Visibility, timing and vernier acuity

Vision Res. Vol. 33, No. 4, pp. 505-526, 1993 Printed in Great Britain. All rights reserved

Copyright

0

0042-6989/93 $6.00 + 0.00 1993 Pergamon Press Ltd

Visibility, Timing and Vernier Acuity SARAH J. WAUGH,*t

DENNIS

M. LEVI*$

Received 20 December 1991; in revised form 10 July 1992

To investigate the relationship between contrast detection and vernier acuity for abutting targets, the effects of varying target exposure duration (122000 msec) on vernier and contrast detection thresholds for long, thin lines and sinusoidal gratings (1 and 8 c/deg), were measured. Vernier thresholds decreased with both increasing exposure duration and increasing target contrast. Predictions made for equally visible targets show that the effect of exposure duration on vernier thresholds is almost completely accounted for by its effect on target visibility. Vernier thresholds and contrast detection thresholds for line targets were also measured in the presence of a spatiotemporal mask, for different exposure durations. Again, once the effect of this mask on target visibility was accounted for, there was virtually no remaining effect of exposure duration on vernier thresholds. The results of these experiments suggest that similar spatial mechanisms mediate both contrast detection thresholds and vernier thresholds for abutting targets; and that the processes involved in target detection and the extraction of relative position information are limited by the same factors. Vernier acuity

Exposure duration

Contrast detection

INTRODUCTION The ability of the human visual system to judge the relative position of two objects in space, such as that required in a vernier acuity task, is an order of magnitude finer than the ability to resolve two targets from one. Because of this exquisite sensitivity, the process whereby relative position information is extracted has sometimes been considered to require more time, than the detection or resolution of spatial targets (e.g. Baron & Westheimer, 1973; Watt, 1987). However, vernier thresholds measured for abutting, or very closely separated targets, are sensitive to changes in experimental conditions, many of which also influence the detectability of a target. It is the goal of this study to examine the experimental hypothesis that vernier acuity thresholds are unaffected by changes in exposure duration providing the target remains equally visible. The hypothesis is examined by comparing the effect of different exposure durations on both detection and abutting vernier tasks, and would be supported by the finding that after accounting for the effect of time on detectability of the target, vernier acuity is independent of time. For detection tasks there is reciprocity between target luminance and exposure duration up to a critical duration. This is known as Bloch’s law (Hartline, 1934; Graham & Kemp, 1938). Bloch’s law also holds for target contrast (Gorea & Tyler, 1986). For durations longer than the critical duration, further increases in *College of Optometry, University of Houston, Houston, TX 772046052, U.S.A. TPresent address: McGill Vision Research Centre, Department of Ophthalmology, McGill University, Montreal, Canada H3A 1Al. $To whom reprint requests should be addressed.

target luminance or contrast lead to lesser improvements in detection thresholds. The results of some studies (Keesey, 1960; Kahneman & Norman, 1964; Baron & Westheimer, 1973; Brown & Black, 1976) suggest that the form acuities, including position acuity, are more complex tasks than detection and require extra time for processing. However, the effect of time on the detectability of acuity targets was not measured in most of the above studies; Baron and Westheimer (1973) although attempting to do so, measured the two tasks over different exposure duration ranges. Since other variables besides exposure duration, such as target size (Graham & Margaria, 1935; Karn, 1936; Barlow, 1958), target configuration (Tolhurst, 1975; Legge, 1978) and retinal adaptation state (Graham & Kemp, 1938; Roufs, 1972) influence target detectability, it is difficult to determine the validity of such a proposal from previous studies. More recent reports which address the importance of time for processing relative position information are conflicting. Hadani, Meiri and Guri (1984) found for a vernier task where three dots were separated from each other by 10min arc, that vernier thresholds are equally good (5-12 set arc) from 2 to 200 msec providing target energy (the product of the target luminance or Weber contrast and exposure duration) is kept constant. Similar results were found for an edge vernier task (Westheimer & Pettet, 1990) where the constituent features were separated by 5 min arc, and the exposure duration range varied between 11 and about 750 msec. The results of these two studies suggest that stimulus energy is the most important factor responsible for the improvement in vernier thresholds with increases in exposure duration, and that time per se is not required to obtain hyperacute relative position thresholds. However in both cases the

505

SARAH

506

J. WAlJGH

vernier features were separated by 5 min arc or more, and because there is evidence for different regimes of position processing for different target separations for the vernier task (Watt, 1984; Waugh & Levi, 1993a), as for the separation discrimination task (Klein & Levi. 1985, 1987; Levi & Westheimer, 1987; Levi. Jiang & Klein, 1990) it is difficult to generalize these results to relative position tasks using abutting vernier targets. In contrast, several studies suggest a specific effect of time on position acuity. For example, Tyler and Gorea measured thresholds for discriminating the position of a line relative to the peak of a sinusoid for different exposure durations (Tyler & Gorea, 1986). They reported a small effect of exposure duration even though the sinusoidal reference stimulus was made equally visible. However in these experiments the visibility of the test line may have varied with stimulus duration. More recently, Watt (1987) found for a range of hyperacuity tasks using line stimuli, that even when stimulus energy was kept constant for the initial 100 msec, thresholds continued to decrease as exposure duration increased up to 1000 msec. In this study, a random noise “energy” mask occupied the stimulus area immediately following the target presentation. To explain these results, Watt suggested an interaction between exposure duration and the geometrical properties of the stimulus. Specifically, he proposed that with the onset of the stimulus, a range of different sized spatial filters is immediately available for position processing, and that this range shrinks as exposure duration is increased, the lowest frequency filters being progressively switched off. The visual system extracts geometrical or position information from the lowest frequency filter available at the end of the target exposure time. However the effect of the noise mask on detectability of the target was not investigated. The purpose of the present study is to examine the effects of target exposure duration on detection and abutting vernier thresholds for similar targets under the same experimental conditions. To address the issue of target visibility, vernier thresholds were measured for targets of different contrast and for different exposure durations. Target contrast could then be scaled by its contrast detection threshold for each exposure duration, and vernier thresholds for equally visible targets could be predicted. In the first experiment, classical line vernier targets were used. To examine the possibility that targets of higher spatial frequency require more time for position processing than targets of lower spatial frequency, the second experiment measured vernier thresholds for abutting repetitive sinusoidal gratings of 1 and 8 c/deg. Finally, in order to eliminate potential effects of neural persistence, a third experiment examined the effect of a spatiotemporal noise mask on both detection and vernier acuity for abutting line targets.

GENERAL

METHODS

The stimuli were presented on a Tektronix 608 oscilloscope screen with a P31 phosphor at a mean luminance of 132.5 cd/m*. The P3 1 phosphor has a peak luminance

and DENNIS

M. l_E\‘:

output at about 525 nm, a bandwidth 01‘bc~ Lvcen ;r~
VISIBILITY, TIMING AND VERNIER

trial one of four near threshold contrasts of the test line, including a blank, was randomly presented. Detection thresholds were again obtained using the ROCFLEX signal detection analysis program. Three estimates of threshold were obtained from psychometric functions where the slope was unconstrained or “free”, and where it was constrained at a value of 1.5 and 2.0. When the slope was free to float, it tended to vary between 1.5 and 2.0. This slope parameter was examined over a wide range of conditions, however for each observer an exponent of 1.5 more often closely represented the floating one, so the thresholds reported were determined using this exponent, unless otherwise indicated. Absolute differences in threshold calculated for the different psychometric function slopes were small (about 20%) and the relative effects of time for example, on thresholds using either exponent were negligible. Data for all experiments were always collected in counterbalanced order. All thresholds reported are the mean of at least four runs weighted by the inverse variance, and the error bars represent f 1 SE, reflecting the larger of the within run and between run variance. Curve fitting was accomplished using Igor@, which uses a Levenberg-Marquardt iterative algorithm to minimize the error between the experimental data and the model fit. For all data analyzed in this way, the fit was weighted by the inverse of the standard error associated with each data point. EXPERIMENT 1: VERNIER ACUITY AND LINE DETECTION

The purpose of this experiment was to assess the effects of varying exposure duration and target contrast on vernier acuity for abutting line targets (Expt la). The effects of varying exposure duration on contrast detection thresholds for a line target were also assessed (Expt lb). In this way, vernier thresholds could be predicted for targets of equal visibility (i.e. equal number of contrast threshold units) across different exposure durations. Methods Three observers, one of the authors (SJW), and two naive observers (FR and TN), participated in this experiment. In Expt la, the effects of target contrast and exposure duration on abutting vernier acuity were measured. The contrast of the line (in %) was defined as AL/L, where AL is the change in luminance and L, is the background luminance. Since the width of our target lines was within Ricco’s area, where there is perfect reciprocity between width and contrast, the line strength or effective contrast, is expressed in units of percent minutes (Ohmin). This unit is useful for describing the visibility of thin lines, because it takes into account line width (Klein, Casson & Carney, 1990), and facilitates comparison with data in the subsequent paper (Waugh & Levi, 1992b) where viewing distance, luminance and eccentricity were varied. Two dark abutting horizontal lines, each two pixels wide (0.62 min arc) and

507

ACUITY

about 40 min arc in length, were presented on the mean luminance background (132.5 cd/m*) and were offset vertically to create the vernier stimulus (Fig. 1). When high contrast lines were used, subpixel offsets were required to measure vernier thresholds. Such an offset was produced by manipulating the contrasts within the line (Watt & Morgan, 1983; Klein et al., 1990), in a manner similar to the centroid method of Morgan and Aiba (1985). Vernier thresholds were measured for target line strengths of between 7 and 52%min (Z 11 and 84%); and for exposure durations of between 12 and 2000 msec, where visible. Data were collected in counterbalanced order where for two observers line strength was held constant while exposure duration was varied, and for the other observer exposure duration was held constant while line strength was varied. In Expt lb, the effects of exposure duration on the contrast detection threshold for a line target were measured. A dark horizontal line, one or two pixels wide (0.31-0.62 min arc) and about 40 min arc in length, was always presented at the same position on the oscilloscope screen (Fig. 1). Note that this line length is equal to that of each of the lines comprising the vernier stimulus. In pilot studies we measured line detection thresholds as a function of line length and found that the 40 min arc line length used was well beyond the “critical” line length, i.e. further increases in line length did not affect the line detection threshold. Contrast detection thresholds were measured for exposure durations of between 12 and 2000 msec. For short durations it was necessary to widen the line to 2 pixels (0.62 min arc) to generate threshold contrasts. Results Figure 2 shows how vernier thresholds vary with increasing exposure duration for targets of different contrast, for three observers. Vernier thresholds decrease both with increasing exposure duration and with increasing contrast. The data are well described by either a three line or a two line fit, on log-log axes, where the initial slope was constrained to a value of - 1. These fits were accomplished by simultaneously fitting two or three power functions to the data. The equations to the three line fit are: th = th, (t/t,)-’

for t < t,

th = th, (t/t,)S’o”2

for t 3 cc

th = th, (t/t2)S’o~2

for t < t,

th = th, (t/t2)dope3

for t 2 t,

(14

and (lb)

where t, the independent variable, is the target exposure duration (set); - 1, slope 2 and slope 3 are the exponents of slopes representing the initial, second and third rates of change of vernier threshold with changes in exposure duration; t, (the critical duration) is the exposure duration where lines with a slope of - 1 and slope 2 intersect, and t, is the exposure duration where lines with slopes 2 and 3 intersect; and th, and th, are the vernier thresholds (set arc) associated with the critical duration

