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Article An Unexpected Spontaneous Motion-In-Depth Pulfrich Phenomenon in Amblyopia

Alexandre Reynaud * and Robert F. Hess McGill Vision Research, Department of Ophthalmology, McGill University, Montreal, QC H3G 1A4, Canada; [email protected] * Correspondence: [email protected]



Received: 28 May 2019; Accepted: 18 October 2019; Published: 22 October 2019


Abstract: The binocular viewing of a fronto-parallel pendulum with a reduced luminance in one eye results in the illusory tridimensional percept of the pendulum following an elliptical orbit in depth, the so-called Pulfrich phenomenon. A small percentage of mild anisometropic amblyopes who have rudimentary stereo are known to experience a spontaneous Pulfrich phenomenon, which posits a delay in the cortical processing of information involving their amblyopic eye. The purpose of this study is to characterize this spontaneous Pulfrich phenomenon in the mild amblyopic population. In order to assess this posited delay, we used a paradigm where a cylinder rotating in depth, defined by moving Gabor patches at different disparities (i.e., at different interocular phases), generates a strong to ambiguous depth percept. This paradigm allows one to accurately measure a spontaneous Pulfrich phenomenon and to determine how it depends on the spatio-temporal properties of stimulus. We observed a spontaneous Pulfrich phenomenon in anisometropic, strabismic, and mixed amblyopia, which is posited to be due to an interocular delay associated with amblyopic processing. Surprisingly, the posited delay was not always observed in the amblyopic eye, was not a consequence of the reduced contrast sensitivity of the amblyopic eye, and displayed a large variability across amblyopic observers. Increasing the density, decreasing the spatial frequency, or increasing the speed of the stimulus tended to reduce the observed delay. The spontaneous Pulfrich phenomenon seen by some amblyopes was variable and depended on the spatio-temporal properties of the stimulus. We suggest it could involve two conflicting components: an amblyopic delay and a blur-based acceleration.

Keywords: Pulfrich phenomenon; interocular delay; stereopsis; motion in depth; amblyopia

1. Introduction The binocular viewing of a fronto-parallel pendulum with a neutral density (ND) filter placed over one eye results in the illusory tridimensional percept of the pendulum following an elliptical orbit in depth, the so-called Pulfrich phenomenon [1]. This is explained as the consequence of the processing delay between the two eyes introduced by the luminance reduction [2–5]. The underlying mechanism might involve either changes in the pure disparities over time for disparity sensors [6–9] or changes to sensors that encode motion/disparity conjointly [10–13]. Some stereo-deficient persons are able to experience the Pulfrich phenomenon [14]. Furthermore, a small percentage (approximately 4%) of mild anisometropic amblyopes who have rudimentary stereopsis experience a spontaneous Pulfrich phenomenon during normal viewing [15]. This is assumed to be due to a delay in the processing of the information coming from the amblyopic eye because of an increased retinocortical transmission time from their amblyopic eye, or because of prolonged neural integration at retinal or cortical sites [16–20]. This delay is observed in the pupillary response to contrast gratings of the amblyopic eye [21,22]. Therefore, it could also be a consequence of the lower contrast gain in the amblyopic eye [23], because a contrast difference between the two eyes also induces

Vision 2019, 3, 54; doi:10.3390/vision3040054 www.mdpi.com/journal/vision Vision 2019, 3, 54 2 of 17 a Pulfrich phenomenon that is assumed to be the result of a contrast-dependent neural delay [24]. The spontaneous Pulfrich phenomenon seen by some amblyopes could be due to either a lowpass temporal deficit or the reduced contrast sensitivity of the amblyopic eye. Indeed, McKee et al. [25] observed a delay correlated with interocular contrast sensitivity difference in amblyopia. The purpose of our study was to assess and characterize this delay. Is it fixed or variable? On what does it depend? To assess and measure the interocular delay (IOD), we used a paradigm where a cylinder rotating in depth is defined by moving Gabor patches of different interocular phases, generating strong to ambiguous depth percepts [24,26,27]. This paradigm allows one to manipulate independently the spatio-temporal properties of the patches to determine their influence on perceived motion-in-depth. Firstly,we assessed the spontaneous Pulfrich phenomenon in amblyopia, and particularly its intersubject variability. Secondly, we manipulated the statistical visual properties of the stimulus to determine if parameters such as density, spatial frequency, and temporal frequency of the stimulus influenced the perceived phenomenon.

2. Methods

2.1. Participants Eight mild amblyopic subjects (two anisometropes, two strabismic, four mixed amblyopes; four males, mean age 35.6 12.4 years) with residual stereoscopic vision participated in this experiment. ± Subject details are reported in Table1. Among the amblyopic subjects we screened, these patients were the only ones able to perform the task. They approximately represent one-third of the amblyopic subjects screened. This research was approved by the Ethics Review Board of the McGill University Health Center (protocol code 1996-1806) and was performed in accordance with the ethical standards laid down in the Code of Ethics of the World Medical Association (Declaration of Helsinki). Written informed consent was obtained from all subjects.

2.2. Apparatus The equipment used was the same as in Reynaud and Hess, 2017 [24]. Stimuli and experimental procedures were programmed with Matlab R2015a (© the MathWorks, Natick, MA, USA) using the Psychophysics toolbox (version: 3.0.12—flavor: beta) [28–30] running on a Linux Mint operating system, on an Apple MacPro computer with an Nvidia GeForce 8800 GT graphics card. Dichoptic presentation was achieved using a polarized passive wide 23-inch three-dimensional (3D)-Ready light-emitting diode (LED) monitor ViewSonic V3D231 in interleaved line stereo mode, so that the two images to the two eyes were presented at the same time but on different scanlines at a refresh rate of 60 Hz. The monitor was gamma-corrected with a mean luminance of 100 cd m 2 and a resolution of 1920 1080 px, placed · − × at a viewing distance of 90 cm, in a dim-lit room. Subjects wore passive polarized ViewSonic 3D glasses that generated a luminance reduction of approximately 60% and a crosstalk of 1% [31]. Vision 2019, 3, 54 3 of 17

Table 1. Clinical details of amblyopic subjects. VA: visual acuity, strab.: strabismus, aniso.: anisometropia, NAE: non-amblyopic eye, AE: amblyopic eye, exo: exotropia, eso: esotropia, IOD: interocular delay. Suppression was measured with the Bagolini striated glasses test. Estimated interocular delay IOD is reported in the last column.

Randot Subject Age/Sex Refraction VA Squint Suppression Patching Surgery Type IOD (ms) (Arcsec)

A1 40/F NAE (OS) plano 20/16 R eso 5◦ weak 60 no no strab. 4.28 AE (OD) plano 20/25 A2 33/F NAE (OS) plano 20/12.5 weak central 100 no no aniso. 4.41 − AE (OD) +2.50 20/16 A3 21/M NAE (OD) 2.75 20/10 L exo 5 no 400 For 5 years no mixed 1.53 − ◦ AE (OS) +1.75/ 1.00 30 20/32 around 11yo − × ◦ A4 25/F NAE (OD) 1.50 20/12.5 no 100 no no aniso. 3.69 − AE (OS) +1.50 20/63 A5 53/M NAE (OD) 1.25/ 0.50 30 20/20 L exo 6 no NA no no mixed 15.62 − − × ◦ ◦ AE (OS) +2.50/ 1.50 75 20/50 − × ◦ A6 27/M NAE (OD) +1.50/ 0.75 163 20/12.5 L eso 5 flickering 60 1 year no mixed 1.97 − × ◦ ◦ AE (OS) +3.50/ 0.75 65 20/20 around 5yo − × ◦ A7 54/F NAE (OD) plano 20/20 L eso 9 weak 100 no strabism surgery strab. 2.97 ◦ − AE (OS) plano 20/32 6 months ago A8 32/M NAE (OD) 1 20/10 L eso 10 weak 400 no no mixed 94.93 − ◦ − AE (OS) +1.5 20/50 Vision 2019, 3, 54 4 of 17

2.3. Stimuli

The stimulus was a structure-from-motion defined rotating cylinder of 18◦ width and 12◦ height, consisting of Gabor patches oscillating horizontally with a sinusoidal speed (Figure1a, supplementary movies). The stimulus was presented dichoptically for 800 ms. In order to generate percepts of the cylinder rotating in depth, Gabor patches were displaced between the two eyes as a function of the interocular phase difference in their oscillation. This interocular phase difference was consistent between all Gabor patch trajectories and was varied from trial to trial to generate strong to ambiguous percepts (Figure1b) [ 24,26,27]. Gabor patch initial positions were randomized in each trial. In the base condition, we used 200 Gabor patches at 80% contrast, each of size 0.15◦ sigma, 2.85 c/d spatial frequency, and 1.36 octave bandwidth with random phase, with a sinusoidal angular speed (degrees of Vision 2019, 3, x FOR PEER REVIEW 5 of 20 phase) of 18◦/s.

