This paper presents a new method for calculating the velocity potential Φ of scattered ultrasonic waves from a rigid sphere placed in the field of waves emanating from a circular concave radiator in an infinite baffle. The solution Φ is given in the form of an infinite series of spherical surface harmonics as a function of reduced quantities ka, krc, kb, kz0, etc., where k is the wave number, a is the radius of the circular concave vibrator, rc is the radius of curvature of it, b is the radius of the sphere, and z0 is the distance from the piston to the center of the sphere. The present theoretical framework has the advantages that it includes no numerical integrations and that it is applicable to elastic or compressible sphere cases with slight modifications of the boundary conditions.
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Hasegawa et al. (1992) studied this question.