508

SARAtI

J. WAUGH

and DENNIS

M. L.E\‘I

FIGURE I. The plate illustrates several of the stimuli used in these studies: the left column shows the line sttmuli for abuttmg line vernier acuity (top). and line detection (middle) in Expts I and 3. An example of the one-dimensional spatiotemporal noise mask which followed the stimulus offset in Expt 3 is shown at the bottom (left column). Note that the mask was actually random, so it varied from trial to trial. The right column shows the sinusoidal stimuli used for abutting vernier acuily (top). and detection (bottom) in Expt 2.

t, and t,, respectively. A two line fit was accomplished by fitting two of these power functions simultaneously [i.e. equation (la) only]. Ultimately the fit which produced the smaller reduced x2 value, was chosen to describe the data (see Table 1 for parameter estimates). A slope of - 1, where threshold is plotted against exposure duration, represents true reciprocity in the

time-contrast domain, i.e. Bloch’s law, and the critical duration (t,) is defined as the point at which the slope first deviates from a slope of - I. When three lines were used to fit the data, the third slope was generally constrained to a value of 0. while the intermediate slope was free to vary. The time at which the intermediate and final slopes intersect represents a second duration

VISIBILITY, TIMING AND VERNIER

ACUITY

509

TABLE 1. Slope and timing characteristics for line vernier

SJW f A A A

Exposure

Duration

Xl

20 %min 40 %min 50 %min

FR W L7 H 0

%min %min %min %min %mln

2

466'

2

4

0.1 Exposure Duration

66'

1 (set)

2

50 40 20 10 7

56 + 3.5 63 * 3.6 74 & 4.8 152 + 12 234 f 18

-0.50 -0.52 -0.39 -0.45 -0.23

f f + f k

FR

50 40 20 10 7

61+8 19 f 8.4 74+ 11.9 259 + 43 371 f 37

-0.50 -0.40 -0.35 -0.26 -0.19

k 0.06 f 0.06 f 0.04 & 0.10 k 0.06

384 f 104 715 f 113

TN

50 40 20 10

43 f 69 k 160 f 173 +

-0.43 -0.36 -0.14 -0.25 -0.17

f 0.03 f 0.06 f 0.06 & 0.05 + 0.04

502 k 70 610 & 164

g 0

l 0

' 0.01

liZI

20 %min 40 %min 50 %min

t 2

466'

2

466'

0.1 Exposure Duration

1 (set)

5.1 9.0 19 21

v

0.03 0.03 0.03 0.04 0.03

342 f 21 408+21 797 * 73 892 + 69

*No duration 2 (tz) given for two line fits. tInsuBicient data for two line fit, single power function used.

TN

4

Slope2

Duration 2* (tz) (msec)

Figure 3(A) shows the data from Fig. 2 replotted as vernier threshold vs target contrast (% top abscissa) or line strength (%min lower abscissa), for several different exposure durations. Vernier thresholds improve with increasing line strength at about the same rate for all but the shortest exposure duration of 23 msec. The data were fit using a single power function, a straight line on log-log co-ordinates, given by:

1

4

’

7 10 20 40 50

Critical duration (1,) (msec)

SJW

(set)

0

0.01

Observer line contrast (% min)

2

FIGURE 2. Vernier thresholds (arc set) are plotted against exposure duration (set) on log-log axes for each of three observers. The symbols in each graph represent thresholds measured for targets of a different contrast indicated in the legends. Target contrasts are specified in units of %min, where the contrast in % is multiplied by the width of the line, which is normally 0.62 min arc. Each straight line segment fit to the data represents a power function whose exponent is the slope of that line on log-log axes. The parameters obtained from these fits are listed in Table 1.

parameter (tz) which in this case, represents the exposure duration after which there is no further improvement in threshold. As the contrast of the target is increased, the critical duration appears to decrease and approach the critical duration for line detection, for all three observers. Power functions fit to the data relating the critical duration (t,) to target contrast, have exponents of -0.48, -0.68 and -0.58 for SJW, FR and TN respectively. This relationship will be further addressed in the results and discussion of Expt 2, and is illustrated in Fig. 10.

th = kc”

(2)

where c, the independent variable, is the target contrast or line strength (Ohmin); th is the vernier threshold (set arc); k is a constant which identifies the position of the function on the threshold ordinate; and it is the exponent or slope of the best fitting function. The exponents estimated for each exposure duration are summarized in Table 2. The average slopes (and standard deviations), across all exposure durations for each observer, were -0.96 f 0.29, - 1.19 + 0.51, and - 1.10 f 0.20 for SJW, FR and TN, respectively. These slopes become -0.88 TABLE 2. Slope (exponent) characteristics for line vernier vs contrast Slope + SE Time (msec)

SJW

2000 1000 500 250 200 150 100 50 23

-0.88 + 0.02 -0.73 * 0.04 -0.92 & 0.02 - 1.oo * 0.03 -0.96 + 0.04 -1.07+0.04 -0.91 + 0.04 -0.58 f 0.07 - 1.65* -0.96 + 0.29 0.93 + 0.01

FR

TN

-0.97 f 0.03 - 1.02 f 0.03 -1.12&0.03

-0.96 k 0.06 -1.10&0.03 -0.92 k 0.03

- 1.10 f 0.08 -0.78 &-0.12 -2.20*

-1.18+0.05 -0.96 + 0.09 - 1.46*

- 1.19 f 0.51 - 1.04 f 0.02

-1.10~0.20 - 1.00 * 0.01

Average

&SD All times?

*Fit between two points. TPower function fit simultaneously to data for all exposure durations [Fig. 2(b)].

SARAH J. WAUGH and DENNIS M. LEVI

510

(A)

Line Contrast

(%)

10

SJW A A

A a A

A A A n

23 50 100 150

SJW

msec msec msec msec

200 msec 250 msec 500 msec 1000 msec 2000 msec

A

A A

A A A A

10

A

Contrast Threshold

23 msec 50 msec 100 msec

150 msec 200 msec 250 msec 500 msec 1000

msec

Units

10

691O

2

I”’

3

4

slope=-1.04

56789

100:

I

86-

n

FR 23 msec

4-

;

15ooo~~

2-

0

m c]

250 msec 500 msec 1000 msec

FR n

23 msec

; 0

0

lEz 250msec 500msac 1000 msec

0

TN 23msec

n

101 864I

I

1

I

5 676Q’

2

10

3

4

56

2

3

4567

'

IO Contrast Threshold Units

2

3

10 2

3

4

56769

slope--l

I

.OO

TN 0 :

0

l 0

23 msec IFIEZ

25Omsec 500 msec 1000 msec

: 0 0 0

10

4

Line

Strength

(%min)

I 1

IzEz 2SOmaec 500msec loo0 msec

t 2

3

4567

'

10 Contrast Threshold Units

2

3

FIGURE 3. (A) Vernier thresholds (arc set) plotted against target contrast (% top abscissa) or line strength (%min bottom abscissa) on log-log axes for each of three observers. The data in these graphs are the same as those in Fig. 2. plotted in a different way to show the effect of increasing target contrast on vernier thresholds. The symbols in each graph represent a different exposure duration indicated in the legends. Each straight line represents a power function, whose exponent is the slope of that line on log-log axes, fit to the data for each exposure duration. T’he slopes obtained from each fit are listed in Table 2. (B) Vernier thresholds (arc set) plotted against target visibility in contrast threshold units for all exposure durations. Contrast threshold units were obtained by dividing the target contrasts on the abscissa of (A) by the contrast threshold of a target lint at each exposure duration. The slopes of the best fitting power functions fit to all the data for each observer are indicated at the top left of each graph.

+ 0.16, - 1.02 + 0.11 and - 1.OO+ 0.14, respectively, if the slopes for the low visibility 23 msec exposure duration are excluded. Contrast detection thresholds across time for all three observers are plotted in Fig. 4. Once again the data were fit with power functions to produce a three line fit [equations (la) and (1 b)], and the slope and timing characteristics for each observer are summarized in Table 3. In this case, we initially fit the data where the first slope was at first allowed to vary [ - 1 in equation

(la)], and then it was constrained to be - 1 as before. The results show that the slope is indeed very close to a slope of - 1. As described in the General Methods section, contrast detection thresholds were obtained using psychometric functions where the slope was either constrained to be 1.5 or 2.0, or was free to vary. Table 3 shows parameter estimates for all three conditions. Generally, for each observer, the slope of the psychometric function when free to vary was close to I .5. However often it appeared that for very short exposure durations.

VISIBILITY. TIMING AND VERNIER

0 2 3

lo-

c

76-

z E

4-

8E

3-

s-

I

’ 2

0.01

3456

I

2

3

l-

,I,

456

2

0.1 Exposure Duration (set)

3

1

FIGURE 4. Contrast detection thresholds (%min) plotted against exposure duration (set), for all three observers. The thresholds plotted here were interpolated to a d’ of 1 from a psychometric function whose slope (exponent) was constrained to be 1.5. The exponents of three power functions fit to the combined data, represented by the lines on this graph are - 1.00, -0.45 and -0.15 respectively. The two points of intersection occur at 55 and 250msec. Parameters for power functions fit to the data for each observer are given in Table 3.

the psychometric function steepened. Examination of the fitting parameters in Table 3 will confirm that timing characteristics were little changed by using different psychometric function slopes. However the intermediate slope (slope 2) did appear to steepen when detection thresholds were calculated using psychometric function slopes that varied across the exposure duration range, suggesting a systematic shift in the psychometric function exponent as the exposure duration is reduced. When thresholds (obtained using an exponent of 1.5) for all three observers were combined, and all parameters were free to vary, the critical duration for line detection