Figure 1. Stimuli. (a) Red/green anaglyph representation of the stimulus. It is composed of 200 Gabor patchesFigure 1. oscillating Stimuli. ( horizontallya) Red/greenand anaglyph presented representation dichoptically. of th (be) stimulus. The phase It di isff composederence in the of oscillation200 Gabor ofpatches the Gabor oscillating patches horizontally between the and two presented eyes generates dichoptically. a percept (b) ofThe a motion-definedphase difference cylinder in the oscillation rotating inof depth.the Gabor If the patches phase between difference the is two negative, eyes generate the cylinders a percept is seen of rotating a motion-defined anticlockwise. cylinder If the rotating phase diinff depth.erence If is the 0◦, thephase percept difference is ambiguous is negative, with the Gabor cylinder patches is seen moving rotating to the anticlockwise. left and to the If right the phase in the samedifference plane. is If0°, it isthe positive, percept the is cylinderambiguous is seen with rotating Gabor clockwise.patches moving Figure to adapted the left from and Referenceto the right [24 in]. 2.4. Proceduresthe same plane. If it is positive, the cylinder is seen rotating clockwise. Figure adapted from Reference [24]. The subjects’ task was to report within a block design paradigm whether they saw the cylinder rotating2.5. Data clockwiseAnalysis or anticlockwise as a function of the interocular phase. Phase was picked with a constant stimuli procedure within [ 1.5, 0.75, 0.375, 0.1875, 0.0938, 0.0469, 0.0234, 0 0.0234, The data were analyzed with− Matlab− R2017b− (©− the MathWorks).− − Figure− 2 depicts the 0.0469, 0.0938, 0.1875, 0.375, 0.75, 1.5]◦ with 10 repetitions in each block. One condition was tested per block.psychometric Each block functions was repeated of the three subjects times reportin in a counterbalancedg a clockwise way. perception as a function of the interocular phase difference. The psychometric functions were fitted with a logistic function 2.5.forced Data between Analysis 0 and 1 (nonlinear least-squares regression, Matlab’s nlinfit function). The estimatedThe data midpoint were analyzed of the with logistic Matlab function R2017b defi (© thenes MathWorks). the point of Figure subjective2 depicts equality the psychometric (PSE), the functionspoint at ofwhich the subjects ambiguous reporting motion a clockwise in plane perception is perceived as a function with of thea report interocular proportion phase diff erence.of 0.5 Theclockwise psychometric and 0.5 functions anticlockwise. were fitted This with PSE a logisticwas then function rectified forced to allow between comparisons 0 and 1 (nonlinear of the effects regardless of which eye was amblyopic of each subject. The rectified point of subjective equality (rPSE) was computed as the actual PSE for subjects whose amblyopic eye was their left eye and its opposite for subjects whose amblyopic eye was their right eye (A1 and A2, see Table 1). Hence, a negative rPSE would mean that the non-amblyopic eye (NAE) was advanced and a positive one would mean that the NAE was delayed. Given the known rotation speed of the cylinder, the rPSE could be converted into interocular delay (IOD) between the amblyopic eye and the non-amblyopic eye (Equation (1)). The interocular delays for the base condition are reported for all amblyopic subjects in Table 1. IOD = rPSE/ω, (1) where ω is the angular speed of the stimulus.

Vision 2019, 3, 54 5 of 17 least-squares regression, Matlab’s nlinfit function). The estimated midpoint of the logistic function defines the point of subjective equality (PSE), the point at which ambiguous motion in plane is perceived with a report proportion of 0.5 clockwise and 0.5 anticlockwise. This PSE was then rectified to allow comparisons of the effects regardless of which eye was amblyopic of each subject. The rectified point of subjective equality (rPSE) was computed as the actual PSE for subjects whose amblyopic eye was their left eye and its opposite for subjects whose amblyopic eye was their right eye (A1 and A2, see Table1). Hence, a negative rPSE would mean that the non-amblyopic eye (NAE) was advanced and a positive one would mean that the NAE was delayed. Given the known rotation speed of the cylinder, the rPSE could be converted into interocular delay (IOD) between the amblyopic eye and the non-amblyopic eye (Equation (1)). The interocular delays for the base condition are reported for all amblyopic subjects in Table1. IOD = rPSE/ω, (1) whereVision 2019ω,is 3, thex FOR angular PEER REVIEW speed of the stimulus. 6 of 20

Figure 2. (a) Psychometric functions of of th thee perceived direction as a func functiontion of the interocular phase differencedifference for all eight amblyopicamblyopic subjects. The midpoi midpointnt of the logistic function at 0.5 performance definesdefines thethe pointpoint ofof subjective subjective equality equality (PSE). (PSE). (b ()b Psychometric) Psychometric functions functions of theof the perceived perceived direction direction as a asfunction a function of the of interocularthe interocular phase ph diasefference difference for the for controlthe control subjects subjects from from our previousour previous article article [24]. [24]. 3. Results 3. Results 3.1. Characterizing the Spontaneous Pulfrich Phenomenon 3.1. Characterizing the Spontaneous Pulfrich Phenomenon We firstly characterized the spontaneous Pulfrich phenomenon that mild amblyopes experience. We analyzedWe firstly the psychometriccharacterized functions the spontaneous of amblyopic Pu subjectslfrich phenomenon reporting a clockwise that mild perception amblyopes of the experience.direction of motion We analyzed of the cylinder the psychometric as a function of thefunctions interocular of phaseamblyopic difference subjects (Figure reporting2a). We can a clockwisesee here that, perception for some amblyopic of the direction subjects, thisof mo psychometriction of the function cylinder is o ffasset a from function 0◦. This of o fftheset interocularcorresponds phase to the difference interocular (Figure delay (IOD) 2a). forWeeach can see participant here that, reported for some in Table amblyopic1 (see Section subjects,2). Allthis of psychometric these delays werefunction significant is offset (for from each 0°. participant, This offset the corresponds PSE was diff erentto the from interocular 0; t-test ondelay the (IOD)bootstrapped for each estimates participant of the reported PSE, α = 0.05).in Table Surprisingly, 1 (see Section these delays2). All did of notthese always delays affect were the non-amblyopic eye (negative values). The amblyopic eye exhibited a negative delay in only three out significant (for each participant, the PSE was different from 0; t-test on the bootstrapped of our eight participants (Table1). Because the delays could a ffect either the non-amblyopic eye or the estimates of the PSE, α = 0.05). Surprisingly, these delays did not always affect the non- amblyopic eye of amblyopes, the average delay for the whole amblyopic group between the amblyopic amblyopicand non-amblyopic eye (negative eye was values). not significantly The amblyopic different eye from exhibited zero (two-sided a negative Wilcoxon delay in signed only three rank out of our eight participants (Table 1). Because the delays could affect either the non- amblyopic eye or the amblyopic eye of amblyopes, the average delay for the whole amblyopic group between the amblyopic and non-amblyopic eye was not significantly different from zero (two-sided Wilcoxon signed rank test, W = 19, p = 0.95). However, when comparing the psychometric functions of the amblyopes to the control group from our previous study (Figure 2b [24]), the PSE of the amblyopic group was much more variable compared to that of the controls. Indeed, the absolute value of the interocular delay |IOD| in the amblyopic group, 16.17 ± 32.13 ms (|PSE| = 0.29 ± 0.58), was significantly longer than in the control group, 1.54 ± 0.68 ms (|PSE| = 0.03 ± 0.01) (one-sided Wilcoxon rank sum test, U = 109, p = 0.001), even excluding the outlier amblyopic subject A8. In order to assess if the variability observed in the amblyopic group may be explained by an internal variability within each subject or if it reveals a consistent delay for each amblyopic subject that varies across the group of subjects, we compared three repeated measurements for each subject on different days in the base condition. The three measured psychometric functions, representing the perceived direction of rotation as a function of the

