Use of Taylor Series Expansions for Time Savings in Computation of Accurate Transducer Pressure Fields

Abstract

In the method of data reduction used in our laboratory to determine acoustic backscatter coefficients in tissues and tissuelike me- dia, computation of the complex acoustic pressure in an attenuating medium due to a nonfocused disk radiator is required at a large num- ber of field points and over a frequency band of about 1 MHz. Com- puter CPU time and input/output time can he 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' ), where r' is the dummy variable and k = k(w) is the complex wave number, makes the integral part of the expansion in a Taylor series straightfor- ward. 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 inputioutput time savings factor of at least 1/6. (The factor 1/7 means, e.g., that a CPU time of 35 min without using the Taylor series becomes 5 min using the Taylor series.)