ACUITY

511

was 55 f 3.2 msec, the second time parameter was 250 + 80.1 msec, and the slopes were - 1.00 f 0.04, -0.45 f 0.19, and - 0.15 f 0.06 respectively (superimposed on data in Fig. 4). Figure 3(B) shows the effect of varying target visibility in contrast threshold units on vernier thresholds. Contrast threshold units were obtained by dividing the line strength (%min) in Fig. 3(A), by the line contrast detection threshold (%min) in Fig. 4 for each exposure duration. Vernier thresholds for all exposure durations collapse to a narrow region no wider than a factor of 2. Best fitting power functions to the combined data for each observer, have slopes of -0.93 f 0.01, - 1.04 f 0.02 and - 1.OOf 0.01 for SJW, FR and TN respectively (Table 2). These slopes were representative for the contrast range from 4 to about 30 times threshold, however slopes fit to the data below 3 times the contrast threshold appeared to be steeper, i.e. - 1.37, - 1.33 and - 1.37. The effect of exposure duration on equally visible vernier targets for each observer is shown in Fig. 5. The points plotted here were derived in the following way: using equations to best fitting lines from Fig. 3(A) (Table 2) and the contrast thresholds of Fig. 4, estimates of vernier thresholds were made for equally visible targets (i.e. in contrast threshold units). The error bars shown with each point are proportional to the errors associated with the slope parameter found for each exposure duration. For the 23 msec exposure duration, since there were only two points to estimate a slope, and because slopes appear to steepen close to threshold, the average slope for all exposure durations was used and this slope was forced through the higher contrast point to obtain a y intercept. The error assigned to this slope was equivalent to the highest error obtained for all other slopes. Because of the small but systematic shift in psychometric function slope with different exposure durations described earlier, this procedure was also performed using contrast thresholds calculated for a psychometric function whose slope was free to vary. The

TABLE 3. Slope and timing characteristics for line detection Exponent TN 1.5 2.0 Free

Critical duration (1,)

Slope 1

Slope2

Duration2 (rz)

Slope3

-1.01 kO.07 - I .03 k 0.06 -1.16+0.10

61 k9.1 58+8.1 78 + 9.4

-0.39 + 0.05 -0.40 + 0.06 -0.37 + 0.09

436 f 103 383 + 87 764 f 222

0.00 + 0.03 0.00 + 0.06 -0.14+0.10

- 1.05 & 0.09 - 1.09 f 0.10 -1.12+0.15

51 f 3.1 50 * 3.3 48 k 8.2

-0.37 + 0.05 -0.38 If:0.04 -0.52 k 0.10

430 + 130 406 f 57 419 f 125

-0.10 & 0.05 -0.08 + 0.04 -0.10 rf:0.05

-1.02+0&t -1.00+0.08 - 1.05 + 0.05

53 + 2.5 52 k 4.7 45 f 7.3

-0.46 + 0.04 -0.46 + 0.04 -0.56 k 0.05

465 f 43 461 f 24 441+73

-0.23 + 0.05 -0.24 + 0.05 -0.24&0.11

55 k 3.2

-0.45

250 + 80

-0.15

FR 1.5

2.0 Free SJW

1.5 2.0 Free

Data for all observers 1.5

-1.00~0.04

combined f 0.19

f 0.06

r,-Time (msec) at which fit deviates from a slope, held to a value of 1.0, on log-log axes. t,-Time (msec) at which the intermediate slope and a slope, held to a value of 0, on log-log axes intersect.

SARAH J. WAUGH and DENNIS M. LEVE

SJW LINE VERNIER A i A

1-j

’

0.01

2

3 x ihreshoid 3 x threshold IO x threshold IO x threshold

(exp=iS) (free) (exp=1.5) (free)

I-4681

2

0.1

468’

2

f

Exposure Duration (set)

FR LINE VERNIER w i ci

3 x threshok! 3 x threshold 10 x threshold 10 x threshofd

(expml.5) (free) (expw1.5) (free)

Exposure Duration (set)

l & 0

TN LINE VERNlER 3 3 10 10

x x x x

thresh&d threshotd threshold threshold

(exp-1.5) (free) (exp-1.5) (free)

Exposure Duration fsec)

FIGURE 5. Vernier thresholds (arc set) plotted against exposure duration (set) for eqtdy rG.vible targets, for each of three observers. These vernier thresholds represent predictions made for target contrasts which are equally visible for each exposure duration. That is, by knowing the effect of exposure duration on contrast detection thresholds for a line (Fig. 4), vernier thresholds for line targets with contrasts equal to some multiple of threshold could be predicted from the power functions relating vernier threshold to target contrast [Fig. 3(A)]. The solid symbols represent vernier thresholds predicted for equally visible targets based on contrast thresholds by extrapolating to a d’ of 1 from a psychometric function whose slope was constrained at 1.5 for all exposure durations. Open symbols represent vernier thresholds predicted for equally visible targets based on contrast thresholds obtained for psychometric functions whose slopes were free to vary, depending on the exposure duration. The slope of the psychometric function often appeared to steepen for very short durations. The small and Iargc symbols used are for predictions made for targets at 3 times and IO times the contrast detection threshold for a line. respectivcl~

slopes of the best fitting lines through the predictions are given in Table 4. For predictions based on a psychometric function whose slope was free to vary, these slopes are between -0.12 and 0.10, and are mostly close to 0. Regression analysis of the points in Fig. 5 shows that none of these slopes were significantly different from 0, i.e. for SJW [t(d.f. = 7)=0.57 and 0.92, P > 0.051 and for FR and TN [t(d.f, = 4) = 0.66-1.16, P > O.OS].

Discussion

The critical duration represents the time after which perfect reciprocity between target contrast and exposure duration begins to fail, and probably represents some physiological limit (Hartline, 1934; Barlow. 1958). The critical durations for our line detection task measured at a mean retinal illuminance of 650 td. and determined using a two line fit. were 63.67 and 84 mscc for FR. SJW

VISIBILITY, TIMING AND VERNIER TABLE 4. Slope characteristics for equally visible line vernier vs exposure duration Slope + SE SJW

FR

TN

3 ctu*

exp = 1.5 (23-1000 msec) (5CrlOOOmsec)

-0.04 f 0.04 -0.04 f 0.04

-0.10 + 0.02 -0.10 + 0.02

0.00 * 0.05 -0.08 + 0.05

exp = free (2331000 msec) (50-1000 msec)

-0.02 + 0.04 -0.03 * 0.04

-0.01 f 0.02 0.00 _+0.02

0.06 k 0.06 -0.03 + 0.06

IO ctu exp = 1.5 (23-1000 msec) (50-1000 msec)

0.02 f 0.03 0.03 + 0.03

-0.18 + 0.07 -0.21 * 0.07

0.03 + 0.06 -0.06 + 0.06

exp = free (2331000 msec) (SO--1000msec)

0.03 * 0.04 0.04 f 0.04

-0.10 + 0.06 -0.12 f 0.06

0.10 k 0.06 -0.01 & 0.06

*ctu, contrast threshold units.

and TN, respectively. These values are reasonably similar to those obtained using the same fitting procedure on previous data for the detection of dark lines on a bright background (Keesey, 1960), i.e. 78-143 msec for LAR and GKS. The background luminance in the Keesey study is not known, and is likely to have been lower than that used in the current study, which might contribute to the slightly longer critical durations found. After the critical duration is reached, thresholds for both line detection and line vernier continue to decrease as exposure duration increases. The rate of this decrease follows a power law with an exponent of between - 0.36 and -0.52 for line vernier, and between -0.37 and -0.46 for line detection (for thresholds derived from a psychometric function with a slope constrained at 1.5). Thresholds do appear to asymptote at a stage sometime after r2, where the effects of additional quanta are probably not physiologically useful and thresholds become limited by other factors such as variability of fixation and accommodation, or loss of attention. An intermediate slope has been similarly reported for the fovea1 detection of sinusoidal targets above about 1.5 c/deg (Legge, 1978) an 8 c/deg sinusoidal target (Gorea & Tyler, 1986), and for small spots of light (Barlow, 1958). It has been attributed to probability summation occurring within the “sustained” mechanism (Legge, 1978) which is postulated to respond best to steady or slowly varying stimuli (Kulikowski & Tolhurst, 1973; Tolhurst, 1975; Gorea & Tyler, 1986). An alternative hypothesis is that “sustained” channels have a longer processing time than “transient” channels (e.g. Breitmeyer & Ganz, 1976) since simple reaction-time is longer for high than for low spatial frequency targets (Breitmeyer, 1975; Harwerth & Levi, 1978). Our results show a decrease in vernier thresholds as target visibility increases, with an exponent, calculated by combining all the data in contrast threshold units for each observer, of -0.93, - 1.04 and - 1.00 for SJW, FR and TN respectively. We pointed out in the Results,

ACUITY

513

that these slopes appear to steepen for target contrasts below about 4 times threshold, which may be a result of the additional uncertainty afforded by such low target visibility (Cohn & Wardlaw, 1985; Cohn & Macleod, 1991). For line contrasts above 4 times the visibility threshold, these slopes become -0.88, - 1.04 and - 0.88 respectively. It is noteworthy, that an ideal detector model predicts both a steepening of this slope for near threshold targets [see Fig. 19(c), Geisler, 19891; and a steeper slope for a dark line on a bright background, than for a bright line on a dark background (Geisler, personal communication). These effects are related to the ratios of the target amplitude and the background photon noise, both of which influence the contrast signal. In general for target contrasts above about 4 times the detection threshold, the slope of the vernier threshold vs target contrast function [Fig. 3(B)] does not vary systematically with exposure duration. Some previous studies which have investigated the effect of increasing target contrast on vernier thresholds have reported shallower slopes. For example, for Gaussian stimuli (c from 2.6 to 42.4min arc) and Gabor stimuli (sine components from 0.25 to 4 c/deg) slopes between - 0.40 and -0.63 have been reported (Krauskopf & Farell, 1991); for edge vernier stimuli, slopes of about -0.50 (Klein et al., 1990) and - 0.48 (Wehrhahn & Westheimer, 1990); for blurred edges, slopes from -0.50 to -0.62 (Watt & Morgan, 1983, 1984); and for sinusoidal stimuli (0.25-8 c/deg) slopes from -0.64 to -0.93 (Bradley & Skottun, 1987) were found. We believe our slopes are steeper than these values primarily because we used 2.5 mm artificial pupils which afforded sharp retinal imagery, and thin line targets, which were within Ricco’s “dimension” (within which contrast and width are perfectly integrated by the visual system). Psychophysical estimates of Ricco’s dimension for foveally viewed long line stimuli such as ours have been estimated to be about 0.8-l min arc under similar background intensity levels (Klein et al., 1990; Banton & Levi, 1991; Waugh & Levi, 1993b). For our experiment, when the lines are offset to create the vernier stimulus (each vernier line subtends 0.61 min), the target still lies primarily within Ricco’s dimension. Thus, any changes in line contrast are fully integrated, or close to fully integrated, by the visual system and result in a concomitant increase in the contrast signal. Since our results suggest that vernier acuity for abutting targets is limited by the same source of noise that limits changes in contrast detection (see General Discussion), the rate of change of vernier thresholds with increasing line strength for our thin line targets is not surprising. There are previous studies which also find that the rate of decrease in vernier thresholds with increasing target contrast are steeper than -0.50. For example, for narrow bar stimuli (each bar being 1.1 min arc wide and 8.31 min arc long), slopes of -0.67 to -0.94 were reported (Wilson, 1986); and for “thin line” stimuli, slopes of -0.71 to - 1.12 (Morgan & Aiba, 1985), -0.70 (Klein et al., 1990) and -0.56 to - 1.09 (Banton & Levi, 1991) were found.

