N-point spatial phase-measurement techniques for non-destructive testing

Complex-wave retrieval from a single off-axis hologram

“…A thorough treatment of the sampling of digital holograms, including aspects related to the nonideal sampling by the CCD can be found in the literature. 51,52 There are also closely related discussions more specific to spatial 31,33,53 and temporal 50 phase shifting.…”

“…Once the change of variables is performed, the remaining mathematics is essentially the same as for phase-shifting algorithms: For specific choices of the reference wave (for example, a plane wave whose wave vector is horizontal) and a suitable one-dimensional weighting function, the linear part of our formulation is equivalent to previously proposed spatial phase-shifting algorithms. 17,24,25,27,31,32 One notable difference, however, is that we consider a two-dimensional spatial weighting function that allows for a much less restrictive choice of the reference wave's form (plane, parabolic, etc.) and orientation.…”

“…The general method has been improved in many ways, for example to compensate for nonideal acquisition devices and conditions. [29][30][31][32][33][34][35] A number of spatial demodulation algorithms have been proposed that are able to demodulate interferograms with closed fringes. [36][37][38][39][40] Thus, they might also form the basis of a two-step procedure to reconstruct digital offaxis holograms acquired in the presence of a microscope lens, since such general setups possibly yield closed fringes.…”

Optical Techniques for Defect Evaluation in Vehicles

“…For the temporal phase-measurement techniques, the phase is measured using a single point in an interferogram as the phase difference between the analyzed and reference beams is changed in a controlled way by the means of a piezoelectric device. The N-frame techniques measure a sequence of interferograms with known phase shifts techniques and they are the most popular type of these (Creath K. et al, 1996).…”

“…Then, a hole is drilled at the desired place, and the Moiré fringes due to stress relaxation are obtained and recorded. A tiltable parallel plate glass was used to promote phase modulation with a four image phase calculation algorithm (Creath K. et al, 1996).…”