The use of the Principal Components Analysis (PCA) for recovering the modulating phase, given a sequence of Phase-Shifted Interferograms (PSI), is a very important contribution to the field. However, its verbatim translation from statistics to PSI has limited the view to consider only constant background illuminations. Here, we show that the Singular Value Decomposition (SVD), used in PCA, actually separates the background illumination (constant or not) and the phase modulation terms. We show that the modulating phase can be correctly recovered if the phase-shifts sample full periods uniformly, independently of the spatial distribution of the number of fringes.
We model a set of Phase-Shifting Interferogram (PSI) images in a new and versatile way that allows exploring
interesting numerical approaches for the analysis of PSI. We show how this representation can be used to recover
the modulating phase if the phase steps are known, and we also show how it can be used as the baseline for an
iterative algorithm. For the case in which the phase steps are known we compare against the four step algorithm.
For the case of unknown phase steps, we compare against the Principal Component Analysis (PCA) and the
Advanced Iterative Algorithm (AIA).
Liquid-crystal variable retarders (LCVRs) are an emergent technology for space-based polarimeters, following its
success as polarization modulators in ground-based polarimeters and ellipsometers. Wide-field double nematic
LCVRs address the high angular sensitivity of nematic LCVRs at some voltage regimes. We present a work
in which wide-field LCVRs were designed and built, which are suitable for wide-field-of-view instruments such
as polarimetric coronagraphs. A detailed model of their angular acceptance was made, and we validated this
technology for space environmental conditions, including a campaign studying the effects of gamma, proton
irradiation, vibration and shock, thermo-vacuum and ultraviolet radiation.
The use of Liquid Crystal Variable Retarders (LCVRs) as polarization modulators are envisaged as a promising novel
technique for space instrumentation due to the inherent advantage of eliminating the need for conventional rotary
polarizing optics hence the need of mechanisms. LCVRs is a mature technology for ground applications; they are wellknow,
already used in polarimeters, and during the last ten years have undergone an important development, driven by
the fast expansion of commercial Liquid Crystal Displays.
In this work a brief review of the state of the art of imaging polarimeters based on LCVRs is presented. All of them are
ground instruments, except the solar magnetograph IMaX which flew in 2009 onboard of a stratospheric balloon as part
of the SUNRISE mission payload, since we have no knowledge about other spaceborne polarimeters using liquid crystal
up to now. Also the main results of the activity, which was recently completed, with the objective to validate the LCVRs
technology for the Solar Orbiter space mission are described. In the aforementioned mission, LCVRs will be utilized in
the polarisation modulation package of the instruments SO/PHI (Polarimetric and Helioseismic Imager for Solar Orbiter)
and METIS/COR (Multi Element Telescope for Imaging and Spectroscopy, Coronagraph).
Reliable inspection of large surfaces with low depth recovery error is needed in a wide variety of industrial applications,
for example in external defect inspection in aeronautical surfaces. Active triangulation measurement systems with a rigid
geometrical configuration are inappropriate for scanning large objects with low measuring tolerances due to the fixed
ratio between the depth recovery error and the lateral extension. Therefore, with a rigid triangulation setup, if we are
interested in defect inspection over extended surfaces then we have to assume errors proportional to the field of view that
can preclude a precise local defect measurement. This problem can be solved by the use of multiresolution techniques.
In this work we demonstrate the application of an active triangulation multiresolution method for defect
inspection of large aeronautical panels. The technique is based on a standard camera-projector system used together with
a second auxiliary camera that can move freely. The result is a global measurement with a superposed local measurement
without any optimization, explicit registration or recalibration process. The presented results show that the depth
recovery error of the local measurement permits the local defects measurement together with a wide-area inspection.
The industry dealing with microchip inspection requires fast, flexible, repeatable, and stable 3-D measuring systems. The typical devices used for this purpose are coordinate measurement machines (CMMs). These systems have limitations such as high cost, low measurement speed, and small quantity of measured 3-D points. Now optical techniques are beginning to replace the typical touch probes because of their noncontact nature, their full-field measurement capability, their high measurement density, as well as their low cost and high measurement speed. However, typical properties of microchip devices, which include a strongly spatially varying reflectance, make impossible the direct use of the classical optical 3-D measurement techniques. We present a 3-D measurement technique capable of optically measuring these devices using a camera-projector system. The proposed method improves the dynamic range of the imaging system through the use of a set of gray-code (GC) and phase-shift (PS) measures with different CCD integration times. A set of extended-range GC and PS images are obtained and used to acquire a dense 3-D measure of the object. We measure the 3-D shape of an integrated circuit and obtained satisfactory results.
3-D triangulation measurement systems with a fixed geometrical configuration have practical limitations that make them inappropriate for a wide variety of applications. The reason is that the ratio between the depth recovery error and the lateral extension is a constant that depends on the geometrical setup. Therefore, with a fixed triangulation setup, there is a tradeoff between field of view and depth resolution. As a consequence, measuring large areas with low depth recovery error necessitates the use of multiresolution techniques. In this work, we propose a multiresolution technique based on a camera-projector system previously calibrated and a second auxiliary camera that can move freely. The method consists of making first a measurement with a large field of view (coarse measurement). Afterwards, the geometrical configuration of the 3-D rig is changed to acquire a small field of view (fine measurement) that is referred to the original reference system and calibration parameters by means of the auxiliary camera. Using this method, a multiresolution reconstruction is possible without any optimization, registration, or recalibration process. Experimental results, which show a decrease of approximately one order of magnitude in the depth recovery error between fine and coarse measures, demonstrate the feasibility of the proposed method.
A novel calibration method for whole field three-dimensional shape measurement by means of fringe projection is presented. Standard calibration techniques, polynomial-and model-based, have practical limitations such as the difficulty of measuring large fields of view, the need to use precise z stages, and bad calibration results due to inaccurate calibration points. The proposed calibration procedure is a mixture of the two main standard techniques, sharing their benefits and avoiding their main problems. In the proposed method, an absolute phase is projected over marked planes placed at unknown positions. The corresponding absolute phase and marks positions are recovered for each plane location. Using Zhang's calibration method, internal camera parameters (also called intrinsic parameters) and the spatial position for each plane are computed. Later on, a polynomial fit of depth with respect to the phase is performed. To obtain the absolute position of an object point, the depth coordinate is obtained by means of the polynomial calibration and its absolute phase. Then the lateral coordinates are computed from the depth, the internal parameters, and the pixel coordinates of the imaged point. Experimental results comparing the proposed method with the standard polynomial-based calibration are shown, demonstrating the feasibility of the proposed technique.
We present a high-speed 3-D spatiotemporal shape measurement technique by means of structured light. Current methods use a constant number of images that do not take into account the available temporal continuity of the measured object. That is, they focus on acquiring and processing as quickly as possible a fixed number of images to solve for the correspondence problem and later obtain the 3-D shape by triangulation. The number of images used imposes the use of some spatial support. The major contribution of our research is a new spatiotemporal scheme that, depending on the object's movement, adaptively uses the maximum number of projected images consistent with the local temporal continuity, therefore solving the correspondence problem with the minimum possible spatial support for each position. This is achieved by the use of a hybrid color pattern composed of an analog sinusoidal periodic code in the red channel and a digital binary spatial code in the blue channel that is cyclically displaced. No subpixel calculation is used and it is possible to implement error correction strategies that make the method fast and reliable, enabling dynamic online 3-D measurement of objects in movement.