SARAH

511

J. WAUGH

In the past, researchers have suggested that vernier acuity requires significantly more time to be processed than detection (e.g. Baron & Westheimer, 1973). However in these studies target contrast was not considered; the duration akin to our second duration (t,) for vernier acuity was often compared to the critical duration (t,) for detection; and values for vernier acuity for abutting targets and for separated targets were not considered to be different. Indeed the values for our second duration (tz) using the highest contrast vernier line target (342-502 msec), which are similar to those found for line detection (430-465 msec), are close to previously reported values for asymptotic vernier acuity of 200-400 msec (Keesey, 1960; Stigmar, 1971; Foley & Tyler, 1976; Hadani et al., 1984). Our results indicate that providing line targets are made equally visible, vernier acuity is equally as precise for exposure durations as short as 23 msec (and probably shorter), suggesting that the same source of noise that limits detection also limits abutting vernier acuity. This alternative approach will be considered more fully in the General Discussion. The present result is essentially in agreement with the results of previous studies where thresholds for a threedot vernier alignment task (Hadani et al., 1984) and an edge vernier task (Westheimer & Pettet, 1990), varied minimally with exposure duration for targets of constant physical energy. However in these studies, the vernier features were separated by 10 min arc (Hadani et ul.. 1984) and 5 min arc (Westheimer & Pettet, 1990), so one should be cautious in directly comparing these results with those found for an abutting vernier task (Waugh & Levi, 1993a). EXPERIMENT 2: VERNIER ACUITY FOR SINUSOIDAL GRATINGS

In this experiment we assessed the effects of varying exposure duration and target contrast on vernier acuity for sinusoidal targets. In this way we could test the possibility that more time is required to extract fine relative position information for medium vs low spatial frequency targets. Since vernier thresholds progressively decrease for sinusoids up to about 4c/deg (Bradley & Skottun, 1987), it may seem reasonable to suspect that more time is required to process the finer relative position thresholds peculiar to spatial frequency mechanisms of about 4 c/deg and above (Breitmeyer & Ganz, 1976). In our first experiment thin lines, which contain a multitude of spatial frequencies were used, so this possibility could not be tested. Sinusoidal stimuli are also useful because the detection thresholds for these stimuli require much lower levels of physical contrast, and therefore it is possible to test at much higher levels of target visibility than are available for the thin line stimulus. In this experiment we investigated the effects of exposure duration on detection and vernier acuity tasks using sinusoidal targets.

Methods The stimuli were abutting sinusoidal gratings of 1 and 8 c/deg, oriented horizontally on the oscilloscope

and DENNIS

M. LFVI

screen (see Fig. 1). The Michelson defmtloir oi ic)ntrasi. i.e. L.,,,,, --- L,,,,, L,,, + L,,,, . specified in units oi‘ percenr. was used. Results were obtained for twi, ~.~b~cr~cr-~.tn~ two authors, for the I c,deg stimulus: .~nd !:,I zinc of. these observers. for the 8 c/de& stimulus. Ohscr\er Dl_ wore an appropriate refractive correcti0rl :~nti vlcwcti the stimulus monocularly with a natural pupil. while the non-viewing eye was occluded with an opaque patch Observer SJW wore goggles as previousl~~ dsuibcd. In Expt 2a, the effects of target contrast ,tnd ~‘xposurc duration on vernier acuity using abutting \inusoidai gratings of 1 and 8 c!deg. were measured. When no offset was introduced, the horizontal grating extended across the entire screen. To create the vernier stimulus, the sinusoidal grating occupying one half of the sc‘rcen. was offset vertically. When the I c/deg stimulus was used, the observer sat 1.33 m from the screen. such that each grating half subtended about 2 deg in horizontal extent. and 4 cycles of the sinusoid were visible When the 8 c,‘deg stimulus was used. the observer sat -%III from the screen, such that each grating half subtended about 40 min arc in horizontal extent. and 10 cycles of the sinusoid were visible. For large suprathreshold offsets, ;I sharp division was perceived between the grating halves. which may have introduced spatial frequencich other than those constituting the sinusoid; however for smaiicr near threshold offsets this sharp division disappeared and was replaced by the perception of a bent or tilted sinusoidal grating. We do not believe that this sharp division provides any useful information in our vcrniel task because (1) as a control, we created a perceptible sharp division by introducing a small separation (I min arc) of mean luminance between the sinusoidal fcalures, and vernier thresholds remained unaffected. and (2) OLIIvernier task is to discriminate the dirrction of the offset. and therefore a sharp division if perceptible does no! provide useful information. Also, it has previously been demonstrated using Fourier analysis (Krauskopf (YL Farell, 1991), that the frequency components of the tilted portion created when a sinusoidal grating is offset. such as is perceived near threshold, are of the same order as those present in the target in the absence of an otTset. To preclude the use of any unwanted position cues available from the circular aperture affixed to the osciiioscope screen, the position of the reference grating was randomly jittered (by about the magnitude of the largest vernier offset) from trial to trial. Vernier thresholds were measured for grating contrasts between 4 and X09/0: and for exposure durations of between 12 and 1000 msec. where visible. In Expt 2b, the effects of exposure duration on contrast detection thresholds for the I and 8 c/deg grating targets (in each instance occupying half of the screen) were measured.

Results Figure 6 shows how vernier thresholds for I and 8 c/deg sinusoidal gratings of different contrasts vary with increasing exposure duration. As for line stimuli, vernier thresholds for sinusoidal stimuli decrease both

VISIBILITY, TIMING AND VERNIER

DL 1CPD 0 5% + 10% 0 20%

2

’

468’

2

468’

Exposure

40%

0

80%

2

0.1

0.01

+

1

Duration

(set)

SJW 1CPD : A

0.01 Exposure

a 2 2 2.

100;

0.1 Duration

z

A

18% 32%

A

80%

1 (set)

t9 6: 4-

-

DL 8CPD

z

2u) E if .-& E

2-

ii w

IO-. 86:

-

H w

1z

20% 40% 80%

ACUITY

515

1 c/deg stimulus across exposure durations and observers was -0.73 + 0.05, and for the 8 c/deg stimulus, across exposure durations for DL, was -0.67 f 0.15. Contrast detection thresholds for the sinusoidal gratings across time for both observers are plotted in Fig. 8. Again, two lines were used to fit the detection data (see Table 7 for parameters). To correspond with line detection data, the thresholds plotted were derived from a psychometric function with a slope of 1.5. The critical durations (t,) were 62 and 55 msec for the 1 c/deg stimulus for DL and SJW respectively; and 53 msec for the 8 c/deg stimulus for DL. As the exposure duration increased above the critical duration, although the function for the 1 c/deg stimulus was almost flat (slopes of -0.04 and -O.lO), thresholds for the 8 c/deg stimulus, as with those for our line vernier stimuli, continued to decrease with a slope of -0.45 until some asymptote is reached (see Fig. 8). Figure 7(A) shows the effect of varying target visibility in contrast threshold units on vernier thresholds for 1 and 8 c/deg sinusoidal gratings. Contrast threshold units were obtained by dividing the target contrast (%) in Fig. 7(A), by the target contrast detection threshold (W) in Fig. 8 for each exposure duration. Vernier thresholds for the 8 c/deg stimulus at all exposure durations collapse to a narrow region with a slope of -0.60 &0.01. Vernier thresholds for the 1 c/deg stimulus are a little more scattered, and the best fitting line has a slope of -0.79 f 0.01 for both observers. As with line vernier, slopes for both the 1 and 8 c/deg vernier stimuli appear to show some steepening below about 4 times threshold. In addition, for the 8 c/deg vernier stimulus, there is evidence of saturation beginning to occur at about 30 times threshold, i.e. the slope begins to flatten.

4-

TABLE 5. Slope and timing characteristics for sine vernier

s al

’

0.01

p

r 4m ‘#I”1 68

’ 0.1

Exposure

r

4’ ““‘I88

2

Duration

1

2’

(set)

FIGURE 6. Vernier thresholds for sinusoidal targets (arc set) are plotted against exposure duration (set) for each of two observers. Data are shown for two observers for a 1 c/deg stimulus, and for one observer for the 8 c/deg stimulus (note change in scale of ordinate). The symbols in each graph represent thresholds measured for targets of a different contrast (%) indicated in the legends. Each straight line segment fit to the data represents a power function whose exponent is the slope of that line on log-log axes. The parameters obtained from these fits are listed in Table 5.

DL (I cldeg) 80

64 & 6.9 78 + 7.4 71 k 7.2 84 f 7.7 67 k 4.6 71 * 10.5

40 20 10 5

Duration2 (12)

Slope2 -0.35 -0.12 -0.16 -0.04 -0.03 -0.03

& 0.16 + 0.04 k 0.04 * 0.04 * 0.05 k 0.06

258 & 90

-0.46 -0.23 -0.28 -0.22 -0.00 -0.14 -0.12

f + f * f f

343 k 76

- 0.26 -0.26 -0.28 -0.18 -0.17 -0.24 -0.25

f 0.03 k 0.03 + 0.06 +0.03 +0.08 f 0.05

SJW (1 cldeg)

80 32

with increasing exposure duration and increasing contrast. Most often the data are better described by a two line fit, with the initial slope constrained to a value of - 1, on log-log axes. Estimates of timing and slope parameters from the best fitting functions are summarized in Table 5. In Fig. 7 the sine data are plotted as vernier threshold vs target contrast, for the different exposure durations. Vernier thresholds improve with increasing target contrast at about the same rate for all exposure durations, for both 1 and 8 c/deg stimuli (see Table 6). The average slope (and standard deviation) for the

Critical duration (t,)

Sine contrast W)

16 8 4’ DL (8 cldeg) 80 40 20 10 7* *Parameters

59 + 72 + 67 + 72 k 113 + 88 + 150 28 25 31 34 68 75 130 manipulated

8.4 5.5 7.3 4.7 4.7 5.9

+ 2.4 + 2.9 k 2.8 + 3.4 rf: 9.0 + 12.2

and held to minimize

0.09 0.04 0.08 0.03 0.03 0.02

x2.

630 + 212

651 & 224 402 k 170

SARAH

516

J. WAUGH

and DENNIS

M

(A)

I.P\‘I

(0)

I

I

slope=-0.79 % 2

DL 1CPD

1000~ 6s

e m

4.

