Equivalent intrinsic blur in amblyopia

Vision Res. Vol. 30, No. 12, pp. 19952022, 1990 Printed in Great Britain. All rights rcscrvtd

0042-6989/90 S3.00 + 0.00 Copyright 0 1990 Pcrgamon F’rcas pk

EQUIVALENT INTRINSIC BLUR IN AMBLYOPIA

DENNIS M. LEVI’ and STANLEY A. KLEIN*

‘University of Houston, College of Optometry, Houston, TX 77004 and *University of California, School of Optometry, Rerkeley, CA 94720, U.S.A.

(Received 21 August 1989; in revbedform 14 December 1989)

Abstract-We used Gaussian blurred stimuli to explore the effect of blur on three tasks: (i) 2-line resolution; (ii) line detection; and (iii) spatial interval discrimination, in observers with amblyopia due to anisometropia, strabismus, or both. The results of our experiments can be summarized as follows.

(i) 2-Line resolution: in normal fovea1 vision, thresholds for unblurred stimuli are approx. 0.5 min arc in the fovea. When the standard deviation (u) of the stimulus blur is less than 0.5 min, it has little effect upon 2-line resolution; however, thresholds are degraded when the stimulus blur, u, exceeds 0.5 min. We operationally ddine this transition point, as the equivalent intrinsic blur, or B,. When the stimulus blur, u. is greater than B,, then the resolurion threshold is approximately equal to u. In ail of the amblyopic eyes, 2-line resolution thresholds for unblurred stimuli were elevated, and the equivalent intrinsic blur was much larger. When the stimulus blur exceeds the equivalent intrinsic blur, resolution thresholds were similar in amblyopic and nonamblyopic eyes.

(ii) Line derec~ion: in both normal and amblyopic eyes, when the stimulus blur, u, is less than B,, then the line detection threshold is approximately inversely proportional to u; i.e. (it obeys Ricco’s law). When u is greater than B,. the equivalent intrinsic blur, then the derecrion threshold is approximately a fixed contrast. All of the amblyopic eyes showed markedly elevated thresholds for detecting thin lines, but normal or near normal thresholds for detecting very blurred lines. Consquently. Ricco’s diameter is larger in amblyopic than in normal eyes.

(iii) @uric/ btervul discriminution: thresholds are proportional to the separation of the lines (i.e. Weber’s law). At the optimal separation, spatial interval discrimination thresholds represent a “hyperacuity” (i.e. they are smaller than the resolution threshold). For unbhrrred lines, the optimal separation is approx. 2-3 times B,. In the normal fovea, and in the amblyopic eyes of anisotnerropic amblyopes the optimal spatial interval discrimination threshold is about one-6fth of the resolution threshold (i.e. a hyperacuity); and over a wide range of separations, spatial interval discrimination thresholds begin to rise when the stimuhrs blur exceeds about one-third of the separation between the lines as long as the contrast is suIRciently high. In contrast, in strubismic amblyopes, like the normal periphery, the optimal spatial interval discrimination thresholds are worse (higher) than would be expected based upon the resolution limit of the strabismic amblyopic eye.

In anisometropic amblyopes the elevated resolution and spatial interval discrimination thresholds are consistent with a raised level of equivalent intrinsic blur, and a reduced contrast response function. In strabismic amblyopia, there appears to be an additional source of loss, which affects spatial localiition to a greater degree than resolution. This extra loss may be modeled in terms of abnormal positional uncertainty due to a sparse cortical spatial sampling grain.

Psychophysics Amblyopia Resolution Spatial interval discrimination Hypcracuity Blur Gaussian blur Intrinsic blur Spatial vision

INTRODUCTION

Amblyopia is a developmental anomaly of spatial vision, which is characterized by reduced visual acuity and reduced contrast sensitivity. Much recent work on amblyopia has centered on the marked losses in positional acuity demonstrated by strabismic and anisometropic amblyopes (Bedell & Flom, 1981; Levi & Klein, 1982, 1985; Bradley & Freeman, 1985; Rentschler & Hilz, 1985; Watt & Hess, 1987). The focus of much of this work has been: (1) to characterize the differences in the nature of the

loss of positional acuity among strabismic and anisometropic amblyopes (e.g. Bedell & Flom, 1983; Bedell, Flom & Barb&to, 1985; Levi & Klein, 1982, 1985); and (2) to attempt to model the losses (Levi & Klein, 1985; Levi, Klein & Yap, 1987; Bradley & Freeman, 1985; Wilson, 1986b; Watt & Hess, 1987).

There is general agreement that amblyopes demonstrate marked losses in both resolution, and in judging the relative position of a target with respect to a nearby reference, i.e. amblyopes show marked losses under conditions which give rise to “hyperacuity” (Westheimer,

1995

1996 DENNIS M. LEVI and STANLEY A. KLEIN

1975) in normal vision (see Fig. 1). However, there is little agreement on how to model the losses (although there is no shortage of ideas). Among the many (not necessarily distinct) explanations which have been proposed to account for the losses are: (1) intrinsic positional uncertainty (Cohn & Wardlaw, 1985); (2) spatial scrambling (Hess, 1982; Watt & Hess, 1987); (3) reduced sensitivity of the putative spatial filters (Bradley & Freeman, 1985; Levi 8z Klein, 1985; Levi et al., 1987; Wilson, 1986b); (4) spatial undersampling (Levi & Klein, 1986; Levi et al., 1987; Wilson, 1986b); and (5) intrinsic blur (Levi & Klein, 1982, 1985; Flom, Bedell & Barbeito, 1986).

The preceding paper examined the role of intrinsic blur in normal vision, where intrinsic blur is defined as the amount of blur that is always convolved with the stimulus blur to produce the effective blur of the stimulus. The notion that amblyopes may have abnormally large degrees of intrinsic blur is consistent with their reduced visual acuity and contrast sensitivity. Moreover, in the case of anisometropic amblyopes, their early visual experience with one defocussed retinal image, might lead to the expectation of increased intrinsic blur. Watt and Hess (1987) argue that the loss in anisometropic amblyopes is not due to intrinsic blur. They measured Vernier acuity (a 2dimensional position task) with lines subjected to differing degrees of l-dimensional Gaussian blur perpen- dicular to the line. They reasoned that when the stimulus ‘blur was small with respect to the intrinsic blur, it would not influence Vernier acuity; however, when the stimulus blur exceeds the intrinsic blur, Vernier threshold would be elevated. Convergence of the thresholds of the two eyes at large stimulus blur values would provide evidence for an additive error of internal blur, whereas, failure of convergence would suggest a multiplicative error that could not be attributed to an additive effect of intrinsic blur. Their results were surprising. For their task, both their normal observers, and their anisometropic amblyopic observers had the same “intrinsic blur” with a standard deviation of about 3-4 min, and the thresholds of the two eyes did not converge at large values of stimulus blur. They concluded, therefore, that the amblyopes’ elevated position thresholds were not a consequence of increased intrinsic blur. Rather, they concluded that anisometropic amblyopes have an additive error of increased positional jitter, because when they added positional jitter

to the Vernier lines, the thresholds of the two eyes converged at large values of positional jitter. We believe that Vernier acuity is not the appropriate task for measuring “intrinsic” blur, since Vernier acuity is so robust to blur (Watt, Morgan & Ward, 1983; Watt & Hess, 1987) and because it may depend upon both the contrast of the stimuli, and, at high contrasts upon the nature of the blur (i.e. l-dimensional vs 2-dimensional) (Carney, Klein & Levi, in preparation). Thus, the Vernier task may not tap the “limiting” intrinsic blur of the visual system. In fact, Watt and Hess interpret their experiments as a measure of the largest filter which supports optimal performance on a particular task (Hess, personal communication).

Spatial interval discrimination tasks, such as bisection represent a l-dimensional position judgment. In normal vision, thresholds depend upon separation (Weber’s law) at large separations, and, at an optimal small separation, thresholds may be extremely acute (Levi & Klein, 1983; Klein & Levi, 1985). In several previous investigations of l-dimensional position acuity, using high contrast, thin bright lines, we found that the optimal thresholds (i.e. performance at the optimal separation) of anisometropic amblyopes (but not strabismics) was commensurate with their resolution loss, and that performance at separations larger than the optimum was essentially normal (Levi & Klein, 1983; Levi et al., 1987). This result is consistent with the possibility that performance at small separations is limited by intrinsic blur, which limits processing by small filters with high sensitivity to spatial position. The notion gets support from the work of Flom et al. (1986), who showed that the position losses of anisometropic amblyopes could be mimicked by optical blurring. Figure 1 shows how Gaussian blur can limit the optimal position threshold of a nonamblyopic eye in a 2-line interval discrimination task.

In the preceding paper (Levi & Klein, 1990), we measured the effects of Gaussian blur upon detection of a line, and upon 2-line resolution and 2-line spatial interval discrimination in central and peripheral vision. In particular, we were interested in obtaining a measure of the fimiting equivalent intrinsic blur (Si). This is the largest amount of stimulus blur that supports optimal resolution, and it represents an estimate of intrinsic error of the visual nervous system which acts like blur. Since several factors con- tribute to the intrinsic blur besides optical blur,

Equivalent intrinsic blur in amblyopia

10 ,

KP

1

.14’

0 so..14'

A SO.1.0

l so.2.u

a sD.4.0’

1997

.Ol ; I I < *l 1 10 1 0

SEPARATION (MINUTES)

Fig. 1. Effects of Gaussian blur on 2-line resolution and spatial interval discrimination for the nonamblyopic eye of observer KP. Each symbol shows data with different amounts of stimulus blur. The open circles are with a standard deviation of 0.14 min. Also shown are data for lines with I (A), 2 (O), and 4 (0) minutes of Gaussian blur. For each condition, the contrast of the lines was 5 times threshold. The effect of blurring the lines is to markedly increase both the resolution thresholds (the resolution thresholds are the four left-most points), and the spatial interval discrimination thresholds at separations less than about 2-3 times the resolution limit. However, at each level of stimulus blur, for separations above 2-3 times the resolution limit, thresholds are in&pen&nr of the level of stimulus blur, so that at

these separations all thresholds he along the same Weber’s law line.

the term equivalent intrinsic blur will be used. In normal fovea! vision, we found the equivalent intrinsic blur to be about 0.5 min (the intrinsic blur values are always reported in units of the standard deviation of the blur function), and suggested that it represents the cascaded effects of optical and sampling blur (Levi & Klein, 1990). We also showed that equivalent intrinsic blur is an important factor in determining the detection threshold in the normal visual system, and in limiting the o#timal spatial interval discrimination threshold. With respect to spatial interval discrimination, we showed that in normal central and peripheral vision, the optimal spatial interval discrimination occurs at a separation 2-3 times the equivalent intrinsic blur. Thus, if amblyopes have increased equivalent intrinsic blur, their optimal threshold should be at a proportionally larger separation than that of normal observers. Because spatial interval thresholds are proportional to separation, the

amblyopic eye’s optimal thresholds will necessarily be elevated.

The present paper extends these experiments to observers with naturally occurring amblyopia. Specifically, we measured resolution, line detection and spatial interval discrimination for Gaussian blurred lines in a group of observers with amblyopia due to anisometropia, strabismus or both (i.e. strabismus and anisometropia). We show that: (i) all our amblyopic observers have elevated 2-line resolution, intrinsic blur and optimal spatial interval discrimination thresholds; (ii) the data of the anisometropic amblyopes can be modeled on the basis of increased equivalent intrinsic blur and a decreased contrast response function, i.e. the anisometropic amblyopic visual system can be mimicked by appropriate scaling in both size and contrast; (iii) strabismic amblyopes show an extra loss in fine positional acuity which cannot be simply modeled on the basis of blur and


contrast. Strabismic amblyopes show an extra loss which may be due to increased positional uncertainty, undersampling, or both.

METHODS AND PROCEDURES

Stimuli

The stimuli in each of the experiments were horizontal black lines that were subjected to Gaussian blur. We used horizontal lines to minimize the effects of image smearing due to the unsteady horizontal fixational eye-move- ments characteristic of amblyopes. Examples of the stimuli are shown in Fig. 1 of the preceding paper (Levi & Klein, 1990), and the methods and procedures used here were identical. For viewing with the amblyopic eye, the stimulus dimensions were “scaled” by varying the viewing distance in proportion to the reduced resolution of the amblyopic eye. Scaling the stimulus size had two main effects: (1) the line became longer. The 1 deg line length for fovea1 viewing is considerably longer than necessary for asymptotic performance (Westheimer & McKee, 1977; Klein & Levi, 1985), thus increasing the stimulus length in the amblyopic eye ensured that the stimuli were su!%ciently long to provide adequate spatial sampling (Levi & Klein, I986). Control experiments verified that further increases in the length of the lines had no effect upon thresholds; (2) the line became wider. For thin lines (less than the eye’s line spread function) on a uniform background, visibility is a function of the product of contrast and width. Thus reducing the distance enabled us to use approximately the same physical contrasts for each eye, and maintain equal visibility. The stimulus width, or spread, as specified by the standard deviation of the Gaussian blur, was the critical independent parameter examined in these experiments.

