OF MERIDIONAL VARIATION EFFECTS VISUAL ON STEADY-STATE EVOKED POTENTIALS’ JAMESG. MAY’ and JOHN K. CULLENJR Louisiana State University Medical Center, Kresge Hearing Research Laboratory of the South, Department of Otorhinolaryngology, 1100Florida Avenue, Building 147. New Orleans, Louisiana 70119. U.S.A., and University of New Orleans. Department of Psychology. Lakefront. New Orleans, Louisiana 70122. U.S.A.

and ANNEMOSKOWITZ-C~DKand JOHN B. SlEGFRiED Pennsylvania College of Optometry, Division of Visual Sciences, 1200 W. Godfrey Avenue, Philadelphia, PA 19141, U.S.A. (Recrired 7 Nocemhrr 1978) Abstract-Two experiments were carried out to assess the influence of meridional variations on the visually evoked potentials (VEPs) elicited by pattern alternation. The first experiment involved a comparison of the oblique effect obtained with grating and checkerboard stimuli. Greater amplitudes resulted using stimuli which contained vertically. as opposed to obliquely. oriented fundamental Fourier components. The second experiment revealed that the peak delay* of the VEP was markedly shorter when subjects wore cylindrical lenses oriented such that they emphasized a fundamental Fourier component of the checkerboard stimulus. These results underline the importance of describing complex patterned stimuli in terms of Fourier analysis when evaluating meridional aspects of visual function.

*[As Regan (1966. 1972. 1978) points out. time to any peak in a steady-state VEP can be a function of numerous variables: (a) transmission time (b) nonlinearity of the amplitude-frequency plot and or (cl differences in the spatial orientation of cortical generators (Halliday and Michaels. 1970: Jeffreys and Axford. 1972). Apparent latency is defined as (?&/(36O?F) where 4 = phase. F = frequency and (?&/(?F) is the slope of the phase vs frequency plot. Thus. the calculation of apparent latency requires measurement of phase changes over a range of different temporal frequencies. The present data were obtained at only a single temporal frequency and it is therefore impossible to assess the individual influence of factors listed above. We have therefore used the term peak delay as opposed to more rigorously defined terms, like apparent latency or phase lag.]

Amplitude and peak delay of steady-state VEPs (Regan. 1966) have been shown to be influenced by various aspects of patterned stimuli. Numerous investigators have found the amplitude of VEPs produced by pattern alternation: (1) changes with spatial frequency and check size (Spekreijse. 1966; Armington et ’ This research was supported by NE1 Post-Doctoral Fellowship No. F32 EYO5106-01 to the third author. an intramural grant from the Pennsylvania College of Optometry. and in part by the National Institutes of Health (USPHS Grant No. NS-I 1647. Program Project). Research was performed in the Electrodiagnostic Laboratory of the Pennsylvania College 0r Optometry. *Address reprint requests to: James G. May, L.S.U. Medical Center, Kresge Hearing Research Lab., 1100 Fla. Ave., Bldg. 147, New Orleans. LA 70119, U.S.A. ’ Note that although removing higher harmonics blurs the edges of checks. there are no spatial-frequency components parallel to the edges of the checks (Kelly, 1976).

~1.. 1971: May er (II.. 197 I : Regan and Richards. 1971): (2) exhibits the oblique effect (Maffei and Campbell, 1970; and Frost and Kaminer. 1975): (3) is sensitive to successive spatial-frequency adaptation (Blakemore and Campbell. 1969: Campbell &nd Maf-

fei. 1970; May er al.. 1974): and (4) is decreased when the high-frequency components of the stimuli are reduced by defocusing (Spekreijse, 1966: Millodot and Riggs, 1970; Regan, 1972, 1973). These findings have led to the suggestion that processes specific to pattern perception may be studied with VEP measures. One approach to the description of the physical characteristics of visual stimuli has involved Fourier analysis in the spatial-frequency domain. Kelly (1976) reported the major spatial frequency components of checkerboard stimuli are oriented at 45. to what appear as the check edges.’ and psychophysical measures of Hicker sensitivity indicate the visual system is more sensitive to checkerboard stimuli in which the major Fourier components are oriented vertically and horizontally, as opposed to obliquely.

