Benito V. Dorrío

Measurement of the complex amplitude of transient surface acoustic waves using double-pulsed TV holography and a two-stage spatial Fourier transform method

We present a technique to measure the mechanical complex amplitude, i.e. the mechanical amplitude and phase of vibration, of an ultrasonic plane wavefield of nanometric amplitude that propagates on a surface. Our aim is to detect perturbations of the initially smooth wavefronts that indicate the presence of flaws in the material. We use bursts of surface acoustic waves (SAWs) and a double-pulsed TV holography system that records two correlograms with time separations down to 1.5 µs. The phases of the correlograms are calculated separately using the spatial Fourier transform method (SFTM) and operated on to obtain the phase change between exposures. In the resultant optical phase map, the field of instantaneous displacements of the surface (that comprises several periods of the SAW) acts as a modulated spatial carrier, now related to the mechanical phase and amplitude, that are extracted by applying the SFTM again.

Detection of transient surface acoustic waves of nanometric amplitude with double-pulsed TV holography.

We describe the detection of bursts of surface acoustic waves by a double-pulsed TV holography technique. We describe mathematically the long- and short-wave bursts in the output correlograms and validate theoretical results with experimental images. The use of short-wave bursts permits us to scan the surface and makes it easier to distinguish, for purposes of nondestructive testing, the disturbances produced by flaws.

Non-destructive testing with surface acoustic waves using double-pulse TV holography

In this paper we present the visualization of the out-of-plane displacement fields produced by Rayleigh and Lamb waves on aluminium surfaces, using a double-pulse TV holography technique. This method presents several interesting characteristics, as a possible way of making whole-field remote measurements of instantaneous acoustic displacements, with good immunity from environmental perturbations. We also show examples where different surface and subsurface flaws have been detected, demonstrating the great potential of this technique for non-destructive testing in industrial applications.

Transient deformation measurement by double-pulsed-subtraction TV holography and the Fourier transform method

We report the measurement of transient bending waves with double-pulsed-subtraction TV holography. The correlation fringe patterns are automatically quantitatively analyzed by the application of Fourier methods. A novel optical setup with two different object-beam optical paths is demonstrated for the generation of carrier fringes. The proposed system is highly immune to environmental disturbances because the optical setup imposes no lower limit on the time separation between laser pulses. One removes the linear phase distribution due to the spatial carrier in the spatial domain by subtracting the phase of the undeformed carrier fringes from the phase of the modulated fringes. Experimental results obtained with an aluminum plate excited by the impact of a piezoelectric translator are presented.

Family of detuning-insensitive phase-shifting algorithms.

The design of phase-shifting algorithms (PSAs) has been carried out with diverse strategies by different authors. A generalized algebraic approach is employed to obtain a family of detuning-insensitive PSAs; their behavior against a linear phase error is analyzed from a geometric point of view. The obtained results are compared with the conditions provided by the Fourier representation of the corresponding sampling reference functions. In our case, new equations as criteria for determining whether a PSA is detuning insensitive, new analytic expressions for the phase error, and new algorithms with interesting properties are achieved.

Fourier analysis of two-stage phase-shifting algorithms

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.

Testing phase-shifting algorithms for uncertainty evaluation in interferometric gauge block calibration

This paper describes the uncertainty contribution of nine different phase-shifting algorithms (PSAs) to a gauge block calibration evaluated using a Monte Carlo method. The phase map and its standard deviation, codified in the output distribution obtained with each PSA, are used as input parameters in the exact fractions method for the final calculation of the gauge block length. Results obtained show the behaviour of each PSA versus different types of error sources. Uncertainty evaluation fits well to a Gaussian distribution for all algorithms tested with more than 104 trials and the central limit theorem is satisfied. As expected, the Symmetric 5 + 1 PSA shows the best behaviour with the lower uncertainty contribution and appears among PSAs used as the best algorithm for this technical application. As the selected PSAs are representative for the main PSA families, the protocol employed can be used for any other specifically tailored algorithm.

Error propagation in differential phase evaluation.

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 DPSAs 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.

Error‐phase compensation properties of differential phase‐shifting algorithms for Fizeau fringe patterns

Many researches have been reported on error‐compensating Phase‐Shifting Algorithms (PSAs) that eliminate or minimize the main error sources during the corresponding phase‐evaluation process. However this kind of analyses have not been carried out in a similar way with respect to the Differential Phase‐Shifting Algorithms (DPSAs) that provide directly the phase‐difference between two fringe patterns, being unnecessary the previous calculation of each individual optical phase or even the phase‐unwrapping process, if the phase‐difference is small. In previous works we have studied, by numerical simulation and in a linear approximation, the quantitative response of several families of DPSAs to detuning errors, nonlinearities of detector and harmonics of the signal, achieving satisfactory results that improve those obtained subtracting the two phases calculated separately with PSAs and that provide valuable information related with the sensibilities of the analysed DPSAs. In this work the combined effect of th...

Measuring Amplitude and Phase of Vibration With Double-Exposure Stroboscopic TV Holography

We present a technique for the measurement of both amplitude and phase of sinusoidal vibrations with double-exposure stroboscopic TV holography combining optical and mechanical phase shifting. Using double-exposure stroboscopic illumination, there is no need of recording a reference state of the object and, consequently, the measurements can be made “in flight”, with a sensitivity to environmental noise much lower and with a more efficient use of the available laser power than with the former single-exposure techniques developed for the same purpose.