Documenta Ophthalmologica 104: 287–302, 2002.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.

A signal-to-noise analysis of multifocal VEP responses:an objective definition for poor records

XIAN ZHANG, DONALD C. HOOD, CANDICE S. CHEN andJENNY E. HONGDepartment of Psychology, Columbia University, New York, NY, USA

Accepted 1 October 2001

Abstract. Sixty local VEP records, called the multifocal VEP (mfVEP), can be obtained overa wide retinal area. From subject-to-subject, from day-to-day, and from location-to-location,these records can vary in quality presenting a challenge to quantitative analyses. Here threeprocedures are described for specifying the quality of mfVEP recordings in terms of signal-to-noise ratios. Monocular mfVEPs were recorded in two, 7-min runs. A ‘2-run signal-to-noiseratio’ (2rSNR) was obtained as [RMS(RunA+RunB)]/[RMS(RunA–RunB)]–1, where RMSis the root-mean-square amplitude of the response over the period from 45 to 150 ms (signalwindow). Two ‘noise-window signal-to-noise ratios’ were obtained with the same numeratoras the 2rSNR but with the denominators based upon the RMS of a signal-free window from325 to 430 ms. In one case, inSNR, the denominator was the RMS of the record’s noisewindow and in the other case, mnSNR, the denominator was the mean of the RMS amplitudesof all the signal-free noise windows for the subject. The SNRs were related to false-positiverates (i.e., detecting a signal when none was present) by recording mfVEPs with some of thesectors of the display occluded. In particular, the outer three rings (36 sectors) of the displaywere occluded so that only noise was recorded; false-positive rates for different values ofSNR were calculated. The 2rSNR had the highest false-positive rate largely due to alpha inthe records of some subjects. The mnSNR had a lower false-positive rate than did the inSNRbecause there was little correlation between the RMS of the noise in the signal-free windowand the RMS of the noise within the signal window. Use of the mnSNR is recommended overthe 2rSNR, especially where alpha contamination can not be eliminated. Ways to improve theSNR of the records are discussed.

Key words: multifocal, visual evoked potential, VEP

Introduction

Optic nerve and ganglion cell damage can alter the visual evoked potential(VEP) (e.g., [1–3]). However, the VEP has its limitations when applied tovisual field testing. It is difficult, for example, to obtain responses to stimula-tion in more than a few field locations within a single session. Baseler et al.[4] argued that this limitation could be overcome by employing the multiple-input method described for the electroretinogram by Sutter and his colleague

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[5,6]. In particular, they showed that 60 or more local VEP responses, calledthe multifocal VEP (mfVEP), could be obtained over a wide retinal area if thestimulus array was scaled to account for cortical magnification. The clinicalimplications of this technique were largely ignored until Klistorner et al. [7]demonstrated a qualitative agreement between visual field defects measuredwith static perimetry and regions of diminished mfVEP responses in patientswith ganglion cell and/or optic nerve damage. Subsequent work showed thatit was possible to quantitatively compare local changes in the mfVEP to localchanges in static (Humphrey) visual fields [8, 9]. Regions of field loss seenwith traditional static visual fields can be detected in the mfVEP, especially ifthe mfVEPs from both eyes of a subject are compared [8–11]. But problemsremain to be solved if the mfVEP is to be of clinical use.

Many of these problems revolve around the well-known inter-subject vari-ability in the VEP and mfVEP responses. The major source of variabilityamong individuals is cortical anatomy. The position of the primary visual areawithin cortical folds [12,13] and the relationship of external landmarks, suchas the inion, to underlying brain structures [9,14] differ widely among indi-viduals. These differences can lead to mfVEP responses that vary markedlyin amplitude across subjects at a given field location and within subjectsacross the visual field. Where appropriate, interocular comparison of mfVEPresponses can be employed to minimize variability due to cortical anatomy[8-11, 15]. However, other problems exist because the responses measureonly a few hundred nano-volts in amplitude.

