It is often desired that a transducer have a polar radiation pattern that is invariant with frequency, but there is currently no way of quantifying the extent to which a transducer possesses this quality (often called "constant directivity" or "controlled directivity"). To address this problem, commonly-accepted criteria are used to propose two definitions of constant directivity. The first, stricter definition, is that the polar radiation pattern of a transducer must be invariant over a specified frequency range, whereas the second is that the directivity index (i.e., the difference, in dB, between the on-axis frequency response and the average response over all directions), must be invariant with frequency. Furthermore, to quantify each criterion, five metrics are derived: 1) Fourier analysis of contour lines (i.e., lines of constant sensitivity over frequency and angle), 2) directional average of frequency response distortions, 3) distortion thresholding of polar responses, 4) standard deviation of directivity index, and 5) cross-correlation of polar responses. These five metrics are computed using measured polar radiation data for four loudspeakers. The loudspeakers are then ranked, from most constant-directive to least, according to each metric, and the rankings are used to evaluate, by comparison with each other and with a predetermined "correct" ranking, each metric's ability to quantify constant directivity. Results show that all five metrics are able to quantify constant directivity according to the criterion on which each is based, while only two of them, metrics 4 and 5, are able to adequately quantify both proposed definitions of constant directivity.
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