Abstract
Acoustic transmission diffraction tomography, which is a technique for reconstructing one or several parameters of an object to be imaged from the observed scattered acoustic field outside of the object, is discussed in this paper. Because the wave length of the incident wave is on the order of 1mm, diffraction effects of the insonifying wave must be taken into account. Conventionally, the first-order Born and Rytov approximation inversion algorithms have been used on the assumption that the parameters of the object to be imaged deviate slightly from the same parameters of the surrounding medium, i.e., inhomogeneities are weakly scattering1–6. For an object characterized by a wave number, the method of the first-order Born perturbation approximation is only valid when the product of the size of the object and the deviation in the circular wave number is small. The method of the first-order Rytov approximation is only valid when the following three conditions are satisfied:
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(a)
The relative wave number deviation is small.
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(b)
The product of the size of the object and the derivation of the relative wave number deviation along the direction perpendicular to the incident wave (hereinbelow, referred to as the effect of inhomogeneity) is small.
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(c)
On wave number discontinuities, including the boundary of the object, junction lines must be ‘steep’ enough (hereinbelow, referred to as the effect of discontinuity).
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Lu, ZQ., Han, XY., Zhang, YY., Chen, GP. (1993). A Comparison of Intermediate, Rytov and Born Transformations in Acoustic Tomography. In: Wei, Y., Gu, B. (eds) Acoustical Imaging. Acoustical Imaging, vol 20. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2958-3_17
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DOI: https://doi.org/10.1007/978-1-4615-2958-3_17
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