José L. Fernández

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.

Fizeau phase-measuring interferometry using the moiré effect

The automation of the fringe pattern analysis in Fizeau interferometry combining the moiré effect with the phase-stepping evaluation method is presented. In this case the phase modulator is a Ronchi grid placed at the interferometer image plane yielding a moiré image, and the necessary phase steps are obtained, simply translating the grid in its own plane, perpendicular to the optical axis. A detailed description of the moiré image formation as an incoherent superposition is developed. Measurements were carried out in a Fizeau interferometer built by the authors, and rms repeatabilities of less than 3 deg in the phase-difference values were attained.

Double-pulsed-carrier speckle-shearing pattern interferometry for transient deformation analysis

We report on a novel technique for the evaluation of transient phase in double-pulsed electronic speckle-shearing pattern interferometry. Our technique requires the acquisition of just two speckle-shear interferograms which are correlated by subtraction to obtain a fringe pattern. A spatial carrier is generated by means of an original optical setup based on the separation and later recombination of the two beams produced by a Nd:YAG twin pulsed laser. One introduces an optical path difference in the curvature radii of the illumination beams by mismatching the distances from two diverging lenses to a beam combiner. This procedure gives rise to a linear phase term in the second speckle- shear interferogram that plays the role of a spatial carrier and allows the use of spatial phase measurement methods to analyze the fringe pattern. We present the theoretical aspects of the technique as well as its experimental implementation.

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.