For all experiments, the stimuli were ramped on over 300 msec, remained at a plateau for 600 msec, and were ramped off for 300 msec, in order to minimize temporal transients.

Viewing conditions

For all experiments, viewing was monocular and with natural pupils. The non-tested eye was occluded with a black patch.

Methods

Experiment I: 2-line resolution and spatial interval discrimination with Gaussian blurred

lines. Unless otherwise specified, the line contrast was approx. 5 times threshold (determined in expt II which was actually done first) for both preferred and amblyopic eyes, and for all blurs; however, in order to minimize contrast cues to resolution or separation, we introduced a contrast jitter of 30% from trial to trial. Absolute position cues were eliminated by randomly varying the position of the line pair from trial to trial.

Thresholds for both 2-line resolution and spatial interval discrimination were measured using a self-paced rating-scale method of constant stimuli. The resolution task measures the smallest separation between the lines that can be discerned (i.e. the smallest separation that can be reliably distinguished from no separation). The spatial interval discrimination task measures the ability to judge the extent of the separation between a pair of lines for a range of base separations. In the present study spatial interval discrimination thresholds were measured for a wide range of base separations and stimulus blurs. The methods were essentially identical to those used in expt I of the preceding paper (Levi & Klein, 1990), and the thresholds reported are the means of 2-5 runs (125 trials per run), weighted by the inverse variance.

Experiment II: lietection of Gaussian blurred lines. Contrast thresholds for detecting single Gaussian blurred lines, as a function of Gaus- sian spread, were measured for each eye using a self-paced rating-scale method of constant stimuli. The methods are identical to those described in the preceding paper (Levi & Klein, 1990) and the thresholds reported are the means of 2-5 runs (100 trials per run), weighted by the inverse variance.

Observers

Twelve highly practised observers participated in the experiments. Observer D& had normal binocular vision and corrected-to- normal visual acuity in each eye, and served as a normal control. The main results were also confirmed on another normal observer, HD, who was naive as to the purpose of the experiments. Ten amblyopes with anisometropia (4), strabismus (3) or both (3) also participated. Each of the observers was given extensive train- ing on these tasks prior to data collection. All observers had clear media, normal fundi, and were carefully refracted for the experiments. Details of the visual characteristics of all of the observers are provided in Table 1.

Observer Age Sex Eye

Equivalent intrinsic blur in amblyopia 1999

Table 1. Visual characteristics

Rx. Acuity’ Fixationb Strabismus

Anisomelropicc KP

JM

TL

RJ

Swabismic KL

RH

PZ

Both MB

cc

WP

Normal DL HD

21

25

19

48

26

23

31

26

40

23

40 21

M

M

F

M

M

M

M

F

F

M

M F

O.D.

z.

:: OS.’ O.D. OS.

+2.25 20/71 Central -OSO/-0.25 x 180 20118 Central -2.75/-0.50 x 180 20115 Central + 1.50/-0.25 x 90 20160 Central -9.00 20150 Central +2.50/-2.00 x 90 20125 Central +0.50/-0.25 x 95 20114 Central +2.50/-0.75 x 125 20157 Central

None

Occasional L. XT lob when tired None

None

O.D. +0.25/-0.50 x 145 20140 0.5 deg Nasal O.S. PL/-0.75 x 60 20112 Central O.D. - I.OO/-0.50 x 170 20115 Central O.S. - 1.50/- 1.50 x 10 201175 Unsteady O.D. +1.00 20155 0.5 deg Nasal OS. +1.00 20120 Central

Constant R. ET., 6A

Microtropia L. ET.. 2” Constant R. ET., l7A

O.D. +7.00 20112 Central O.S. +9.00 20/140 0.5-l deg Nasal O.D. +2.25 20/155 1.5 dcg Nasal OS. -0.75 20/15 Central O.D. -2.00 20120 Central O.S. +2.00/-2.00 x 180 20/110 0.5-I deg Superior

Constant L. ET., 6A Constant R. ET., 37A

Constant L. ET., 6”

O.S. -1.00 20115 Central None O.D. +0.50 20115 Central None

‘75% correct on Davidson-Eskridge charts. bFixation determined with Haidinger’s brushes and visuoscopy. No constant strabismus, and hyperopic anisometropia > + I .5D or myopic anisometropa > 4D.

RESULTS AND DISCUSSION

Experiment I: resolution and spatial interval discrimination

Eflect of separation, Gaussian blur and contrast. Figure 1 shows the effects of Gaussian blur on 2-line resolution and spatial interval discrimination for the nonamblyopic eye of observer KP. The different symbols show data with different amounts of stimulus blur. The open circles are for a standard deviation of 0.14 min (these are thin lines compared to the eye’s line spread function, and will therefore be referred to as unblurred lines). Also shown are data for lines with 1 (A), 2 (0) and 4 (0) ‘min of Gaussian blur. For each condition, the contrast of the lines was 5 times threshold. For each curve, both the ordinate and the abscissa value of the left-most point is the 2-line resolution threshold. Consider the data with unblurred lines: for separations slightly larger than the resolution limit, thresholds improve dramati- cally, reaching an optimum which is a “hyperacuity” (Westheimer, 1975) at about 2 times the resolution limit. As separation increases further, thresholds increase approximately proportional to the separation. This is the well known “Weber’s law” for separation (Westheimer & McKee, 1977; Levi, Klein & Yap, 1988), and

is shown by the solid line with a slope of 1. The effect of blurring the lines is to markedly increase both the resolution thresholds (the left-most points) and the spatial interval discrimination thresholds at separations less than about 2-3 times the resolution limit. However, at each level of stimulus blur, for separations above 2-3 times the resolution limit, thresholds are independent of the level of stimulus blur, so that at these separations all thresholds lie along the same Weber’s law line. This result is in close agreement with the 3-dot bisection results of Toet, van Eekhout, Simons and Koenderink (1987).

Figure 2 shows the effects of separation on 2-line spatial interval discrimination in the two eyes of an anisometrope (Fig. 2A), a strabismic (Fig. 2B), and an observer with both strabismus and anisometropia (Fig. 2C). The data of the amblyopic eyes were obtained with unblurred lines and are shown by the solid symbols. Also shown in each panel of Fig. 2 are the unblurred data of the. nonamblyopic eye (O), and data of the nonamblyopic eye with the lines blurred with standard deviation of 3 min (0 in Fig. 2A) or 4 min (0 in Fig. 2B and C). For the anisometropic amblyope at 10 times threshold (A in Fig. 2A), both the resolution threshold (the leftmost point) and the entire spatial

DENNIS M. LEVI and STANLEY A. KLEXN 2000

(A) 10

(B) 10

an - SrRA8

# if

a^

r_ l-

9 . 8 . 0 * E .

A KiO’Tt8iwl

.l 1

..__.

(C) 10 3

wP-smB&*tuso

.t I 1 10 1

SEPARATION (MINUTES)

Fig. 2


interval discrimination curve for the amblyopic eye are closely modeled by the data of the blurred nonamblyopic eye. The physical contrast for the amblyopic eye was also higher than that of the fellow eye. To equate performance in the two eyes, it was necessary to set the contrast of the lines to 10 times the (elevated) contrast threshold of the amblyopic eye, while that of the nonamblyopic eye was 5 times threshold (above about 5 times contrast detection threshold, contrast has little effect in the preferred eye as shown by Morgan & Regan, 1987, and Klein & Levi, 1989). As may be noted here, contrast does have a significant effect in the anisometropic amblyopic eye. At 5 times threshold (0) the amblyopic eye’s thresholds are elevated by about 50% (compared to the data at 10 times threshold) at separations smaller than 20 min. Interestingly, at the largest separations interval discrimination thresholds at 5 and 10 times detection threshold are almost identical. These data strongly suggest that the deficit in resolution and spatial interval discrimination of unisometropic amblyopes may be modeled as a consequence of increased equivalent intrinsic blur, and abnormal contrast response. This possibility will be investigated further in the section on equivalent intrinsic blur.

Figure 2B and C show data for two strabismic amblyopes (from hereon, we shall refer to all amblyopes with constant unilateral strabis-

mus as strabismic amblyopes whether or not they have anisometropia). Thresholds of their amblyopic eyes are shown for unblurred stimuli with contrast set to 5 (0) and 10 (A) times threshold. Note that while the resolution thresholds for each observer are closely approximated by that of a nonamblyopic eye with a Gaussian blurred stimulus whose standard deviation is 4 min, the optima1 thresholds are 2-4 times worse than that of the nonamblyopic eye, and the thresholds at separations up to 30 min remain elevated. Summaries of the threshold, T,, near the optimal separation are tabulated in Table 2. For WI’, who was tested at larger separations, the data of the two eyes converge at about 40 min. This is consistent with our previous bisection results, in which the thresholds of the amblyopic eyes are most elevated at small separations (where normal eyes perform best), and become nearly normal at large separations (Levi et al., 1987). Our previous work also suggested differences between strabismic and anisometropic amblyopes in the bisection task. These results suggest that the data of strabismic amblyopes may not be simply modeled by a single increased equivalent intrinsic blur factor. Nor are these results simply modeled as a consequence of a reduction in the effective contrast of the strabismic amblyopic eye, since increasing the contrast of the ambly- epic eye from 5 to 10 times threshold had little effect.

Fig. 2 (Opposite). The effects of separation on 2-line spatial interval discrimination in the two eyes of an anisometrope (A), a strabismic (B), and an observer with both strabismus and anisometropia (C). The data of the amblyopic eyes were obtained with unblurred lines and am shown by the solid symbols. Also shown are the unblurred data of the nonamblyopic eye (O), and data of the nonamblyopic eye with the lines blurred with a standard deviation of 3 min (0 in A) or 4 mm (0 in B and C). For each amblyopic eye, thresholds were obtained at a contrast of 5 times threshold (0) or 10 times threshold (A). For the amblyopic eye of the anisometropic amblyope at 10 times threshold (A in A), both the resolution threshold (the leftmost point) and the entire spatial interval discrimination curve for the amblyopic eye are closely modeled by the data of the blurred nonamblyopic eye. As may be noted here, contrast does have a significant effect in the anisometropic amblyopic eye. At 5 times threshold (0) the amblyopic eye’s thresholds are elevated by about 50% (compared to the data at 10 times threshold) at separations smatter than 20 min. The contrast of the nonarnblyopic eyes was 5 times threshold. These data suggest that the deficit in resolution and spatial interval discrimination of onisowutropic amblyopes may be modeled as a consequence of increased equivalent intrinsic blur, and a reduced local contrast response. Thresholds of the amblyopic eyes of the two strabismic amblyopes are shown in B and C for unblurred stimuli with contrast set to 5 (a) and 10 (A) times threshold. Note that while the resolution thresholds for each observer are closely approximated by that of a nonamblyopic eye with a Gaussian blurred stimulus with a standard deviation of 4 min. the optimal thresholds are 2-4 times worse than that of the nonamblyopic eye, and the thresholds at separations up to 30min remain elevated. These results suggest that the data of strabismic amblyopes are not simply modeled by a single increased equivalent intrinsic blur factor. Nor are these results simply modelled as a consequence of a reduction in the effective contrast of the amblyopic eye, since increasing the contrast of the amblyopic eye from 5 to 10 times threshold had little

effect.

“R 30/12-F


Task

Table 2. Detection resolution and interval discrimination parameters

Spatial interval discrimination

Detection Resolution (near optimum) Bd T, T, Bi T, B, Snellen

Amblyopic eyes Anisometropic

KP 1.75 JM 1.79 TL 2.72 RJ 1.33

Strabismic KL 2.38 RH 1.57 PZ 1.37

Both

Et 1.71 1.83 WP 3.86

Normal periphery DL 2.5 1.5 5.0 2.17 & 2.84

2.5 1.7 5.0 2.03 10 2.76

Non -amblyopic eyes x 0.72 SD 0.18

1.07 1.15 1.75 1

1.67 1.69 1.12

1.65 2.88 1.14

0.84 0.95 1.04

1.52 1.62 1.7

3.9 (2.P) 0.86 (0.5’) 1.4 3.8 3.7 (1.7’)

:::8 0.82 (0.5’) 0.92 3

5.17 ;::

1.16 4.6 2.5 2.51 (1.34’) 0.55 (0.2’) 2.29 2.8

0.94 1 0.36 1.1 2 3.24 (2.7”) 2.36 1.64(1.gb) 3.2 8.8 1.32 1.47 0.38 1.4 2.8

1.35 1.97 0.67 1.64 7.0 2.75 2.9 1.46 5.8 7.8 3.34 (3.4’) 5.7

1.25 1.68 0.64 2.51 1.59 1.85 0.87 2.19 2.06 2.88 1.04 5.13

1.56 1.71 1.24 2.42 2.1 2.3 0.96 2.95 3.64 4.36 1.62 4.04

0.67 0.77 0.12 0.31 0.82 0.19 0.22 0.01 6.03 0.19

1.5 (2.V) 5.1 5.5

‘The data shown in parentheses were obtained at 10 times threshold. %s poiut was measured directly with contrast 10 times threshold.

