Here we describe a 2-step temporal phase unwrapping formula that uses 2-sensitivity demodulated phases for measuring static surfaces. The first phase demodulation has at most 1-wavelength sensitivity and the second one is G-times (G>>1.0) more sensitive. Measuring static surfaces with 2-sensitivity fringe patterns is well known and recent published methods combine 2-sensitivities measurements mostly by triangulation. Two important applications for our 2-step unwrapping algorithm is profilometry and synthetic aperture radar (SAR) interferometry. In these two applications the object or surface being analyzed is static and highly discontinuous; so temporal unwrapping is the best strategy to follow. Phase-demodulation in profilometry and SAR interferometry is very similar because both share similar mathematical models.

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Fringe projection profilometry is a well-known technique to digitize 3-dimensional (3D) objects and it is widely used in robotic vision and industrial inspection. Probably the single most important problem in single-camera, single-projection profilometry are the shadows and specular reflections generated by the 3D object under analysis. Here a single-camera along with N-fringe-projections is (digital) coherent demodulated in a single-step, solving the shadows and specular reflections problem. Co-phased profilometry coherently phase-demodulates a whole set of N-fringe-pattern perspectives in a single demodulation and unwrapping process. The mathematical theory behind digital co-phasing N-fringe-patterns is mathematically similar to co-phasing a segmented N-mirror telescope.

Abstract:In this paper we apply the frequency transfer function (FTF) formalism to analyze the red, green and blue (RGB) phase-shifting fringeprojection profilometry technique. The phase-shifted fringe patterns in RGB fringe projection are typically corrupted by crosstalk because the sensitivity curves of most projection-recording systems overlap. Crosstalk distortion needs to be compensated in order to obtain high quality measurements. We study phase-demodulation methods for null/mild, moderate, and severe levels of RGB crosstalk. For null/mild crosstalk, we can estimate the searched phase-map using Bruning's 3-step phase-shifting algorithm (PSA). For moderate crosstalk, the RGB recorded data is usually preprocessed before feeding it into Bruning's PSA; alternatively, in this paper we propose a computationally more efficient approach, which combines crosstalk compensation and phase-demodulation into a single process. For severe RGB crosstalk, we expect non-sinusoidal fringes' profiles (distorting harmonics) and significant uncertainties on the crosstalk calibration (which produces pseudo-detuning error). Analyzing these distorting phenomena, we conclude that squeezing interferometry is the most robust demodulation method for RGB fringe-projection techniques. We support our conclusions with numerical simulations and experimental results.Centro de Investigaciones en Optica, 2016-05-13.

In this paper we describe a high-resolution, low-noise phase-shifting algorithm applied to 360 degree digitizing of solids with diffuse light scattering surface. A 360 degree profilometer needs to rotate the object a full revolution to digitize a three-dimensional (3D) solid. Although 360 degree profilometry is not new, we are proposing however a new experimental set-up which permits full phase-bandwidth phase-measuring algorithms. The first advantage of our solid profilometer is: it uses base-band, phase-stepping algorithms providing full data phase-bandwidth. This contrasts with band-pass, spatial-carrier Fourier profilometry which typically uses 1/3 of the fringe data-bandwidth. In addition phase-measuring is generally more accurate than single line-projection, non-coherent, intensity-based line detection algorithms. Second advantage: new fringe-projection set-up which avoids self-occluding fringe-shadows for convex solids. Previous 360 degree fringe-projection profilometers generate self-occluding shadows because of the elevation illumination angles. Third advantage: trivial line-by-line fringe-data assembling based on a single cylindrical coordinate system shared by all 360-degree perspectives. This contrasts with multi-view overlapping fringe-projection systems which use iterative closest point (ICP) algorithms to fusion the 3D-data cloud within a single coordinate system (e.g. Geomagic). Finally we used a 400 steps/rotation turntable, and a 640x480 pixels CCD camera. Higher 3D digitized surface resolutions and less-noisy phase measurements are trivial by increasing the angular-spatial resolution and phase-steps number without any substantial change on our 360 degree profilometer.