Application of fourier analysis to the visibility of gratings

Abstract

SUMMARY1. The contrast thresholds of a variety of grating patterns have been measured over a wide range of spatial frequencies.2. Contrast thresholds for the detection of gratings whose luminance profiles are sine, square, rectangular or saw-tooth waves can be simply related using Fourier theory.3. Over a wide range of spatial frequencies the contrast threshold of a grating is determined only by the amplitude of the fundamental Fourier component of its wave form.4. Gratings of complex wave form cannot be distinguished from sinewave gratings until their contrast has been raised to a level at which the higher harmonic components reach their independent threshold. 5. These findings can be explained by the existence within the nervous system of linearly operating independent mechanisms selectively sensitive to limited ranges of spatial frequencies.

The influence of bandwidth and temporal properties of spatial noise on binocular masking-level differences

“…We can thus legitimately make a different and potentially interesting comparison between the effects of broad-and narrowband noise when they have been equated for noise power per cycle per degree. This comparison is interesting because it allows us to estimate the effective bandwidth of the spatial frequency channels hypothesized by Campbell and Robson (1968). Provided we assume that the ratio of signal to noise power within a channel is the determining factor in detection, the channel widths at each frequency are given simply as the ratio of the square of the threshold contrasts in the broad-and narrowband noise conditions.…”

Higher-harmonic adaptation and the detection of squarewave gratings

“…The fundamental frequency of this grating was in the low-frequency region of the contrast sensitivity function where sensitivity to squarewaves exceeds that to sinewaves by more than 4/n (cf. Campbell and Robson, 1968). Thus, at threshold the fundamental component of the squarewave remains below its detection threshold, so that only the higher harmonics contribute to detection.…”

“…) rather than the fundamental frequency (f) determines threshold for the low-frequency squarewave grating. Campbell and Robson (1968) further showed that a single-channel system, represented by a single contrast sensitivity function, could not account for the difference between the sensitivity to sinewave and squarewave gratings at low spatial frequencies. They, therefore, suggested the existence of multiple channels, each tuned to a different spatial frequency, acting independently (see also, Sachs et al, 1971;Graham and Nachmias, 1971).…”

“…At low spatial frequencies, sensitivity to sinewave gratings falls off linearly, but remains approximately constant for squarewave gratings (Campbell and Robson, 1968). These differences may be explained in terms of linear filtering theory, according to which the sensitivity to the higher harmonics (3f, 5S, etc.…”

The influence of level and polarity of figure‐ground contrast on vision

“…The observations of Campbell & Robson (1968) introduced a concept of human visual processing which has proved fertile ground for much subsequent experimental investigation. Snellen letter recognition, for example, is considered to be founded upon the ability of the visual system to detect and code the contrast components of the range of spatial frequencies comprising the test optotype subsequent to filtering by the CSF.…”