amplitude than elicited by normally oriented checkerboards. A second aim or this study concerned the influence upon the VEP of selective attenuation of various spatial-rrequency components distributed along a number of meridians in checkerboard stimuli. The second experiment constituted another assessment of the degree to which the Fourier spectrum affects the steady-state VEP. Subjects viewed a normally oriented checkerboard through a cylindrical lens oriented to emphasize the various spatial-frequency components in the pattern.

/ @

/

OwQlE

Fig. 1. Examples of the stimulus patterns

used in Experi-

ment I.

EXPERI\IE\T

;Liay and Matteson (1976) and Green er (I/. (1976) have shown that orientation-contingent color altereffects are associated with the fundamental components of checkerboard stimuli. These results support the contention that our understanding of pattern-perception mechanisms can be expanded by conceptualizing physical stimuli within a Fourier-analysis model. However. there are some reasons to doubt that characteristics of VEPs elicited by checkerboard stimuli will agree with obtained psychophysical results. Kelly (1976) found flicker sensitivity was greater [or gratings than for checkerboard stimuli and suggested pattern detection depends on sensitivity to the maximum amplitude of the two-dimensional Fourier components. On the other hand. numerous studies (Rietveld er al., 1967; MacKay, 1969; Armington et al.. 1971) indicate VEP amplitude is greater when checkerboards. rather than gratings, are used as stimuli. Furthermore. the defocusing or gratings and checkerboards composed of small stimulus elements [e.g. 13’ element widths) results in a decrease in VEP amplitude. while producing a prominent perception of the hrndamental spatial-frequency components. Thus, it is quite possible the VEP is influenced more by spatial contrast. and influenced by different neural mechanisms, than those responsible for psychophysical measures of pattern detection. One purpose of the present investigation was to determine if the amplitude of the steady-state VEP elicited by normally and obliquely oriented checkerboards reflects the same kind of oblique effects noted in Kelly’s (1976) counterphase flicker experiments. If VEP amplitude is influenced more by the major Fourier components, obliquely oriented checkerboard stimuli would be expected to evoke greater VEP

s: JM

Fig. 1. Examples of VEPs obtained from one subject. indicating the amplitude and peak delay measurements employed in experiment I.

I

Strbjecrs Three

adults

with

all had uncorrected astigmatism. Each VEP experiments.

vision served as subjects: 20/20 acuity and no significant had previously participated in

normal

Appcmrrts Stitntdi. The stimuli were vectographic grating and checkerboard patterns (American Polartzers, Inc.. Division of Smith, Kline, and French) consisting of orthogonally polarized adjacent bars or checks. mounted on circular Plexiglas discs. Light from a tungsten lamp was projected through a Polaroid onto the stimulus targets using a Kodak Carousel slide projector (Model 800). Constant-speed rotation of this Polaroid resulted in sinusoidal alternation of the dark- and light-pattern elements. The targets. viewed at a distance of 16 ft. subtended 5.15’ visual angle and were equated to have a lundamental spatial frequency of 4.0 cideg (i.e. check width was 1.4 x bar width; see Kelly. 1976). Thus, the bar widths were 7’30” and the check widths were 10’30”. The luminance or the stimulus field was 0.93 R-L and the contrast was 85”,0. Targets were presented in two orientations. vertical and oblique (45.). as shown in Fig. I. This terminology is straightforward with erating patterns. but needs clarification when describing checkerboards. The differently oriented checkerboards will be In the referred to as “squares” and “diamonds”. squares condition, the edges of each check are vertically and horizontally oriented. but the major Fourier components are along 45’ and 135’ axes. Conversely. in the diamonds condition, check edges are obliquely oriented and the major Fourier components are along the vertical and horizontal axes (see Appendix). Recording syaw~. Cortical potentials were recorded differentially using gold EEG electrodes (Grass, G6). The active electrode was attached to the scalp ap proximately 3.5 cm above the inion on the midline (at 0~: IO?/, of inion-nasion distance). The reference electrode was placed on the right mastoid and the ground on the left mastoid. Inter-electrode impedance was maintained below ZOOOR. At the beginning or each session. the electrical system was calibrated using a square-wave generator (Grass, Model SWCI B). The EEG was led through two preamplifiers (Grass, Model Pl5B) connected in cascade with a total gain of IO’ and a bandpass of 0.1-100 Hz. Amplified signals were led into a signal averaging computer (Nicolet Instrument Corp.. Model 1072). .A