As the mfVEP responses can be very small, deciding what constitutes aresponse can be a problem. Electrical noise from the environment and cor-tical noise from, for example, alpha waves can vary from day to day andeven moment to moment. To improve an analysis of the mfVEP, records thatare too noisy and/or records with signals that are too small to be measuredreliably should be eliminated from the analysis. For example, records withpeak-to-trough (PtT) amplitudes less than a criterion value could be excludedfrom further analysis [16]. However, there are problems with using the PtTamplitude as a criterion for eliminating records when responses are contam-inated by alpha waves or are unduly noisy due to higher frequency noise.Consider the three records in the first row of Figure 1A (described further inthe next section). The first two records do not contain a signal but have aboutthe same PtT amplitude as the third record because alpha is present in the firstrecord, and high frequency noise is present the second. The root-mean-square(RMS amplitude), defined below, has advantages over the PtT amplitude asa criterion for eliminating records, but it suffers from the same problem. Inthis paper, two signal-to-noise ratios are evaluated as criteria for eliminatingrecords of poor quality.

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Figure 1. (A) The top row contains three waveforms with approximately the same peak totrough and RMS amplitudes. The first record has an alpha contribution, the second has highfrequency noise while the third has a discernible signal. See the text for details. The recordsfor the second run, Run B, are in the second row. And the third and fourth rows are (Run A +Run B)/2 and (Run A – Run B)/2. The 2rSNR calculated with the formulas in panels (B) and(C) appear at the bottom of the records. (C). The equation for calculating the RMS amplitudewhere Rt is the response amplitude at time t, µ is the average of the amplitudes from 45 to150 ms, and N is the number of samples in the time period. (D) The equation for calculatingthe 2rSNR where RMS is defined as in panel (C). (E) The signal and noise windows used inthe calculation of the inSNR and mnSNR. F. The general equation for calculating nwSNRs.

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Introduction to the two-run signal-to-noise ratio (2rSNR)

The approach adopted here is described in Baseler et al. [4] who employed itto assess the reproducibility across two recording sessions. Here two mfVEPresponses obtained for the same location in the same session are compared(see also Ref. [17]). Figure 1A illustrates the logic behind the approach.The upper row of mfVEP records in Figure 1A represents three hypothet-ical records from a single run, Run A. These records are actually from theoccluded display experiment described below. The first two columns do notcontain a signal (i.e., there was no stimulus present) while the third contains aclear signal (there was a stimulus present). The first record contains an alphacomponent. The second was amplified in amplitude to illustrate the appear-ance of a very noisy record as is occasionally recorded from some subjects.These three examples were chosen to have nearly identical RMS amplitudes.By RMS amplitude we mean the root-mean-square (RMS) calculated oversome time interval (see Figure 1B for equation). The RMS measure has theadvantage over the PtT measure in that it does not depend upon a particularaspect of the response waveform but merely requires the specification of atime interval. The interval of analysis employed here is 45–150 ms shown asthe dashed lines in Figure 1A. The records in Run A of Figure 1A have nearlyidentical RMS amplitudes; they also have similar peak-to-trough amplitudes.The logic and advantage of the ‘two-run signal-to-noise ratio’, 2rSNR, isshown in the rest of Figure 1A. First, a second set of responses is obtained,shown as Run B in the second row of the figure. The two responses are addedand averaged to get the row labeled ‘SUM/2’, and they are subtracted andaveraged to get the row labeled ‘DIFF/2’. The SUM gives us an estimate ofthe signal plus noise and the DIFF a measure of the noise. Notice that if thesignals were identical in both runs then the DIFF record would be only noise.The 2rSNR is obtained as the ratio of the RMS values for the SUM and DIFFresponses (see formula in Figure 1C). This is not a true SNR in the sense thatthe numerator, in addition to containing a signal term, contains a noise term aswell as a term representing an interaction between the signal and noise [18](see also Eq. (A5) in Ref. [4]). The minus 1 is in the equation (Figure 1C)so that 2rSNR will be, on average, equal to 0 when no signal is present. InFigure 1A, the two records without a signal have a 2rSNR close to 0 whilethe records with the large signal have a 2rSNR of 4.6.