The effect of contrast can be seen more clearly in Fig. 3, where spatial interval discrimination thresholds are plotted as a function of stimulus contrast (specified in threshold units). Data are shown for the amblyopic eyes of anisometropic amblyope KP (Fig. 3A) and strabismic amblyope WP (Fig. 3B) for three separations. For KP, for each separation, thresholds improve rapidly, as stimulus contrast increases from 2.5 to 5 times threshold, and then they continue to improve slowly up to 15 or 20 times threshold (the highest level tested). Watt and Hess (1987) also noted that increasing the luminance of their Vernier target resulted in improved thresholds in the amblyopic eye of an anisometropic amblyope. Strabismic amblyope WP’s data also show a marked increase between 2.5 and 5 times threshold; however, for each separation, thresholds show no further improvement when the contrast is increased.

Equivalent intrinsic blur (B,). Consider the following simple model proposed by Watt and Hess (1987): the visual system has an internal error due to blur, and to this is added the stimulus blur. When the stimulus blur is small, it will have little influence upon thresholds; however, when it exceeds the equivalent intrin-

sic blur, B,, then threshok-l is proportional to the stimulus blur. Thus, the equivalent intrinsic blur can be estimated by measuring thresh&is for resolution as a function of stimulus blur (in the discussion section we consider the nature of this equivalent intrinsic blur in the amblyopic visual system). The model is:

Th = k,/mj; (1)

where Q is the stimulus blur, specified as the standard deviation of the individual Gaussian bar, B, is the equivalent intrinsic blur and 7% is the resolution threshold. The multipli&ive fat- tor, k, might depend on a variety of factors such as the d’ level at which threshold is d&ned and the stimulus contrast. This is the formulation proposed by Watt and Morgan (1985), and later used by Watt and Hess (1987), to estimate the “intrinsic blur” in a Vernier acuity task. This model is based on the assumption that thb: visual system has an internal error (BJ that acts like blur. Thus, I3, is an additive error. The variance of the stimulus blur is expacted to add to the variance of the intrinsic blur as in equation (1), since the two are uncorrelated.

Figure 4 shows 2-line resolution thresholds as a function of the standard deviation of the


(A) 10

UP - Allgo

1 10 100

CONTRAST (THRESHOLD UNITS)

Fig. 3. Spatial interval discrimination thresholds vs stimulus contrast (specified in threshold units). Data are shown for the amblyopic eyes of anisometropic amblyope KP (A) and strabismic amblyope WP (B) for three separations. For both observers, thresholds improve rapidly, as stimulus contrast increases from 2.5 to 5 times threshold. For anisometropic amblyope KP, they continue to improve slowly up to I5 times threshold (the highest level tested). However, for strabismic amblyope WP at each separation, thresholds show no further improvement when the contrast is increased

beyond 5 times threshold.

Gaussian lines. Data are shown for each eye of two anisometropes (top), two strabismics (middle), and two observers with both strabismus and anisometropia (bottom). The open symbols are data of the preferred eyes, solid symbols are the amblyopic eyes. For each eye of each observer, there is a range of small stimulus blur values, where the blur has little effect; at larger stimulus blur spreads, thresholds rise in proportion to the stimulus blur. The filled and dotted lines fit to the data are of the form:

Th = T,[l + (a/B,)2]“2; (2)

where T, is the resolution threshold for an unblurred stimulus (i.e. the asymptotic threshold value), e is the stimulus blur, and Bi is the equivalent intrinsic blur (i.e. the horizontal position of the knee in the function). (Note that equation 2 is simply a restatement of equation 1 obtained by making the substitution T, = kBi .) Thus, when the stimulus blur is small, it has no influence upon thresholds; however, when it exceeds the equivalent intrinsic blur (Bi), then threshold increases. The function provides a reasonable (though not perfect) fit to the data, and allows an estimate of the parameters T, and Bi, and their standard errors. There are several points of note in Fig. 4: (I) each of the amblyopic eyes have higher resolution thresholds (T, at small stimulus blur values) than the fellow eyes; (2) each of the amblyopic eyes has a larger equivalent intrinsic blur (Bi) than its fellow (this is shown quantitat- ively in Table 2 and in Fig. 5); (3) for stimuli with large standard deviations (i.e. very blurred stimuli), thresholds for the two eyes converge, so that they are either identical (e.g. KP and WP), or close, with the amblyopic eye remaining slightly worse (e.g. RH). Since increased stimulus blur causes the performance of the two eyes to converge, this suggests an additive error (equivalent intrinsic blur) rather than a multiplicative error of stimulus blur in the amblyopic eye.

Ta,ble 2 gives the values of T, and Bi for each of the amblyopic eyes. The additive error is shown in the column labeled Bi (column 4) in Table 2. The multiplicative error (k) is shown in column 3 of Table 3 (labeled TJB,). Table 3 also summarizes the loss at large values of stimulus blur for all of the observers (i.e. AE T,/NAE T, at large SD). Note that all of the observers show losses in resolution for unblurred stimuli (i.e. T, ratios of 1.4 to almost 8) and increases in the size of the equivalent intrinsic blur (ratios from 1.5 to almost 15). However, at large stimulus blurs, the ratios average approx. 1, i.e. resolution thresholds are essentially equal in the two eyes when the stimulus blur is large. Only two observers, RH (see Fig. 4, middle), and JM (not shown here), deviate significantly from this pat- tern, by showing interocular ratios of 1.7 at large stimulus blur values. Note that these losses are considerably smaller than their losses with unblurred stimuli. Moreover, for anisometropic observer JM, increasing the contrast of the lines lowered the thresholds of the amblyopic eye, but not the preferred eye, so that at large standard


deviations thresholds were essentially equal (i.e. doubling the contrast gave a ratio of 1.04). These losses, and the role of additive and multiplicative errors will be examined further in the general discussion section.

The numbers in parentheses in Tables 2 and 3 are data taken at a contrast of 10 times detection threshold. The resolution threshold, T,, in anisometropes is about halved when the contrast is doubled. Intrinsic blur, Bi, was measured for KP at 10 times detection threshold.and was also found to be halved, implying that the multiplicative factor, k = T,/B,, is independent of contrast. Thus the column labeled “k” in Table 3 does not show contrast dependence. Inspection of Fig. 4 shows why it is to be expected that k is relatively independent of contrast for amblyopes. Any decrease in T, would have to be matched by a comparable decrease in Bi, or else thresholds for the ambly- epic eye would be lower than for the nonambly- epic eye. The strong contrast dependence of Bi and constancy of k in anisometropes is opposite from the dependence on contrast found in normals as discussed in the preceding paper (Levi & Klein, 1990). In normals, Bj is independent of contrast whereas k has a slight dependence on contrast. In order to further investigate the role of contrast on Bf and k, intrinsic blur was measured for each eye of observer KP at several contrast levels (from 2 to 10 times threshold in the preferred eye, and 2.5 to 20 times threshold in the amblyopic eye). The data are shown in Fig. 5. Figure 5A shows 2-line “resolution” thresholds vs blur. Open symbols are data of the preferred eye, filled symbols show data of the amblyopic eye. The stimulus contrast is coded by the size of the symbols (i.e. the smallest

symbols show the lowest contrast, the largest symbols show the highest contrast). For KP’s preferred eye, lowering the contrast has a small multiplicative effect, increasing thresholds at all levels of stimulus blur. Thus, in the preferred eye, Bi is approximately independent of contrast (0 in Fig. 5B), while T, shows a slight contrast dependence (A in Fig. 5B). The data of the amblyopic eye show a different picture. Increas- ing contrast from 2.5 to 10 times threshold resulted in a lowering of both T, and Bi. Further increases in contrast (to 20 x threshold) had little effect. Figure 5B shows clearly the linear and parallel changes in both Bi and T,, from 2.5 to 10 times threshold. Thus, in anisometropic amblyopic eyes, there appears to be a raised level of intrinsic blur (Bi) even at high contrast; however, at low contrast, the intrinsic blur and the effect of contrast are additive. The multiplicative factor k = T,/B, can be determined from Fig. 5B as the difference between T, and Bj on the log axis. Figure 5B shows that k for the amblyopic eye is smaller than for the nonambly- epic eye. This would imply that at large blur values the amblyopic eye’s “resolution” would be better than that of the fellow eye. Unfortu- nately, the fellow eye was not measured at sufficiently large blur so a direct comparison between the two eyes is not possible.

Much of the resolution data is summarized in Fig. 6, where the equivalent intrinsic blur (Bi) estimated from the model fit is plotted against the resolution threshold (T,). Plotted here are the data of the preferred (A) and amblyopic (solid symbols) eyes of strabismics (A), anisometropes (0) and both (m). Also shown is the preferred eye of WP with dioptric defocus (A) and with eccentric viewing at 2.5, 5 and 10

Fig. 4 (Opposite). Two-line resolution thresholds are plotted as a function of the standard deviation of the Gaussian lines. Data are shown for each eye of two anisometropes (top), two strabismics (middle), and two observers with both strabismus and anisometropia (bottom). The open symbols are data of the preferred eyes, solid symbols are the amblyopic eyes. For each eye of each observer, there is a range of small stimulus blur values, where the blur has litte e&t; at larger stimulus blur spreads, thresholds rise in proportion to the stimulus blur. The solid and dotted lines fit to the data are of the form:

r /D \211/2 Th=T,.Ll+k;)] ,

where T, is the threshold for an unblurred stimulus (i.e. the asymptotic threshold value), B, is the stimulus blur, arid Bi is the equivalent intrinsic blur (i.e. the horizontal position of the knee in the function). Thus, when the stimulus blur is small, it has no influence upon thresholds; however, when it exceeds the equivalent intrinsic blur, then threshold is proportional to the stimulus blur. Note that: (1) each of the amblyopic eyes has higher asymptotic resolution thresholds (at small stimulus blur vahtes) than the fellow eyes; (2) each of the amblyopic eyes has a larger equivalent intrinsic blur than its fellow; and (3) for stimuli with large standard deviations (i.e. very blurred stimuli), thresholds for the two eyes converge, so that they are either identical or close. Since increased stimulus blur causes the performance of the two eyes

to converge, this suggests an additive error (equivalent intrinsic blur) in the amblyopic eye.


deg in the lower visual field (0). In addition is the data of normal control observer DL in the fovea, and at 2.5, 5 and 10 deg in the lower visual field (0). The dotted line is the 1.1: 1 line fit to the normal data of the preceding paper. Note that, like the data of the normal fovea and periphery, the data of amblyopic observers (both with and without strabismus) are compat-

1 KP-AMSO

ible with this line, suggesting that in the ambly- epic visual system, the resolution threshold is approximately equal to B,, the equivalent intrinsic blur. This is also evident in Table 3 where the ratio of resolution threshold to the equivalent intrinsic blur (the multiplicative factor, k) is approx. 0.9 (i.e. & shown in the column labeled Z-“/B,).

.I I

10

1

.I J .l 1 10 loo

GAUSSIAN STANDARD

Fig. 4

OM r-l l &E

‘I . . . . . . ..I . . ., . . ..I . . -...r

Nrn.eol?t8&A

L ONAE I l AE

.I 1

OEVIATIDN (MINUTES)

DENNIS M. LEVI and STANLEY A. KLEIN

GAUSSIAN STANDARD DEVIATION (MINUTES) CONTRAST (THRESHOLD UNITS)

Fig. 5. (A) Two-line “resolution” thresholds vs blur for the preferred (open symbols) and amblyopic eyes of anisometropic amblyope KP at contrast levels of 2, 5 and 10 times threshold in the preferred eye and 2.5, 5, 10 and 20 times threshold in the amblyopic eye. Stimulus contrast is indicated by the symbol size (the smaller the symbol, the lower the contrast). (B) ‘This lignre shows B, (circles) and T, (triangles) estimated by the model fits to the data (the lines in A). Note that for the preferred eye (open symbols) 7’, improves slightly with contrast, while B, shows little effect. For the amblyopic eye (Wed symbols), both B, and r, improve more or less linearly with increasing contrast up to 10 times threshold. 7’, is consistently lower than B, for the amblyopic eye so the multiplicative factor, k, is less than unity. Thus for large blur,

the amblyopic eye might be better than the nonambiyopic eye.

