Object spatial frequencies, retinal spatial frequencies, noise, and the efficiency of letter discrimination

To determine which spatial frequencies are most effective for letter identification, and whether this is because letters are objectively more discriminable in these frequency bands or because can utilize the information more efficiently, we studied the 26 upper-case letters of English. Six two-octave wide filters were used to produce spatially filtered letters with 2D-mean frequencies ranging from 0.4 to 20 cycles per letter height. Subjects attempted to identify filtered letters in the presence of identically filtered, added Gaussian noise. The percent of correct letter identifications vs s/n (the root-mean-square ratio of signal to noise power) was determined for each band at four viewing distances ranging over 32:1. Object spatial frequency band and s/n determine presence of information in the stimulus; viewing distance determines retinal spatial frequency, and affects only ability to utilize. Viewing distance had no effect upon letter discriminability: object spatial frequency, not retinal spatial frequency, determined discriminability. To determine discrimination efficiency, we compared human discrimination to an ideal discriminator. For our two-octave wide bands, s/n performance of humans and of the ideal detector improved with frequency mainly because linear bandwidth increased as a function of frequency. Relative to the ideal detector, human efficiency was 0 in the lowest frequency bands, reached a maximum of 0.42 at 1.5 cycles per object and dropped to about 0.104 in the highest band. Thus, our subjects best extract upper-case letter information from spatial frequencies of 1.5 cycles per object height, and they can extract it with equal efficiency over a 32:1 range of retinal frequencies, from 0.074 to more than 2.3 cycles per degree of visual angle.