Effects of meridional variation on steady-state VEPs

I397

small hole in an opaque mask surrounding the periphery of the rotating polaroid allowed light to faii onto a photocell. the output of which provided pulses to trigger computer averaging. The Polaroid was rotated at a rate of 6 Hz, resulting in I:! reversals of contrast per second. Twelve VEPsJsec were recorded with a 256 msec epoch. Each record graphed on an X-Y plotter (Hewlett-Packard. Model 7044A). showed averaged responses to three consecutive contrast reversals. Procedure All subjects viewed the patterns monocularly with the right eye and eight VEPs were recorded under each stimulus orientation for each subject. They fixated a point at the center of each stimulus pattern.’ The VEPs were recorded in sets of four, and the order in which the stimulus orientations were presented was randomized and counterbalanced (abed. dcba) for each subject. The peak-to-trough amplitude of two successive VEPs was measured for each trace. yielding a total of 16 measurements per condition for each subject. Results

Figure 2 shows four replications of typical, averaged responses for subject JM evoked by one stimulus condition. Also shown are the response features measured. VEP amplitudes for the four conditions are shown in Fig. 3. For all subjects, VEP amplitude was greater for the vertically oriented than for the obliquely oriented grating. thus confirming the existence of the typical oblique effect. For the checkerboard patterns. the VEP amplitude of all subjects was greater for diamonds than for squares, indicating that horizontal- and vertical-fundamenta1 Fourier components predominated. No differences in peak delay were found between vertical and oblique orientations of gratings or checkerboards. EXPERl3lENT Z

Subjects

Two adult males with normal vision, both practiced observers. served as subjectsin this experiment. Both had uncorrected 20120 acuity and no significant astigmatism. Apparatus

Fig. 3. Mean VEP amplitude obtained with vertical gratings (V). oblique gratings (O), diamond patterns (Dt. and square patterns (S1 for each subject. Vertical lines depict

_+ 1.0 SE.

(lens axis aligned with the vertical edges of the checks): (2) horizontally (lens axis orientation aligned with the horizontal edges); or (3) obliquely (lens orientation at 45” or 135’ to the orientation of the check edges). Pattern alternation rate and ail other stimulation particulars were identical to Experiment 1. Procedure At the canning of each session, four control VEPs were recorded without cylindrical lenses. Thereafter, four VEPs were recorded in each lens orientation and the order of lens orientation was randomized. Two sessions were run for each subject. yielding a total of eight VEP traces for each lens orientation. Two measurements of amplitude and one of peak delay were made for each trace. resulting in 16 amplitude and 8 peak-delay measurements per condition for each subject. Mean measurements of peak delay and amplitude were calculated for the control VEPs for each session. All measurements of peak delay and amplitude obtained from lens conditions were normalized to the mean control measurements. Resulrs

Four replications of averaged VEPs for each lens orientation for subject JS are presented in Fig. 4. No differences in peak-to-trough amplitude were found among lens-orientation conditions for either subject.

