Wide-field, low-cost mapping of power ultrasound fields in water by time-average moiré deflectometry

Abstract

Mapping of acoustic fields in the power ultrasound range in water is a rather common problem in diverse application areas like sonochemistry, biomedicine, or industrial cleaning. Different approaches have been developed for the visualization and mapping of such acoustic fields, being a classical solution the mechanical scanning with pressure sensors (typically, hydrophones) over a grid of points. For high intensity ultrasound, the analysis of bubbles trajectory has also been employed. Alternative optical techniques are the scanning of a pointwise sensor (PIV, LDV), and also full field techniques like deflectometry or schlieren, smooth wavefront interferometry, holographic interferometry, ESPI and similar interferometric speckle techniques, or more exotic approaches like a Fabry-Perot sensor combined with a high-speed camera. In spite of the wide variety of existing methods, most of them present shortcomings like the need of maintaining the acoustic field stable during the whole measurement process (that may be several minutes for a mechanical scanning instrument), or the sensitivity to environmental perturbations (very high for interferometric techniques) or the complexity or expensiveness of the equipment, or its fragility or lack of portability that may prevent making measurements in the field. One of the well-known techniques to analyze phase objects is moire deflectometry. This technique, developed in the nineteen-eighties, employs a well-shaped laser illumination (collimated or spherical) and two gratings to analyze the deflections of the rays after passing through the phase object (the acoustic field in water in our case). Although its sensitivity in practical terms is smaller than that of interferometric techniques, when the acoustic fields to map have enough intensity (as those employed for ultrasonic cleaning), moire deflectometry combines a sufficient sensitivity to the measurand with appropriate insensitivity to perturbations (environmental seismic and thermal effects, laser noise, etc.), with the additional benefit to covering a wide field of view (typically 30x30 cm2) at a low cost, overcoming most of the aforementioned limitations. We present the development of a moire deflectometry laboratory setup to map the acoustic field launched in a water tank by a piezoelectric transducer designed for ultrasonic cleaning purposes. As the temporal spectrum of the excited wave is not monochromatic, we avoided in principle stroboscopic techniques, choosing instead to record time-average images of the moire fringe pattern under CW illumination, employing a standard digital CCD camera with an exposure time much higher than the central acoustic period. Although this acquisition scheme loses the acoustical phase, we still retain information about the acoustic amplitude, which is enough for many practical engineering tasks. We developed a specific differential data processing procedure, based on extracting the variations of the contrast of the moire fringes across the images, with and without the acoustic excitation, by means of filtering the carrier, the speckle and evaluating the moire pattern with the Fourier transform method.