Differential phase-shifting algorithms (DPSAs) and sum phase-shifting algorithms (SPSAs) recover directly the phase difference and the phase sum, respectively, encoded in two patterns. These algorithms can be obtained, for instance, by an appropriate combination of phase-shifting algorithms (PSAs), which makes unnecessary the previous calculation and subtraction or addition of each individual optical phase by means of conventional PSAs. A filtering process in the frequency domain is presented that allows us to obtain in a simple and elegant manner a qualitative characterization with a Fourier description of the two-stage phase-shifting evaluation that reveals possible phase shifter miscalibration errors and unexpected harmonics in the signal.
Narrowband ultrasonic surface acoustic waves are of the greatest current interest for the nondestructive testing of thinwalled members and shell structures like plates, pipes, bridge girders, cans and many others. The measurement and characterization of ultrasonic displacement elds of Lamb waves by pulsed TV holography (TVH) is presented. Narrowband ultrasound is generated in a few millimeters thick aluminum plate by the prismatic coupling block method using a tone-burst excitation signal in the range of lMHz. At this frequency, the plate supports only a few Lamb wave modes, mainly the A0 and S0 ones. The simultaneous presence of these modes produces a beating clearly detectable as a spatial amplitude modulation. Our self-developed TVH system performs the optical phase evaluation by the Spatial Fourier Transform Method and renders the instantaneous out-of plane mechanical displacement eld along the whole inspected area. From this eld, the wavenumber of each Lamb mode can be obtained and, by combining them with the value of the ultrasound frequency and with the Rayleigh-Lamb theoretical frequency spectrum, information about the elastic constants of the specimen material is obtained.
In many metrological applications the data being measured is associated to the phase difference codified in two fringe patterns. This phase difference can be recovered directly with what are called Differential Phase Shifting Algorithms (DPSAs) by using a combination of irradiance values from both patterns in the arctangent argument. Use of such algorithms requires characterisation mechanisms to inform of their sensitivity to the various random and systematic error sources, which is the same as for well-studied Phase Shifting Algorithms (PSAs). Thus, we present a new analysis of error propagation for DPSAs taking into account the frequency shifting property of the employed arctangent function. The general analysis is verified for significant specific cases associated to large errors that appear during phase difference evaluation using the Monte Carlo method, which provides a characterisation of a DPSA's sensitivity; this is an alternative to spatial and temporal techniques but has wholly coinciding results. Monte Carlo simulation opens up the possibilities for the analysis of other error types for any DPSA.
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