Ángel F. Doval

Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile

The spectrum of the intensity profile of multiple-beam Fizeau interferograms is presented. Knowledge of this spectrum provides valuable information about the characteristics of Fizeau interferograms, allowing one to calculate the phase error when the Fizeau profile is evaluated by means of two-beam phase-stepping algorithms, as is usual for low-reflectivity coefficients.

Comparison of carrier removal methods in the analysis of TV holography fringes by the Fourier transform method

Carrier removal is a key step in the Fourier transform method (FTM) of fringe pattern analysis because it can give rise to significant errors in the recovered phase. The existing methods of fringe carrier removal in the FTM are reviewed and a comparison of three different methods, translation of the sidelobe to the frequency origin, leastsquares fit and subtraction of the phase of the undeformed carrier fringes, are presented. Computer-generated fringe patterns are used to determine the differences between the original and the retrieved phase distributions. Several figures of merit are proposed to assess the performance of the mentioned methods. Experimental fringe patterns, obtained by double-pulsed-subtraction TV holography, are analyzed by the methods considered here, and the retrieved phase distributions are also compared.

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.

Determination of thickness and elastic constants of aluminum plates from full-field wavelength measurements of single-mode narrowband Lamb waves

A method based on fitting the theoretical dispersion curves of Lamb waves to experimental data is presented to determine the thickness and two independent elastic constants of aluminum plates a few millimeters thick. The waves are generated by means of the wedge method using a narrowband source, selecting the wedge angle and the acoustic frequency f so that mainly one mode is excited. A self-developed pulsed electronic speckle pattern interferometry system renders a two dimensional map of the out-of-plane acoustic displacement field at the plate surface, which allows an accurate measurement of the acoustic wavelength lambda(1). For any mode, the relation between lambda(1) and f depends on the three unknown parameters, so at least three experimental measurements (lambda(1i),f(i)) with different frequencies and/or different modes are required to calculate them. The suitability of different Lamb modes to determine each parameter when the others are known is studied, as well as the conditions that the experimental set of values must fulfill to calculate all three parameters. Numerous Lamb modes at different frequencies are generated in each plate, and a fitting is made based on the minimization of the error function, resulting in an accuracy better than 1%.

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.

Spatiotemporal Fourier transform method for the measurement of narrowband ultrasonic surface acoustic waves with TV holography

The measurement of ultrasonic surface acoustic waves of nanometric amplitude by TV holography (TVH) was demonstrated some years ago. The spatial periodicity of the wavefield across the optical phase difference maps was exploited to yield the mechanical amplitude and phase of the propagating wave. Now we present a refinement of the technique where we also profit from the temporal periodicity, at each point of the surface, of the displacement induced by the wave. We record a series of sets of primary correlograms, which are processed to yield optical phase-difference maps. We change slightly the delay between the excitation of the wave and the measurement from one recording to the next, so that the position of the wavefield on the resultant images is shifted accordingly. Every point on the surface, which oscillates at the frequency of the wave, is thus recorded at several instants of its oscillation cycle in consecutive optical phase difference maps of the sequence. We have then spatial periodicity at a given instant across each image and temporal periodicity at a given point on the surface across the series of images. This feature is exploited to calculate a three-dimensional Fourier transform of the data. As we employ narrowband ultrasonic waves, the spatial content of the spectrum is contained in a small region of the spatial frequency plane and within a thin slice of temporal frequencies, and can be easily filtered and inverse Fourier transformed to obtain the mechanical amplitude and phase of the wave. This method intends to extend the detection capability of the TVH technique to ultrasonic waves of lower amplitude.

Contrast enhanced and phase controlled stroboscopic additive fibre optic TV-holography for whole field out-of-plane vibration analysis

Abstract A new technique for real-time contrast enhancement and phase control of fringes in additive Stroboscopic TV-holography applied to out-of-plane vibration analysis and its implementation on a fibre-optic electronic speckle pattern interferometer (FOESPI) are presented. Synchronous Stroboscopic illumination, firing two pulses per object vibration period, is combined with simultaneous inter-pulse (high frequency) and inter-frame (low frequency) phase modulation in the reference arm of the ESPI yielding a sequence of frames (interferograms) that are grabbed and processed in real-time. With this technique both speckle and fringe phases are independently controlled by means of the parameters of modulation enabling speckle contrast inversion, as required to enhance the visibility of fringes by sequential subtraction, as well as dynamic fringe phase shifting to solve peakvalley ambiguities.

Multimode vibration analysis with high-speed TV holography and a spatiotemporal 3D Fourier transform method.

The combination of a high-speed TV holography system and a 3D Fourier-transform data processing is proposed for the analysis of multimode vibrations in plates. The out-of-plane displacement of the object under generic vibrational excitation is resolved in time by the fast acquisition rate of a high-speed camera, and recorded in a sequence of interferograms with spatial carrier. A full-field temporal history of the multimode vibration is thus obtained. The optical phase of the interferograms is extracted and subtracted from the phase of a reference state to yield a sequence of optical phase-change maps. Each map represents the change undergone by the object between any given state and the reference state. The sequence of maps is a 3D array of data (two spatial dimensions plus time) that is processed with a 3D Fourier-transform algorithm. The individual vibration modes are separated in the 3D frequency space due to their different vibration frequencies and, to a lesser extent, to the different spatial frequencies of the mode shapes. The contribution of each individual mode (or indeed the superposition of several modes) to the dynamic behaviour of the object can then be separated by means of a bandpass filter (or filters). The final output is a sequence of complex-valued maps that contain the full-field temporal history of the selected mode (or modes) in terms of its mechanical amplitude and phase. The proof-of-principle of the technique is demonstrated with a rectangular, fully clamped, thin metal plate vibrating simultaneously in several of its natural resonant frequencies under white-noise excitation.