We show how a sinusoidal fringe pattern can be obtained by using a single cube beam splitter based on the Gates’ interferometer configuration. When an expanded and collimated laser beam hits the binding edge of a nonpolarizing cube beam splitter parallel to the splitter coating, it generates interference fringes at the exit due to the internal reflections and refractions of the laser beam passing through the cube. Unlike common digital projection systems, the proposed optical arrangement generates a perfectly sinusoidal and continuous fringe pattern, minimizing the problems associated with the discretization of a synthetic digital signal. The fast Fourier transform and phase-shifting techniques are used to demodulate the captured fringe patterns. Experimental results are presented for the three-dimensional shape reconstruction of the relief of a coin and of a spherical indentation on a piece of aluminum with a maximum height of about 150 μm. In addition, we evaluate the accuracy and resolution of the proposed measuring device: shape reconstruction accuracy is about 1.4% and axial resolution is 0.15 μm. Due to its simple and compact setup, the proposed system is particularly suited to be miniaturized.
In optical interferometry, noise and distortions in the recovered wrapped phase are very common, and their nature is inherent to the quality and visibility of the fringe patterns that modulate the phase. Filtering these phase imperfections from the wrapped phase is not straightforward since we cannot directly apply filters without damaging their information, that is, its modulus 2π phase jumps. However, having a way to filter noise and distortions from the wrapped phase is desirable and very important because, at the end, the filtered phase is closer to the expected, errors are reduced, and the unwrapping task can be less complex. We propose a modulus 2π filtering method to remove noise and distortions directly from the wrapped phase without damaging its information. The presented method is a global filtering process, but we use the local frequencies from the wrapped phase in such a way that each pixel is tuned to its instant frequency.
The most known and used phase shifting interferometry (PSI) demodulation methods are one-dimensional temporal linear systems. These methods use the information of the interferogram sequence at a single pixel to recover the modulating phase. Accordingly, scanning all pixels, we obtain the two-dimensional (2-D) modulated phase sought. As PSI demodulation methods do not take into account spatial information, these methods cannot remove unwanted harmonics or noise from the interferogram image space (spatial domain). To remove these unwanted artifacts from the image space, spatial information must be included in the demodulation model. We are going to show that the well-known least-squares system for PSI can be used as a full-field 2-D linear system that uses the temporal and spatial information in conjunction in order to recover the modulating phase while removing noise, unwanted harmonics, and interpolating small empty sections of the image space all in the same process with a low computational time.
In this work, we develop a regularization technique to demodulate a phase-shifting interferogram sequence with arbitrary inter-frame phase shifts. With this method, we can recover the modulating phase and inter-frame phase shifts in the same process. As all phase-shifting algorithms, the assumption is that the wavefront under test does not change over time, but the introduction of phase-shifts can vary in a nonconstant way. A notable characteristic of this demodulation method is that not only can it recover the modulating phase, but it is also capable of filtering-out large amounts of corrupting noise. We will show numerical experimental results and comparisons with another already published method to see the performance of the demodulation technique developed herein.