Table 3. Comparison of parameters

Observer Bd

T;

AE T, Bd NAE T, T, B, Snellen

+I I s, at large 0 7;;

2 @,I - Bi S T,

Anisomerropic KP 0.45 (0.9) JM 0.48 (1.P) TL 0.53 RJ 0.53(1.~)

Mean 0.498 (0.97”)

Strabismic KL RH ::: (0.58’) PZ I.0

Mean 1.3

Both CMC” 0.7 1.3

WP 1.2(1.1’) Mean I.1

Periphery DL

2.5 1.2 5.0 1.4

WF 1.4

2.5 1.1 5.0 1.0 10 0.8

Mean I.3

Normal NAE Mean 1.1

0.72 0.3 (0.6’) 1.62 0.77(1x?) 0.53 0.27 0.76 0.27 (0.8’) 0.91 0.41(0.87*)

0.7 (0.7’) 1.7 (1.V)

::: 0.9 (0.85)

0.22 (0.25) 0.26 0.61 (0.36’) 0.22 (0.29) (0.54’) 0.22

:: 0.89 0.25

0.22 (0.15) 0:69 0.24 (0.08.) 0.22 (0.23) 0.46 0.50 (0.33”)

1.0 0.8 0.5 1.1 0.85

0.9 2.25 1.4 0.7 (0.81’) 0.9 0.9 1.07 1.39

0.9 1.7 0.9 I.2

0.38 0.5 (0.7) 0.29 0.39

1.10 0.33 1.35 0.51 (0.22) 0.93 0.27 1.13 0.37

2.1 2.7 2.1 2.3

83 0:6 0.74

0.9

::‘: (0.7a) 0.81

1.0 0.50 0.83 0.41 5.2 1.0 0.53 2.00 0.25 2.8 0.7 0.45 0.90 0.29 (0.36’) 1.7 0.9 0.49 1.24 0.32 2.8

8:; 0.9

1.08 0.9 0.51 0.98 1.0 0.55 1.26 0.8 0.51

0.9

8.: d.85

0.99 1.1 0.79 0.8 1.1 0.46 0.64 1.0 0.45 I.11 1.1 0.55

1.49 0.25 1.18 0.40 1.78 0.20

1.42 0.51 1.28 0.33 0.93 0.46 1.35 0.35

0.87 0.96 0.18 0.40 0.39 1.2

“The data shown in parentheses were obtained at IO times threshold.


AWC=-

AWEEMOFYES

0 ANlscMmc

A STRASISMIC

n SOTH(S&A)

ASYMPTOTIC RESOLUTION (MINUTES)

Fig. 6. Equivalent intrinsic blur estimated from the model fit to the resolution data is plotted against the asymptotic resolution threshold. Plotted here are the data of the preferred (A) and amblyopic (solid symbols) of strabismic (A), anisometropic (0) and both (H). Individual data can be seen in Table 2. Also shown is the preferred eye of WP with dioptric defocus (0) and viewing eccentrically at 2.5, 5 and 10 deg in the lower visual field (0). The open circles show the data of normal control observer DL at 0, 2.5, 5 and 10 deg in the lower visual field. The dotted line is the 1.1: 1 line fit to the normal data in the preceding paper. The data of amblyopic observers (both with and without strabismus) are compatible with this line, suggesting that in the amblyopic visual system, equivalent intrinsic blur for resolution is

approximately equal to the resolution threshold.

Eflect O;,f blur on spatial interval discrimination (B,). In the preceding manuscript (Levi & Klein, 1990), we showed that in the normal fovea, spatial interval discrimination thresholds begin to rise when the standard deviation of the stimulus blur exceeds approx. one-third of the interline separation. We term the critical blur for spatial interval discrimination ,B,, the separation blur. Figure 7A shows spatial interval discrimination threshold plotted against stimulus blur for each eye of anisometropic amblyope KP for a base separation of 4.8 min. The open and solid circles are data of the preferred and amblyopic eyes respectively, with the stimulus contrast set to 5 times the detection threshold. Thresholds for the amblyopic eye are about 4 times higher than for the nonamblyopic eye. This multiplicative loss is similar to that reported by Watt and Hess for their Vernier task. We believe that this multiplicative loss may be the result of reduced eflective contrast in the amblyopic eye. The open triangles show the

data of the preferred eye at twice threshold. The effect of reducing the stimulus contrast is to elevate thresholds at all contrast levels, but not to significantly alter B,, the separation blur which was similar to that of the amblyopic eye, between 1.1 and 1.4 min (about one-third of the 4.8 min separation), over a wide range of contrasts (Levi & Klein, 1990). The solid squares are data of the amblyopic eye at 10 times threshold. Note that increasing the stimulus contrast improved the thresholds of the ambly- epic eye, and brought them into close proximity with the results of the preferred eye at twice threshold. Thus, for spatial interval discrimination, the amblyopic eye of this anisometropic amblyope is similar to a normal eye with lower contrast. Note that the separation blur, B,, is independent of contrast, contrary to the situ- ation with B,, associated with the resolution task.

Figure 7B shows spatial interval discrimination data for both eyes of strabismic ambly-


(Al

10

KP - ANISO

AE 5’ THRESKW

l AElO’THRESttCLD

.l 1

GAUSSIAN STANDARD DEVIATION (MINUTES)

WP - BOTH (S 6 A)

GAUSSIAN STANDARD DBVIATION (YIMJTEB)

Fig. 7. (A) Spatial interval discriminatron threshold plotted against stimulus blur for each eye of anisometropic amblyope KP for a separation of 4.8min. The open and solid circks are data of the preferred and amblyopic eyes respectively, with the stimulus contrast set to 5 times the detection threshold. The open triangles show the data of the preferred eye at twice threshold. The effect of reducing the stimulus contrast is to elevate thresholds at all contrast levels, but not to signifkantly alter the equivalent intrinsic blur which was similar to that of the amblyopic eye over a wide range of contrasts. The solid squares are data of the amblyopic eye at 10 times threshold. Note that increasing the stimulus contrast improved the thresholds of the amblyopic eye, and brought them into close proximity with the results of the preferted eye at twice threshold. Thus, fo: spatial interval discrimination, the amblyopic eye of this anisometropic amblyope is similar to a normal eye with lower contrast. (B) Spatial interval discrimination thresholds versus stimulus blur for both eyes of strabismic amblyopa WP. The lines had a base sqtration of 5 min, and a contrast 5 times threshold. Note that for this observer, the thresholds ofthe amblyopic eye are about 3-4 times higher than those of the preferred eye at all kvels of stimuIus blur, aud the equivaknt intrinsic blur of the.amblyopic eye is more than twice as large. In the ambtyopic eye, sigmas of 2.5 and 5 min do not degrade performance contrary to the performance of the preferred eye, or of the anisometropic amblyope (see A). Thus, it appears that at small separations, the amblyopic eyes of strabismic amblyopes may show increased tolerance to stimulus blur for spatial interval discrimination, and hence an increased

level of equivalent intrinsic blur.

ope WP. The lines had a base separation of 5 min, and a contrast 5 times threshold. Note that for this observer, the thresholds of the amblyopic eye are about 3-4 times higher than those of the preferred eye at all levels of stimulus blur, and the separation blur, S,, of the amblyopic eye is more than twice as large (slightly > half the separation of the line-pair) as that of the preferred eye (3.2 rfr 0.45 min vs 1.26 f 0.27 min). In Fig. 3B we showed that increasing the contrast in this observer’s ambly- epic eye did not improve his interval discrimination thresholds. Similarly, at a separation of 10 min (data not shown), his amblyopic eye had a separation blur of 5.1 4 0.66 min, compared to 2.1 & 0.45 min in the preferred, eye. Thus, at small separations (near the optimum) strabismic amblyopes, like the normal periphery (Levi & Klein, 1990), show an extra increase in interval threshold, beyond what is expected from the intrinsic blur (B,), which results in an elevated

8,. This point will be examined further’ below. The values of B, and T, for all the observers tested are presented in Table 2 and the multiplicative factor k, = TJB, is given in Table 3. These parameters were obtained by fitting the data with a model in which T,, B, and k in equations (1) and (2) are replaced with T,, B,, and k,.

A matter of scale? Figure 8 plots spatial interval discrimination thresholds vs blur standard deviation for several base separations in a different format. In Fig. 8, borh the thresholds and the stimulus blur have been divided by the interline separations. Thus, the thresholds are expressed as a Weber fraction (AS/S), and the stimulus blur standard deviation is also expressed as a fraction (e/S). In this figure the open symbols are data of the preferred eye, and the solid symbols are for the amblyopic eye. Each symbol size represents a different separation, with the smallest symbols, (connected by


(A) (B) 10 10

K. P. J z - a .

‘; . Z c r m

ii : 1:

5 -

2 . f

0 ‘l:: 0

2 . c” . g . t f . e .

.Ol , . . . . . . . . . . . . . ..I . . . . . ..I . . . . . . . I . . . ..e .Ol .l 1 10 .Ol I . . . . . ..I

.Ol .l 1

Stimulus blur (units of sepsrstion) Slmulus blur (units of separstion)

Fig. 8. Spatial interval discrimination thresholds versus blur standard deviation for several base separations are plotted in a different format. Both the thresholds and the stimulus blur have been divided by the interline separations. Thus, the thresholds are expressed as a Weber fraction (AS/S), and the stimulus blur standard deviation is also expressed as a fraction (u/S). Open symbols are data of the preferred eye, and the solid symbols are of the amblyopic eye. Each symbol sixe represents a different separation with larger symbols denoting larger separations. The smallest symbols, connected by lines, are the data near the optimal separation. For anisomefropic atnblyope, KP (A), the smallest solid circles connected by dotted lines represent the data at the optimal separation at a contrast 5 times the detection threshold. Note that these data appear to be elevated by about a factor of three at all blur spreads. Increasing the contrast to 20 times threshold (shown by A-.-A) brings the amblyopic eye into close agreement with the preferred eye data at 5 times threshold. At larger separations (e.g. 20min shown by l ), at 5 times threshold the amblyopic eye data is quite similar to that of the fellow eye. (B) shows the data of srrubismic umblyope, WP. At large separations, the data of the amblyopic eye are quite similar to those of the preferred eye when plotted in these coordinates. However, the data near the optimal separation (0 .. ~0) differ in two main respects from the fovea1 data (0): (i) at small stimulus blur values the amblyopic eye threshold Weber fractions are 3-4 times higher than the fovea1 values; and (ii) the amblyopic eye thresholds begin to rise when the stimulus blur exceeds about 0.5 (i.e. half the interline separation) and thresholds of the two eyes at all separations converge. Near the optimal separation,

increasing the contrast to 10 times threshold (A-u-A) does not improve performance.

lines) representing the data near the optimal separation. First consider the data of the preferred eyes (open symbols). The most striking feature of this plot, is that the data, when plotted in these coordinates, collapse into an almost unitary curve, with thresholds between about 0.06 and 0.09 for KP, and 0.08 and 0.12 for WP for stimulus blurs less than about 0.3 (i.e. one-third of the interline separation), and rising sharply as the stimulus blur increases. Thus, when plotted in this fashion, the fovea1 data of the preferred eyes appear to be scale invariant (Toet et al., 1987).

The data of the amblyopic eyes are rep- resented by the solid symbols. For anisometropic amblyope, KP (Fig. 8A), the smallest solid circles connected by dotted lines represent the data at the optimal separation at a contrast 5 times the detection threshold (from Fig. 7A). Note that these data appear to be

elevated by about a factor of three at all blur spreads. Two manipulations can reduce the threshold elevation: (1) increasing the contrast to 20 times threshold (shown by A-.-A) brings the amblyopic eye into close agreement with the preferred eye data at 5 times threshold; (2) at larger separations (e.g. 20 min shown by a), at 5 times threshold the amblyopic eye data is quite similar to that of the fellow eye.