Introduction to the noise window signal-to-noise ratio (nwSNR)

The nwSNR ratio is a more conventional measure. We asked whether therewas a part of the record that was far enough in time from the onset of thepattern reversal so as to be free of the response but not so far in time that it

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Figure 2. (A) The standard mfVEP display. (B) The occluded display with the peripheral 36sectors covered.

is affected by so-called ‘kernel overlap’ [5]. For the 7-min m-sequence usedhere, the epoch from 325 to 430 ms (the same period as our analysis epochof 45–150 ms) appears to contain, to a first approximation, only noise. Thiswas based upon an analysis of its frequency content. This was confirmed byaveraging the mfVEP responses from the 14 control subjects in Ref. [19]. ThemfVEPs in Figure 1D are the averages of the responses to the 30 sectors aboveand below the midline (see Figure 3). As previously reported [4,7,8], thesemfVEPs are reversed in polarity. Notice that the ‘noise window’, defined asthe period from 325 to 430 ms, does not appear to have a response. To obtaina nwSNR (Figure 1E), the RMS for the ‘signal window’, which will containboth signal and noise, is divided by the RMS for the ‘noise window’, whichto a first approximation contains only noise. Two nwSNRs were obtained foreach record, one based upon the RMS of the noise window for that individualrecord alone (inSNR) and the other based upon the mean of the RMS valuesof all the noise windows for a particular subject (mnSNR).

Choosing a criterion value of SNR

An advantage of a SNR over a RMS or PtT criterion is that it can be definedindependent of noise level. That is, the biologically and environmentally pro-duced noise in recordings can vary from day-to-day, individual-to-individual,and laboratory-to-laboratory. Since noise is in both the denominator and nu-merator, the SNR will have the same meaning for different days, individuals,or laboratories while the RMS and PtT measures will not. But, what valuedoes one choose when rejecting ‘poor’ records based upon SNR values? Thelarger the SNR, the more likely the records provide a good measure of the real

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Figure 3. (A) A histogram of the 2rSNR values of the noise-only records from eight subjects(288 pairs of noise-only records). (B) Histograms of the inSNR and mnSNR values for the288 pairs of noise-only records. (C) The cumulative distribution for the histograms in panels(A) and (B). It provides an estimate of the false positive rate as a function of a criterion valueof the SNR.

signal. At the same time, the larger the SNR criterion the fewer the responsesthat can be included in our analysis. One way to express this trade-off is in

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terms of false-positive rates. As the criterion value of the SNR is increased,the percentage of records falsely identified as having a signal will decrease.The main purpose here is to relate the values of the SNR to false-positiverates. A preliminary report was presented at the ARVO 2001 meeting [22].

Methods

Stimuli

Figure 2A shows the ‘standard’ display employed in previous work and Fig-ure 2B the ‘occluded display’ employed here. These stimulus arrays were pro-duced with VERIS software (Dart Board 60 With Pattern) from EDI (Electro-Diagnostic Imaging, San Mateo, CA). The array in Figure 2A consists of60 sectors each with 16 checks, eight white (200 cd/m2) and eight black(< 1cd/m2). The entire display has a diameter of 44.5◦. For the ‘occludeddisplay’ in Figure 2B, the outer three rings (36 sectors in all) were coveredwith white cardboard. The central 24 sectors remained to help the subjectmaintain fixation and attention as in the standard display of Figure 2A.

Recording the mfVEP

The mfVEPs were recorded with gold cup electrodes placed at 4 cm abovethe inion (active), at the inion (reference), and on the forehead (ground). Thecontinuous record was amplified with the low and high frequency cutoffs setat 3 and 100 Hz (1/2 amplitude; Grass preamplifier P511J, Quincy, MA),and it was sampled at 1200 Hz (every 0.83 ms). The m-sequence had 215-1elements and required about 7 min for a single run.

All mfVEPs were obtained with monocular stimulation. Within a session,two runs were obtained with the occluded display (Figure 2B). The two runsare needed to calculate the 2rSNR. The records from the two runs were av-eraged before the nwSNRs were calculated. To improve the subject’s abilityto maintain fixation, the run was broken up into overlapping segments eachlasting about 27 s. Second-order local response components were extractedusing VERIS 4.1 software from EDI (San Mateo, CA). All other analyseswere done with programs written in MATLAB (Mathworks, MA).

