Spatial frequency tuning studies: weighting as a prerequisite for describing psychometric curves by probability summation.

The visibility of sine-wave gratings was determined as a function of their width and modulation depth. The psychometric curves were described by probability summation. resulting in weighting functions which under certain conditions indicate the existence of tuning. i.e. a maximum sensitivity outside the fovea at an eccentricity inversely proportional to the spatial frequency. The disagreement in the literature about the existence of tuning can be understood in terms of our present findings. Btyngdahl (1966) found that the subjective modulation depth for visual stimuli has a maximum at a certain eccentricity (measured from the fovea) which is a function of the spatial frequency. This finding is in agreement with the assumption of “tuning” in the perception of visual stimuli. van Doom et al. (1972) confirmed Bryngdahl’s observations, on the basis of theoretical considerations using a scatingensemble formalism. van der Wildt et al. (1976) suggested that their results, obtained with a stimulus of increasing width, could be explained on the assumption that the most sensitive part of the retina for iow spatial frequencies is not the fovea. However, measurements of the contrast sensitivity for small stimuli as a function of the eccentricity have not yet yielded &finite proof of the existence of tuning (HiIz and Cavonius 1974: Koenderink er al., 1978; Kroon et al., 1980; Rovamo et al., 1978; Rijsdijk et al., 1980). Evidence for the existence of tuning is only found for stimuli of a certain limited extent. van der Wiidt et al. (1976) found that a statistical approach to the dependence of sensitivity on width does not give adequate agreement with experiment. They used probability summation, assuming a homogen~us retina. The purpose of the present study is to investigate whether the visibility of a grating as a function of the width can be described by probability summation, if a weighting function is used. * Present address: lnstituut voor Perceptie Onderzoek. Den Dolech 2. 5612 AZ Eindhoven. The Netherlands. t The visibility (P,) in percent can be derived from the Percentage correct answers (P,) as follows: P, = P, + ~(100 PC1 so: P, = ZP, 100. When the percentage correct answers was below SO%, which results in a negative visibility, P, was taken to be 0%. EQL’IPMENT AND METHODS Stif?lUlUS Jle stimulus in all experiments was a onedimensionally modulated sine-wave grating, with a height of 5” and a variable width. This pattern was generated on a picture monitor (Tektronix 632, with phosphor WA D6500). The surrounding field was rectangular, with a width of 20’ and a height of 5’. A red fixation spot was presented in the centre of this field. The mean stimulus luminance was 10 cd/m’, equal to the luminance of the surrounding field. The viewing distance was 85 cm. No artificial pupil was used. The me~urements were carried out monocularly (right eye). A chin rest and a forehead rest were used The sine-wave signal was produced by a function generator (Wavetek 144X the gate input of which was controlled by a puise generator (Datapulse IOOA). The pface of the stimulus on the screen could be adjusted with the aid of the pulse delay, and the pulse width determined the width of the stimulus. A whole number of sine-wave periods was displayed, starting at phase zero. The centre of the grating was always presented in the centre of the surrounding field. The contrast is given as the percentage modulation depth (M): M = L ma= Lmin x 1009~‘. Lln,X + Lmin x3 Experimentni procedure The visibility of the grating (defined as the percentage probability of seeing it) was determined by a twoalternative forced-choice procedure. During each run, two pairs of clicks could be heard. One of these pairs coincided with the beginning and end of the stimulus presentation time: the choice of which pair to use for this purpose was made at random. The subject was asked to indicate which of the two click pairs coincided with the presentation of the pattern. The visibility was determined from the percentage of correct resp0nses.t Each session consisted of 20 runs, and was 253 1. N. KR~OH and G. J. VAN DER W/~LDT I / t I IIIII I I , IllIf I IO 100 number of perKzus Fig. I. The visibility of sine-wave gratings as a function of the number of periods. F, = 0.5 cdeg. The lines are drawn by eye through the data. repeated 4 times. The time interval between the clicks of each pair. and between pairs, was 1 sec.