Figure 8B shows the data of strabismic amblyope, WP. At large separations, the data of the amblyopic eye are quite similar to those of the preferred eye when plotted in these coordinates. However, the data near the optimal separation (a . . . 0) differ in two main respects from the fovea1 data (0): (i) at small stimulus blur values the amblyopic eye threshold Weber fractions are 3-4 times higher than the fovea1 values; (ii) the amblyopic eye thresholds begin to rise when the stimulus blur exceeds about 0.5


- 0 MmMLFfE

. A PFEFEllREDEYES

. ANlSOMETW+‘K:

A STRABISMIC

n BOTH (S 6 A)

. •1 PERlRERl

.l 1 10

ASYMPTOTIC RESOLUTION THRESHOLD (WWTES)

Fig. 9. Asymptotic spatial interval discrimination thresholds for a separation near the optimum (2-3 times the resolution limit) are plotted against resolution. The data of the normal control observer is shown by an open circle, and that of the preferred eyes of several amblyopic observers by open triangles. The data of the amblyopic eyes of anisometropes, strabismics and those with both strabismus and anisumetropia, are shown by solid circles, triangles and squares mspectively (individual data is shown in Table 2). Also shown in these figures are data of the normal periphery (from Levi UL Klein, 199O-shown by 0). The dotted line shows a ratio of 5: 1, indicating that the optimum fovea1 spatial interval discrimination thresholds of the nonamblyopic eyes are approx. 5 times smaller than the resolution limit, i.e. they are a hyperacuity. Note that the data of the anisometropic amblyopes fall close to this lint, suggesting that resolution and spatial interval discrimination thresbokis are al&ted to the same degree. The data of the amblyopes with constant unilateral strabismus, like the data of the normal periphery he rilong a line with a steeper slope, showing that spatial interval discrimination thresholds are affected to a gmater degree than resolution in strabismic amblyopes. The solid curve has the form S = 0.65 R - 0.3, where Sis the optimum spatial interval discrimination threshold, and R is the resolution We&told. This curve is derived from the data of the normal periphery (see text for details). This curve shows the factor of 3 more rapid decline in spatial interval discrimination threshokis than resolution in the periphery, and provides a reasonabk

fit to the data of all but the most mild strabismic amblyope.

(i.e. half the interline separation). Note that when the stimulus blur exceeds about half the interline separation, thresholds of the two eyes at all separations converge. In Figs 2C and 3B, we showed that increasing the contrast of the stimuli does not improve performance for this observer, and this point is also illustrated by the solid triangles in Fig. 8B, which show data near the optimal separation at 10 times threshold (A).

Figure 9 summarizes the spatial interval discrimination results for separations near the optimum (between about 2 and 3 times the resolution limit) by plotting the asymptotic separation thresholds (T,) against resolution (r,). In this figure the data of the normal control

observer is shown by an open circle, and that of the preferred eyes of sever@ amblyopic observers by open triangles. The data of the amblyopic eyes of anisometropes, strabismics and those with both strabismus and anisometropia, are shown by solid circles, triangles and squares respectively. Also shown are data of the normal periphery (from Levi & Klein, 1990-shown by 0). The dotted line shows a ratio of 5: 1, indicating that the optimum spatial interval discrimination threshold of the nonamblyopic eyes is approx. 5 times smaller than the re&ol- ution limit, i.e. it is a hypermity. Note that the data of the anisometropic amblyopes falLclose to this line, suggesting that resolution and spatial interval discrimination thresholds are


affected to the same degree. The data of the amblyopes with constant unilateral strabismus, like the data of the normal periphery lie along a line with a steeper slope, showing that spatial interval discrimination thresholds are affected to a greater degree than resolution in strabismic amblyopes. These trends can also be seen in Table 3. For example, in the anisometropic amblyopes, optimal spatial interval discrimination thresholds are approx. f of the resolution threshold (column labeled TJT,), similar to the preferred eyes, whereas in the strabismic observers, and in the normal periphery the ratio is larger. These results are consistent with our previous studies of resolution and hyperacuity in amblyopic observers (Levi & Klein, 1982, 1983, 1985; Levi et al., 1987); however, in the present study the stimuli for both tasks are identical. Moreover, as opposed to the three- line bisection task, two-line spatial interval discrimination is not influenced by “crowding” which occurs at small separations (Yap, Levi & Klein, 1989) and is especially detrimental in the periphery and in strabismic amblyopia. The solid curve in Fig. 9 has the form T, = 0.65T, - 0.3,’ where T, is the optimum spatial interval discrimination threshold, and T, is the resolution threshold. This curve is derived from the data of the normal periphery, and arises by eliminating eccentricity (E) from the equations T, = T,O (1 + E/0.65) and T, = T,O (1 + E/2.0) where T,O = 0.1 min and T,O = OSmin (see Levi & Klein, 1985 for further details). These two equations describe the linear fall-off of resolution and separation thresholds in the periphery. The curve in Fig. 9 shows the factor of 3 more rapid decline in spatial interval discrimination thresholds than resolution in the periphery, and provides a reasonable fit to the data of all but the most mild strabismic amblyope (PZ).

It is also interesting to note from Table 2 that near the optimal separation, the separation blur (B,) for optimal spatial interval discrimination is smaller than that for resolution in the normal fovea and in the anisometropic amblyopes; however, in the periphery, and in the amblyopic eyes of strabismics, the separation blur is larger than the equivalent intrinsic blur, B,. This can be seen in Table 3. The column labeled B,/Bi shows the separation blur of normal and anisometropic observers is about half the equivalent intrinsic blur, whereas, in the strabismic amblyopes, and in the normal periphery, it is equal to or larger than the equivalent intrinsic

blur. For anisometropic amblyopes, both the optimal spatial interval discrimination threshold, and the separation blur are increased in proportion to the observer’s resolution. In contrast, the amblyopes with constant unilateral strabismus, like the normal periphery, show more marked losses in spatial interval discrimination thresholds, and show additional separation blur.

To summarize, our spatial interval experiments show that all amblyopes have elevated optimal spatial interval thresholds (T, in Table 2). For the anisometropes the threshold elevation for spatial interval discrimination is consistent with the threshold elevation f6r resolution, whereas in strabismic amblyopes, there is an extra loss in optimal spatial interval discrimination thresholds (Fig. 9, and T,/T, in Table 3). For the anisometropic amblyopes, increasing the stimulus contrast improves both the spatial interval threshold and the resolution threshold. For the strabismic amblyopes, increasing the stimulus contrast improves neither.

Experiment II: detection of Gaussian blurred lines

In the preceding manuscript (Levi & Klein, 1990), we showed that equivalent intrinsic blur plays an important role in limiting contrast detection. In this section, we show how contrast detection for local stimuli is affected in amblyopes. Figure 10 shows detection thresholds plotted as a function of the standard deviation of the Gaussian blurred lines for each eye of two amblyopes with anisometropia (top), strabismus (middle) and both (bottom). Open symbols are the data of the nonamblyopic eyes, while the solid symbols are the data of the amblyopic eyes. For each eye, thresholds first decrease approximately linearly as the Gaussian standard deviation increases and then level off near I%, almost independent of either width or eye. In fact, it is interesting to note that while the thresholds for large Gaussian standard deviations are slightly elevated in the amblyopic compared to the preferred eyes of MB and TL, they are actually slightly lower in WP and PZ’s amblyopic eyes.

The curves fitted to the data have the form:

Th = Td* BJa for e < B,,

Th = Td for u > Bd

where 0 is the standard deviation of the Gaussian blur, Bd is critical stimulus blur value,


KP - AMSO f TL - AN/SO

1 * . . . . . ..I * . . . ...*. . f . .,..T

.1

’ lo ’ Pf - STRAB

GAUSSIAN STANtMRl? DEVIATION MINUTES)

Fig. 10. Detection thresholds pfotted as a function of the standard deviation of the Gaussian blurred lines for the preferred (0) and ambtyopic fr)) eyes of two amblyopts with ~~~ (top). strabiamw (middle) and both (bottom). For each eye, thresholds first decrease approxirnntsfy Enearly as the Gaussktt standard deviation increases and then level off near I%, almost independent of either width or eye. The curves fitted to the data have the form:

Th = Td for o > Bd Tir = Tp Bd/u for D c Bd

where u is the standard deviation of the Gaussian blur, B,, is the critical bhtr, above which thrcshotds arc independent of the standard deviation of the blur, and T, is the asymptotic thmshoid.

0


above which thresholds are independent of the

OIKHMLEMS

APiSSfEDEES

l mitsamm A STRABlsMlC

n SOTH(S6A)

.1 1

ASYMPTOTIC CONTRAST THRESHOLD (%)

Fig. 11. The critical blur standard deviation (in minutes) is plotted against the asymptotic contrast threshold (in pcramt). The data contained within the box are the data of the normal control observer (0). and of the prcferrcd cycs (A). Because of ineomplctc data, two of the preferred eyes have been omitted. Data of the amblyopic eyes are shown by the solid symbols (~-anisometropes; ~-strabismics; and l -amblyopes with both strab~~ and a~ome~opia). Note the oritical blur of the amblyopie eyes is enlarged, while the asymptotic thresholds of all but one of the amblyopcs fall within the range of the

preferred eyes.

standard deviation of the blur (we shall refer to this as the detection blui), and Td is the asymptotic detection threshold. These curves provide a reasonable fit to the data, and demonstrate Ricco’s law at small blur spreads (threshold is equal to the product of line spread and contrast), We specify B,+ as the standard deviation of the critical blur, so Bd should be multiplied by (2n)‘p in order to relate these data to the more usual Ricco’s diumeter for targets with a rectangular rather than a Gaussian profile.

Figure 10 has three points of note: (1) each of the amblyopic eyes shows increased contrast thresholds for small blur spreads; (2) the diameter of Ricco’s area, as indicated by B,+ is larger in the amblyopic eyes; and (3) at larger blur spreads the two eyes have nearly equal sensitivity.

The detection data of all of the observers are summarized in Figs 11 and 12, and in Tables 2 and 3. Figure 11 plots B,, (the detection blur, in minutes) against T,, (the asymptotic contrast threshold, in percent). The data contained

within the box are the data of the normal control observer (O), and of the preferred eyes of the amblyopic observers (A). There is a range (about a factor of 2) in both the size of the critical blur, and the asymptotic sensitivity of the preferred eyes; however, the main point of this figure is to show that the pooling area for contrast (BJ of ail of the amblyopic eyes (solid symbols) is enlarged, extending from a standard deviation of about 1.5 to approx. 3.5 mm, while the asymptotic thresholds (Td) of all but one of the amblyopes falls within the range of the preferred eyes. These data are consistent with the well-documented loss of high but not low spatial frequency contrast sensitivity in amblyopes (e.g. G&alder & Green, 1971; Hess & Howell, 1977; Levi & Harwerth, 1977; Bradley & Freeman, 1981), and with older studies of spatid summation (Miller, 1955; Grosvenor, 1957; Flynn, 1967), and suggest that pooling of spatial contrast extends over larger distances in the amblyopic visual system. The first two data columns in Table 2 show the size of Bd (in minutes), and the asymptotic detection


ASVWTOTIC FtESOLUTtON THRESHOLD (MINUTES)

Fig. 12. Plots the critical blur for contrast detection (Ricco’s extent) against the ohaervers’ 2-line resolution threshold at 5 times threshold. The dgta in the box are that of the normal control observer (O), and the preferred eyes of the amblyopes (A). The solid circks, triangles and squares an data of the amblyopic eyes of anisometropes, strabismics and observers with both. For several amblyopes, resolution was also measured at 10 times threshold, and the data are shown by the smaller symbols m by lines to the corresponding data at 5 times threshold. Also included on this graph (a) are data from the normal periphery (from the preceding paper). The dashed line shows the 1: 1 line; i.e. resolution equal to the

standard deviation of Rkco’s diameter.

thresholds (Td in %) in the amblyopic eye of each observer. Also shown in the last row is the mean and standard deviation of the data of the nonamblyopic eyes. It is clear from these data that B,, is larger in the amblyopic eyes (1.6 to almost 6 times), while there is little difference in the asymptotic thresholds, Td (amblyopic to nonamblyopic eye ratios between 0.7 and 2.1, with a mean ratio of about 1.2). For comparison, data of the normal periphery at 2.5, 5 and 10 deg in the lower visual field are also shown both in Fig. 12 (lJ--discussed below) and in Table 3, where the ratios, B,/T,, in the periphery and fovea of the same observer are given. It is interesting to note the similarity of the peripheral data to that of the amblyopic observers.

Figure 12 plots B., against the observers’ 2-line resolution threshold measured at a contrast of 5 or 10 times threshold (see next section). The data in the box are that of the normal control observer (O), and the preferred eyes of the amblyopes (A). The solid symbols are data of the amblyopic eyes of anisometropes,

strabismics and observers with both. Also included on this graph (0) are data from the normal periphery (from the preceding paper). The dashed line shows the 1: 1 line. Note that much of the data falls near the line, suggesting that resolution and the detection blur are essentially equal. Interestingly, the data of each of the 4 anisometropic amblyopes and 1 of the strabismic amblyopes (large solid symbols) fall below the line and are consistent with a 0.5: 1 line (i.e. the critical blur for detection is about one-half the resolution limit). When we measured the amblyopic eye’s resolution at twice the contrast (10 times threshold) in three of the anisometropes (JM, RJ and KP), the resolution thresholds improved by about a factor of two, making the ratio of B,/T, approximately equal to 1. These data are shown by the smaller solid circles, which are connected to the lower contrast data by a line. In two strabismic amblyopes (WP and RH) increasing the stimulus contrast had little (RH-A) or no (WP-m) effect.