Vision 2019, 3, 54 6 of 17 test, W = 19, p = 0.95). However, when comparing the psychometric functions of the amblyopes to the control group from our previous study (Figure2b [ 24]), the PSE of the amblyopic group was much more variable compared to that of the controls. Indeed, the absolute value of the interocular delay |IOD| in the amblyopic group, 16.17 32.13 ms (|PSE| = 0.29 0.58), was significantly longer than in ± ± the control group, 1.54 0.68 ms (|PSE| = 0.03 0.01) (one-sided Wilcoxon rank sum test, U = 109, ± ± p = 0.001), even excluding the outlier amblyopic subject A8. In order to assess if the variability observed in the amblyopic group may be explained by an internal variability within each subject or if it reveals a consistent delay for each amblyopic subject that varies across the group of subjects, we compared three repeated measurements for each subject on different days in the base condition. The three measured psychometric functions, representing the perceived direction of rotation as a function of the interocular phase difference, are reported in Figure3. It appears that the psychometric functions are quite similar from day to day, except for subject A8. To quantify the repeatability of this measure, we computed the intraclass correlation coefficient of the estimated PSE for the three repetitions for all subjects. It revealed a good correlation (r = 0.68) between the three repetitions, indicating that the IOD was consistent across sessions and, therefore, the variation that we observed previously was between, not within, amblyopes. Initially, we wondered if this delay could be the consequence of the loss of sensitivity in the amblyopic eye. Indeed, a contrast reduction in one eye can retard the processing of the information coming from that eye at the neurophysiological [32–34] and behavioral levels [35,36]. In particular, we previously showed in observers with typical vision that such a contrast difference could induce an illusion of depth (i.e., the Pulfrich phenomenon) and shift the psychometric function measured with an identical stimulus [24]. Therefore, in order to test if the delay observed with the amblyopic subjects was associated with the lower contrast gain in their amblyopic eye, we report in Figure4a the correlation between the observed interocular delay and their interocular contrast sensitivity ratio at the same Gabor spatial frequency used in the stimulus (see AppendixA). This correlation was significant (coefficient of determination R2 = 0.56, p = 0.03); however, it was mainly driven by the data of subject A8. Excluding him resulted in a coefficient of determination R2 = 0.27, p = 0.23 (Figure4b). Given that, in this regression, most subjects (five out of eight) presented a positive value of the interocular delay (i.e., a delay in the non-amblyopic eye), we conclude that this correlation, while significant, may not be meaningful.

3.2. Influence of the Stimulus Parameters Any measured delay could be fixed, for example, due to slower optic nerve transmission; thus, it would not depend on stimulus parameters. Alternatively, the delay could be the result of a longer neural integration in the processing of visual information, in which case it would likely show a stimulus dependence [23]. To determine the type of delay, we manipulated the density, the spatial frequency, and the speed of the Gabor patches seen by the two eyes. An example is given in Figure5a, where the psychometric functions of the perceived direction of rotation as a function of the interocular phase difference are displayed for one amblyopic subject. Results are shown for different numbers of Gabor patches defining the stimulus (100, 200, or 400). In this figure, it seems that the psychometric function shifted to the left and the PSE approached 0◦ when the number of Gabor patches was increased. The rPSE as a function of the number of Gabor patches defining the cylinder stimulus is then presented in Figure5b for the eight amblyopic subjects. For most subjects, the rPSE approached 0◦ when more Gabor patches were presented. The data were fitted by linear regressions with slopes significantly converging, i.e., slopes were positive when the initial rPSE for 100 Gabor patches was negative, and they were negative when the initial rPSE was positive (one-sided Wilcoxon signed rank test, W = 1, p = 0.008). However, only two of these slopes were significant (see Table S1, Supplementary Materials). It should be noted that the rPSE values of subject A8 were scaled (divided) by a factor of 10 to be represented with other data. The slopes of the psychometric functions as a function of the number of Gabor patches are reported in Figure5c. Vision 2019, 3, x FOR PEER REVIEW 7 of 20 interocular phase difference, are reported in Figure 3. It appears that the psychometric functions are quite similar from day to day, except for subject A8. To quantify the repeatability of this measure, we computed the intraclass correlation coefficient of the Vision 2019, 3, 54 7 of 17 estimated PSE for the three repetitions for all subjects. It revealed a good correlation (r = 0.68) between the three repetitions, indicating that the IOD was consistent across sessions Theyand, didtherefore, not show the any consistentvariation pattern,that we indicating observed that thepreviously density of was the stimulus between, had nonot consistent within, eamblyopes.ffect on the quality of the performance in the task.

Figure 3. Variability of the PSE. The three repetitions (10(10 blocks each, light to dark shades) of the psychometric functions of the perceivedperceived direction of rotation as a function of the interocular phase didifferencefference forfor all all amblyopic amblyopic subjects subjects (A1 (–A1A8–inA8 each in each panel). panel). Data pointsData points are fitted are by fitted a logistic by a function. logistic function.

Vision 2019, 3, x FOR PEER REVIEW 8 of 20

Initially, we wondered if this delay could be the consequence of the loss of sensitivity in the amblyopic eye. Indeed, a contrast reduction in one eye can retard the processing of the information coming from that eye at the neurophysiological [32–34] and behavioral levels [35,36]. In particular, we previously showed in observers with typical vision that such a contrast difference could induce an illusion of depth (i.e., the Pulfrich phenomenon) and shift the psychometric function measured with an identical stimulus [24]. Therefore, in order to test if the delay observed with the amblyopic subjects was associated with the lower contrast gain in their amblyopic eye, we report in Figure 4a the correlation between the observed interocular delay and their interocular contrast sensitivity ratio at the same Gabor spatial frequency used in the stimulus (see Appendix A). This correlation was significant (coefficient of determination R2 = 0.56, p = 0.03); however, it was mainly driven by the data of subject A8. Excluding him resulted in a coefficient of determination R2 = 0.27, p = 0.23 (Figure 4b). Given that, in this regression, most subjects (five out of eight) presented a positive value of the interocular delay (i.e., a delay in the non-amblyopic eye), we conclude that this correlation, while significant, may not be meaningful.

3.2. Influence of the Stimulus Parameters Any measured delay could be fixed, for example, due to slower optic nerve transmission; thus, it would not depend on stimulus parameters. Alternatively, the delay could be the result of a longer neural integration in the processing of visual information, in which case it would likely show a stimulus dependence [23]. To determine the type of delay, we manipulated the density, the spatial frequency, and the speed of the Gabor patches seen Vision 2019, 3, 54 8 of 17 by the two eyes.

Vision 2019, 3, x FOR PEER REVIEW 9 of 20

presented in Figure 5b for the eight amblyopic subjects. For most subjects, the rPSE approached 0° when more Gabor patches were presented. The data were fitted by linear regressions with slopes significantly converging, i.e., slopes were positive when the initial rPSE for 100 Gabor patches was negative, and they were negative when the initial rPSE was positive (one-sided Wilcoxon signed rank test, W = 1, p = 0.008). However, only two of these Figure 4. slopesFigure were 4.Correlation Correlationsignificant between between (see Table the the observedobserved S1, Supplementa interocularinterocular delay ry Materials). and and the the interocular interocular It should contrast contrast be noted sensitivity sensitivity that the rPSEratio.ratio. values (a )(a Interocular) Interocular of subject delay delay A8 aswere as a a function function scaled ofof (divided) thethe interocular by a contrast contrastfactor of sensitivity sensitivity 10 to be ratio represented ratio at at the the same same with spatial spatial other 2 data.frequencyfrequency The slopes of of the the of Gabor Gabor the psychome patches patches used usedtric inin thefunctionsthe stimul stimulusus as for for a all function all subjects. subjects. ofCoefficient Coetheffi numbercient of determination of determinationof Gabor patchesR2 =R = 0.5641,0.5641, p == 0.0317. ( (bb) )Inset Inset of of the the dotted dotted frame frame area area of of (a (a) )excluding excluding subject subject A8. A8. Coefficient Coefficient of of are reported in 2Figure 5c. They did not show any consistent pattern, indicating that the determination R =2 0.2677, p = 0.2343. densitydetermination of the stimulus R = 0.2677, had p no= 0.2343. consistent effect on the quality of the performance in the task. An example is given in Figure 5a, where the psychometric functions of the perceived direction of rotation as a function of the interocular phase difference are displayed for one amblyopic subject. Results are shown for different numbers of Gabor patches defining the stimulus (100, 200, or 400). In this figure, it seems that the psychometric function shifted to the left and the PSE approached 0° when the number of Gabor patches was increased. The rPSE as a function of the number of Gabor patches defining the cylinder stimulus is then