+

DL 1CPD

: + 0

l

23 12 msec 50msec 100 msec 200 msec

;j + 0 +

23 12 msec 50 msec 100 msec 200 msec

0

1000 msec

0

1000 msec

10-l

I

’

2

466’

10 Contrast

1

2

4

’

66’

100

1

(%)

2

466’

2

4

66’

10 100 Contrast Threshold Units

SJW 1CPD A 12 msec

SJW 1CPD A 12msec

: A A A

: A A A

23 50 msec 100 msec 200 msec 1000 msec

23 50 msec 100msec 200 msec 1000 msec

1 o’

2

466’

10 Contrast

1

2

4

66’

100

10

1

100

Contrast Threshold Units

(%)

00

DL 8CPD H 12msec : W H W

1

8 6

slope=-0.60 a I

DL 8CPD n 12msec : W H W

50 23 msec 100 msec 200 msec 1000 msec

23 50 msec IOOmsec 200 msec 1000 msec

l-

’

1

2

466’

10 Contrast

2

4

6BT

100 (%)

Contrast Threshold Units

FIGURE 7. (A) Vernier thresholds (arc set) plotted against target contrast (%) for each of two observers Data are shown for two observers for a 1 c/deg stimulus, and for one observer for the 8 c/deg stimulus. The data in these graphs are the same as those in Fig. 2, plotted in a different way to show the effect of increasing target contrast on vernier thresholds. The symbols in each graph represent a different exposure duration indicated in the legends. Each straight line represents a povver function. whose exponent is the slope of that line on log-log axes, fit to the data for each exposure duration. The slopes ohtaincd i’rom each fit are listed in Table 6. (B) Vernier thresholds (arc set) plotted against target visibility in contrast threshold umts for all exposure durations. Contrast threshold units were obtained by dividing the target contrasts on the abscissa of Fig. 7(A) by the contrast threshold for the sinusoidal target at each exposure duration, The slopes of the best fitting power functarn~ fit to ail the data for each observer are indicated at the top right of each graph

The effect of exposure duration on equally visible vernier targets for each observer is shown in Fig. 9. The points plotted here were derived using the best fitting lines from Fig. 7(A) and the contrast thresholds of Fig. 8. This procedure was more fully described previously (results of Expt 1). As for Expt 1, predictions were also made using contrast thresholds calculated for a psychometric function whose slope was free to vary, which is reasonable because of the systematic steepening in psychometric function found with decreasing exposure

duration. For the 1 c/deg stimulus, the predictions based on a psychometric function whose slope was,fiee to vary have slopes between -0.09 and -0.03 (see Table 8). Although regression analysis reveals that many of these slopes are not significantly different from 0 [for SJW t(d.f. = 4) = 2.2 and 2.5, and for DL r(d.f. = 4) = 2.6. P > 0.051, for DL the slope of -0.09 k 0.02 found for stimuli at 10 times the visibility level. is significantly different [t(d.f. = 4) = 4.5. P < 0.051. For the 8 c:deg stimulus, the slope of the best fitting lines for equally

VISIBILITY, TABLE

6. Slope characteristics

for sine vernier

1000 200 100 50 23 15

+ SDAll times* *Power function [Fig. 6(b)].

DL

vs contrast Slope (8 c/deg)

Slope (1 c/deg) Time (msec)

TIMING

SJW

DL

0.03 0.03 0.05 0.07 0.06 0.12

-0.77 *0.04 -0.73 + 0.03 -0.74 f 0.04 -0.79 + 0.06 -0.82 f 0.16 -0.74+0.18

-0.52 -0.52 -0.59 -0.64 -0.83 -0.89

-0.69 f 0.04 -0.79 f 0.04

-0.77 * 0.04 -0.79 f 0.06

-0.67 kO.15 -0.60 f 0.03

-0.75 -0.71 -0.66 -0.65 -0.67 -0.72

* + * f + f

fit simultaneously

to data for all exposure

k 0.03 +0.03 f 0.06 k 0.03 +0.13 k 0.24

durations

visible targets for observer DL vary from -0.05 to 0.02 for the same exposure duration range of 12-1000 msec, neither of which are significantly different from 0 [t(d.f. = 4) = 0.84 and 1.6, P > 0.051. Results for the 8 c/deg grating, as for the line target, show that as the contrast of the target is increased, the critical duration (as determined from a two line fit) decreases with an exponent of -0.67 f 0.09 (see Fig. 10). However for the 1 c/deg vernier results, the critical duration is fairly constant at least for target contrasts of 5% and above (slopes of -0.11 f 0.05 and 0.05 f 0.05, for SJW and DL respectively). Since the critical durations for the 4% contrast 1 c/deg and the 7% contrast 8 c/deg sinusoidal stimuli were estimated by eye, they were not included in the fitting procedure. 1

AND

VERNIER

517

ACUITY

Discussion

As for the line stimulus, vernier thresholds for both sinusoidal stimuli are virtually independent of exposure duration (from 12 to 1000 msec), providing the targets are equally visible. On average, across observers, the slope of the power function relating vernier thresholds for equally visible targets to exposure duration is - 0.05 f 0.03 for the 1 c/deg stimulus; and for DL, the slope for the 8 c/deg stimulus is about -0.02 f 0.05. These data reveal that even though vernier acuity for abutting sinusoidal gratings is finer for the 8 c/deg than for the 1 c/deg grating stimulus, once the effect of time on detection is accounted for, more time is not required to attain these thresholds. While we cannot rule out differences in processing time for the 1 and 8 c/deg stimuli, our results are consistent with the hypothesis that for each target (as well as for our line stimuli), detection and vernier acuity are limited by similar mechanisms. However, the slightly negative slope found for the 1 c/deg sinusoidal stimuli suggests that although the spatial mechanisms that mediate target detection and vernier thresholds are similar, they are not the same. Other evidence exists to support this suggestion. For example, Krauskopf and Fare11 (1991) found that vernier thresholds measured using “equally detectable” narrow bars or narrow Gaussian stimuli are lower for luminance defined than for chromatically defined stimuli. They attributed this difference to the increased detectability of low frequency components of the chromatic targets, which are of little use in the assessment of offsets. In addition, using a spatial noise masking paradigm and line targets, we have found that masks most effective at elevating detection thresholds are centered at slightly lower spatial frequencies than those most effective at elevating vernier thresholds (Waugh, Levi & Carney, 1993). In combination, these findings suggest that for low spatial frequency stimuli, the vernier offset may be mediated by slightly higher spatial frequency mechanisms with timing characteristics which are different enough from those that mediate detection of the stimuli, to result in a small residual effect of exposure duration.

TABLE

7. Slope and timing characteristics

Observer

for sine detection

Exponent

Critical duration (f,)

1.5 2.0 Free

62 & 3.0 61 + 2.9 67 k 8.5

1.5 2.0 Free

55 * 3.9 53 f 2.7 63 + 6.5

-0.10 -0.10 -0.22

1.5 2.0 Free

53 + 7.0 54 f 9.6 69 &- 14.0

-0.36 + 0.03 -0.39 + 0.11 -0.39*0&l

Slope2

DL (I cldeg)

Exposure

Duration (set)

FIGURE 8. Contrast detection thresholds (%) plotted against exposure duration (set), for both observers, and for both sinusoidal stimuli. The thresholds plotted here were interpolated to a d’ of 1 from a psychometric function whose slope (exponent) was constrained to be 1.5. The solid lines represent two power functions fit to the data obtained for the 1 c/deg stimulus, and the dotted lines represent two power functions fit to the data obtained for the 8c/deg stimulus. Parameters for the power functions fit to these data for each observer are given in Table 7.

0.04 * 0.03 0.00 + 0.07 0.11 & 0.06

SJW (I cjdeg) * 0.05 If: 0.03 * 0.04

DL (8 cl&)

&--Time (msec) at which fit first deviates of 1.0, on log-log axes.

from a slope, held to a value

SARAH

.I WAUGH

and DENNIS

M. LIZ\‘1

DL 1CPD l

g 0

3 3 IO IO

x x x x

threshold threshold threshold threshold

(exp= (free) (exp= (free)

1 OY 6:

I: ’

0.01

2

466’

0.1

2

466’

1

2

Exposure Duration (set)

SJW 1CPD A

101, ,, ) “,,“,

0.01

i A

3 3 IO 10

x x x x

threshold threshokf threshold threshold

(exp= ,5) (free) (exp= .5) (free)

, , “““,

2 4 6“0.12 4 -1

2

Exposure Duration (set)

DL 8 CPD H i w

0.01

3 3 10 10

x x x x

threshold threshold threshold threshold

(expl S) (free) (exp=1.5) (free)

1 0.1 Exposure Duration (set)

FIGURE 9. Vernier thresholds (arc set) plotted against exposure duration (set) for equally visible targets, for both obscrvm and for both sinusoidal stimuli. These vernier thresholds represent predictions made for target contrasts which are equally visible for each exposure duration. That is, by knowing the effect of exposure duration on contrast detection thresholds (i>r the sinusoidal stimuli (Fig. 8), vernier thresholds for sinusoidal targets with contrasts equal to some multiple of threshold could be predicted from the power functions relating vernier threshold to target contrast [Fig. 7(A)]. The solid symbols represent vernier thresholds predicted for equally visible targets based on contrast thresholds by extrapolating to a d’ of 1 from a psychometric function whose slope was constrained at 1.5 for all exposure durations. Open symbols represent vernier thresholds predicted for equally visible targets based on contrast thresholds obtained for psychometric functions whose slopes were free to vary, depending on the exposure duration. The slope of the psychometric function often appeared to steepen for very short durations. The small and large symbols used are for predictions made for targets at 3 times and 10 times the contrast detection threshold for the stimuli, respectively.

In several respects, detection and vernier thresholds obtained for the 8 c/deg sinusoidal stimulus and those obtained for a line stimulus behave similarly. For example, for the detection paradigm, critical durations are similar, and for exposure durations greater than the critical duration and less than the asymptote, an intermediate slope with an exponent between -0.37 and -0.46, occurs for both stimuli. For the vernier paradigm, intermediate slopes for both types of stimuli

(line and 8 c/deg) are similar, although they are perhaps steeper for the line stimuli. Also, as the target contrast increases, the critical duration for vernier acuity decreases at a similar rate (see Fig. IO). However vernier thresholds for targets of comparable visibility are about a factor or 2 lower for the line vernier stimuli than for the 8 cideg sinusoidal stimuli. These findings suggest that the peak of the spatial frequency mechanism optimal for mediating relative position thresholds for abutting line stimuli.