Table 3 summarizes a large number of parameters from each of the experiments, by comparing the amblyopic eye’s performance on several different tasks. For example, column 1 shows the ratio of Bd (e.g. the detection blur) to the observer’s resolution for that eye (T,). As is evident from Fig. 12, for the preferred eyes, that ratio is about 1, while for the anisometropic amblyopes, it is about 0.5 for resolution measured at a contrast x5 times threshold. When the stimulus contrast was increased, the ratio increases to approx. 1 (shown in parentheses in Table 3). Note that the data in parentheses in all columns show the ratios determined at 10 times threshold. Since there are a large number of different aspects of detection, resolution and spatial interval discrimination to consider, Table 3 will be of value in cornparing performance across conditions, while Table 2 will be useful in making comparisons across observers (see Discussion section). As shown in Table 3, Bi and T, are also approximately equal to the extent of Ricco’s summation diameter, Bd. Thus, the equivalent intrinsic blur B, appears to play a triple role in determining both the resolution threshold and the detection threshold as well as setting the breakpoint below which blur has no effect on resolution and on spatial interval discrimination. Bi corresponds to the “R&o’s diameter” for spatial summation in a detection task, and it also corresponds to the resolution threshold for thin lines. The values of B,., T, and Bd are given for each of the amblyopic eyes in Table 2. When compared to the fellow eye, all the amblyopic eyes have raised levels of equivalent intrinsic blur and correspondingly larger resolution thresholds and Ricco’s diam- eters.

SUMMARY AND GENERAL DISCUSSION

In the experiments described above, we have estimated the equivalent intrinsic blur of the amblyopic visual system, i.e. the smallest amount of stimulus blur that supports high resolution. This equivalent intrinsic blur provides a measure of the intrinsic error of the visual nervous system which acts like blur. Our main result is that the visual system of observers with naturally occurring amblyopia due to strabismus, anisometropia, or both, have raised amounts of equivalent intrinsic blur, consistent with the reduced visual acuity and cutoff spatial frequency of the amblyopic eye. The main evi-

dence for this is shown in Figs 4 and 6. Figure 4 shows that increasing stimulus blur causes the 2-line resolution of the two eyes to converge, suggesting an additive error of increased equivalent intrinsic blur in the amblyopic eye. Figure 6 shows that for the amblyopic observers tested here, this equivalent intrinsic blur is between 1 min (at the high end of the normal range for a mild strabismic amblyope) to almost 10 min (for a severe anisometropic amblyope). These results are not explained on the basis of the optics of the amblyopic visual system, which is normal (Frankhauser & Rohler, 1967), and our observers were carefully corrected for these experiments. In the section on “Implications For Anatomy and Physiology,*’ we will discuss the nature of the neural alterations which might result in increased equivalent intrinsic blur.

In the second experiment, we showed that contrast sensitivity for thin lines is decreased in the amblyopic eye (see the column labeled Td in Table 2), consistent with the well documented loss of contrast sensitivity at high spatial frequencies (e.g. Gstalder & Green, 1971; Hess & Howell, 1977; Levi & Harwerth, 1977; Bradley & Freeman, 1981). Also spatial contrast is pooled over an extended distance in the ambly- epic eye. This increase in the diameter of R&o’s area (B,,) is consistent with previous studies of spatial summation in amblyopic eyes (Miller, 1955; Grosvenor, 1957; Flynn, 1967), and appears to be closely related to the resolution threshold (Fig. 12) and the size of the equivalent intrinsic blur (Table 3, the column labeled BJB,). Thus, our results suggest that three quantities, the resolution threshold, the equivalent intrinsic blur, and the diameter of R&o’s area are closely related. Interestingly, the detection blur, Bd, of the anisometropes is about half their resolution limit measured at a contrast level 5 times threshold. For normal observers, or strabismic amblyopes, increasing the stimulus contrast to 10 times threshold has little effect upon resolution thresholds. However, increasing the line contrast for the resolution task in three of the anisometropes (JM, KP and RJ), resulted in a two-fold improvement in the resolution thresholds, making the ratio of B,/T, approximately equal to 1 (Table 3 column 4- data in parentheses, and Fig. 12), suggesting that the deficit in anisometropic amblyopes is, at least in part, contrast related.

Both spatial interval discrimination thresholds, and the separation blur, B,, depend upon the base separation of the stimulus. Thus,


increased equivalent intrinsic blur, Bi, would be expected to influence spatial interval discrimination and the size of the separation blur when the line separation is small compared to the equivalent intrinsic blur. This point is illustrated in Figs 1 and 2, where the effect of equivalent intrinsic blur is mimicked by blurring the stimulus. For separations equal to or less than the stimulus blur, thresholds are markedly elevated; however, for separations greater than about twice the stimulus blur, separation thresholds are unaffected by stimulus blur. At any level of blur,the form of the function is similar, there is a sharp transition from the resolution limit to the optimal spatial interval discrimination threshold, which is about a factor of 5 smaller than the resolution threshold (i.e. a hyperacuity). Our results suggest a very similar result in the amblyopic eyes of anisometropic amblyopes: when the separation of the lines is about twice the resolution limit (or twice the intrinsic blur), thresholds are about 5 times better than for resolution (in Table 3, the ratio TJT, is about 0.2 for the anisometropic amblyopes, and in normals). Thus, in anisometropic amblyopes, the spatial interval discrimination thresholds are elevated to a degree consistent with the intrinsic blur. For spatial interval discrimination, at separations near the optimum, anisometropic amblyopes also demonstrate increased separation blur. This is to be expected since the optimal separation is larger than that of normals (see Fig. 2); the interesting point is that for the anisometropic amblyopes, the increase in separation blur is commensurate with their increased intrinsic blur (in Table 3, the ratio BJBi is approx. 0.46 in the anisometropic amblyopes, similar to the value of 0.4 in the nonamblyopic eyes), and it is similar to that of the normal eye for the same physical separation (e.g. Fig. 6A). In contrast, strabismic amblyopes, like the normal periphery, show an additional increase in separation thresholds and in separation blur over and above that predicted from their resolution, or from their equivalent intrinsic blur. Table 3 shows the ratio of spatial interval to resolution thresholds, T,/T,, is about 0.4 for the strabismics, twice as high as that for normals and anisometropes; similarly, the ratio of separation blur to equivalent intrinsic blur, B,/Bi, is about 1.2 in the strabismics, about a factor of three larger than in the anisometropic and nonambly- epic eyes. These effects can also be seen clearly in Fig. 8, where spatial interval discrimination

thresholds are plotted against the stimulus blur, with both axes normalized to account for the effects of separation. The striking results of Fig. 8 show that the amblyopic eye of M- isometropic amblyope KP is similar to the normal eye, when the effects of intrinsic blur and low signal-to noise ratio are taken into account by (i) scaling the results according to separation, and (ii) increasing the contrast in the amblyopic eye (triangles in Fig. SA). On the other hand, near the optimal separation, neither scaling nor increased contrast normalize the data of strabismic amblyope WP (compare the triangles in Fig. 8B to the triangles in Fig. 8A).

Table 3 also compares the loss of Snellen acuity (75% correct, measured with David- son-Eskridge charts) to the loss of resolution (the last column, labeled Snellen/T,). It is of interest to note that for the anisometropic amblyopes, Snellen acuity and resolution are nearly equal (mean ratio of 0.85, suggesting that both may be limited by equivalent intrinsic blur). In contrast, the strabismic amblyopes show an extra loss of Snellen acuity (ratios between 1.7 and 5.2). This is consistent with our previous studies comparing grating acuity and Snellen acuity (Levi & Klein, 1982, 1983, 1985); however, in previous studies resolution was measured with a repetitive stimulus. In the present study, the extra loss of Snellen cannot be explained by the local nature of the Snellen target since the 2-line resolution task is also local.

kfodelling the umblyopic loss

In this section we consider four broad hypotheses regarding the nature of the amblyopic loss. These hypotheses are neither exhaustive, nor necessarily exclusive, but provide a context for understanding both the present results, and those of other studies.

Signal-to-noise/equivulent intrinsic blur hypothesis: Several recent models for position discrimination are based on the contrast response function of localized spatial filters (Klein & Levi, 1985; Wilson, 1986a). Thus, it is plausible that reduced contrast sensitivity or signal-to-noise ratio of the small (high spatial frequency) filters may result in reduced pos- tional sensitivity. The selective loss of high spatial frequency (small) mechanisms, would be equivalent to increased neural blurring of the amblyopic eye, and therefore it should be possible to mimic amblyopia either by Gaussian blur, or by reduced contrast. Figure 2 shows


that it is indeed possible to do so for anisometropic, but not strabismic amblyopes. Reducing the contrast in the preferred eye produced quite similar data to that of the amblyopic eye of anisometropic observer KP (Fig. 7A). Conversely, increasing the contrast in his amblyopic eye, made it similar to that of the preferred eye (Fig. 2A). Taken together, these findings suggest that at least to a first order approximation the position losses of M- isometropic amblyopes for a variety of conditions (Vernier acuity; bisection and 2-line spatial interval discrimination) can be understood in terms of a reduced contrast sensitivity (signal-to-noise ratio) of the filters of the amblyopic eye. This reduced signal-to-noise hypothesis for anisometropic amblyopia is contro- versial! Watt and Hess (1987), have argued against this, because, making their target lines brighter in the amblyopic eye did not equate performance in the two eyes. However, in the present study, and in the data of Watt and Hess (1987), increasing the line contrast did improve performance in the amblyopic eyes of anisometropic amblyopes.

Saturation in the contrast vs spatial interval discrimination function (Morgan & Regane, 1987) may set a ceiling on performance. Thus, it seems more reasonable to ask whether the amblyopic eye’s performance may be mimicked by reducing the contrast in a normal eye. The present results, and those of Bradley and Free- man (1985) showed that the poor positional acuity of the amblyopic eye could also be mimicked in the nonamblyopic eye by markedly reducing the contrast of the stimulus. The present study suggests that the data of anisometropic amblyopes may be modeled as a consequence of a reduced signal-to-noise ratio of the small spatial filters. Because the loss in signal-to-noise ratio is selective for high spatial frequency mechanisms, it is equivalent to a raised extent of equivalent intrinsic blur, and Fig. 2 shows that the data of the anisometropic but not strabismic amblyopes can be mimicked by increused stimulus blur, and reduced stimulus contrast, i.e. the anisometropic amblyopic visual system can be mimicked by the appropriate scaling in both size and contrast.

In our resolution and interval tasks, thresholds of normal observers show very little effect of stimulus contrast above about 5 times threshold (Morgan & Regan, 1987; Klein 8z Levi, 1989); whereas the performance of anisometropic amblyopes continues to improve at

much higher contrast levels (see e.g. the data of KP, Figs 3 and 7). A similar effect is seen in the Vernier acuity study of Watt and Hess (1987). Watt and Hess found that increasing the inten- sity of their line stimuli had almost no effect in normal observers, but had a dramatic effect in anisometropic amblyopes. In fact, the spatial interval data of KP shown in Fig. 7 are quite reminiscent of Watt and Hess’s (1987) Vernier results, in showing a multiplicative error (i.e. thresholds in the amblyopic eye are uniformly elevated at all stimulus blurs).

The present data suggest that this multiplicative error in anisometropic amblyopes (but not in strabismics) can be attributed to a weak effective contrast signal at low contrasts. Simply equating the perceived contrast of the lines is not sufficient because the position judgment is based upon somewhat higher spatial frequency mechanisms than the line detection judgment, so an extra contrast compensation must be based on the observer’s performance on a dipole detection task (Levi & Klein, in preparation). In our previous studies of position acuity in amblyopes (Levi & Klein, 1982, 1983, 1985, 1986), we used very high contrast stimuli. Under those conditions, the position thresholds of anisometropic amblyopes are consistent with their resolution thresholds, and both can be simply accounted for on the basis of equivalent intrinsic blur. However, the present study suggests that two sources of error in the amblyopic eye of anisometropes: an additive error of equivalent intrinsic blur, and a multiplicative error due to a weak or ineffective local contrast signal. Both of these errors may be largely understood on the basis of the contrast sensitivity function of the anisometropic amblyope. Previously (Levi et al., 1987) we have pointed out that contrast scaling by simply making the lines equally visible may not be adequate because the mechanisms detecting the lines may not be the same as those which detect the position cue, and the present study appears to bear this out. The position cue is at higher spatial frequencies than the detection cue, so an extra boost in contrast should be needed, compared to what would be expected based on the relative detection thresholds.

