Generalized performance parameter for single-threshold detection systems

A new generalized performance parameter for single-threshold detection systems is investigated that providesa more consistent measure of system performance than the conventional signal-to-noise ratio (SNR).It is shown explicitly that this parameter decreases monotonically as the Bayes risk and probability of errorincrease, and that it reduces to the SNR under appropriate conditions. An example is presented in whichthis parameter is monotonic with system performance, but the SNR is not. The analysis, which utilizes normalizingtransformations, is also useful in the direct calculation of the Bayes risk, probability of error, andsensitivity, as is considered in detail subsequently (P. R. Prucnal, Applied Optics 19, 3606 (1980)).