Spatial-Frequency Discr~~Inat~Qn of Drifting Gratings

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0042-6989190$3.00+ 0.00 VisionRes. Vol. 30.No. 9, pp. 1331-1339, 1990 Printedin Great Britam.AH rights reserved CopyrightQ 1990Pergamon Press plc

SPATIAL-FREQUENCY DISCR~~INAT~QN OF DRIFTING GRATINGS

MARK W. GREENLEE,‘*KJRCEN GERLING* and STEPHAN WALTENSPIEL’ ‘Neurologische ~niversit~tskli~ik, Abt. Neurophysiologie, Hansastr. 9, 7800 Freiburg I. Br. and 2Universitlts-Augenklinik, Abt. Neuroophthalmologie, Killianstr. 5, 7800 Freiburg I. Br., F.R.G.

(Received 17 October 1989; in revised form 8 January 1990)

Abstract-Spatial-frequency discrimination thresholds were measured for briefly (300 msec) presented sinewave gratings having a contrast one logarithmic unit above detection threshold. The gratings were drifted at rates varying from I. 1 to 40 Hz. In a two-interval forced-choice paradigm thresholds were determined for vertically and obliquely oriented gratings. Three reference spatial frequencies (I, 4, 12 c/deg) were tested. For the I c/deg reference spatial frequency, spatial-frequency di~~mination thresholds were constant over the wide range of drift rates used. For 4 and 12 c/deg reference gratings, discrimination thresholds were constant for drift frequencies up to 14 Hz. For drift frequencies beyond 14 Hz, spatial-frequency discrimination thresholds increased abruptly, rising from approx. 6% at 14 Hz to 25% at 40 Hz drift rate. Measurements with obIiquely oriented gratings yielded comparable results. The increase in the spatial-frequency discrimination threshold for medium-high spatial frequencies and high temporal frequencies might reflect an increase in the spatial frequency bandwidth of the mechanisms sensitive to these stimulus frequencies.

Spatial-frequency discrimination Stimulus velocity Contrast Channels

INTRODUCTION is associated with a certain probability that the grating will be detected. This finding suggests The human observer is capable of discriminat- that the detection of a grating and the identifi- ing a difference of as little as 2-4% in the spatial cation of its spatial frequency are performed by frequency of two suprathreshold gratings the same mechanisms. (Campbell, Nachmias & Jukes, 1970; Hirsch & It is well known that the visual system is less Hylton, 1982; Mayer & Kim, 1986; Thomas, sensitive to rapidly moving grating stimuli. The 1983). For a grating of high spatial frequency, temporal modulation transfer function of the say, 20 c/deg, having a period length of only human visual system has a maximum between 3 min arc, this means that spatial frequency 5-10 Hz and falls off rapidly for temporal fre- discrimination can be successfully performed, quencies above 10 Hz (Kelly, 1961; Robson, although the period lengths of two gratings 1966; Watson, 1986). The present study investi- differ by only 3.6-7.2 set arc. Spatial frequency gates whether the detection and spatial- discrimination can thus be thought of as a form frequency discrimination of gratings would, in of hyperacuity (Westheimer, l975), because the a parallel fashion, covary with drift frequency. smallest resolvable difference is approximately a If the same mechanisms are involved in the factor of 10 less than that of the average spacing detection and discrimination of spatial fre- between the centers of the fovea1 cones (Hirsch quency then stimulus motion should affect both & Hylton, 1984; Williams & Collier, 1983). types of performance in a similar manner. We Thomas (1983) has shown that, near contrast here report the findings of experiments in which threshold, the detection of a grating and the the spatial-frequency discrimination of supra- identification of its spatial frequency are related threshold drifting gratings was measured. The by a proportionality rule: for a given near- gratings had a wide range of drift rates and threshold contrast level and spatial-frequency three different spatial frequencies. We also ex- difference the probability that the spatial fre- plore the effect of grating orientation on the quency of the grating will be correctly identified spatial-frequency discrimination of drifting gratings. The results indicate that spatial- *To whom all correspondence should be addressed. frequency discrimination thresholds for gratings

