Abstract

We have measured the form of a nonlinear transformation of retinal illuminance in the human visual system by measuring the detectability of the distortions it produces and approximating the transformation with orthogonal polynomials. Superimposing two interference fringes, of frequencies f₁ and f₂, produces a neural distortion product that can be more easily detected than the fringes themselves. The amplitudes of difference frequencies produced at (2f₂ − f₁) and (f₂ − f₁) were measured separately by finding the contrast of superimposed fringes necessary to produce a threshold grating of 10 cpd. These thresholds, along with the threshold for a 10 cpd fringe, determine a set of simultaneous equations that yield the coefficients of the polynomials. As no distortion products of spatial frequency (mf₂ – f₁) could be detected when m > 2, we approximated the transformation with a third-order polynomial. The function that results depends somewhat on mean retinal illuminance, but it has the shape of a simple, saturating function that is more linear, and saturates more abruptly, than the function V = l/(l + s). A tenfold change of mean illumination changes the sale of intensity by slightly less than tenfold.

© 1985 Optical Society of America