FigureFigure 5. 5.E ffEffectect of of density. density. ( a()a) Psychometric Psychometric functionsfunctions of of the the perc perceivedeived direction direction of of rotation rotation for for one one representativerepresentative amblyopic amblyopic subject subject (A3) (A3) as aas function a functi ofon the of interocular the interocular phase phase difference difference for three for dithreefferent numbersdifferent of numbers Gabor patches of Gabor composing patches composing the stimulus: the stimulus: 100 (light-gray 100 (light-gray symbols), symbols), 200 (mid-gray 200 (mid-gray symbols), andsymbols), 400 (dark-gray and 400 symbols). (dark-gray Data symbols). points Data are fittedpoints by are a fitted logistic by function. a logistic (function.b) Rectified (b) Rectified PSE (rPSE) PSE as a function(rPSE) ofas thea function number of of the Gabor number patches of Gabor for the patc eighthes amblyopicfor the eight subjects. amblyopic * rPSE subjects. values * rPSE for subject values A8 werefor dividedsubject A8 by were 10. (c )divided Slopes by of the10. psychometric(c) Slopes of the functions. psychometric Dashed functions. lines represent Dashed linearlines represent regression. Qualitylinear ofregression. fit and regression Quality of parameters fit and regression are reported parameters in Table are S1 report (Supplementaryed in Table S1 Materials, (Supplementary Sheet 1). Materials, Sheet 1). Secondly, in order to test the effect of the spatial frequency on the IOD, we manipulated the size of theSecondly, Gabor patchesin order whichto test definedthe effect the of stimulus. the spatial The frequency psychometric on the functions IOD, we ofmanipulated the perceived directionthe size of of rotation the Gabor as apatches function which of the defined interocular the stimulus. phase diff Theerence psychometric for one amblyopic functions subject of the are presentedperceived in Figuredirection6a. Resultsof rotation are shownas a function for four of di fftheerent interocular sizes of Gabor phase patches: difference 0.15, for 0.3, one 0.45, oramblyopic 0.6◦, which hadsubject spatial are frequenciespresented in of 2.85,Figure 1.43, 6a. 0.95, Results and 0.71are shown c/d, respectively. for four different For these sizes four sizes,of theGabor numbers patches: of Gabor 0.15, patches 0.3, 0.45, were or respectively 0.6°, which set had to 200, spatial 100, 66,frequencies and 50 in orderof 2.85, to minimize1.43, 0.95, overlap. and The0.71 psychometric c/d, respectively. function For shifted these tofour the sizes, left and the the numbers PSE approached of Gabor 0patches◦ when were the size respectively of the Gabor patchesset to was200, enlarged 100, 66, (scaled).and 50 in The order rPSE to asminimi a functionze overlap. of the sizeThe of psychometric the Gabor patches function is reported shifted in Figureto the6b forleft alland amblyopic the PSE subjects.approached For most0° when of them, the thesize rPSE of the approached Gabor patches 0 ◦ when was the enlarged size of the Gabor(scaled). patches The was rPSE increased, as a function i.e., when of the the spatialsize of frequencythe Gabor was patches decreased. is reported This was in Figure indicated 6b byfor the significantlyall amblyopic converging subjects. slopes For most of the of linear them, regressions the rPSE approached (one-sided Wilcoxon0° when the signed size rank of the test, GaborW = 4, p =patches0.03) although was increased, only three i.e., of thesewhen regressionthe spatial slopes frequency were significantwas decreased.(see Table This S1, wasSupplementary indicated Materials).by the significantly The slopes of converging the psychometric slopes functionsof the linear are reportedregression ins Figure (one-sided6c. The Wilcoxon slopes significantly signed increasedrank test, as aW function = 4, p = of0.03) the sizealthough of the only Gabor three patches, of these which re indicatedgression slopes that the were psychometric significant functions (see wereTable getting S1, steeperSupplementary (one-sided Materials). Wilcoxon signedThe slopes rank testof the on thepsychometric slopes of the functions linear regressions, are reportedW = 31, p = 0.04). This would indicate that participants’ performance got more reliable at low spatial frequency. in Figure 6c. The slopes significantly increased as a function of the size of the Gabor patches, which indicated that the psychometric functions were getting steeper (one-sided Wilcoxon signed rank test on the slopes of the linear regressions, W = 31, p = 0.04). This would indicate that participants’ performance got more reliable at low spatial frequency.

Vision 2019, 3, 54 9 of 17 Vision 2019, 3, x FOR PEER REVIEW 10 of 20

Figure 6. EffectEffect of spatial frequency. ( a) Psychometric functions of the perceived direction of rotation for one amblyopic amblyopic subject subject (A3) (A3) as as a afunction function of of the the interocular interocular phase phase difference difference for for different different sizes sizes of ofthe the Gabor Gabor patches patches composing composing the thestimulus: stimulus: 0.15°, 0.15 0.3°,◦, 0.30.45°,◦, 0.45 and◦ ,0.6° and (from 0.6◦ (fromlight gray light to gray dark to gray). dark gray).Data points Data are points fitted are by fitted a logistic by a function. logistic function. (b) rPSE as (b a) rPSEfunction as aof function the size of the Gabor size of patches the Gabor for patchesthe eight for amblyopic the eight amblyopicsubjects. * subjects.rPSE values * rPSE for values subject for A8 subject were A8divided were dividedby 10. ( byc) Slopes 10. (c) Slopesof the ofpsychometric the psychometric functions. functions. Dashed Dashed lines linesrepresent represent linear linear regression. regression. Quality Quality of offit fit and and regression parameters are reported inin TableTable S1S1 (Supplementary(Supplementary Materials,Materials, SheetSheet 2).2).

Finally, we we manipulated manipulated the rotationthe rotation speed speed of the cylinder of the cylinder stimulus. stimulus. In Figure7a, In the Figure psychometric 7a, the functions for one amblyopic subject are displayed for different angular speeds: 4.5, 9, 18, 36, and 72 /s. psychometric functions for one amblyopic subject are displayed for different angular◦ The psychometric function shifted to the right and the PSE approached 0◦ when the rotation speed of speeds: 4.5, 9, 18, 36, and 72°/s. The psychometric function shifted to the right and the PSE the Gabor patches was increased. The rPSE of all subjects as a function of the angular rotation speed approached 0° when the rotation speed of the Gabor patches was increased. The rPSE of all of the cylinder stimulus is presented in Figure7c. For most subjects, the rPSE approached 0 ◦ as the rotationsubjects speedas a function increased. of However,the angular the rotation convergence speed of of the the slopes cylinder was notstim significantulus is presented in this case in becauseFigure 7c. of the For outlier most data subjects, of subject the A7, rPSE which approa was probablyched 0° due as tothe fusion rotation issues speed at very increased. high speed (allHowever, of her other the convergence data were aligned, of the describing slopes was a positivenot significant slope). in This this result case was because diagnostic of the because, outlier atdata high of speed, subject if thereA7, which was a fixed was transmission probably due delay, to onefusion would issues expect at thatvery the high resultant speed displacement (all of her and,other hence, data were the equivalent aligned, phasedescribing would a increase, positive not slope). decrease This as result the data was suggest. diagnostic This because, observation at suggestshigh speed, that itif mightthere bewas more a fixed reasonable transmission to interpret delay, the change one would in rPSE expect in terms that ofa the longer resultant neural integrationdisplacement time and, than hence, delayed the transmission equivalent per phase se. Thewould slopes increase, of the psychometricnot decrease functions as the data as a function of angular speed of the stimulus are reported in Figure7c. The slopes which were initially suggest. This observation suggests that it might be more reasonable to interpret the change shallow did not change much. However, the slopes which were initially steep decreased when the in rPSE in terms of a longer neural integration time than delayed transmission per se. The speed of the stimulus was increased. This indicates that the task was getting harder and less reliable at slopesVision of 2019 the, 3 , psychometricx FOR PEER REVIEW functions as a function of angular speed of the stimulus11 of 20 are high speeds, which confirmed the irrelevance of the rPSE value of subject A7 at 72◦/s. reported in Figure 7c. The slopes which were initially shallow did not change much. However, the slopes which were initially steep decreased when the speed of the stimulus was increased. This indicates that the task was getting harder and less reliable at high speeds, which confirmed the irrelevance of the rPSE value of subject A7 at 72°/s.