VISIBILITY, TIMING

AND VERNIER ACUITY

519

1000-I a66

A

SJW lcpd sine

4-

$ s.

lo-

I 1

I I I III, 2

3

4567

’

IO Target Contrast

I

I I,,,,,

2

34567

’

100 (%min or %)

FIGURE 10. The critical durations (msec) determined from two line fits for vernier acuity plotted against target contrast (%) for four observers and for both line vernier and the sine vernier tasks. The open symbols and the solid line describe the trend found for three observers for the line vernier task; the large solid diamonds and the dot-dashed line describe the trend for one observer for the 8 c/deg sine vernier task; and the smaller solid symbols and the dotted line describe the trend for two observers for the 1 c/deg task. The lines represent power functions with exponents of -0.53 f 0.07, -0.67 rt: 0.09 and -0.06 + 0.06 for the combined data for the line, 8 and 1 c/deg targets, respectively. The corresponding symbols at the right ordinate represent critical durations obtained for detecting the vernier targets obtained from a two line fit. Note that the critical duration for vernier thresholds can be shorter than that obtained for detection of the stimulus (e.g. 8 c/deg sinusoidal stimulus).

is not centered about 8 c/deg. Instead it is probably centered about a higher spatial frequency (Waugh et al., 1993). On the other hand, the 1 c/deg sinusoidal stimulus behaves quite differently from either the line stimulus or the 8 c/deg sinusoidal stimulus. For example, for exposure durations longer than the critical duration, contrast thresholds for the 1 c/deg stimulus change very little. The critical duration for vernier acuity for the I c/deg stimulus, over a wide range of target contrasts, also changes very little (see Fig. IO). For targets of comparable visibility, vernier thresholds for the 1 c/deg stimulus are relatively poor, i.e. about a factor of 6 and 12 higher than the 8 c/deg stimulus, and the line stimulus, respectively. Reaction-time studies suggest that low spatial frequency mechanisms are particularly sensitive to temporal transients (Tolhurst, 1975; Breitmeyer & Ganz, 1976; Legge, 1978; Harwerth, Boltz & Smith, 1980), and the present experiments show that they are also less precise at discriminating fine changes in relative position than higher spatial frequency mechanisms. Since vernier threshold is proportional to stimulus blur this would be expected from statistical considerations (Watt & Morgan, 1983; Morgan, 1991). EXPERIMENT

3: A SPATIO-TEMPORAL AND VERNIER ACUITY

MASK

The results of the first two experiments suggest that once target visibility is taken into account, there is no specific effect of timing on vernier acuity. However, one potential di~~ulty is retinal or neural persistence.

Indeed, Watt (1987) used an “‘energy” mask in his study in order to circumvent this problem. Watt found for a number of spatial discrimination tasks, that thresholds continued to decrease as exposure duration increased up to at least 1000 msec even though the stimulus energy (the product of target luminance and exposure time) was kept constant for durations up to 100msec. In these experiments, the target offset was simultaneous with the onset of a random-dot mask. Thus, it is possible that the failure of the present experiments to find a specific effect of timing on vernier acuity resulted from retinal or neural persistence after the target was extinguished. On the other hand, vernier thresholds for briefly presented line stimuli are detrimentally affected by spatial interference following the stimulus within about 150 msec (Westheimer & Hauske, 1975). Thus it is plausible that the differences in the results of Watt (1987) and the results of our Expt 1 could be explained by the interference produced by the mask on the spatial discrimination TABLE 8. Slope characteristics for equally visible sine vernier vs exposure duration Slope (I c/deg) L?L.

SJW

Slope (8 c/deg) DL.

3 ctu* Exp = 1.5 Exp = free

-0.08 f 0.03 -0.05 f 0.04

-0.13 _+0.07 -0.03 + 0.05

-0.08 f 0.03 -0.05 * 0.04

IO ctu Exp = 1.5 Exp = free

-0.12+0.02 -0.09 + 0.02

-0.13 * 0.05 -0.13 & 0.05

-0.01 + 0.01 0.02 * 0.05

‘ctu, contrast threshold units.

520

SARAH

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tasks. The question of whether such a mask has additional effects on spatial discrimination tasks, above and beyond those effects it would have on the detectability of the target (Sekuler, 1965; Houlihan & Sekuler, 1968), remains unanswered. In this experiment we sought to limit retinal and or neural persistence by using a spatiotemporal mask. Separate effects of the mask on detection and vernier tasks would provide evidence for different processing mechanisms for the two tasks, whereas similar effects would support the hypothesis that the tasks are processed by contrast dependent mechanisms limited by the same sources of noise. Methods The three observers who participated in Expt 1 also participated in parts of this experiment; FR and SJW completed Expt 3a, and TN, FR and SJW completed various parts of Expt 3b. An example of the spatial noise mask, the spatial content of which was randomly varied from trial to trial, is shown in Fig. 1. For each trial, the noise mask was created by randomly assigning a luminance level to each horizontal raster line. Two noise mask conditions were conducted for both the vernier and detection experiments. In condition 1, the mask both immediately preceded (for an exposure duration of 1 frame or about 4 msec) and also immediately followed the stimulus. In condition 2 the mask followed the stimulus after a 43 msec interval of uniform mean luminance. The exposure time for the mask in both conditions remained at 500 msec. Neither the mask, nor the blank time altered the mean luminance of the screen (which was always 132.5 cd/m*). In Expt 3a, the effect of the mask under both conditions 1 and 2 on contrast detection thresholds for a line was measured. As with Expt 1, a dark horizontal line, one or two pixels wide (0.31-0.62 min arc) and about 40 min arc in length, was always presented at the same position on the oscilloscope screen. Data were collected on two observers for each of these conditions. In Expt 3b, the effect of the mask on vernier thresholds for lines which were equally visible under unmasked conditions (using the line detection thresholds from Expt l), was assessed under both mask conditions. This is somewhat akin to the experiment performed by Watt (1987) in which spatial discrimination thresholds were measured for approximately equal energy unmasked stimuli, in conjunction with a random-dot mask. Also in Expt 3b we assessed the effect of the mask on vernier thresholds for lines which were equally visible under both mask conditions (using the line detection thresholds from Expt 3a). Results of this experiment would demonstrate the extra effect, if any, that the mask had on vernier acuity above the effect it had on detectability. In Expt 3c, the effect of increasing the vernier line contrast on vernier thresholds under unmasked and masked conditions, was assessed for at least two exposure durations. The exposure durations were chosen to be both where the mask had some effect and where it had very little effect on line detection thresholds. From these

and DENNIS

M. LFVI

results, we could assess whether the mash ;rtlectct’i tir contrast dependence of abutting vernier ICUI’\ in ;$!I’ way.

Results Figure 11 illustrates the effect that the spatiotemporal mask had on the line detection threshold for different exposure durations, under condition I (mask 1) and condition 2 (mask 2) for all observers. Partial data for mask 1 were collected for observer TN. and thcsc points are included on the graph for comparison. For line detection thresholds collected under both mask con. ditions, a two line power function provided the best lit. The parameters estimated from these fits are provided in Table 9, along with parameters estimated from two line fits carried out on the unmasked detection data from Expt lb. For the two line tit. we defined the critical duration (t,) as the intercept between a slope ot’ I and the second slope, which was free to vary. To bc consistent with previous analysis, the detection thresholds reported are those calculated where the slope of the psychometric function was constrained to be 1.5. The timing and slope characteristics listed in Table 9, were virtually unchanged when detection thresholds calculated for other psychometric function slopes were used. Two line fits to the combined detection vs exposure duration data for two observers (FR and SJW), for mask and tie mask conditions, are superimposed in Fig. 11. Mask 1 (which immediately preceded and followed the stimulus) significantly affected line detection thresholds below about 250 msec; whereas mask 2 (which followed the stimulus after an interval of 43 msec) aflected line detection thresholds to a lesser degree, and only for target exposure durations below about 100 msec. The effect of both masks on detection was to shift the threshold \‘\ exposure duration function laterally along the exposure duration axis. On average. this shift amounts to about 0.69 and 0.23 log units for mask 1 and mabk 2. I’Cspectively; and serves to increase the critical duration on average by 254 and 46 msec. Figure 12(A) shows the effects of mask 1 on vernier thresholds for observers TN and SJW. This graph shows three curves for each observer. First, the open symbols connected by the solid lines, represent unmasked vernier thresholds obtained for equally visible targets based on the unmasked contrast detection thresholds for each exposure duration. These data confirm the findings 01 Expt 1, that vernier thresholds for equally visible targets are virtually independent of time over the range 01‘ exposure durations measured. Second. the solid symbols connected by the solid lines, show the effect of mask I on vernier thresholds for targets with these same contrasts. It appears that mask 1 does not alfect vernier thresholds unless the exposure duration of the target IS below about 200-250 msec, where it has a marked effect. Third, the solid symbols connected by the dotted line\. are vernier thresholds measured for equally visible masked targets, taking into account the effect of mask I on line detection thresholds. That is. using the data ohtained in Expt 3a. the vernier target was made an equal

VISIBILITY, TIMING AND VERNIER

521

ACUITY

76-

mask2

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0

FR nomask

3-

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I

I

I,,,,,,

I

2

3

45676

2

0.1 Exposure Duration

I-

I,,,,,,, 45676

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2

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FIGURE 1I. Line contrast detection thresholds (%min) plotted against exposure duration (set) for three observers under conditions of no mask, mask 1 and mask 2. The open symbols and the solid line describe the effect of exposure duration on line detection thresholds for three observers, where there is no spatiotemporal mask. These are the same data replotted from Fig. 4. The solid symbols and the solid line describe the effect of exposure duration on line detection thresholds for three observers, when a spatiotemporal mask immediately precedes and immediately follows the line detection target (mask 1). The semi-open symbols and the dot-dashed line describe the effect of exposure duration on line detection thresholds for two observers, when a spatiotemporal mask follows the line detection target by 43 msec. Parameters to the best fitting power functions for each observer are given in Table 9.

number of times above threshold, and masked vernier thesholds were again measured. With this experimental manipulation, vernier thresholds once again become practically independent of time, and are slightly below those measured for equally visible thresholds for unmasked stimuli. Figure 12(B) shows the effects of mask 2 on vernier thresholds, for FR and SJW. The format is the same as for Fig. 12(A). Mask 2 does not affect vernier thresholds until the target exposure duration is reduced below about 100 msec, where it reduces thresholds to a lesser degree than mask 1. In agreement with the results for mask 1, once the effect of mask 2 on detection thresholds is taken into account, vernier thresholds are independent of the target’s exposure duration. Figure 13 compares our averaged data for mask 1 (for TN and SJW), with the curvature sensitivity data of Watt (1987), averaged across three observers. In this curvature discrimination task, observers judged whether a short region of a long line appeared to the right or the left. The key comparison is between the solid and open squares. The open squares are the data of Watt, and the solid squares are masked vernier thresholds from the present study where the stimulus was 5 times the unmasked line detection threshold at each exposure duration. Thus both types of stimuli have equal target energy for short durations. If one considers the two tasks to be similar, then the close agreement between the shapes of these curves below about 250 msec suggests the possibility that Watt’s “energy” mask acted in much the

same way as our spatiotemporal mask. The solid circles show our masked vernier thresholds for stimuli that were equally visible, i.e. 5 times the masked line detection threshold. Clearly, the dramatic increase in vernier thresholds at brief durations seen in our data (solid squares) can be attributed to the effects of the mask on target visibility. Our results and Watt’s do differ somewhat at long durations: Watt’s data continue to improve at durations beyond 300 msec, while our data do not. The most likely explanation is that line detection thresholds TABLE 9. Slope and timing characteristics for line detection with and without spatio-temporal mask

Slope1

Critical duration (t,) (mask)

Slope2

1 2

- 1.03 f 0.05 - 1.07 * 0.04 - 1.02 f 0.04

63 f 3.8 289 k 49 126 f 15

-0.23 f 0.02 -0.29+0.11 -0.09 f 0.04

None 1 2

-1.05+0.04 - 1.07 f 0.04 - 1.OO+ 0.08

67 f 3.8 349 f 34 95 * 13.9

-0.31 f 0.02 -0.14 f. 0.11 -0.25 f 0.03

Observer Mask FR None

sJw

FR =,,d,SJW combined

None 1 2

-1.05*0.04 - 1.08 k 0.03 -0.97 f 0.03

68 + 2.5 336 k 27 126 + 5.2

-0.26 k 0.01 -0.17 + 0.08 -0.17 f 0.02

TN

None

- 1.10 * 0.07

84 + 5.7

-0.20 &-0.03

r,-Time (msec) at which fit first deviates from a slope, held to a value of 1.0, on log-log axes.