The recording apparatus was identical to that used in Experiment I. The rectangular stimulus field subtended a visual angle of 23.2” vertically and 29.8’ horizontally and contained a ‘1.5 c!deg pattern of squares (i.e. normaily oriented checkerboard-25 check widths) viewed at a distance of 7.Oft. Subjects viewed the pattern. with the right eye. through a + I .75 diopter lens which was oriented: (I) vertically ’ It has been reported that central fixation may resuh in a cancellation of response generated in upper and lower half fields (Jeffrey and Axford. 1971). Central fixation was used in these experiments. however. so that the results might be directly cornbared to a previous electrophysiological study of the oblique effect (Maffei and Campbell 1970) which also used central fixation and because it is not clear whether the upper and lower half fields differ regarding the degree to which the oblique effect is demonstrable.

Fig. 4. VEPs obtained from one subject under four conditions of cylinder orientation. Four replications are presented for each condition. Responses in (HI and (V) were obtained when the cylinder axis was aligned with the horizontaf and vertical edges of the checks. In conditions 0, and Oa. the cylinder axis was oriented along the oblique meridians.

Fig. 5. Normalized VEP peak delay obtained with various cylinder orientations for both subjects. Vertical lines depict + 1.0 SE.

The peak delay of averaged VEPs, however, was markedly increased in vertical- and horizontal-lens conditions. The mean normalized latency for each condition. together with the standard error of the means, are plotted in Fig. 5. For both subjects, the peak delay is shortest when the cylindrical lens is oriented to emphasize one or the other fundamental Fourier component. DISCUSSlO\

Results of the first experiment indicate the amplitude of steady-state VEPs is greater when grating stimuli are vertically. rather than obliquely, oriented. This finding is in agreement with previous psychophysical (Appelle, 1972) and electrophysiological data (Frost and Kaminer. 1975) and confirms the notion that meridional anisotropies exist in some subjects free from refractive error and astigmatism. All of the spatial frequencies contained in the grating stimuli have the same orientation. however. and offer little information regarding the relative importance of the fundamental and higher harmonic contributions to the observed oblique effect. The fact that the steady-state VEP amplitudes are greater for oblique. as opposed to normally oriented checkerboards, suggests that it is the fundamental component that is most import,ant in producing these meridional differences. These findings agree with psychophysical experiments reported by Kelly (1976) in that he also reported that subjects were relatively more sensitive to checkerboards which contained vertical and horizontal as opposed to obliquely oriented fundamental components. Thus. VEP amplitude and psychophysical detection measures indicate that the oblique effect is mediated more by the fundamental frequency components rhan it is by the edges (higher harmonics) of the pattern. Although numerous ekperiments have pointed out the importance of higher harmonic frequencies in the production of pattern alternation VEP (Spekreijse, 1966; Millodot and Riggs, 1970; Regan, 1972, 1973), it is possible to record steady-state VEPs with simple,

‘See latency.