FigureFigure 7. E ff7.ect Effect of speed.of speed. (a )(a Psychometric) Psychometric functionsfunctions of of the the perc perceivedeived direction direction of rotation of rotation for one for one amblyopicamblyopic subject subject (A3) (A3) as aas function a function of of the the interocular interocular phase phase difference difference for for different different rotation rotation angular angular speedsspeeds of the of the stimulus: stimulus: 4.5, 4.5, 9,9, 18,18, 36, 36, and and 72 72 °/s◦ (from/s (from light light gray grayto dark to gray). dark Data gray). points Data arepoints fitted are fittedby by a alogistic logistic function. function. (b) rPSE (b) as rPSE a function as a function of the angular of the sp angulareed for the speed eight foramblyopic the eight subjects. amblyopic * subjects.rPSE *values rPSE for values subject for A8 subject were divided A8 were by divided10. (c) Slopes by 10. of the (c) psychometric Slopes of the functions. psychometric Dashed functions. lines Dashedrepresent lines representlinear regression. linearregression. Quality of fit Quality and re ofgression fit and parameters regression are parameters reported in are Table reported S1 in Table(Supplementary S1 (Supplementary Materials, Materials, Sheet 3). Sheet 3).

4. Discussion We confirm the observation made by Tredici and von Noorden [15] on three of their 70

patients that a spontaneous Pulfrich phenomenon exists in amblyopia. We developed a more sensitive method where we accurately measured the point of subjective equality as a function of stimulus disparity. Using this approach, we showed that the spontaneous Pulfrich phenomenon in amblyopia occurs in a significant percentage of patients and it depends on various stimulus parameters. Most notably, the observed dependence of the IOD on rotation velocity makes it more likely that the delay reflects changes in temporal integration within neurons rather than changes in transmission time between neurons. Also, the integration time within the amblyopic network was not always longer; sometimes, it was shorter, compared with that of the non-amblyopic eye stimulation. This resulted in a large variability in the basis for the spontaneous Pulfrich phenomenon between different amblyopic subjects. Barbur et al. [21] also observed that, at low spatial frequency, the pupillary response to contrast gratings could be slightly faster in the amblyopic eye of anisometropes compared to their non-amblyopic eye. Nevertheless, our observation that in some cases the processing associated with the amblyopic eye could be faster than that associated with the non- amblyopic eye seems inconsistent with previous psychophysical studies on reaction times [16,23,37] and magnetoencephalography [38]. We speculate that this difference comes from the fact that these studies tested strong amblyopes, whereas we tested only mild amblyopes who exhibited a degree of stereopsis (mean acuity differences between the two eyes were respectively 0.8, 1.0, and 0.7 logMAR for Levi et al. (1979) [23], Loshin and Levi (1983) [37], and Chadnova et al. (2017) [38], compared to 0.38 logMAR in our cohort; data were unavailable in Hamasaki and Flynn (1981) [16]). Indeed, in a previous study using more severe amblyopes, we measured neural delays using frequency-tagged magnetoencephalography (MEG) [38]. In these more severe amblyopes, all the delays we measured involved the amblyopic eye function. For comparison, we combined the data from these two studies (the present one using psychophysics with mild amblyopes and the previous one using MEG with more severe amblyopes) to see if there was a correlation between the interocular delay (IOD) and the

Vision 2019, 3, 54 10 of 17

4. Discussion We confirm the observation made by Tredici and von Noorden [15] on three of their 70 patients that a spontaneous Pulfrich phenomenon exists in amblyopia. We developed a more sensitive method where we accurately measured the point of subjective equality as a function of stimulus disparity. Using this approach, we showed that the spontaneous Pulfrich phenomenon in amblyopia occurs in a significant percentage of patients and it depends on various stimulus parameters. Most notably, the observed dependence of the IOD on rotation velocity makes it more likely that the delay reflects changes in temporal integration within neurons rather than changes in transmission time between neurons. Also, the integration time within the amblyopic network was not always longer; sometimes, it was shorter, compared with that of the non-amblyopic eye stimulation. This resulted in a large variability in the basis for the spontaneous Pulfrich phenomenon between different amblyopic subjects. Barbur et al. [21] also observed that, at low spatial frequency, the pupillary response to contrast gratings could be slightly faster in the amblyopic eye of anisometropes compared to their non-amblyopic eye. Nevertheless, our observation that in some cases the processing associated with the amblyopic eye could be faster than that associated with the non-amblyopic eye seems inconsistent with previous psychophysical studies on reaction times [16,23,37] and magnetoencephalography [38]. We speculate that this difference comes from the fact that these studies tested strong amblyopes, whereas we tested only mild amblyopes who exhibited a degree of stereopsis (mean acuity differences between the two eyes were respectively 0.8, 1.0, and 0.7 logMAR for Levi et al. (1979) [23], Loshin and Levi (1983) [37], and Chadnova et al. (2017) [38], compared to 0.38 logMAR in our cohort; data were unavailable in Hamasaki and Flynn (1981) [16]). Indeed, in a previous study using more severe amblyopes, we measured neural delays using frequency-tagged magnetoencephalography (MEG) [38]. In these more severe amblyopes, all the delays we measured involved the amblyopic eye function. For comparison, we combined the data from these two studies (the present one using psychophysics with mild amblyopes and the previous one using MEG with more severe amblyopes) to see if there was a correlation between the interocular delay (IOD) and the interocular visual acuity (VA) difference in the amblyopic population. The delay observed in the amblyopic eye is reported as a function of the difference in VA between the NAE and the AE for mild (this study) and strong (data from Reference [38]) amblyopes in Figure8. It is, however, important to note that the IOD was assessed with two very different methodologies in the two studies. There seemed to be a trend of longer delays associated with larger interocular VA differences, although, for this sample size, this correlation was not significant (coefficient of determination R2 = 0.17, p = 0.14). This correlation slightly improved excluding subject A8 (R2 = 0.22, p = 0.11). A conclusion that there is a processing delay correlated with the degree of amblyopic deficit would receive some support from studies of reaction time differences to visual stimuli for amblyopic versus non-amblyopic eyes [16,23]. Our starting hypothesis was that, since we already demonstrated a contrast-dependent Pulfrich phenomenon in normals [24] (we replicated these results in amblyopes in AppendixB), any spontaneous Pulfrich phenomenon in amblyopes could be due to the known interocular difference in contrast sensitivity in amblyopia [39,40]. The finding that the polarity of the rPSE can differ between amblyopes rules this out as a general explanation. The same is true for any explanation that involves interocular suppression. The fact that there is only small intra-subject variability (i.e., the variability is between subjects not within subjects) rules out any explanation based on an instability in interocular timing. An alternative hypothesis could come from recent finding that blur induces a “reverse” Pulfrich phenomenon [41]. Indeed, in their paper, Burge et al. showed that removing the high spatial frequencies in one eye by optically blurring the image sped up the processing of that eye, resulting in the perception of a Pulfrich phenomenon in the direction of the blurred eye. In that case, the blur experienced by amblyopes in their amblyopic eye [42,43] could speed up the processing of the amblyopic eye and, thus, induce such reverse Pulfrich phenomena. Vision 2019, 3, x FOR PEER REVIEW 12 of 20 interocular visual acuity (VA) difference in the amblyopic population. The delay observed in the amblyopic eye is reported as a function of the difference in VA between the NAE and the AE for mild (this study) and strong (data from Reference [38]) amblyopes in Figure 8. It is, however, important to note that the IOD was assessed with two very different methodologies in the two studies. There seemed to be a trend of longer delays associated with larger interocular VA differences, although, for this sample size, this correlation was not significant (coefficient of determination R2 = 0.17, p = 0.14). This correlation slightly improved excluding subject A8 (R2 = 0.22, p = 0.11). A conclusion that there is a processing delay correlated with the degree of amblyopic deficit would receive some support from studies of reaction time differences to visual stimuli for amblyopic versus non-amblyopic Vision 2019, 3, 54 11 of 17 eyes [16,23].

