Abstract
The analysis of sound scattered by a rough surface and measured by multiple microphones positioned in the far field yields an estimate of the unknown scattering surface profile. Expanding from previous work, the approach used in this paper is based on an expansion and linearization of the Kirchhoff integral equation, and applies to a low density of receivers. Here, the original algorithm is modified in order to reduce the measurement bias, and extended to broadband signals to over-constrain the problem and improve its robustness. The improved method is rigorously assessed alongside the original algorithm and its small perturbation version, for a two-dimensional geometry and for scattering surfaces with a spatial power-function spectrum. The impact of the measurement setup and surface characteristics on the reconstruction uncertainty are evaluated by means of numerical simulations. Additional experimental data obtained for three known surface profiles reveal the impact of noise and measurement uncertainties. The optimal measurement configuration requires a trade-off between resolution (higher at high frequencies), and robustness (higher at low frequencies). This limit is overcome at least partially by the proposed multiple-frequency extension. The resulting measured uncertainties were close to the theoretical expectation of approximately 2% of the acoustic wavelength.
Highlights
Measurements of the shape of the interface between two media are ubiquitous across engineering and geophysics, including applications such as non-destructive testing, microscopy, and remote sensing
This work provided a systematic comparison of various approaches to reconstruct a rough surface from measurements of the scattered acoustic field with a linear array of microphones
For the range of conditions examined in this work, the linearization of the scattering equations proposed in [17] was found having a small effect on the reconstruction error
Summary
Measurements of the shape of the interface between two media are ubiquitous across engineering and geophysics, including applications such as non-destructive testing, microscopy, and remote sensing. Examples include the ocean bottom [1], sea waves [2,3], or river surfaces [4,5]. If transmission through the interface can be neglected (this is the case, for example, of high frequency sound on the water-air or air-water interface), the surface shape can be estimated based on a model of scattering and a measurement of the scattered signal by a number of sensors distributed in space. Surface reconstruction techniques based on this principle have been developed for optical [6,7], electromagnetic [8,9,10,11,12,13], elastic [14], and acoustic [15,16,17] wave signals
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