In this paper, we present a theoretical model of a parametric array for tomographic applications. The array in the model is assumed to extend right up to the receiver and its cross section is assumed not to be negligible. These two assumptions have not been previously made in applications concerned with tomography. We invoke conditions that permit the derivation of a simple relation for tomographic reconstruction of variations in the acoustic nonlinear parameter throughout the cross section of an object.
LawW. K.FrizzellL. A.DunnF., Determination of non-linear parameter B/A of biological media, Ultrasound Med. Biol.11, 307–308 (1985).
2.
SehgalC. M.PorterB.GreenleafJ. F., Measurements of the acoustic non-linearity parameter B/A in human tissues by a thermodynamic method, J. Acoust. Soc. Amer.76, 1023–1029 (1984).
3.
SehgalC. M.BrownG. M.BahnR. C.GreenleafJ. F., Measurement and use of acoustic nonlinearity and sound speed to estimate composition of excised livers, Ultrasound Med. Biol.12, 865–874 (1986).
4.
IchidaN.SatoT.LinzerM., Imaging the nonlinear ultrasonic parameter of a medium, Ultrasonic Imaging4, 295–299 (1983).
5.
NakagawaY.NakagawaM.YoneyamaM.KikuchiM., Nonlinear parameter imaging computed tomography by parametric acoustic array, in IEEE 1984 Ultrasonic Symposium Proceedings, pp. 673–676 (IEEE Cat. No. 84CH2112-1).
BerktayH. O.LeahyD. J., Farfield performance of parametric transmitters, J. Acoust. Soc. Amer.55, 539–546 (1974).
8.
FenlonF. H., On the performance of a dual frequency parametric source via matched asymptotic solution of Burgers' equation, J. Acoust. Soc. Amer.55, 35–46 (1974).
9.
RolleighR. L., Difference frequency pressure within the interaction region of a parametric array, J. Acoust. Soc. Amer.58, 964–971 (1975).
10.
MoffettM. B.MellenR. H., Nearfield characteristics of parametric acoustic sources, J. Acoust. Soc. Amer.69, 404–409 (1981).
11.
NakagawaY.HouW.CaiA.ArnoldN.WadeG.YoneyamaM.NakagawaM., Nonlinear parameter imaging with finite-amplitude sound waves, in IEEE 1986 Ultrasonics Symposium Proceedings, pp. 901–904 (IEEE Cat. No. 86CH2375-4).