footnote to

abstract

for the definition

ol apparent

spatial. sine-wave gratmgs (Blakemore and Campbell. 1969; Campbell and MaKei. 1970: MaKei and Camp bell, 1970). Levi and Harwerth (1978) have shown that the peak of the amplitude-spatial frequency functions occur at about 3.0c,‘deg for steady-state VEPs Gth such stimuli. The magnitude of the higher-harmonic’ components in a checkerboard declines rapidly with each higher harmonic and. in this light, it is not surprising that the amplitude of the steady-state VEPs is maximally influenced by the fundamental. Data from the second experiment also indicate the relative importance of the iundamental Fourier component in the production of steady-state VEPs. The peak delay of these VEPs. elicited with cylindrial lenses in various orientations. is shortest when one of the two orthogonally oriented fundamental Fourier is maximally components in focus (minimsll) attenuated). When the lenses are oriented such that vertical or horizontal edges are minimally affected. peak delay is considerably greater. Since the orientation tuning of these cylmders is broad enough to attenuate, to some extent, the components oriented 45’ from the axis of the lens, the orthogonally oriented fundamentals together w?th one set of higher harmonics are attenuated when the cylinder is aligned with the edges of the patterns. When the cylinder is aligned such that its axis has the same orientation as one of the fundamentals. that fundamental together with the orthogonally oriented higher harmonics 3:s attenuated. Mathematical analysis (see Appendix) oi the filtering characteristics of the cylindrical I:ns reveals that a 45’ orientation produces minimun attenuation of one set of Fourier components N bile maximizing the attenuation of the orthogonal set. These results suggests a complex relationship between the spatial properties of the stimulus and VEP amplitude and peak delay. The amplitude oi VEPs is reduced when gratings and checkerboards are oriented at 45’ and 135’ (Experiment 2). but amplitude is not significantly altered when cylindrical lenses are rotated similarly (Experiment 1). OX explanation for this might be that both higher hsrmonies and fundamental components contribute :o VEP amplitude. but that the neuronal mechanisms which mediate sensitivity to high and low spatial frequencies have different apparent latencies5 The VEP obtained with pattern alteration has been suggestti to arise from a mixture oi pattern responses and r:sponses to local luminance (Spekreijse, 1966; Regan and Richards, 1970, 1973; Regan. 1978). Recenill;. Regan (1978) has argued that checkerboards of medium spatial frequencies can result in a VEP composed of a mixture of pattern components and local frequency components. The contributions from pattern and local flicker mechanisms may derive from different cortical sites and have different transmission times. If the apparent latency of the pattern (i.e. high spatial frequency) mechanisms is slower than that of the local flicker (lower spatial frequency) mechanisms (see Levi and Harwerth, 1978). then the effect of blurring the edges (or selectively filtering high spatial frequencies) of checkerboards might be expected to result in shorter VEP peak delay when the highfrequency responses vanish. When the low-frequent! responses are reduced by blurring the fundamental. losses in amplitude due to this source may be com-

Effects of meridional variation on steady-state pensated for by increased contributions from highfrequency mechanisms with an overall increase in peak delay. This analysis is admittedly speculative and predicated on the assumption that the recording electrodes are positioned such that the high- and lowfrequency mechanisms exert approximately the same influence on amplitude. These data may also hold some implications for clinical assessment of the visual system. Many electrodiagnostic approaches employ the methodology reported here (i.e. sinusoidal modulation of patternalternated, normally oriented checkerboards). Results of both present experiments suggest the orientation of the fundamental Fourier component together with complex spat&temporal relationships described could interact significantly with refractive astigmatism or meridional amblyopia. The use of a normally oriented checkerboard with subjects exhibiting such problems in tht oblique meridians might yield reduced VEP amplitude and increased VEP latency to an even greater degree than in normal subjects. Thus, unless these responses are evaluated in terms of norms which reflect the orientation of the fundamental Fourier components, spurious conclusions may result.

VEPs

I399

May J. G., Forbes W. B. and Piantanida T. P. (1971) The visual evoked responses obtained with an alternating barred pattern: Rate. spatial frequency and wave length. Elecrroenceph. clin. NrurophJsioi. 30. 2X-228. May J. G.. Leftwich D. A. and Aptaker P. (1974) Evoked potentiai correlates of adaptation to wave length and orientation. Vision Res. 14. 143-146. Millodot M. and Riggs L. A. (1970) Refraction determined electrophysiologically. Archs Ophrhul. 84, 172-275. Regan D. (1966) Some characteristics of average steadystate and transient responses evoked by modulated light. E:lectroenceph.

clin. Neurophysiol. 20. 23-248. Porenrials in Psychology. Sensor! and Clinical Medicine. p. 77. Chapman &

Regan D. (1972) Ecoked

Physio/ogy Hall, London. Regan D. (1973) Objective refraction using evoked brain potentials. Inresr. Ophthul. 12, 569-679. ,Regan D. (1978) Assessment of visual acuity by evoked potential recording: Ambiguity caused by temporal dependence of spatial frequency selectivity. Vision Res. 18, 439-443. Regan D. and Richards W. (1971) Independence of evoked potentials and apparent size. Vision Res. I I, 679-684. Regan D. and Richards W. (1973) Brightness and contrast evoked potentials. J. opt. Sot. Am. 63, 606-61 I. Rietveld W. J., Tordior W. E.. Hagenouw J. R. B., Lubbers J. A. and Spoon Th. A. C. (1967) Visual evoked responses to blank and to checkerboard patterned flashes, Acra ph_vsiol. pharmoc. neerl. 14, 259-285. Analysis of’ EEG Responses in Man.

