Detectability of a luminance increment*

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Abstract
The psychometric function for the detection of a foveal luminance increment was studied in human observers. The signal to be detected was a modulation of a 1300 cd/m2 6′ circular red target. For an ideal photodetector, the theory of signal detectability predicts that d′, the index of detectability, should rise linearly with the luminance, E, of the luminance increment unless the observer has some uncertainty concerning the parameters of the signal to be detected. Uncertainty is expressed by the parameter M that indicates the number of orthogonal signals possible. If M is greater than 1.0, (d′)2 = In{1-1/M +(1/M) exp(E2/N2)} where N2 is the variance of the noise that obscures the signal. In addition, the theory predicts that the slope of the receiver operating characteristic (ROC curve) should decrease with increasing M. In one experiment, in which E was varied, a nonlinear psychometric function and an ROC curve of relatively low slope were found. In another experiment that included a pulsed background (pedestal) whether or not the signal was presented, the predicted linear M = 1 psychometric function was found. Finally, the ROC slope that was measured in rating experiments increased when the pedestal was used. Presumably, the pedestal provides the signal-parameter information that the observer could not remember. We conclude that the human observer acts like an ideal photodetector that has imperfect memory concerning the signal to be detected.

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