepped by 2π/k in (k-1) equal steps where k is an integer. It is normal practice to restrict the value of k to 3,4, or even 5 as a compromise between accuracy 4362

Generating fringe-free images from phase-shifted interferometry data

Applied Optics, 2005

Weighted averaging of a sequence of phase-shifted interference patterns yields a fringe-free intensity image that can be useful for machine vision, lateral metrology, defect detection, and other supplementary tasks in a surface-profiling interferometer. Coefficients for effective fringe-removal algorithms follow from a Fourier analysis of phase-shifting errors. Theoretical and experimental examples illustrate the substantially improved performance of a well-designed weighted average over a simple linear sum of data frames.

Phase and fringe order determination in wavelength scanning interferometry

A method to obtain unambiguous surface height measurements using wavelength scanning interferometry with an improved repeatability, comparable to that obtainable using phase shifting interferometry, is reported. Rather than determining the conventional fringe frequency-derived z height directly, the method uses the frequency to resolve the fringe order ambiguity, and combine this information with the more accurate and repeatable fringe phase derived z height. A theoretical model to evaluate the method's performance in the presence of additive noise is derived and shown to be in good agreement with experiments. The measurement repeatability is improved by a factor of ten over that achieved when using frequency information alone, reaching the sub-nanometre range. Moreover, the z-axis non-linearity (bleed-through or ripple error) is reduced by a factor of ten. These order of magnitude improvements in measurement performance are demonstrated through a number of practical measurement examples.

Phase difference determination by fringe pattern matching

Optics & Laser Technology, 1996

A method of phase difference determination in interferomet~ is presented. In this method, the phase difference between two interferograms is determined by fringe pattern matching with subpixel accuracy. The signal-to-noise ratio is significantly improved due to the region-based fringe pattern matching and its effect of averaging noise. The experiment shows that this method is useful for the determination of phase difference between two equi-spaced fringe patterns, and it has the advantages of high precision of measurement and high resistance to noise.

Fringe detection in noisy complex interferograms

Applied Optics, 1996

A new algorithm to estimate the two-dimensional local frequencies of phase interferometric data is described. With a complex sine-wave model, demonstration is given that a conventional multiplesignal classification 1MUSIC2 algorithm can be used in spite of multiplicative noise perturbations. A faster algorithm dedicated to the processing of interferograms is developed and a measure of confidence in the estimate is proposed. We studied numerical performances using synthetic fringes. As a result of the frequency estimation, knowledge of the fringe local width and orientation can be applied to restore noisy phase data. Results of a complex phase filter are presented for real interferograms obtained from synthetic aperture radar images.