Spekreijse H. (1966) Junk, The Hague. REFERENCES

Appelle S. (1972) Perception and discrimination as a function of stimulus orientation: The “oblique effect” in man and animals. Psycho/. Bull. 78. 266278. Armington J. C., Crowin T. R. and Marsetts R. (1971) Simultaneously recorded retinal and cortical responses to pattern stimuli. J. opr. Sot Am. 65, 1514-1521. Blakemore C. and Campbell F. W. (1969) On the existence in the human visual system of neurones selectively sensitive to the orientation and size of retinal images. J. Physiol. 203, 237-260. Campbell F. W. and Maffei L. (1970) Electrophysiological evidence for the existence of orientation and size detectors in human visual system. J. P&o/. 207, 635-652. Frost B. J. and Kaminer J. J. (1975) The orientation anisotropy and orientation constancy: A visual evoked potential study. Perception 4, 51-58. Green M., Corwin T. R. and Zemon V. (1976) A comparison of Fourier analysis and feature analysis in patternspecific color aftereffects. Science 182, 147-148. Halliday A. M. and Michael W. F. (1970) Changes in pattern-evoked responses in man associated with the vertical and horizontal meridians of the visual field. J. Physiof. 208, 499-5 13. Jeffreys D. A. and Anford J. G. (1972) Source locatbns of pattern related visual evoked potentials I. Components of striate cortical origin. Expl brain Res. 16. 22& Kellv D. H. (1976) Pattern detection and the two-dimensiorta! Fourier transformation: Flickering checkerboards and chromatic mechanisms. Vision Res. 16, 277-279. Levi D. M. and Harwerth R. S. (1978) A sensory mechanism for amblyopia: electrophysiological studies. Am. J. Oprom. phgsiol. Opt. 55, 163-l 71. MacKay D. M. (1969) Evoked brain potentials as indicators of sensory information processing. Neurosci. Res. Program Bufl. 7, l-276. Maffei L. and Campbell F. W. (1970) Neurophysiological localization of the vertical and horizontal coordinates in man. Science 167, 386387. May J. G. and Matteson H. H. (1976) Spatial frequency contingent color aftereffects. Science 194, 145-147.

APPENDIX

Let marked squares have a value of + I. Let unmarked squares have a value of -I. Consider the origin to be at 0. The x spatial period then equals 2n and the y spatial period equals 2b. The Fourier series for a squarewave across the I direction is given by:

The Fourier series for a square-wave direction is given by :

across the y

ff.Y)= ir&siny. The series for the two dimensions is therefore:

x

Fig. 6. Square checkerboard pattern.

JA.MESG

1100 Now : coslrt

+

8) = cos I cos j3 - sin x sin b

(1)

cojtx

- /?I = cos I cos b 2 sin x sin p.

(2)

Subtracting

(2) cost2

er al

MAY

checkerboard with its curvature curvature m the XI plane.

t

(I) we have

in the y: plane.

2

rk

- fl) - cos(x + /?J = 2 sin x sin b

Of

,,...I

sin x sin fi = I Q[cos(x Re-writing j’(*, y) =

- 8) - cos(x + p)]

,.~.

,-’

2. c __,,,(!f_!?)_,,,.~~+!y). ’ ii2 ,k ml,, of two sets of

Y

/

lens positroned

along

the z-axis.