522

SARA11 .I. WAUGH

and DENNIS M. LEVI

(A)

0 TN CTU no mask CTNCTU+maskl ,+-, TN CTU mask 1 cmask 1 -A-A-

SJW CTU no mask SJW CTU + mask 1 ,-A-- SJW CTU mask 1 + mask 1

Exposure Duration (set)

0 FR CTU no mask +FRClU+mask2 ,-E, FR CTU mask 2 + mask 2

-A-B&VCNnorartsk -&sJwcnJ+ma8k2 ,-.A.- SJW CTU mask 2 + mask 2

Exposure Duration (set)

FIGURE 12(A). Vernier thresholds (arc set) plotted against exposure duration (set) for two observers for IWOconditions. IX. no mask and with mask 1. The open symbols are unmasked vernier thresholds measured for targets with contrasts at 5 times the contrast threshold for a line under unmasked conditions. The solid symbols connected by the solid lines are vernier thresholds measured in conjunction with mask 1, for targets which were at 5 times the contrast threshold for a line under unmasked conditions. The solid symbols connected by the dotted lines are vernier thresholds measured in conjunction with mask 1, for targets which were at 5 times the contrast threshold for a line under masked conditions. (B) Vernier thresholds (arc set) plotted against exposure duration (set) for two observers for two conditions, i.e. no mask and with mask 2. The open symbols are vernier thresholds measured for targets with contrasts at 5 times the contrast threshold for a line under unmuskrd conditions. The solid symbols connected by the solid lines are vernier thresholds measured in conjunction with mask 2. for targets which were at 5 times the contrast threshold for a line under unmasked conditions. The solid symbols connected by the dotted lines are vernier thresholds measured in conjunction with mask 2, for targets which were at 5 times the contrast threshold for a line under masked conditions.

improve as duration increases up to at least 1 set (see Figs 4 and 11); thus, targets with constant contrast (like Watt’s) become more visible as duration increases, while our targets had constant visibility at long durations (since the effect of the mask was only at short durations). A summary of the results of Expt 3c, where we measured the effects of both masks on vernier thresholds for different target contrasts, is given by Fig. 14(A, B). Here the vernier thresholds are plotted against target contrast in threshold units. As for Expts 1 and 2 [Figs 3(B) and 7(B)], vernier thresholds again collapse to a region where there is no systematic effect of exposure duration. The slopes of the power functions for vernier thresholds measured under condition 1 (mask l), and under unmasked conditions are - 1.01 + 0.04 and -0.95 + 0.13 respectively. These slopes, superimposed on the data of Fig. 14(A), were obtained by averaging the slopes

across all observers and exposure durations shown. Interestingly, the masked data mostly fall slightly below the unmasked data, suggesting that the mask had more of an effect on detection thresholds than on vernier thresholds (see Discussion). The slopes of the power functions for vernier thresholds measured under condition 2 (mask 2), and under unmasked conditions are - 1.13 + 0.13 and -0.93 + 0.17 respectively. These slopes are superimposed on the data of Fig. 14(B). Thus neither spatiotemporal mask appears to have significantly affected the contrast dependence of unmasked abutting vernier acuity, or the temporal dependence of vernier thresholds for equally visible stimuli. Discussion

We performed this experiment in an attempt to circumvent the potential effects of retinal and/or neural

523

VISIBILITY. TIMING AND VERNIER ACUITY

l~~~~~m~k, / 0

curvature disc~mination (Watt ‘87)

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Exposure Duration (set) FIGURE 13. Vernier thresholds and curvature amplitude thresholds (arc set) from Watt (1987) are plotted against exposure duration (XC). The large open squares are curvature discrimination thresholds replotted from Watt (1987) and averaged from three observers. The curvature disc~mination thresholds were measured in conjunction with a random-dot mask which imm~iately followed the di~~mination target. In that study (Watt, 1987), the product of the target luminance and its exposure duration was kept constant for the first 100 msec. For longer exposure durations, a constant contrast target was used. Open circles are unmasked vernier thresholds for equally visible stimuli (i.e. at 5 times the line detection threshold at each duration) from the present study averaged for the two observers [TN and SJW also shown in Fig. 12(A)]. Solid squares are masked vernier thresholds for the same observers where the stimulus was 5 times the unmasked line detection threshold at each exposure duration. Solid circles show their masked vernier thresholds for stimuli that were equally visible, i.e. 5 times the masked line detection threshold. persistence.

To achieve this, we presented a spatiotemporal mask following extinction of the stimulus. Our main conclusion is that if the effect of a spatiotemporal mask on contrast detection for different exposure durations (at least from 50 to 1000 msec) is accounted for, then no additional effect of exposure duration on vernier acuity for long abutting lines is found. This finding is supported by detection and vernier acuity data for a spatial mask under two different temporal conditions. The pattern of our results, in fact, agrees with that found for other spatial discrimination tasks reported by Watt (1987) (e.g. see Fig. 13) despite possible differences in the tasks (curvature discrimination vs vernier discrimination), the geometrical properties of the stimuli (Watt used lines 1 deg long; our lines were each 40 min long) and the masks (Watt used an “energy” mask comprised of 240 bright random dots; we used a one-dimensional spatiotemporal pattern mask, with no change in mean luminance) used in these studies. The close agreement suggests the possibility that Watt’s “energy” mask may have affected his target visibility in much the same way as our spatiotemporal mask. As noted in the Results, the effect of a spatiotemporal mask on line detection thresholds is to produce a lateral shift in the thresholdexposure duration function along the exposure duration axis (on a log-log plot). This suggests that for short exposure durations, a spatiotemporal mask serves to

reduce the effective visibility of the target, or the sensitivity of the visual system in a nonlinear way; such that a fixed proportion of extra time or contrast is required for the visual system to reach a given level of sensitivity. For long target exposure durations the mask does not significantly affect visual sensitivity. An alternative possibility is that our vernier task and the curvature discrimination task of Watt (1987) provide very different stimulus cues. For the curvature task, the cue may be very local, while for the vernier task it may be extended. Although the overall length of the line targets in the two studies is similar, this approach would view the curvature discrimination and vernier targets as effectively short and long line stimuli, respectively, and would suggest that the effects of exposure duration for the two would be quite different (Watt, 1987; personal communication). Our experiments do not address this possibility. Interestingly, vernier thresholds for equally visible masked targets, at least for mask 1, were often lower than those for equally visible unmasked targets. Assuming equal slopes for the unmasked and masked functions relating vernier threshold to target visibility, the magnitude of this effect is about 0.2 log units, such that thresholds for equally visible masked targets were about 37% lower than equally visible unmasked thresholds. This suggests that the effect of the mask on line detection

SARAH J. WAUGH and DENNIS M. LEVI

(A)

I

A 0 1 A

for the line detection SJW 50,100.150,250 msec no mask TN 100,250 msec msac no mask mask 1 SJW 50,100,150,250 msac mask 1

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masks used was the same for hot\! r:tbk\. to the horizontal line targets. Previous stud& employing both backward (Sekuler, 1965) atid f;~rwar-cl (Houlihan & Sekuler. 1968) spatioternpoui masking paradigms, and one study employing a simultaneou\ masking paradigm (Waugh et cl/., 1993). suggest that the strongest masking effect on line detection occur\ whcu the orientation of the mask is parallel to the te\r targer. However there is evidence from simultancou~ spaua! masking studies that the strongest effect 01‘ ;in optimal spatial mask on abutting vernier thresholds. occurs when the mask is between 5 and 20deg away from the orien tation of the constituent lines (Findlay. 1973; Waugh et al., 1993) or high frequency sinusoidal gratings (Carney & Klein. 1991). The effect of a spatiotemporai mask (a black and white grating) on the detection of‘ ;I line oriented between 10 and 20 deg from the mask i\ reduced by about 0. I6---0.30 log units. relative to IIS effect when it is oriented parallel to the test line (Sekuler, 1965: Houlihan & Sekuler, 1968). Results from a simultaneous masking study (Waugh CI al., 1993) reveal that the line detection thresholds for an optimal spatial mask were reduced by between 0.10 and 0.40 log units as the mask orientation relative to the line varied from 5 to 2Odeg respectively. Thus it might be expected that vernier thresholds for targets made equally detectable taking into account the effect of mask I, would be lower than those measured without any spatiotemporal mask. The magnitude of the decrease, assuming for now that vernier thresholds improve in proportion to target contrast. should be between about 0.10 and 0.40 log units. I‘or longer intervals (ISIS) between the mask and the test stimulus, both the magnitude of the masking and the effect of changing the angle between the two, decreases (Sekuler, 1965). For a 60 msec ISI, Sekuler (1965) found that changing the mask angle had no significant effect on detection thresholds, although there was still ;I small masking effect. About a 7 -10% effect of the mask angle was estimated for an IS1 of 40msec. This would explain why the effect found for mask 1 was not noticeable for mask 2. which followed the target by about 43 msec. i.e. parallel

6-

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line vernier experiments.

of the noise

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et ml., 1993). In the present

Units

FIGURE 14. (A) Vernier thresholds (arc set) measured with and without mask 1, plotted against target visibility in contrast threshold units for two observers. The open symbols are vernier thresholds measured without the presence of any mask for a few different exposure durations (see legend). The solid line represents the best fitting power function (exponent = -0.95 + 0.13) to these data. The solid symbols are vernier thresholds measured for the mask 1 condition. The dotted line represents the best fitting power function to these data (exponent = - 1.01 + 0.04). (B) Vernier thresholds (arc set) measured with and without mask 2, plotted against target visibility in contrast threshold units for two observers. The open symbols are vernier thresholds measured without the presence of any mask for a few different exposure durations (see legend). The solid line represents the best fitting power function (exponent = -0.93 + 0.17) to these data. The semi-open symbols are vernier thresholds measured for the mask 2 condition. The dot-dashed line represents the best fitting power function to these data (exponent = - 1.13 + 0.13).