Figure 8. Correlation between interocular delay and intero interocularcular visual acuity (VA) didifferencefference in the amblyopic population.population. The The delay delay observed observed in thein amblyopicthe amblyopic eye is eye plotted is plotted as a function as a offunction the diff erenceof the indifference VA between in VA the between non-amblyopic the non-amblyopic eye (NAE) and eye the (N amblyopicAE) and the eye amblyopic (AE) for mild eye (filled(AE) for color mild symbols) (filled andcolor strong symbols) (open and black strong symbols) (open amblyopes. black symbols) Data foramblyopes. strong amblyopes Data for werestrong taken amblyopes from Reference were taken [38]. 2 Thefrom dashed Reference line represents[38]. The lineardashed regression line represents across the linear full population regression (coe acrossfficient the of determinationfull populationR 2 =(coefficient0.17, p = 0.14; of determination excluding subject R2 = 0.17, A8: Rp == 0.14;0.22, excludingp = 0.11). subject A8: R2 = 0.22, p = 0.11). Hence, one possible explanation could be that the interocular timing difference could be governed Our starting hypothesis was that, since we already demonstrated a contrast-dependent by two components for the processing associated with the amblyopic eye: (i) a delay correlated with Pulfrich phenomenon in normals [24] (we replicated these results in amblyopes in Appendix the strength of amblyopia, up to 156 ms [16], supported by the mild correlation we observe (Figure8), andB), (ii)any a modestspontaneous acceleration, Pulfrich in the phenomenon range of 4ms, due in toamblyopes blur [41]. For could mild amblyopes,be due to the the blur-based known accelerationinterocular mightdifference dominate, in contrast whereas, sensitivity for more severe in amblyopia amblyopes, [39,40]. the dominant The finding factor might that bethe a neuralpolarity processing of the rPSE delay can associated differ between with the amblyopicamblyopes eye. rules this out as a general explanation. The Thesame observation is true for that any all explanation but one subject that had invo a negativelves interocular rPSE at low suppression. speed (4.5◦/ s),The while fact some that ofthere them is only switched small their intra-subject polarity at variability high speeds (i.e., (Figure the 7variability), could also is findbetween an explanation subjects not with within this blur-basedsubjects) rules acceleration out any suggestion. explanation Indeed, based an objecton an moving instability quickly in might interocular appear moretiming. blurred An thanalternative an object hypothesis moving slowly, could thus come generating from recent a faster finding acceleration. that blur It couldinduce alsos a explain“reverse” the Pulfrich decrease inphenomenon the slope of the[41]. psychometric Indeed, in their function paper, at highBurge speeds, et al. whichshowed in that caseremoving could indicatethe high a spatial sort of position uncertainty. frequencies in one eye by optically blurring the image sped up the processing of that eye, One could argue that the fact that we changed the number of elements as we changed their resulting in the perception of a Pulfrich phenomenon in the direction of the blurred eye. In size between the different spatial frequency conditions could have influenced the effect we observed. We cannot completely rule out this hypothesis. However, the density of the elements had only a mild effect on the PSE (mean absolute difference 0.07◦ between the minimum (100) and maximum (400) number of elements), whereas the spatial frequency had a much larger effect of 0.25◦ between the most extreme conditions with a similar ratio of 4:1 elements. Furthermore, such an effect of spatial frequency was not observed in a control population (see AppendixC). Moreover, while an increase in the number of elements reduced the absolute |rPSE|, The increase in the size of the elements, which also produced a reduction of the |rPSE|, was accompanied by a decrease in the number of elements. Therefore, the putative influence of the number of elements would have opposed the |rPSE| decrease observed in this condition, suggesting that the effect of spatial frequency might indeed be even bigger. On the other hand, the area covered by the Gabor patches increased with their size despite Vision 2019, 3, 54 12 of 17

the decreasing number of elements. Hence, the absolute reduction in rPSE observed could be driven by spatial summation mechanisms. This effect of spatial frequency could be supported by the fact that, in amblyopia, the two eyes are more balanced at low spatial frequency [44–47]. The absolute |rPSE| might be reduced regardless of its initial polarity because the amblyopic delay might be reduced due to the eyes being more balanced, and the blur effect [41] might also be decreased due to blurring having less of an effect on low-spatial-frequency images. It seems to us, on the basis of the stimulus dependence of the effect, that the spontaneous Pulfrich phenomenon experienced by a subgroup of amblyopes (those with mild amblyopia and some residual stereopsis) is likely caused by an alteration in temporal summation associated with the processing of information by the amblyopic visual system rather than a simple transmission delay [17–20]. This processing could involve two conflicting components: an “amblyopic delay” [16,23,38] and a “blur-based acceleration” [41]. In the aim of developing treatment procedures, if we want conditions under which the amblyopic eye is not put at a competitive disadvantage to that of the non-amblyopic Vision 2019, 3, x FOR PEER REVIEW 14 of 20 eye (i.e., conditions that optimally favor binocular vision), then dynamic visual stimuli should be chosenSupplementary to minimize Materials: not only The the following interocular are available contrast online sensitivity at www.mdpi.com/xxx/s1: difference but also Supplementary the interocular Videos delay diff1,erence. 2, and 3 Stimulishow not-to-scale of low spatial anaglyph and examples high temporal of the stimulus frequency presented achieve with bothan interocular objectives. phase difference making the stimulus rotation ambiguous (Supplementary Video 1), clockwise (Supplementary Video 2), or Supplementarycounterclockwise Materials: (SupplementaryThe following Video 3). are These available videos online can be at viewed http:// www.mdpi.comwith standard red/green/2411-5150 anaglyph/3/4/54/ s1: Supplementaryglasses, with Videosthe red 1,filter 2, andover 3 the show left not-to-scale eye. Supplementary anaglyph Table examples S1 presents of the stimulusfit quality presented and regression with an interocular phase difference making the2 stimulus rotation ambiguous (Supplementary Video 1), clockwise (Supplementaryparameters in all Video tested 2), conditions. or counterclockwise R : coefficient (Supplementary of determination; Video MSE: 3). mean These squared videos error; can be a: viewedregression with standardslope; pf: red p/-valuegreen of anaglyph the F-statistic; glasses, pt: withp-value the of red the filter two-tailed over thet-statistic. left eye. Supplementary Table S1 presents fit quality and regression parameters in all tested conditions. R2: coefficient of determination; MSE: mean squared error;Author a: regression Contributions: slope; pf:A.R.p -valueand R.F.H of the designed F-statistic; the pt:researchp-value and of wrote the two-tailed the manuscript.t-statistic. A.R. performed the experiments and analyzed the data. Author Contributions: A.R. and R.F.H. designed the research and wrote the manuscript. A.R. performed the experimentsFunding: This and research analyzed was the funded data. by the Canadian Institutes of Health Research grand number 228103 and the ERA-NET NEURON grant number JTC 2015 to RFH. Funding: This research was funded by the Canadian Institutes of Health Research grand number 228103 and the ERA-NETConflicts NEURON of Interest grant:The numberauthors declare JTC 2015 no to conflict RFH. of interest.: Conflicts of Interest: The authors declare no conflict of interest. Appendix A. Contrast Sensitivity of Amblyopic Subjects Appendix A Contrast Sensitivity of Amblyopic Subjects The contrast sensitivities of the amblyopic eye (AE) and the non-amblyopic eye (NAE) of Theall amblyopic contrast sensitivities subjects as of a the function amblyopic of the eye spatial (AE) and frequency the non-amblyopic are presented eye in (NAE) Figures of all amblyopicA1a,b. They subjects were as measured a function with of the the spatial quick frequencycontrast sensitivity are presented function in Figure (qCSF) A1 [48]a,b. with They the were measuredsame apparatus with the quickand procedure contrast sensitivity as used in function Reference (qCSF) [44]. [48 Then,] with the the ratio same between apparatus the and proceduremonocular as used sensitivity in Reference AE/NAE [44]. Then,was calculated; the ratio between it is plotted the monocular as a function sensitivity of the AE /NAEspatial was calculated;frequency it isin plotted Figure asA1c. a function of the spatial frequency in Figure A1c.