The refracting power m the 5)’ plane equals zero. The refracting power in the yz plane = F, The refracting power in any plane on an angle tJ with the x axis will equal F, COS’ B + F, sin’ H (Euler’s formula) or F,, = F, sin: 0. since F, equals 0. Expressing the power in diopters. this relation becomes D, = D, sin’ 0. Assume the checkerboard is positioned at the far point of a non-accomodated eye such that a grating with strips parallel to the x-axis is perfectly focused on the retina. The effective image formed along any other meridian will lie in front of the retina, with the retinal image distance incrsasing with D. The degree of blur (and hence. the reductren in contrast) will vary as a function of the retinal image distance.

for 1. m = 1. 3

,,.~.i,=~~cos.(~-~)+~cos.(~-~)

+;cOSn(~-~)+;cOs3n(~

” e

x

Fig. 7. Sample cylindrical

Expanding

..fl

_,I’

j‘(.~, y) with x = (nl.~), a and /? = (;rmy)‘b

This can be viewed as the superposition functions.

and no

-$)+

-~{cO+~)+fcOs~(~+~)

+jjcOsn(~+;j+;cos3n(~+~j+

Let u = b (a square f(.x.y)

grid). Then

= ${cosn(y)

+ ;c,sn(.Gj

+;c,s.(%j

+ ;cos3n(yj

+

- -$os.(~)

+ ;c,s.(3+)

+ ;cosn~~j

+ ;cos3ri(l;li)

+

Fig. 8. Image projection of an object located a simple cylindrical lens.

at x through

Referring to Fig. 8, d = lens-retina distance. e)e lens-retinal distance, s, = l/D, where D is the total dioptric power, and the object is effectively at zc. Let k = the distance between extreme rays; we have then k

Considering the first set of functions. these will correspond to sine-wave grids with stripes oriented at an angle 0 with respect to x as follows :

e = 18.4

(.x - 3~);

0 = 71.6’.

and

= g (d =k

e = -45’.

90” re:

s,)

1

The second set of functions yields sine-wave 90” with respect to the first set. i.e. (x + y):

s2=d-s,

2s,

L = Z(tan x)s2 = Z(tan z)(d - s,)

(I - y); 0 = 4sz (3.x - I’):

tanx=--_;

grids rotated

(x - .v)

(3,x + y);

6 = -18.4’.

90”re:

(x - 3~)

(x + 3~);

0 = -71.6’.

90”re:

(3x -4’).

The coefficients for each cosinusoidal term in the function sets can be looked upon as representing the peak contrast. Now consider a cylindrical-planar lens placed before the

d-l ( SI

=(kD-I) j

The total dioptric power D equals D,,,, + D,,,. and d is approximately equal to the cornea!-retinal distance. Thus. = I and the expression for L reduces to D L’z kDd = KD where K is constant and D is the dioptric power of the cylindrical lens. The reduction of coefficients in the series representing the checkerboard equals I/( I + De) where De is the effectt\e power of the lens for any meridian measured relative to the center line of the cylinder. When the lens is positioned

Effects of meridional variation on steady-state VEPs such that its center line is parallel to the .r-axis, the first four terms of the first function set are attenuated by I:(1 + OSKD). I!(1 + IKD). I;‘(1 + 0.9KD). I:(I + OSKD). respectively. The orthogonal components to these first four components are attenuated by a similar amount. When the lens is oriented such that the center line is at 15’ relative to the .y-axis. the first four terms of the first

1401

function set are attenuated by I. I,‘(1 + O.XD), I,(1 + O.ZKD). 1. The first four components of the second set are attenuated by I ‘(I + KD). I :(I + 0.8KD). li(l + 0.8KD). I:(I + KD). Thus. a -t5’ lens orientation produces a simplification in the patterned stimulus as opposed to a reduction in contrast without significant simplification (0’ orientation).

Effects of meridional variation on steady-state visual evoked potentials.

OF MERIDIONAL VARIATION EFFECTS VISUAL ON STEADY-STATE EVOKED POTENTIALS’ JAMESG. MAY’ and JOHN K. CULLENJR Louisiana State University Medical Center,...
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