was greater than its effect on line vernier thresholds. One plausible explanation for this effect, is that the orientation of the most effective mask, appears to be different

GENERAL

DISCUSSION

The results of our experiments suggest that the mechanisms mediating vernier thresholds for long abutting targets, are limited by the same factors that mediate changes in contrast detection. This conclusion is based on our findings that once the effect of time on target detection is accounted for, little if any additional time ih required to extract the finest relative position information from an abutting vernier task. Experiment 3. where a spatiotemporal mask was employed with both line detection and line vernier tasks, adds further support to this hypothesis. In the recent literature. spatial discrimination thresholds were found to be both stimulus energy dependent. that is independent of exposure duration

VISIBILITY,

TIMING

AND

(Hadani et al., 1984; Westheimer & Pettet, 1990); and exposure duration dependent (Watt, 1987). Our results suggest that abutting vernier thresholds are energy dependent to the extent that increases in target energy lead to increases in target visibility. They also agree with the data obtained by Watt for his “geometrical” spatial discrimination tasks, e.g. curvature discrimination, in that vernier thresholds for equal energy targets do improve with exposure duration if a spatiotemporal mask immediately follows the target. However, if the effect of the mask on target detectability across time is accounted for, there are no additional effects of time on vernier thresholds, at least for long line targets. Local contrast and spatial discrimination tasks A number of recent models attempt to explain how relative position information is extracted from spatial discrimination tasks (e.g. separation discrimination, vernier acuity and curvature discrimination), by assuming that such tasks are limited by the same sources of noise that limit contrast discrimination (Watt & Morgan, 1984; Klein & Levi, 1985; Regan & Beverley, 1985; Wilson, 1986). These models each consist of a range of spatial filters, available at a specific retinal location, with sensitivity profiles varying in spatial frequency tuning and orientation tuning characteristics. The models differ in the number of spatial filters proposed; whether the spatial discrimination information is mediated by the output of a single filter, or whether it results from a combination of outputs from more than one filter; how such a combination, if proposed, is achieved; and whether the source of noise limiting the output of these filters is the only source of noise limiting the spatial discrimination threshold. A recent analysis of these different models (Bowne, 1990) suggests that the sources of noise limiting contrast discrimination and some other discrimination tasks, e.g. spatial frequency discrimination, temporal frequency discrimination and orientation discrimination, are different. These findings are not in conflict with our hypothesis that abutting vernier acuity is limited by the same source of noise as contrast discrimination. Rather as proposed by Bowne (1990) it suggests that for tasks such as spatial frequency discrimination, another contrast independent but task-dependent source of noise, e.g. positional uncertainty, is limiting discrimination thresholds. Detectability and visibility In the analysis of our results, we have normalized vernier target contrasts by the contrast detection threshold of the target for the different exposure durations. Although there is evidence that the slope of the psychometric function relating d’ to contrast is slightly steeper for contrast detection than contrast discrimination (Nachmias & Sansbury, 1974; Stromeyer & Klein, 1974; Legge, 1984), the two tasks are closely related by a shape invariant “dipper” function (Nachmias & Sansbury, 1974; Legge & Foley, 1980). Thus for many experimental manipulations, normalizing by the contrast detection threshold has led to superimpositions of this function

VERNIER

525

ACUITY

(Legge, 1981; Legge & Kersten, 1983; Bradley & Ohzawa, 1986). This slight difference in psychometric function exponents is inconsequential to our conclusions. Indeed our results suggest that changes in abutting vernier acuity with time are well accounted for by changes in target detectability with time. Although it is likely that the spatial mechanisms that mediate target detection and abutting vernier thresholds are similar, there are clearly exceptions to the hypothesis that they are the same. As mentioned previously, there is evidence to suggest that those mechanisms most sensitive to the vernier offset are of a slightly higher spatial frequency (Morgan & Aiba, 1985; Krauskopf & Farell, 199 1; Waugh et al., 1993) and are oriented differently (Findlay, 1973; Carney & Klein, 1991; Waugh et al., 1993) to those most sensitive to detecting the target itself. Several previous studies have attempted to directly relate positional thresholds to local contrast detection (e.g. Hartridge, 1922; Morgan & Aiba, 1985; Morgan, 1986; Klein et al., 1990). For example, Morgan (1986) and Morgan and Aiba (1985) showed that vernier thresholds could be derived by a consideration of the threshold intensity increments between neighboring photoreceptors. More recently Klein et al. (1990) showed that vernier thresholds under optimal conditions such as for long lines which abut, are predictable from detection thresholds for the “cue” produced by the vernier offset, which in the case of a line target, is a dipole (an adjacent black and white line pair). The results of this study and the subsequent study (Waugh & Levi, 1993b) provide further support for the hypothesis that detection thresholds are appropriate for scaling the visibility of abutting vernier stimuli. Conclusion In conclusion, our results suggest that rather than vernier thresholds for abutting targets requiring more time than contrast detection to be processed, the same factors or “sources of noise” limit both spatial tasks. This conclusion is based upon experimental results which show that for exposure durations ranging from 12 to 2000 msec, vernier thresholds for equally visible targets are practically the same. REFERENCES Banton, T. & Levi, D. M. (1991). Binocular summation in vernier acuity. Journal of the Optical Society of America A, 8, 673-680. Barlow, H. B. (1958). Temporal and spatial summation in human vision at different background intensities. Journal OfPhysiology, 141, 337-350. Baron, W. S. & Westheimer, G. (1973). Visual acuity as a function of exposure duration. Journal of the Optical Society of America, 63, 212-219. Bowne, S. F. (1990). Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination. Vision Research, 30, 449-46 1. Bradley, A. & Ohzawa, I. (1986). A comparison of contrast detection and discrimination. Vision Research, 26, 991-997. Bradley, A. & Skottun, B. C. (1987). Effects of contrast and spatial frequency on vernier acuity. Vision Research, 27, 1817-1824. Breitmeyer, B. G. (1975). Simple reaction time as a measure of the temporal properties of transient and sustained channels. Vision Research, 15, 411-415.

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Breitmeyer, B. G. & Ganz, L. (1976). Implications of sustained and transient channels for theories of visual pattern masking, saccadic suppression. and information processing. Psychological Rez,ie~r. 8.1. I-36. Brown, J. L. & Black, J. E. (1976). Critical duration for resolution 01 acuity targets. Vision Research, 16, 309 315. Carney. T. & Klein, S. A. (1991). Orientation masking of grating vernier acuity. Inoestigatice Ophthalmology and Visual Science (Suppl.), 32, 1023. Cohn. T. E. & Macleod, D. 1. A. (1991). Effect of stimulus area on psychometric function slope. Inaestigative Ophthalmology and Visual Science (Suppl.), 32, 1023. Cohn, T. E. & Wardlaw, J. C. (1985). Effects of large spatial uncertainty on fovea1 luminance increment detectability. Journal of the Optical Society qf America A, 2, 820-825. Findlay, J. M. (1973). Feature detectors and Vernier acuity. Nature, 241, 135-137. Foley, J. M. & Tyler, C. W. (1976). Effect of stimulus duration on stereo and Vernier displacement thresholds. Perception and Psychophysics, 20, 125-- 128. Geisler, W. S. (1989). Sequential ideal-observer analysis of visual discriminations. Psychological Reviews, 96, 2677314. Gorea, A. & Tyler. C. W. (1986). New look at Bloch’s law for contrast. Journal of the Optical Society q/ America, 3, 52-61. Graham, C. H. & Kemp, E. H. (1938). Brightness discrimination as a function of the duration of the increment in intensity. Journal qf General Physiology, 21. 635-650. Graham, C. H. & Margaria, R. (1935). Area and the intensity-time relation in the peripheral retina. American Journal of Physiology, 113, 299 -305. Hadani, I., Meiri, A. Z. & Guri, M. (1984). The effects of exposure duration and luminance on the 3-dot hyperacuity task. Vision Research, 24, 871-874. Hartline, H. K. (1934). Intensity and duration in the excitation of single photoreceptor units. Journal c~f Cellular and Comparative Physiology, 5, 229.-247. Hartridge, H. (1922). Visual acuity and the resolving power of the eye. Journal of Physiology, 57, 52-67. Harwerth, R. S. & Levi, D. M. (1978). Reaction time as a measure of suprathreshold grating detection. Vision Research, 18, 1579-l 586. Harwerth. R. S., Boltz, R. L. & Smith, E. L. (1980). Psychophysical evidence for sustained and transient channels in the monkey visual system. Vision Research. 20, 15-22. Houlihan, K. & Sekuler, R. W. (1968). Contour interaction in visual masking. Journal qf Experimental Psychology, 77, 281-285. Kahneman, D. & Norman, J. (1964). The time-intensity relation in visual perception as a function of observer’s task. .lournal qf E.xperimenral Psychology, 68, 2 15-220. Karn. H. W. (1936). Area and intensity-time relation in the fovea. Journal of‘ General Psychology. 14, 360-369. Keesey, U. T. (1960). Effects of involuntary eye movements on visual acuity. Journal of the Optical Society c!f‘America,50, 769-774. Klein, S. A. & Levi, D. M. (1985). Hyperacuity thresholds of I second: Theoretical predictions and empirical validation. Journal of the Optical Society qf America A. 2. 1170- 1190. Klein, S. A. & Levi, D. M. (1987). Position sense of the peripheral retina. Journal of the Oprical Socieiy of America A, 4, l543- 1553. Klein, S. A., Casson, E. & Carney, T. (1990). Vernier acuity as line and dipole detection. Vision Research, SO, 1703 1719. Krauskopf, J. & Farell, B. (1991). Vernier acuity: Effects of chromatic content, blur and contrast. Vision Research, 31, 735-749. Kulikowski, J. J. & Tolhurst. D. J. (1973). Psychophysical evidence for sustained and transient detectors in human vision. Journal of Physiology, 232, 149-162. Legge, G. E. (1978). Sustained and transient mechanisms in human vision: Temporal and spatial properties. Vision Research, 18, 69-81. Legge, G. E. (1981). A power law for contrast discrimination. Vision Research, 21, 457-461. Legge. G. E. (1984). Binocular contrast summation--l. Detection and discrimination. Vision Research, 24, 373 383. Legge, G. E. & Foley, J. M. (1980). Contrast masking in human vision. .lournal of the Optical Socie!,, of America. 70, 145% 1470.

and DENNIS

M. LEVI

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Acknowledgemenf.r--We thank Thorn Carney for his help in setting up the experiments, and Stan Klein for his assistance with lgor. We also thank Harold Bedell, Nancy Coletta, Wilson Geisler. Michael Morgan, Earl Smith, Roger Watt and an anonymous reviewer for helpful comments on an earlier version of the manuscript. This research was supported by grant ROlEY01728 from the National Eye Institute. and a Sigma Xi Grant in Aid of Research