The filtered Fourier difference spectrum predicts psychophysical letter discrimination in the peripheral retina

We wished to devise a measure of dissimilarity (D) which could predict psychophysical discrimination performance for Snellen letter pairs in peripheral vision. Threshold size for discriminating 33 pairs of Snellen letters was measured at 30 degrees eccentricity in the nasal retina for two subjects. D was computed for each pair by performing an overlap subtraction in the spatial domain, followed by a Fast Fourier Transform on this difference image, and dividing the total power in the resultant 'difference spectrum' by the sum of the powers of the individual letter spectra. A plot of D vs. psychophysical threshold letter size gave a mean correlation of R = -0.81. When D was calculated for letters that were low-pass filtered at different cut-off frequencies, the correlation with psychophysical performance was greatest when cut-off was between 1.25-1.9 cycles/letter (R = -0.85). Conversely, when the difference spectrum was high-pass filtered at different cut-off frequencies, the correlation decreased continuously as the cut-off increased. These results imply that the band of frequencies between zero and 1.25 cycles/letter are most important for letter discrimination in peripheral vision.