VR 3019-F 1331 1332 MARK W. GREENLEE et al of medium-high spatial frequency increase for (the Best-PEST, Lieberman & Pentland. 1982). drift rates above 14 Hz. On the contrary, the Each measurement was initiated with a para- spatial-frequency discrimination of a low spatial metric value (i.e. contrast or delta spatial fre- frequency grating (1 c/deg) is unaffected by drift quency) which was roughly 3-4 times that of the frequencies up to 40 Hz. expected threshold value. By pressing one of two switches the observer communicated his reponse to the computer and the parametric METHOD value was sought that would produce a 75% The sinewave luminance gratings used in the correct response rate for the task under investi- experiments were presented on a high-resolution gation. The experimental parameter was con- cathode ray tube (Joyce Electronics, Cam- trolled using a 20-step single staircase with a bridge, U.K.) with white (P4) phosphor and a resolution of 1 dB in contrast or I % spatial-fre- frame rate of 100 Hz. The control vottages quency difference for the contrast detection and determining the spatial frequency, contrast, frequency discrimination tasks, respectively. A spatial position and temporal frequency of the total of 40 trials were conducted for each gratings were under the control of a micro- threshold measurement. Approximately 30 processor. The display had a space-average trials suffice for reliable threshold estimates luminance of 60cd/m2. It was masked by a using this procedure (Lieberman & Pentland, back-illuminated semi-circular surround to a 1982). The results shown in the figures are based rectangular field of l0 x IS deg at I 14 cm view- on the average of two or more such threshold ing distance. The mean luminance and color measurements. The standard error of the para- temperature of the surround were adjusted to metric estimation in most cases did not exceed closely match that of the display. Precautions 2 dB for contrast thresholds or 2% for spatial- were taken to minimize the effects of stray light frequency di~~mination thresholds. Three spa- from the surround onto the screen. Photometric tial frequencies (1, 4 and 12 c/deg) and 10 drift measurements were performed on a regular frequencies (1.140 Hz) were used. For the spa- basis to control the linearity of the voltage- tial-frequency discrimination task, the contrast contrast characteristic of the display for the of the gratings was adjusted to be 1 log unit contrast range used. above its respective detection threshold. The Spatial-frequency discrimination thresholds contrast of the gratings varied from 2 to 95%. were determined using a two-interval forced- Owing to its high contrast threshold, for the choice procedure. Sinewave gratings were highest drift frequency used (40 Hz) grating presented in two temporal intervals. The spatial contrast was less than 1 log unit above the frequency of the one of the gratings was respective contrast threshold for each spatial incremented by a defined amount (Af). The frequency tested. However, both subjects re- subject’s task was to discriminate which ported that these gratings were clearly visible grating had a higher spatial frequency. The and that the apparent contrast of the drifting contrast of the gratings was incremented gratings was similar to that of the gratings and decremented as a Gaussian function of drifting at lower rates. time. The standard deviation of the To reduce the effects of fixed spatial and temporal Gaussian envelope was 50 msec temporal cues over time, we designed the pro- and total presentation time was 3OQmsec. The gram controlling the experiment in such a way two stimuli were separated in time by 1.0 sec. as to add or subtract for each stimulus presen- These two intervals were announced by tation a random value (“jitter”) to such stimulus computer-generated tones 100 msec prior to the parameters as grating contrast, temporal fre- ~ginning of each stimulus presentation. The quency, the initial spatial phase of the test test gratings drified at rates varying between 1.1 gratings, as well as the reference spatial fre- and 4OHz. The direction of drift (leftward vs quency itself. This manipulation appeared to be rightward) was randomized by the computer important since the subject could have other- over presentations. wise based his judgements on such spurious cues Contrast thresholds were also measured at as the apparent contrast or velocity of the each drift frequency for the two observers reference and test gratings, which would vary tested. Contrast detection and spatial-frequency systematically with spatial frequency. The maxi- discrimination thresholds were determined mum size of such randomized jitter never ex- using a maximum-likelihood search algorithm ceeded 10% of the base value and these values Spatial-frequency discrimination 1333 averaged to approx. 0 over 40 trials, so as not The observers were two of the authors (MWG to bias the average value over time. and JG). JG is an emmetrope and MWG is In a subsidiary set of experiments we varied optimally refracted for his myopia and astigma- the orientation of the test gratings from vertical tism. Both subjects have had extensive experi- to horizontal in 15 deg steps. The base spatial ence with similar psychophysical experiments. frequency in this experiment was 1 c/deg and the Therefore, no noticeable effect of learning was drift frequency was either 5 or 20Hz. In a evident over the period of experimentation. further experiment we measured spatial-fre- RESULTS quency discrimination thresholds for gratings oriented at 45 deg and drifting at rates varying Contrast sensitivity to drifting gratings from I. 1 to 40 Hz. The spatial frequency in this Figure 1 presents the findings of the experi- experiment was either 4 or 12 c/deg. ments where we measured the contrast sensi-

