In this work, we deduce explicit conditions to design phase shifting algorithms (PSAs) in order to suppress errors in phase measurement, the double-frequency ripple distortion and the spurious piston. These errors arise when non-uniform phase-shifting interferograms are processed with conventional PSAs which assume uniform phase shifts. By modeling the non-uniform phase shifts as a polynomial of the unperturbed phase shift value !0, we show that the conditions for eliminating those errors are associated to the m-th derivative of the PSA's frequency transfer function (FTF). Thus, we propose an approach to design robust algorithms based on the FTF formalism, and we present a ready-to-apply eight-frame PSA. Finally, our conclusions are supported by computer simulations.
In this work, we introduce the windowed generalized phase-shifting algorithms (WG-PSAs) using static and dynamic weighting functions/widows. These algorithms are derived from a weighted least square fitted to the monochromatic temporal fringe, thereby, the selection of the window plays an important role due to the fact that it shall reduce the influence of those intensities jeopardizing the phase estimation. In order to make the best selection, we propose to employ an adaptive/dynamic window which has the ability to detect the fringe patterns that jeopardize the phase retrieval. This window is computed iteratively by analyzing the error between the measured and fitted intensities. Furthermore, we provide the analysis of our scheme using the frequency transfer function (FTF) formalism for phaseshifting algorithms. Finally, we executed numerical experiments with synthetic data in which we compare the performance of the dynamic window versus several static ones from the state-of-the-art; although our scheme is more computationally expensive due to the iterative procedure, it works better than the traditional generalized PSAs with a window included or not.
We propose a fringe-projection profilometry technique for shape defects measurement, which can be employed for three-dimensional (3-D) quality inspection. The proposal consists of using a template surface to design phase-shifting algorithms with special-purpose phase response via the frequency transfer function. These algorithms can jointly and directly estimate the spatial phase deviations in a 3-D inspection. Phase deviations correspond to shape differences between the template shape and a testing one. The phase-unwrapping procedure is unnecessary when phase differences are small, as is usual in quality inspections. Experimental results show that our technique is so sensitive that the ripples in a fingerprint can be retrieved.
The characterization of the superficial topography of a thin film, obtained from an interferometer installed in our Optics Laboratory, is done using bi-dimensional images of its surface overlaid with interference fringes (interferogram1). These images differ among them only by a constant variation of the optical phase2. The total number of images to acquire depends on the image processing algorithm to apply; this algorithm allows to determine the value of the phase introduced by the surface form.
We describe the control of a piezoelectric device (PZT), mounted in an interferential microscope (IM) to introduce phase steps by mean of modifications light optical path, which is reflected from a sample surface. Both the piezoelectric control as the interferogram acquisitions from the interferometry system are made in a program designed in LabVIEW®. The program gives a stepped voltage by means PZT controller to a piezoelectric; causing deformation of the piezoelectric which in turn produces a shift in the surface mounted over it, resulting in a shift in the fringes pattern, besides the program controls a camera for acquiring an image at each voltage change. We use image processing to measure the displacement of the fringes finding out the position of the pixels which have a maximum of intensity, the first interferogram is set as a reference, in the following images the position of the pixel higher intensity is moving to fill the following pixel position with major intensity pixel of reference interferogram. Between two consecutive maximum and minimum of interference, the phase difference is 2π, then we can obtain the phase-shifting for each voltage change as well as the voltage needed to introduce a 2π phase-shifting in the fringe pattern, and finally obtain interferograms with a constant phase-shifting to reconstruct surface shape of thin films.
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