USE OF TAYLOR SERIES EXPANSIONS FOR TIME SAVINGS IN COMPUTATION OF ACCURATE TRANSDUCER PRESSURE FIELDS.

In the method of data reduction used in the authors' laboratory to determine acoustic backscatter coefficients in tissues and tissuelike media, computation of the complex acoustic pressure in an attenuating medium due to a nonfocused disk radiator is required at a large number of field points and over a frequency band of about 1 MHz. Computer CPU time and input/output time can be considerable because of the need to evaluate an integral corresponding to each field point P and frequency, w. The fact that the frequency dependence of this integral is restricted to a factor in the integrand of the form exp (ikr prime ), where r prime is a dummy variable and k equals k(w) is the complex wave number, makes the integral part of the expansion in a Taylor series straightforward. The first five terms of the Taylor series have been derived, and tests of the accuracy of the expansion are presented. While maintaining adequate accuracy, the CPU time savings accrued through use of the series corresponds to a factor of 1/7 and an input/output time savings factor of at least 1/6.