I (a)

10 100 Drift Frequency (Hz)

(bl

10 100 Drift Frequency (Hz) Fig. I. Contrast sensitivity (l/threshold contrast) is plotted as a function of the drift frequency of briefly presented (300 msec) sinewave gratings. Results for three spatial fkquencies (squares I c/deg, triangles 4 c/deg, circles 12 c/deg) are shown. (a) Presents the findings for observer MWG and (b) for JG. 1334 MARKW. GREENLEE et al

tivity to gratings drifting at different rates. The from 5 to 8%. Observer MWG exhibited parameter is the spatial frequency of the grat- slightly lower discrimination thresholds for ings (I,4 and 12 c/de&. The findings for subject medium temporal frequencies, MWG are shown in Fig. l(a) and those for JG We next explored the spatial frequency dis- in Fig. l(b). For both observers, contrast sensi- crimination of gratings having a reference tivity peaks around 5 Hz and falls off rapidly spatial frequency of 4 c/deg. The results for above 10 Hz. In accordance with earlier reports observer MWG and JG are presented in Fig. 3. (Robson, 1966; Watson, 1986) the temporal For this medium spatial frequency, both sub- modulation transfer function shows a low-pass jects exhibit di~~~nation thresholds which are characteristic for medium-to-high spatial fre- more or less constant up to around 14Hz. quencies and a bandpass characteristic for low However, for drift frequencies beyond 14 Hz, spatial frequencies. the Weber fraction increases substantially. MWG shows a change from 6% at 14.1 Hz to 24% at 40 Hz and JG indicates a threshold change from 6% at 20Hz to 25% at 4OHz drift frequency. This increase in discrimination Figure 2 presents the findings of the experi- threshold occurred despite the fact that grating ments where we measured the spatial-frequency contrast was adjusted to remain a constant discrimination for gratings having a reference amount above threshold (see Method). The spatial frequency of 1 c/deg. As mentioned observers reported that, although the grating above, the contrast of the gratings was adjusted was clearly visible as a grating, they had to be approx. 1 log unit above the respective difficulty discriminating between the reference contrast threshold for each drift frequency and test gratings with respect to their spatial tested. The Weber fraction of spatial-frequency frequency. discrimination, or the ratio of the difference In the next experiment we increased the refer- frequency to the reference frequency (Af /f ), is ence spatial frequency to 12 c/deg. To compen- plotted as a function of the drift rate of the sate for the resolution limits of the display, in gratings. Results for MWG are shown by solid, this experiment the viewing distance was in- those of JG by open symbols. Spatial frequency creased to 228 cm. The increase in viewing discrimination thresholds are fairly constant distance decreased the angular subtense of the over a large range of drift frequencies. Values display at the eye to 5 x 7.5 deg. The same for MWG vary from 2 to 6% and those for JG viewing distance was used to measure contrast

0.3 . 1 cldeg

0.25 * l MhKJ 0 JG 02

Afff 0.15

o:. i;

0 4 1 10 100

Drift Frequency (Hz) Fig. 2. Spatial-frqmcy dircriminrtion WeshoW (Af1-f) are prmmmi as a function of the drift fivqcncy of the grating. The spatid ftequcncy of the mfwmce g&q was I #deg. Rcwits for MWG shown by solid, thoec for JG by open symbols. Spatial-frequency discrimination 1335