Subjects

Eight subjects ranging in age from 20 to 58 years (mean 31 years) with noknown abnormalities of the visual system participated in the study. Proced-ures followed the tenets of the Declaration of Helsinki and the protocol was

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approved by the committee of the Institutional Board of Research Associatesof Columbia University.

Calculating the SNRs

As described above, the 2rSNR was calculated for each pair of 36 noise-onlyrecords from each subject using the equations in Figures 1B,C. To obtain anwSNR for the same pairs of records, the responses from Runs A and B werefirst averaged. Two nwSNRs were then defined. One, called the ‘individualnoise window SNR’ (inSNR), was defined for the ith sector of the jth subjectas

inSNR = [RMSij (45 to 150ms)/RMSij (325 to 430ms)] − 1. (1)

where RMS(t1 to t2) is the RMS defined by the equation in Figure 1B forthe interval from t= t1 to t= t2. The second nwSNR, called the ‘mean noisewindow SNR’ was defined for the ith sector of the jth subject as

mnSNR = {RMSij (45 to 150ms)/[�iRMSij (325 to 430ms)/n]} − 1 (2)

where the denominator is the average of the individual RMS values for jthsubject.

Notice that all three SNRs have the same numerator. The denominators areof the same form. They are all based upon the RMS of the combined recordsfrom Runs A and B. They differ in terms of whether the RMS is based uponthe record for the signal window (2rSNR), the noise window (inSNR) or themean of the RMS values of the noise windows (mnSNR).

Results

To obtain a distribution of the SNR values when no signal is present, the SNRswere calculated for all 36 pairs of responses (two runs were obtained with the36 occluded sectors) from all eight subjects. The distribution of these 288SNR values is shown in Figure 3A,B for the three different types of SNRs.The cumulative distribution of these histograms can be found in Figure 3C.Since there can be no signal present in this experiment, the cumulative dis-tribution provides an estimate of the ‘false positive rate’ as a function of thevalue of a SNR criterion. The false positive rate is the percentage of time thatone would conclude there is a signal present when in fact there is no signalpresent. For example, a false positive rate of 5% (dashed line in Figure 3C)is associated here with SNR values of about 1.0, 0.8, and 0.5 for the 2rSNR,inSNR and mnSNR, respectively. Notice that for any given SNR value, the

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false-positive rate is highest for the 2rSNR and lowest for the mnSNR. Recallthat the numerator of all three SNRs is the same. To understand why we getdifferent false-positive values, we need to understand the implications of thedifferent denominators.

Consider the difference between the two measures of nwSNR. Each pointin the scatter plot in Figure 4A shows the inSNR (Eq. (1)) and the mnSNR(Eq. (2)), for each of the 288 noise-only records from the occluded displayexperiment. As expected from Figure 3C, the mnSNR, based upon the meanfor each subject, exhibits less variability than the inRMS which is based uponthe individual records. Notice, for example, the number of points falling bey-ond a value of 1.0 (solid lines) for each measure. The reason can be foundin Figure 5. In Figure 5, the RMSij (45 to 150 ms), the numerator of bothnwSNRs is shown versus the RMSij (325 to 430 ms), the denominator of theinSNR. For clarity only the data for four of the subjects are shown. Thesesubjects were chosen as they represent examples of subjects with the lowestmean RMS value (triangles), the highest mean RMS value (pluses), the largestrange of RMS values (open circles), and the best correlation between theRMS values for the two windows (filled circles). It is clear in Figure 5 that,for any given subject, the noise in the two windows is poorly correlated. Onaverage, the correlation coefficient (r2) of the two RMS values was 0.07 witha range from 0.00 to 0.29 (filled circles). Since the noise outside the signalwindow is poorly correlated with the noise in the signal window, the meanof the RMS from all the noise windows of a given subject supplies a betterestimate of the noise in an individual record.