Positional uncertainty/spatial scrambling hypothesis. One recent idea, is that there is a high degree of positional uncertainty in the ambly- epic visual system (Cohn & Wardlaw, 1985). Increased positional uncertainty might be expected to produce elevated contrast detection thresholds for localized stimuli (such as thin


lines), because the observers would not be able to appropriately direct their attention to the target; however, it would not be expected to have as large an effect upon resolution or spatial interval discrimination thresholds for stimuli that were suprathreshold. This theory is not supported by our data which shows that the loss in detection is exactly what is expected from the loss in resolution (Fig. 1 l), when one compen- sates for contrast as discussed above.

A variant of the spatial uncertainty hypothesis was suggested by Hess (1982), who proposed that there may be a local scrambling or distortion of the metric of visual space. This is an appealing idea, since it implies that there should be a high degree of relative positional uncertainty in the amblyopic visual system for nearby stimuli, consistent with the results of a large number of previous studies (Bedell & Flom, 198 1; Levi & Klein, 1982, 1985; Bradley & Freeman, 1985; Rentschler & Hilz, 1985; Watt & Hess, 1987), as well as the present experiments. Watt and Hess (1987), recently measured the Vernier acuity of several anisometropic amblyopes with targets whose elements were subjected to positional jitter. Their results showed positional jitter profoundly degraded performance of the nonamblyopic eye, but not ‘of the amblyopic eye, suggesting elevated positional uncertainty in the amblyopic eye. In a separate study, Pointer and Watt (1987) suggested that the reduced sensitivity of the amblyopic eye for shape discrimination could be mimicked by the introduction of pos- itiona! jitter. Watt and Hess (1987) reported that blur and jitter had different effects in their anisometropic amblyopes. In normal vision, Vernier acuity is fairly robust to stimulus blur, thus this task may not tap the limiting equivalent intrinsic blur. Based upon their experiments Watt and Hess concluded that anisometropic amblyopes do not have raised equivalent intrinsic blur. Our results with one-dimensional stimuli show that they do.

There are several aspects of the performance of anisometropic amblyopes that are difficult to reconcile with the scrambled spatial metric hypothesis. Watt and Hess (1987) suggest that there is a limiting positional uncertainty of about 5 set in normal observers, and that it is larger in anisometropic amblyopes. Watt and Hess estimate the “limiting position uncertainty” by measuring Vernier acuity with lines comprised of unresolved dots, whose positions are subjected to position jitter. Not surprisingly,

they find that when the jitter is smaller than the (unjittered) Vernier threshold, stimulus jitter has no effect, and when it exceeds the (unjittered) Vernier threshold, threshold is proportional to the stimulus jitter, since the error in the actual position of the lines adds to the Vernier threshold. Thus, by tautology, the “limiting positional uncertainty” must be similar to the Vernier threshold. Anisometropic amblyopes show losses in Snellen acuity, grating acuity and contrast sensitivity which are commensurate with their reduced positional acuity (Levi & Klein, 1982, 1985; Bradley & Freeman, 1985). Consider for example an amblyope with a “limiting positional uncertainty” of 15 set arc, about three times higher than normal (e.g. Watt & Hess, 1987). It is difficult to see how this would reduce grating acuity to 20 c/deg (also a factor of three), or reduce contrast sensitivity over a wide range of spatial frequencies. On the other hand, the spatial jitter hypothesis may apply to strabismic amblyopes, in whom the loss of positional acuity is greater than the loss of resolution or contrast sensitivity (this will be discussed further in the section on spatial undersampling). However, a more parsimonious explanation for the losses of Snellen acuity, resolution, and hyperacuity of anisometropic amblyopes is based upon their loss of contrast sensitivity at high spatial frequencies and a weak local contrast response. This would lead to raised equivalent intrinsic blur, and decreased signal-to-noise ratio of the underlying mechanisms. This notion is consistent with what is known about the physiology of primates reared with monocular defocus (Movshon, Eggers, Gizzi Hendrickson, Kiorpes & Boothe, 1987- see section on anatomy and physiology). It should be noted that we agree with Watt and Hess (1987) regarding the increased relative positional uncertainty in anisometropic amblyopes; however, we disagree about the cause. Watt and Hess (1987) argue that the reduced resolution, contrast sensitivity, and position acuity are a consequence of local spatial scrambling. We argue that the losses of anisometropic amblyopes can be understood on the basis of raised internal blur, and reduced signal-to-noise of the underlying spatial filters. In order to convincingly ascribe the loss to scrambling, Watt and Hess would have to show that the position loss was larger than the contrast loss and the resolution loss. To clarify the role of blur, contrast and the contrast sensitivity function, we restate our hypothesis presented


at the beginning of this modeling section. Anisometropic amblyopes have a loss in contrast sensitivity that is most severe at high spatial frequencies (Levi & Harwerth, 1977; Bradley & Freeman, 1981). This high spatial frequency loss is equivalent to an increased intrinsic blur. The selective loss at high spatial frequencies also explains why simply scaling the line contrast is not sufficient. When using line stimuli (as in the present study, or that of Watt & Hess, 1987), the line stimulus to the ambly- epic eye must have much higher contrast (in line threshold units) than the preferred eye, because the discrimination cue is at higher .spatial frequencies than the line. Thus, the peak contrast in the amblyopic eye must be increased so that the cue contrast in the two eyes is the same.

Spatial undersampling hypothesis. A fundamental issue from the perspective of modeling positional acuity, is the spatial sampling of the mechanisms (spatial filters) responsible for the position acuity with respect to their receptive field size (Wilson, 1986b; Klein & Levi, 1985). Sparse spatial sampling (i.e. increased distance between neighboring receptive fields of the same size) would result in reduced resolution, but a more marked loss in position acuity, since critical localized cues may be missed (Wilson, 1986b; Klein 8c Levi, 1985). Since the resolution and position losses of anisometropic amblyopes are commensurate, we have argued that a reduced signal-to-noise ratio of high spatial frequency mechanisms is sufficient to account for the losses of anisometropic amblyopes, but that the extra loss of position acuity seen in strabismic amblyopes may be a consequence of sparse spatial sampling (Levi & Klein, 1985, 1986). There are several circumstantial lines of evidence to support the sparse spatial sampling grain hypothesis in strabismic amblyopes. First is the close qualitative and quantitative corre- spondence between the performance of strabismic amblyopes and the normal periphery (Levi & Klein, 1985; Levi et al., 1987 and Fig. 9 of the present paper). In the normal periphery, positional acuity is degraded to a greater extent than resolution, and the variation in positional acuity with eccentricity is consistent with several recent physiological estimates of the variation in the spatial sampling grain of the striate cortex (Dow, Snyder, Vautin & Bauer, 1981; Dow, Vautin & Bauer, 1985; Tootell, Silverman, Switkes & DeValois, 1982; Van Essen, New- some & Maunsell, 1984; Levi, Klein 8t Aitse- baomo, 1985; Tolhurst & Ling, 1988; also see

Levi & Klein, 1990). Second, both the normal periphery, and the central field of strabismic (but not anisometropic) amblyopes benefit from the addition of discrete spatial samples (Levi & Klein, 1986; Levi et al., 1987). This would be expected in a sparsely sampled visual system, where positional noise would be uncorrelated between sampling elements in the visual system, and each sample of the stimulus would be independently localized, resulting in a square root relationship between sampling elements in the visual system. Third, in normal fovea1 vision, and in the anisometropic amblyopes, the separation blur, E,, is about one-quarter of the separation of the line-pair for separations between about 2 and 10 times the resolution limit (Levi & Klein, 1990, and Fig. 7A). On the other hand, in the periphery, and in the central field of strabismic amblyopes, separation blur is larger (e.g. Fig. 7B) even after making allowance for the effects of separation (0 -. . l in Fig. 8B). In other words, the normal periphery and the amblyopic eye of strabismics tolerate blur over larger distances than does the fovea. Snyder (1982) suggested that blurring the stimulus may actually improve positional acuity in peripheral vision, where spatial sampling is sparse. Our results with long lines do not support his hypothesis since there is no dipper in Fig. 8B to illustrate facilitation. However, they do suggest that the mechanisms responsible for optimal spatial interval discrimination are more tolerant to blur in the periphery and in strabismic amblyopia than in normal fovea1 vision or anisometropic amblyopia (see column BJB, in Table 3). In the preceding paper (Levi & Klein, 1990), we suggested that the increased separation blur in the periphery reflects increased spatial uncertainty which is proportional to the reduced cortical representation. A similar explanation would also account for the data of strabismic amblyopes. Thus, our working hypothesis is that in strabismic amblyopia, the extra loss of positional acuity, the effectiveness of adding discrete samples to the stimulus, and the extra separation blur, all have their basis in sparse spatial sampling, due to insufficient cortical neurons to provide accurate relative position signals. A scrambling of the neural signals may be very difficult to distinguish experimentally from undersampling, and may well be a consequence of undersampling.

While all of our amblyopic observers show an additive error of increased equivalent intrinsic blur that has important consequences for resol-


ution, detection and spatial interval discrimination, anisometropic amblyopes also have a multiplicative error, which we ascribe to a weak local contrast signal. This error affects both resolution and spatial interval discrimination. Strabismic amblyopes, on the other hand also show a greater loss in spatial interval discrimination than for resolution, which cannot be accounted for on the basis of equivalent intrinsic blur or a weak signal. We suggest that this extra loss in strabismic amblyopes is a consequence of increased positional uncertainty, undersampling, or both.

Implications for anatomy and physiology

The present results, and those of other experiments suggest that there may be fundamental differences in the neuronal losses which accom- pany anisometropic and strabismic amblyopia (Hess, Campbell & Zimmem, 1980; Hess & Pointer, 1985; Levi BE Klein, 1982, 1985; Levi et al. 1987). In this section we briefly review anatomical and physiological studies of experimental amblyopia. Eggers and Blakemore (1978) have studied the contrast sensitivity of neurons in kittens reared with experimental anisometropia. They discovered that neurons driven through the amblyopic eye showed reduced contrast sensitivity, particularly at high spatial frequencies. Their electrophysiological contrast sensitivity function shows reduced contrast sensitivity in the “amblyopic” eye, much like that seen in humans. Similar results have also been obtained in monkeys reared with chronic‘atropinization (Movshon et al., 1987). While atropinization only results in blur at close viewing distances, the behavioral consequences of early rearing with chronic atropinization of one eye are remarkably similar to the results seen in human anisometropic amblyopia (Kiorpes, Boothe, Hendrickson, Movshon, Eggers & G&i, 1987). The results suggest that the selective deprivation of high spatial frequencies in the retinal image, produced by monocular defocus, is reflected in the behavioral deficits. More importantly, these investigators also studied the anatomy (Hendrickson, Movshon, Boothe, Eggers, Gixzi & Kiorpes, 1987) and physiology (Movshon et al., 1987) of the retina, LGN, and cortex in the same animals. These studies provide strong support for the notion that the primary effects of monocular blur on the developing visual nervous system are cortical. They found that the retina and all other eye

tissues were normal. Cells in the parvocellular layer (P) of the LGN were slightly smaller in the deprived than the nondeprived laminae, but with normal physiological properties and normal resolution. However, monocular blur produced marked effects on the spatial properties of neurons in striate cortex. Neurons driven by the defocussed eye tended to have lower optimal spatial frequencies, poorer spatial resolution, and lower contrast sensitivity than neurons driven by the untreated eye. These effects were mainly found in neurons with parvocellular inputs, with little effect upon neurons with magnocellular inputs. Thus, it appears that monocular defocus has its main physiological effects upon the P pathway. Rearing with monocular blur also reduced the degree of binocular interaction in striate cortical neurons, and shifted.eye dominance toward the untreated eye. One interesting finding of this study concerns the spatial tuning of binocular neurons encoun- tered in the cortices of these animals. Binocular interactions were more or less normal when tested with low spatial frequency stimuli, but were abnormal at high spatial frequencies, in line with the psychophysical findings of Holopi- gian, Blake and Greenwald (1986). Thus, the functional changes in the physiology of animals reared with monocular blur are a loss of spatial resolution and contrast sensitivity, primarily at high spatial frequencies.