0.3 4 ctdeg 0.25 a

0 JG P 0.2

Af/f 0.15

0.1

0.05

0 1 10 100 Drift Frequency (Hz)

Fig. 3. Spatial-frequency discrimination thresholds as a function of drift frequency for a reference spatial frequency of 4 c/deg.

sensitivity for the 12 c/deg condition. All other Spatial -frequency discrimination of obliquely stimulus parameters remained as before. The oriented gratings results are shown in Fig. 4 for the two subjects tested. Here again, we observe good perfor- Figure 5 presents the results of the experiment mance for medium-to-low drift rates and poor in which we explored the effect of grating orien- performance for high drift rates. Note that the tation on the spatial-frequency discrimination transition in thresholds for medium to high drift of drifting gratings. In Fig. 5, the Weber frac- rates occurs rather abruptly. tion is plotted as a function of the orientation of

0.3 12 cldeg 0.25 l tvMG 0 JG 0.2

Aftf 0.15

0 1 10 100 Drift Frequency (Hz)

Fig. 4. Spatial-frequency discrimination thresholds as a function of drift frequency for a reference spatial frequency of 12 c/deg. 1336 MARK W. GJEENLEE et al.

0.3

0.25 o 5Hz 1 Meg l 20 Hz 0.2

Aflf 0.15

0.1 0.05 z-7 0 90 120 150 180 210 Grating Orientation (deg) Fig. 5. Spatial-frequency discrimination thrubob aa a funaion of the orientation of the grptingf. The spatial frequency of the nfcrcnoc grating wus 1c&g and the drift fiqimcy was either 5 Hz (0) or 20 Hz (0). a grating with a 1 c/deg base frequency and a gratings is unimpaired by stimulus motion for a contrast that was one log unit above detection wide range of drift frequencies (Fig. 2). Con- threshold. The parameter corresponds to the trary to this 6niiing, spatial-frequency diserimi- drift frequency of the grating (open circles 5 Hz, nation is substantially impaired for gratings solid circles 20Hz). The results indicate that having a reference frequency of 4cldeg and spatial-fmuency discrimination performance is greater, w&never the driR rate of these gratings independent of the orientation of the drifting exceeds 15 Hz (Figs 3 and 4). For the two higher grating for this low spatial frequency. They also spatial frequencies tested (4 and 12cfdeg) the indicate that there is no interaction between the temporal frcquenoy, where disuimkation per- orientation of the grating and drift fmuency. formance bcgks to break down, corresponds to We further tested whether the increase in the point in the contrast transfer function where discrimination thresholds found for medium-to- sensitivity begins to decline rapidly (Fig. 1). high spatial frequency gratings and high drift It might be argued that eye movements may rates would be more pronounced for obliquely be causing the effect at spatial frequencies of oriented gratings. Figure 6 compares discrimi- 4c/deg and above. A low spatial frequency nation thresholds for vertically oriented and grating could be followed easier and thus drift obliquely oriented gratings as a function of the would have less e&t on discrimination drift frequency. For the sake of comparison, tbe thresholds. Certain precautions were taken, results presented in Figs 3 and 4 for vertical howcvcr, to reduce the effkts of pursuit eye gratings are depicted by the curves in Fig. 6. The mov~en~ and spurious cues due to stimulus symbols show the results for the condition motion and changes in spatiaf frequency. First, where the gratings were oriented at 45 deg for we wed short stimulus durations and random a 4 (triangles) and 12c/deg (circles) reference stimulus dinactions (Ichard or rigbkard drift) spatial frequency. The findings indicate that to reduce the eflects of smooth pursuit eye there is no marked diRerence between perfor- movements. Tbe gratings were only visible for mance for vertical and oblique gratings. approx. 150 msec and this duration is leas than that usually required to voluntarily initiate eye movements (Fischer, 1987). We can thus be DlscusslON fairly certain that cyt movements could not The present ~dings indicate that spatial-fre- have been rehabiy made by the subjects to quency discrimination of low spatial-frequency reduce image motion on tbe retina thereby Spatial-frequency discrimination 1337