Figure 4B shows a comparison of the mnSNR (Eq (2)) and the 2rSNRvalues for all 288 noise-only records. Although the 2rSNR and mnSNR arecorrelated, the correlation is far from perfect. To better understand why thesemeasures differ, the individual records associated with 2rSNR values greaterthan 1.0, the symbols to the right of the vertical line in Figure 4B were ex-amined. Fourteen of these 16 records came from three of the eight subjects.In 14 of the 16, the records in the signal window of both Runs A and Bhad a low frequency component that was approximately in phase in the tworuns and appear to be attributable to alpha. Figure 6A provides an example.Notice that by chance a slow component, presumably due to the presence ofalpha waves in the continuous VEP record, is in phase in the two runs. Thisresults in a 2rSNR of 1.9. The mnSNR (Eq (2)) was 0.59. When the noise isin phase as in Figure 6A, the 2rSNR will be larger than the nwSNR becausethey share the same numerator and the denominator of the 2rSNR will besmaller. Recall that the denominator is the RMS of the difference betweenRuns A and B and thus includes the difference of the two alpha components.By a similar argument, the 2rSNR will be smaller than the mnSNR when the

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Figure 4. (A) The inSNR is plotted against the mnSNR. Each point is for a single sector anda single subject for the combined records of Runs A and B. There are 36 points (the occludedsectors) for each subject. The different symbols denote different subjects. (B) Same as in (A),but for mnSNR versus 2rSNR.

alpha components are out of phase. [This would be easier to see in Figure 4had the −1 in the SNR equations been removed and a log scale used. Theequivalent points to those falling between 1 and 2 on these scales would fallbetween −0.5 and −0.33.]

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Figure 5. (A) The RMS amplitude for the epoch between 45 and 150 ms is plotted against theRMS amplitude for the window from 325 to 430 ms. Each point is for a single sector and asingle subject for the combined records of Runs A and B. There are 36 points (the occludedsectors) for each subject. The four different symbols denote different subjects.

Figure 6. (A) A set of noise-only records illustrating a case where the 2rSNR is large becausethe noise in both Runs A and (B), most likely alpha wave in origin, is in phase. B. A set ofnoise-only records illustrating a case where the 2rSNR measure will be superior to the nmSNRmeasures.

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Figure 7. The first 600 ms of the mfVEP records from five of the locations in the occludeddisplay experiment. Records from the same locations are shown for all eight subjects.

Discussion

Measuring the quality of the mfVEP records

The mfVEP responses are inherently small. In fact, for some subjects thesignal may be essentially zero in some locations. This is not necessarilycaused by abnormal vision but can be present in control subjects due to localfolding of the cortex. In particular, the activity of cells oriented parallel to therecording electrodes will not be seen. Since the mfVEP signals can be small,distinguishing them from noise becomes a problem. Some investigators haveemployed a criterion amplitude (PtT or RMS) in the signal window to identifypoor records (e.g., Ref. [16]). As can be seen in Figure 5, this procedure is lessthan optimal. Placing the criterion at 0.04 would accept all of one subject’snoise-only signals (pluses) while rejecting all of another’s (triangles). A betterprocedure involves estimating the noise level and calculating a SNR for eachrecord. Based upon the analysis in this paper, it is probably best to obtainone estimate of noise level for the entire set of records. Using this average

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value as an estimate of the RMS noise in the signal window, a SNR can becalculated for each record and records can be rejected if this value falls belowsome criterion value.

A priori, one might expect that the 2rSNR is a better way to detect thepresence of a signal in noise since it uses an estimate of the noise in thesame epoch as the signal to be detected. Figure 6B, for example, shows a pairof responses from the occluded display experiment. In this case, the 2rSNRwill provide the best estimate of the noise in the signal window. But, there is aproblem for the 2rSNR when there is a source of noise, alpha in this case, witha reasonably high probability of occurrence and with a dominant frequencythat is low relative to the analysis window. Under these circumstances, thiscomponent will appear in phase in the two runs on some occasions and out ofphase in others. In general, a slow component in phase will give a 2rSNR thatis greater than a nwSNR and one out of phase a 2rSNR that is smaller than anwSN. Thus, under these circumstances the 2rSNR is not a good metric forrejecting noisy records. By a similar logic, however, for a fixed value of theSNR, the nwSNR will lead to more or less false-negatives, saying a signalis not present when in fact it was, than the 2rSNR depending upon whetherthe alpha components are in or out of phase. In sum, the fact that a givenvalue of the 2rSNR has a higher false-positive rate than the same value ofthe nwSNR does not tell the whole story. What we really need to know iswhich measure produces ‘better records’ when the same percentage of therecords is removed. This is a more complicated issue to resolve, but unlessthe contamination from alpha can be removed the mnSNR will provide a lessvariable estimate of the noise.

