Two-step phase shifting algorithms: Where are we?

Abstract

Two steps phase shifting interferometry has been a hot topic in the recent years. We present a comparison study of 12 representative self-tunning algorithms based on two-steps phase shifting interferometry. We evaluate the performance of such algorithms by estimating the phase step of synthetic and experimental fringe patterns using 3 different normalizing processes: Gabor Filters Bank (GFB), Deep Neural Networks (DNNs) and Hilbert Huang Transform (HHT); in order to retrieve the background, the amplitude modulation and noise. We present the variants of state-of-the-art phase step estimation algorithms by using the GFB and DNNs as normalization preprocesses, as well as the use of a robust estimator such as the median to estimate the phase step. We present experimental results comparing the combinations of the normalization processes and the two steps phase shifting algorithms. Our study demonstrates that the quality of the retrieved phase from of two-step interferograms is more dependent of the normalizing process than the phase step estimation method.

Optical phase retrieving of a projected object by employing a differentiation of a single pattern of two-beam interference

“…On one hand, fringe-projection is based on the projection of pre-defined interference fringes on an object in order to change their phase distribution due to the shape of this object’s tomography 1 , 2 , 5 – 8 . On the other hand, the phase-shifting methods can be used for “pixel by pixel” extraction of an interference pattern’s phase distribution with high resolutions 1 , 2 , 5 , 10 – 12 .…”

“…But, retrieving the phase values from multiple images is a time-consuming process which persecutes the real-time measurements 1 , 2 . Therefore, recent attempts are presented to overcome this problem; e.g., algorithms based on only two-step phase-shifting of a certain phase shift which is capable of speeding up the phase retrieving process with keeping the same quality level of the retrieved object’s shape 1 , 2 , 12 . Despite considering more than one pattern, the phase-shifting profilometry is still preferable compared to Fourier-transform profilometry which requires only one image for phase extraction.…”

“…These two equations are less than the three unknown parameters; (1) background term (or carrier), (2) intensity and (3) phase of each pixel in the interference pattern 1 , 2 , 7 , 14 , 15 . Therefore, different approaches are presented to extract the phase data using the two-step phase-shifting methods such as those based on the slow variable background term and the specific phase-shift 2 , 12 , 16 , 17 . Moreover, it was reported that the intensity of the slow variable background of the fringe patterns (i.e.…”

A two steps phase-shifting demodulation method using the VU factorization

“…This sign ambiguity is solved by the phase-shifting interferometry techniques [1]. In phase shifting interferometry, if we know the phase shift, a formula can be deduced to obtain the modulating phase [7,8], but, if this is unknown, a non-linear process is involved [9].…”

“…In this work, we show a method to demodulate the phase given only two fringe patterns with unknown phase shift. The method presented here follows a completely different approach that makes it interesting and an important contribution to the state of the art [9]. This method does not require any pre-filtering process to the fringe patterns in order to remove the background illumination and normalize them.…”