A 4 cldeg o 12 cfdeg

Aflf

10 100 Drift Frequency (Hz)

Fig. 6. Spatial-frequency di~~mination thresholds as a function of drift frequency for gratings oriented at 45 deg. Results for a 4 c/deg reference shown by triangles, those for a 12 c/deg reference grating by circles. Continuous (4c/deg) and broken (12 c/deg) lines show for comparison the results (data points omitted) for gratings of vertical orientation.

improving thresholds for low spatial fre- and McKee (1977) is that the info~ation re- quencies. The results that the orientation of quired to solve the spatial-frequency discrimi- the grating had no effect on discrimination nation task was oriented orthogonal to the threshold further argues against a role of eye direction of motion, whereas the vernier offset movements as a possible contaminating factor cues were oriented obliquely to the axis of in these results. stimulus displacement. Such differences appear to be critical for di~~mination performance. Eflect of grating orientation on spatial-frequency discrimination thresholds Discrimination performance and stimulus motion Westheimer and McKee (1975, 1977) have For the vernier targets, Westheimer and shown that discrimination thresholds for the McKee (1975) restricted their observations to offset of two vertically oriented lines remains stimulus velocities of 3.5 degjsec and less. In a unaffected by image motion for a range of recent report, Morgan and Benton (1989) repli- velocities between 0.5 and 3.5 deg/sec. Inter- cated the findings of Westheimer and McKee estingly, vernier-resolution thresholds were and expanded their observations to stimulus affected by oblique motion, when the vertical velocities up to 6 degjsec. Morgan and Benton targets were moved along the 45 and 135 deg (1989) did, however, find an effect of stimulus meridians. Compared to thresholds for horizon- motion for another form of hyperacuity- tal motion, vernier-offset thresholds for oblique spatial interval discrimination-for two parallel motion began to diverge for stimulus velocities line segments separated, on average, by 4.5 min greater than 2 deg/sec. In contrast, the present arc. By varying the standard interval between results indicate that the good discrimination the two line segments from 4.5 to 36min arc, performance exhibited for low spatial frequency these authors could explore the interaction be- gratings is unaffected by grating o~entation tween line separation and stimulus velocity. (Fig. 5). In addition, the effect of drift frequency They found that stimulus motion had little effect on spatial-frequency discrimination for on width discriminations for widely separated medium-high spatial frequencies was the same line segments, but did attenuate performance for vertically and obliquely oriented gratings for closely spaced stimuli (Morgan & Benton, (Fig. 6). An important difference between the 1989; Fig. 2). The present results indicate that present experiments and those of Westheimer stimulus motion had no effect on spatial-fre- 1338 MARKW. GREENLEEet al quency discrimination thresholds for low spatial the human visual system is remarkably capable frequencies (1 c/deg), but had a large effect for of detecting minute differences in the spatial medium-high spatial frequencies. Thus. the find- frequency of two suprathreshold gratings. ings of Morgan and Benton (1989) for spatial- Above 15 Hz the fidelity of the visual system interval discrimination of two line segments and begins to break down at least for spatial fre- our present observations appear to be related to quencies of 4 c/deg and above. We suggest that the same underlying mechanisms. Stimulus vel- this change in discrimination efficiency is related ocity affects discrimination of line separation or to an increase in the spatial-frequency band- grating spatial frequency when the critical infor- width of mechanisms sensitive to high temporal mation is contained in the medium-high spatial frequencies. frequency range and has little effect when this Acknowledgements-This research was supported by the information is stored in the low spatial fre- Deutsche Forschungsgemeinschaft (SFB 325, 83 and 84). quency range. The results of computer simu- The authors would like to thank Drs S. Magnusscn and L. lations in our laboratory suggest that this might Spilimann for critical comments on an earlier version of this be caused by mechanisms having a broader manuscript. spatial-frequency tuning to high stimulus vel- REFERENCES ocities (or high temporal frequencies). An in- Andrews, B. W. & Pollen. D. A. (1979). 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