The effect of prism rearing (to simulate strabismus), is to reduce the proportion of binocu- larly activated cells, and to shift the ocular dominance of the cells which do respond. Craw- ford and von Noorden (1980) have suggested that the loss of binocular cells is associated with the loss of functional binocularity (and stere- opsis), while the shift in ocular dominance is associated with visual acuity loss. Movshon has suggested that the loss of functional connections may be much more profound in the visual cortices of surgically strabismic than monocu- larly blurred monkeys, and that the losses may involve both P and M pathways (Movshon’s fantasy, personal communication), while the effects of blur primarily involve the P pathways. While it is tempting to speculate that the mas- sive loss of functional input from the deviated eye to the visual cortex is the source of spatial undersampling evident in the psychophysical performance of strabismic amblyopes, to date there have been no quantitative studies of spatial resolution in the cortices of strabismic monkeys.


Amblyopia as a developmental abnormality

Amblyopia is a developmental abnormality of spatial vision; thus, it seems reasonable to ask whether the differences in the performance of strabismic and anisometropic amblyopes reflect fundamental differences in the underlying mechanisms of amblyopia, or whether strabismus and anisometropia exert their effects at different stages of development. This question is under- lined by the recent finding that resolution (grating acuity) and Vernier acuity have different developmentals time courses in the primate visual system (Kiorpes & Movshon, 1988). Simi- larly, the studies of Vernier acuity in human infants (e.g. Manny & Klein, 1985; Shimojo & Held, 1987) suggest that the Vernier acuity of infants (6-8 months of age) is only about twice as good as resolution, while in adults it is 4-10 times better. It seems likely that this very high level of spatial processing develops well beyond the age range studied to date, and may coincide with the late development of finely sampled, fovea1 high spatial frequency mechanisms in the cortex, and possibly the “calibration” of cone positions in the cortex (Maloney, 1989). The critical point is that vernier acuity and grating acuity must have a different developmental time course from birth until they reach adult levels of performance. If the developing visual system were highly susceptible to the effects of binocular misalignment (decorrelation of retinal images of the two eyes on corresponding points) at an early stage, when Vernier acuity was relatively less developed than grating acuity, then the loss of Vernier acuity would be large compared to the loss of grating acuity. If on the other hand, the visual system were relatively unaffected by monocular retinal image blur until later in development, when the ratio of Vernier to grating acuity is adult-like, then both Vernier acuity and resolution might be affected to the same degree by uncorrected monocular defocus. In other words, we hypothesize that the high degree of intrinsic blur present in the infant visual system may serve as a buffer against the effects of uncorrected refractive error early in life. The answer to this question will require a clear definition of the period(s) of susceptibility to strabismus and to monocular defocus.

To summarize, our results show that (i) contrary to the results of Watt and Hess (1987), all of the ambiyopic observers we tested have raised equivalent intrinsic blur, (ii) the data of the anisometropic amblyopes can be modeled on

the basis of increased equivalent intrinsic blur and a decreased local contrast response, i.e. the anisometropic amblyopic visual system can be mimicked by the appropriate scaling in both size and contrast, (iii) the data of strabismic amblyopes show an extra loss in fine positional acuity which cannot be simply modeled on the basis of blur and contrast. Strabismic amblyopes show an extra loss which may be due to increased positional uncertainty, undersampling, or both.

Acknowledgement-Supported by grants ROI EY01728 and ROl EY04776 from the National Eye Institute.

REFERENCES

Bedell, H. E. & Flom, M. C. (1981). Monocular spatial distortion in strabismic amblyopia. Investigative Ophthal- mology and Visual Science, 20, 263-268.

Bedell, H. E. & Flom, M. C. (1983). Normal and abnormal space perception. American Journal of Optometry and Physiological Optics, 60, 426-435.

Bedell, H. E., Flom, M. C. & Barbeito, R. (1985). Spatial aberrations and acuity in strabismus and amblyopia. Investigative Ophthalmology and Visual Science, 26, 909-916.

Bradley, A. & Freeman, R. D. (1981). Contrast sensitivity in anisometropic amblyopia. Investigative Ophthalmology and Visual Science, 21, 467-476.

Bradley.. A. & Freeman, R. D. (1985). Is reduced vernier acuity in amblyopia due to position, contrast or fixation deficits? Vision Research, 25, 55-66.

Cohn, T. E. & Wardlaw, J. C. (1985). Effects of large spatial uncertainty on fovea1 luminance increment de- tectability. Journal of the Optical Society of America, A 2, 820-825.

Crawford, M. L. J. & von Noorden, G. K. (1980). Gptically- induced concomitant strabismus in monkeys. Investigative Ophthalmology and Visual Science, 19, 1105-I 109.

Dow, B. M., Snyder, R. G., Vautin, R. G. & Batter, R. (1981). Magnification factor and receptive field sixe in fovea1 striate cortex of the monkey. Experimental Brain Research, 44, 2 13-228.

Dow, B. M., Vautin, R. G. & Bauer, R. (1985). The mapping of visual space onto fovea1 striate cortex in the macaque monkey. Journal of Neuroscience, 5, 890-902.

Eggers, H. M. & Blakemore, C. (1978). Physiological basis of anisometropic amblyopia. Science, 201, 262-267.

Fankhauser, F. & Rohler, R. (1967). The physical stimulus, the quality of the retinal image and fovea1 brightness discrimination in one amblyopic and two normal eyes. Documenta Ophthalmologica, 23, 149-184.

Flom, M. C., Bedell, H. E. & Barbeito, R. (1986). Spatial uncertainty and acuity in anisometropic amblyopia. Investigative Ophthalmology and Visual Science (Suppl.), 26, 80.

Flynn, J. T. (1967). Spatial summation in amblyopia. Archives of Ophthalmology, 78, 470-474.

Grosvenor, T. (1957). The effects of duration and background luminance upon the brightness discrimination of an amblyope. American Journal of Optometry and Physiological Optics, 34, 634-663.


Gstalder, R. 3. & Green, D. G. (1971). Laser interferometric acuity in amblyopia. Journal of Pediatric Ophthalmology, 8, 251-256.

Hendrickson, A., Movshon, J. A., Boothe, R. G., Eggers, H., Giui, M. & Kiorpes, L. (1987). Effects of early unilateral blur on the macaque’s visual system. II. Anatom- ical observations. Journal of Neuroscience, 7, 1327-I 339.

Hess, R. F. (1982). Developmental sensory impairment: Amblyopia or tarachopia? Human Neurobiology, I, 1 l-29.

Hess, R. F. & Howell, E. R. (1977). The threshold contrast sensitivity function in strabismic amblyopia: Evidence for a two-type classification. Vision Research, 17, 1049-1055.

Hess, R. F. % Pointer, J. S. (1985). Differences in the neural basis of human amblyopias: The distribution of the anomaly across the visual field. Vision Research, 25, 1577-I 594.

Hess, R. F., Campbell, F. W. & Zimmem, R. (1980). Differences in the neural basis of human amblyopias: The effects of mean luminance. Vision Research, 20,295-305.

Holopigian, K., Blake, R. & Greenwald, M. J. (1986). Selective losses in binocular vision in anisometropic amblyopes. Vision Research, 26, 621-630.

Kiorpes, L. & Movshon, J. A. (1988). Development of Vernier and grating acuity in strabismic monkeys. Inves- tigative Ophthalmology and Visrucl Science (Suppl.), 29,9.

Kiorpes, L., Boothe, R. G., Hendrickson, A., Movshon, J. A., Eggers, H. M. 8c Gizzi, M. S. (1987). Effects of early unilateral blur on the macaque’s visual sytem. I. Behav- ioral observations. Journal of Neuroscience, 7, 13 18-l 326.

Klein, S. A. & Levi, D. M. (1985). Hyperacuity thresholds of 1 second: Quantitative predictions and empirical vali- dation. Journal of the Optical Society of America, A 2, 1170-l 190.

Klein, S. A. & Levi, D. M. (1989) A simple model of resolution and position thresholds for blurred lines. Irwes- tigative Ophthalmology and VisualScience (Suppl.), 30,245.

Levi, D. M. 8c Harwerth, R. S. (1977). Spatio-temporal interactions in anisometropic and strabismic amblyopia. Investigative Ophthalmology and Visual Science, 16, 90-95.

Levi, D. M. & Klein, S. A. (1982). Hyperacuity and amblyopia. Nature, London, 298, 268-270.

Levi, D. M. & Klein, S. A. (1983). Spatial localization in normal and amblyopic vision. Vision Research, 23, 1005-1017.

Levi, D. M. & Klein, S. A. (1985). Vernier acuity, crowding and amblyopia. Vision Research, 25, 979-991.

Levi, D. M. & Klein, S. A. (1986). Sampling in spatial vision. Nature, London, 320, 360-362.

Levi, D. M. & Klein, S. A. (1990). Equivalent intrinsic blur in spatial vision. Vision Research, 30, 1971-1993.

Levi, D. M., Klein, S. A. & Aitsebaomo, A. P. (1985). Vernier acuity, crowding and cortical magnification. Vision Research, 25, 963-977.

Levi, D. M., Klein, S. A. Jr Yap, Y. L. (1987). Positional uncertainty in peripheral and amblyopic vision. Vision Research, 27, 581-597.

Levi, D. M., Klein, S. A. & Yap, Y. L. (1988). “Weber’s Law” for position: Unconfounding the role of separation and eccentricity. Vision Research, 28, 597-603.

Maloney, L. T. (1989). Combining information across multiple sampling arrays. Investigative Ophthalmology and Visual Science (Suppl.), 30, 54.

Manny, R. E. & Klein, S. A. (1985). A three alternative tracking paradigm to measure vernier acuity of older infants. Vision Research, 25, 1245-1252.

Miller, E. F. II (1955). The nature and cause of impaired visual acuity in amblyopia. American Journal of Oprom- etry and Archives of the American Academy of Optometry, 32, 10-28.

Morgan, M. J. M. & Regan, D. M. (1987). Opponent model for line interval discrimination: Interval and Vernier performance compared. Vision Research, 27, 107-l 18.

Movshon, J. A., Eggers, H. M., Giai, M. S., Hendrickson, A., Kiorpes, L. & Boothe, R. G. (1987). Effects of early unilateral blur on the macaque’s visual system--III. Physiological observations. Journal of Neuroscience, 7, 1340-1351.

Pointer, J. S. & Watt, R. J. (1987). Shape recognition in amblyopia. Vision Research, 27, 651660.

Rentschler, I. & Hilx, R. (1985). Amblyopic processing of positional information. Part I: Vernier acuity. Experimen- tal Brain Research, 60, 270-278.

Shimojo, S. & Held, R. (1987). Vernier acuity is less than grating acuity in 2- and 3-month-olds. Vision Research, 27, 77-86.

Snyder, A. W. (1982). Hyperacuity and interpolation by the visual pathways. Vision Research, 22, 1219-1220.

Toet, A., van Eekhout, M. P., Simons, H. L. % I&n&rink, J. J. (1987). Scale invariant features of differential spatial displacement discrimination. Vision Research, 27, 441-452.

Tolhurst, D. J. & Ling. L. (1988). Magnification factors and the organization of the human striate cortex. Human Neurobiology, 6, 247-254.

Tootell, R. B., Silverman, M S., Switkes, E. & De Yalois, R. L. (1982). Deoxyglucose analysis of retinotopic organization in primate striate cortex. Science, 218, 902-904.

Van Essen, D. C., Newsome, W. T. & Maunsell, J. H. R. (1984). The visual Beld representation in striate cortex of the macaque monkey: Asymmetries anisotropies, and individual variability. Vision Research, 24, 429-448.

Watt, R. J. UC Hess, R. F. (1987). Spatial information and uncertainty in anisometropic amblyopia. Vision Research, 27, 661-674.

Watt, R. J. & Morgan, M. J. (1985). A theory of the primitive spatial code in human vision. Vision Research, 25, 1661-1674.

Watt, R. J., Morgan, M. J. &Ward, R. M. (1983). The use of different cues in Vernier acuity. Vision Research, 23, 991-995.

Westheimer, G. (1975). Visual acuity and hyperacuity. Investigative Ophthalmology, 14, 570-572.

Westheimer, G. & McKee, S. P. (1977). Spatial con- figuration for visual hyperacuity. Vision Research, 17, 940-947.

Wilson H. R. (1986a). Responses of spatial mechanisms can explain hyperacuity. Vision Research, 26, 453-470.

Wilson, H. R. (1986b). Model of peripheral and amblyopic hyperacuity. Investigative Ophthalmology and Visual Science (Suppl.), 27, 95.

Yap, Y. L., Levi, D. M. & Klein, S. A. (1989). Peripheral position acuity: Retinal and cortical constraints on 2-dot separation discrimination under photopic and scotopic conditions. Vision Research, 29, 789-802.

Equivalent intrinsic blur in amblyopia

Documents

Transcript of Equivalent intrinsic blur in amblyopia