FigureFigure A1. A1.Contrast Contrast sensitivity sensitivity of of (a ()a the) the amblyopic amblyopic eye eye (AE) (AE) and and ( b(b)) the the non-amblyopic non-amblyopic eyeeye (NAE)(NAE) of allof amblyopic all amblyopic subjects subjects as a function as a func oftion the spatialof the frequency.spatial frequency. (c) Ratio (c between) Ratio between the monocular the monocular sensitivity AEsensitivity/NAE as a AE/NAE function as of a the function spatial of frequency. the spatial frequency.

Appendix B. Contrast-Dependent Pulfrich Phenomenon in Amblyopia The interocular delay can be manipulated by reducing the luminance or contrast seen by one eye in normal observers [24,49]. Thus, we then wanted to test if the delay observed in the amblyopic group could be compensated for by reducing the luminance or contrast in the non-amblyopic eye. An example is given in Figure A2a. The psychometric functions of one amblyopic subject who reported a clockwise perception as a function of the interocular delay for five luminance conditions are displayed, where an ND filter was placed in front of the non-amblyopic eye: no-filter, 0.1ND, 0.3ND, 0.6ND, and 1ND. One can see that the psychometric function shifted to the right when the luminance was decreased over the non- amblyopic eye (NAE), meaning that the rotation was seen more anticlockwise. The estimated rPSE for changes in the interocular phase is then plotted as a function of the interocular luminance difference between the non-amblyopic and the amblyopic eyes in Figure A2b for all subjects. It should be noted that the rPSE values of subject A8 were scaled

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Appendix B Contrast-Dependent Pulfrich Phenomenon in Amblyopia The interocular delay can be manipulated by reducing the luminance or contrast seen by one eye in normal observers [24,49]. Thus, we then wanted to test if the delay observed in the amblyopic group could be compensated for by reducing the luminance or contrast in the non-amblyopic eye. An example is given in Figure A2a. The psychometric functions of one amblyopic subject who reported a clockwise perception as a function of the interocular delay for five luminance conditions are displayed, where an ND filter was placed in front of the non-amblyopic eye: no-filter, 0.1ND, 0.3ND, 0.6ND, and 1ND. One can see that the psychometric function shifted to the right when the luminance was decreased over the non-amblyopic eye (NAE), meaning that the rotation was seen more anticlockwise. The estimated rPSE for changes in the interocular phase is then plotted as a function of the interocular luminance difference between the non-amblyopic and the amblyopic eyes in Figure A2b for all subjects. It should be noted that the rPSE values of subject A8 were scaled (divided) by a factor of 10 to be represented with other data. When an ND filter was placed in front of the NAE, the rPSE increased for all subjects, meaning that the processing of the information coming from the NAE was retarded by the luminance reduction. The data were fitted by linear regressions in a fashion similar to Carkeet et al. [49]. The estimated slopes were significantly positive for all subjects (mean slope 0.42 0.20, one-sided Wilcoxon signed rank test, W = 36, p = 0.004). On average, the rPSE increased ± from 0.17 when there was no luminance difference to 0.30 at 1ND interocular luminance difference, − ◦ ◦ which falls in the same range as we previously observed in the normal population [24]. Thus, for participants whose rPSE was initially positive, meaning that their NAE was actually delayed compared to their AE, applying an ND filter in front of the NAE drove the rPSE away from 0◦ and aggravated the interocular delay (IOD). For subjects A2 and A7 whose rPSE was initially negative, meaning that their AE was delayed compared to their NAE, applying an ND filter in front of the NAE brought the rPSE close to 0◦ for small ND values, but at some point continued to increase it and drove it beyond 0◦ for high luminance reductions, as can be observed by the continuous shift to the right of the psychometric function with increasing ND values in Figure A2a. Subject A8 presented an initial rPSE negative value so large that even the largest tested luminance reduction did not bring his rPSE to 0◦. All of these results indicate that the reduction of luminance to one eye results in slowing down the processing of the information coming from that eye and is independent of the initial polarity of the delay. The slopes of the psychometric functions as a function of the interocular luminance difference are presented in Figure A2c. Most of them decreased and this decrease was significant, which indicates that the task was getting harder and less reliable at high luminance differences (one-sided Wilcoxon signed rank test on the slopes of the linear regressions, W = 5, p = 0.04). We showed previously on normals that a contrast reduction in one eye could induce a delay in the processing of the signal coming from this eye [24]. Hence, we wanted to assess if this effect was reproducible in the amblyopic population. Hence, we reduced the contrast of the Gabor patches seen by the non-amblyopic eye. This is actually a typical manipulation that reduces the interocular suppressive imbalance that amblyopes exhibit when viewing with both eyes open. In Figure A3a, the psychometric functions are displayed for one amblyopic subject who reported a clockwise perception as a function of the interocular delay for three contrast conditions where the contrast of the Gabor patches was reduced in the image seen by the NAE: no reduction, 40% reduction, and 60% reduction. One can see that the psychometric function was shifted to the right when the contrast was decreased in the non-amblyopic eye image, meaning that the rotation was seen more anticlockwise. The estimated rPSE for changes in the interocular phase is then plotted as a function of the interocular contrast difference in Figure4b for all subjects. Here again, the rPSE values of subject A8 were scaled by a factor of 10 to be represented with other data. When the contrast of the Gabor patches seen by the NAE was decreased, the rPSE on average increased from 0.17 at 0% to 0.06 at 60% interocular contrast difference (Figure A3b). The data − ◦ ◦ were fitted by linear regressions with significantly positive slopes (mean slope 0.41 0.60, one-sided ± Vision 2019, 3, x FOR PEER REVIEW 16 of 20

Visionsignificantly2019, 3, 54 higher than in the normal population (one-sided Wilcoxon rank sum test,14 ofU 17= 73, p = 0.08; normal population data from Reference [24]). This comparison was still Wilcoxonsignificant signed if the rank outlier test, amblyopicW = 32, p = subjects0.03) despite A1 and one A8 subject were (subjectexcluded A1) from presenting the analysis a negative and slope.led to Thisa slope negative approximately slope was due 2.5 totimes his negative higher than rPSE atfor 60% normals. contrast difference, which we think is probablyThe relatedslopes to of a visibilitythe psychometric or fusion issue functions when the as contrast a function is reduced of the too interocular much, rather contrast than an actualdifference switch are in the presented interocular in delay. Figure These A3c. estimated Most slopesof them of the decreased rPSE as a function and this of the decrease interocular is contrastsignificant, difference which were indicates significantly that higherthe task than was in the getting normal harder population and (one-sidedless reliable Wilcoxon when rank the sum test, U = 73, p = 0.08; normal population data from Reference [24]). This comparison was still contrast difference was severe (one-sided Wilcoxon signed rank test on the slopes of the significant if the outlier amblyopic subjects A1 and A8 were excluded from the analysis and led to a linear regressions, W = 3, p = 0.02). slope approximately 2.5 times higher than for normals. TheSimilar slopes to ofthe the results psychometric above for functions interocular as a functionchanges ofin theluminance, interocular for contrast participants difference whose are presentedrPSE was ininitially Figure positive,A3c. Most reducing of them the decreased contrast and of thisthe Gabor decrease patches is significant, presented which to the indicates NAE thatdrove the the task rPSE was away getting from harder 0° and lessaggravated reliable when the IOD. the contrast For subjects difference whose was rPSE severe was (one-sided initially Wilcoxonnegative, signed meaning rank that test their on the AE slopes was of delayed the linear co regressions,mpared to theirW = 3, NAE,p = 0.02). reducing the contrast of theSimilar image to seen the results by the above NAE for brought interocular the changes rPSE cl inose luminance, to 0°. It foreven participants continued whose to increase rPSE was it initiallyand drove positive, it away reducing from 0° the for contrast subject of A7 the for Gabor large patches contrast presented reductions to the, NAEas can drove be observed the rPSE awayby the from continuous 0◦ and aggravated shift to the the right IOD. of For the subjects psychometric whose rPSE function was initially with decreasing negative, meaning contrast that in theirFigure AE A3a. was All delayed of these compared results to suggest their NAE, that reducingthe contrast the contrastreduction of theresults image in seena slowing by the down NAE brought the rPSE close to 0 . It even continued to increase it and drove it away from 0 for subject A7 of the processing of the information◦ coming from the eye independent of the initial◦ polarity for large contrast reductions, as can be observed by the continuous shift to the right of the psychometric of the delay, which is comparable to what was previously described for changes in function with decreasing contrast in Figure A3a. All of these results suggest that the contrast reduction resultsinterocular in a slowing luminance. down of the processing of the information coming from the eye independent of the initialAs we polarity previously of the delay,observed which in iscontrols, comparable a mo tonocular what was reduction previously of describedluminance for or changes contrast in interocularin the input luminance. received by the non-amblyopic eye would slow down its processing, independentlyAs we previously of the observed initial indelay. controls, Thus, a monocular it could reduction compensate of luminance for or oraggravate contrast in any the inputspontaneous received byinterocular the non-amblyopic delay observed eye would in slowambl downyopia. its In processing, controls, independentlywe previously of observed the initial delay.a correlation Thus, it couldbetween compensate the regression for or aggravate slopes anyof the spontaneous angular interocularPSE as a delayfunction observed of the in amblyopia.interocular Incontrast controls, difference we previously and observed the slopes a correlation of the angular between PSE the regressionas a function slopes of of the angularinterocular PSE asluminance a function difference of the interocular [24]. However, contrast di forfference amblyopes, and the slopesthis same of the correlation angular PSE using as a function of the interocular luminance difference [24]. However, for amblyopes, this same correlation the rPSE was only significant because of the outlier subject A8 (coefficient of determination using the rPSE was only significant because of the outlier subject A8 (coefficient of determination R2 = 0.5563, p = 0.0336); without his data, the coefficient of determination dropped to R2 = R2 = 0.5563, p = 0.0336); without his data, the coefficient of determination dropped to R2 = 0.1037 with p0.1037= 0.4812. with p = 0.4812.

