As well-documented, the loss of contrast sensitivity with eccentricity was sharper for higher spatial frequencies and for L/M cone-opponent stimuli than for achromatic or S-cone-opponent stimuli. For a study, researchers sought to examine two competing hypotheses and investigate how eccentricity affected perceived contrast when stimuli are given at suprathreshold contrasts. 

Contrast constancy predicted that, regardless of changes in detection threshold, there would be no decrease in perceived contrast across the visual field; appearance was solely dependent on physical contrast. On the other hand, perceived contrast may scale similarly to the detection threshold, indicating the proportionate rise in stimulus contrast above the threshold. Using a 2AFC contrast matching approach between the fovea and periphery, they assessed perceived contrast for stimuli presented to the L/M cone-opponent, S-cone opponent, and Ach up to 18 degrees of eccentricity. 

They experimented with various reference contrasts, ranging from low (near the detection threshold) to high suprathreshold contrasts, and they compared the perceived suprathreshold contrast to the observed detection thresholds. They showed support for a hybrid model in which perceived contrast was lowered with eccentricity for stimuli in the low and middle contrast range, and contrast constancy was only obtained at the greatest contrasts. In addition, they found no distinction between chromatic and Ach contrast responses when equated for comparable sensitivity losses.

Reference: jov.arvojournals.org/article.aspx?articleid=2783813