The individual mfVEP records give the appearance of local periods ofalpha. Thus, we initially thought that the inSNR, based upon the same record,might provide a better measure than the mnSNR. But, as we should have sus-pected, the alpha contamination is largely global, not local in time. Figure 7illustrates this point by showing the first 600 ms of records for five randomlychosen locations for the eight subjects. The alpha contribution is particularlyobvious in three of these subjects. Notice that there is some fluctuation in thenoise with periods of prominent alpha seen within these records, but thesefluctuations do not have any consistent structural basis. The lack of correla-tion between the signal and noise windows in Figure 5 reinforces this point.Since this correlation is poor, the alpha contamination affects the inSNR ina manner similar to its effects on the 2rSNR, resulting in a more variableestimate of the noise in the signal window. For example, an examination ofthe records for the extreme values of the inSNR in Figure 4A (points abovehorizontal line) revealed that these records usually had an alpha componentout of phase in the noise window.

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Improving the quality of the mfVEP records

Regardless of the signal-to-noise measure employed, rejecting records froman analysis involves a trade off between a loss of data on one hand, and again in the quality of the data on the other. Our purpose here was to relate theSNR criteria to false-positive rates so as to allow the experimenter to assessthis trade-off. The fact that we recommend the use of the mnSNR means thatthe experimenter can obtain false positive rates from the actual recordings byanalyzing the records outside the signal window [19].

To obtain a false-positive rate of 5% or better the mnSNR should be equalto or better than about 0.5. We will show in the following paper that, onaverage, as many as 17% of the responses from normal controls may fail tomeet this criterion level. This is an unacceptably large number for many pur-poses. There are two methods readily available for improving the SNR. Oneinvolves summing responses from neighboring sectors and the other addingadditional electrodes (e.g., Refs. 8,11,16,19). The following paper examinesthese methods in detail.

There are also precautions that the experimenter can take to improve theSNR. First, it is important to keep the resistance of all electrodes as low,and as similar, as possible. Second, attempts should be made to reduce theintrusion of alpha waves. Figure 6A illustrates how alpha contamination canbe mistaken for a signal no matter what SNR measure is employed. Reducingalpha or, in fact, any low frequency noise, will reduce the false positive ratesfor any given SNR value.

There are two classes of techniques one might consider for reducing thecontamination of the records by alpha. First, the experimenter can continu-ously monitor the VEP record and provide feedback to the subject. For ex-ample, we have recently found that many ‘alpha-producers’ can suppressalpha if they are told to pay close attention to the edges of the small checks inthe center of the display and if the experimenter provides feedback wheneveran alpha burst appears on the screen. The second technique involves softwarerejection of alpha bursts. This is not available in the current versions of theVERIS software, but it should be possible to implement.

More than a methodology for rejecting poor records

Beyond providing an objective method for rejecting poor records, there arebenefits to a measure that takes into consideration both signal and noise. Asignal-to-noise measure allows for a quantitative answer to questions such as:‘Is condition A better than B’, where A and B refer to different numbers of re-cording channels (see following paper [19]), records obtained from differentlaboratories, different methods of analysis or different experimental condi-

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tions. Whatever the question, ‘better’ usually implies a larger signal-to-noiseand thus a SNR should be employed.

Acknowledgements

Supported by grants from the National Eye Institute (R01-EY-02115 andR01-EY-09076). The authors gratefully acknowledge the support and ad-vice of Drs. Greenstein and Odel. We also thank Nazreen Karim and An-nemarie Gallagher for their help in recording mfVEPs and Drs. Fortune andGreenstein for helpful comments on earlier versions of this paper.

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Address for correspondence: D.C. Hood, Department of Psychology, Schermerhorn Hall,Room 406, Columbia University, 1190 Amsterdam Ave., New York, NY 10027-7004, USAFax: +1-212-854-3609; E-mail: dch3@columbia.edu