FigureFigure A2.A2. Interocular luminanceluminance didifference.fference. (a)) PsychometricPsychometric functionsfunctions ofof thethe perceivedperceived directiondirection ofof rotationrotation forfor oneone representativerepresentative amblyopicamblyopic subjectsubject (A7)(A7) asas aa function of the interocular phase difference difference forfor fivefive luminanceluminance conditions.conditions. Neutral density (ND) filtersfilters were placedplaced inin front ofof thethe non-amblyopic eye:eye: no-filter, no-filter, 0.1ND, 0.1ND, 0.3ND, 0.3ND, 0.6ND, 0.6ND, and and 1ND 1ND from from light- light- to dark-gray to dark-gray symbols. symbols. Data Datapoints points are fitted are fitted by a logistic function. (b) rPSE as a function of the interocular luminance difference for the by a logistic function. (b) rPSE as a function of the interocular luminance difference for the individual individual eight amblyopic subjects. * rPSE values for subject A8 were divided by 10. (c) Slopes of eight amblyopic subjects. * rPSE values for subject A8 were divided by 10. (c) Slopes of the the psychometric functions. Dashed lines represent linear regression. Quality of fit and regression psychometric functions. Dashed lines represent linear regression. Quality of fit and regression parameters are reported in Table S1 (Supplementary Materials, Sheet 4). parameters are reported in Table S1 (Supplementary Materials, Sheet 4).

Vision 2019, 3, 54 15 of 17 Vision 2019, 3, x FOR PEER REVIEW 17 of 20

FigureFigure A3. A3.Interocular Interocular contrast contrast di difference.fference. ((aa)) Psychometric functions functions of ofthe the perceived perceived direction direction of of rotationrotation for onefor one amblyopic amblyopic subject subject (A7) (A7) asas aa functionfunction of of the the interocular interocular phase phase difference difference for three for three contrastcontrast conditions. conditions. Contrast Contrast was was decreased decreased inin thethe non-amblyopic eye eye (NAE) (NAE) image: image: 0% (light-gray 0% (light-gray symbols),symbols), 40% 40% (mid-gray (mid-gray symbols), symbols), and and 60% 60% (dark-gray (dark-gray symbols)symbols) reduction. reduction. Data Data points points are are fitted fitted by by a logistica logistic function. function. (b) rPSE (b) rPSE as aas function a function of of the the interocular interocular contrast contrast difference difference for for the theeight eight amblyopic amblyopic subjects.subjects. *rPSE *rPSE values values for for subject subject A8 A8 were were divideddivided by by 10. 10. (c ()c Slopes) Slopes of ofthe the psychometric psychometric functions. functions. DashedDashed lines lines represent represent linear linear regression. regression. QualityQuality of of fit fit and and regression regression parameters parameters are reported are reported in in TableTable S1 (Supplementary S1 (Supplementary Materials, Materials, Sheet Sheet 5). 5).

AppendixAppendix C Eff C.ect Effect of Density of Density and Spatialand Spatial Frequency Frequency on Control on Control Subjects Subjects In FigureIn Figure A4a A4a are presentedare presented the rectifiedthe rectified points poin oftssubjective of subjective equality equality (rPSE) (rPSE) of eightof eight control subjectscontrol (including subjects the (including two authors) the astwo a functionauthors) ofas thea function number of of the Gabor number patches of Gabor (with size patches 0.15◦ and spatial(with frequency size 0.15° 2.85 and c/d). spatial Forcontrol frequency subjects, 2.85 c/d) the. rPSEFor control was computed subjects, asthe the rPSE actual was PSEcomputed for subjects whoseas dominantthe actual eyePSE was for theirsubjects right whose eye and dominant its opposite eye was for their subjects right whose eye and dominant its opposite eye was for their left eye.subjects The rPSEwhose values dominant were mucheye was less their variable left ey thane. The in therPSE amblyopic values were population much less and variable significantly convergedthan in when the amblyopic the number population of Gabor and patches signific wasantly increased converged (one-sided when Wilcoxonthe number signed of Gabor rank test, on thepatches slopes ofwas the increased linear regressions, (one-sidedW Wilcoxon= 4, p = 0.03). signed In Figurerank test, A4b on are the presented slopes theof the rPSE linear values of regressions, W = 4, p = 0.03). In Figure A4b are presented the rPSE values of the control the control subjects as a function of the size of the Gabor patches: 0.15, 0.3, 0.45, or 0.6◦, which had spatialsubjects frequencies as a function of 2.85, 1.43, of the 0.95, size and of 0.71 the c /Gabod respectively.r patches: For 0.15, these 0.3, four 0.45, sizes, or 0.6°, the numberwhich had of Gabor patchesspatial was respectivelyfrequencies setof 2.85, to 200, 1.43, 100, 0.95, 66 and and 50. 0.71 Here c/d again, respectively. the rPSE valuesFor these were four much sizes, less the variable thannumber in the amblyopic of Gabor population,patches was particularly respectively at set high to spatial200, 100, frequencies 66 and 50. (small Here sizes).again, Converselythe rPSE to whatvalues is observed were withmuch amblyopes, less variable for than control in subjects,the amblyopic it seems population, that the rPSE particularly became more at high variable whenspatial the spatial frequencies frequency (small of thesizes). Gabor Conversely patches to was what decreased, is observed characterized with amblyopes, by a divergence for control in the rPSEsubjects, as a function it seems of the that size the of therPSE patches. became However, more variable this divergence when the wasspatial not frequency significant of (one-sided the Gabor patches was decreased, characterized by a divergence in the rPSE as a function of the WilcoxonVision signed 2019, 3, rankx FOR PEER test, REVIEW on the slopes of the linear regressions, W = 19, p = 0.47). 18 of 20 size of the patches. However, this divergence was not significant (one-sided Wilcoxon signed rank test, on the slopes of the linear regressions, W = 19, p = 0.47).

Figure A4.FigureEff A4.ect Effect of density of density and and spatial spatial frequency frequency on control control subjects. subjects. (a) rPSE (a) rPSE as a function as a function of the of the numbernumber of Gabor of Gabor patches patches for eightfor eight control control subjects. subjects. (b (b) )rPSE rPSE as asa function a function of the of size the of size the ofGabor the Gabor patchespatches for eight for controleight control subjects. subjects. Dashed Dashed lines lines representrepresent linear linear regression. regression.

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