The Effects of Astigmatism on Sensitivity to Sinusoidal and Square Wave Gratings

Transcription

1 <fc?r~ O /80/ $02.00/0 AMERICAN JOURNAL OF OPTOMETRY & PHYSIOTOGICAL OPTICS Vl. 57, N. 6, pp June 1980 Cpyright 1980 American Academy f Optmetry Printed in U.S.A. The Effects f Astigmatism n Sensitivity t Sinusidal and Square Wave Gratings t*s JO ANN S. KINNEY* Naval Submarine Medical Research Labratry, Naval Submarine Base, Grtn, Cnnecticut Abstract Cntrast threshlds fr different spatial frequencies were measured fr fur individuals with ptimum ptical crrectin and with 2 D f astigmatismm induced at varius meridians. Sensitivity fr sine waves f lw spatial frequencies was unaffected by the astigmatism; hwever, grss changes were fund at high spatial frequencies when the astigmatism was induced with the pwer meridian perpendicular t the rientatin f the stripes. Fr square waves, the results were cmparable at high spatial frequencies, but astimgatism als prduced a decrement at 0.2 cycles/degree. This latter effect can be predicted by assuming that astigmatism results in a lss f higher rder harmnics in the respnse t square waves. Key Wrds: spatial cntrast threshlds, astigmatism Althugh the effects f astigmatism n spatial cntrast sensitivity have nt been subjected t extensive investigatin, results can be predicted frm the ptics f astigmatic systems and frm the data n the effects f defcusing by spherical lenses. An astigmatic ptical system fcuses a pint surce as tw fcal lines, with cnturs parallel t the emmetrpic meridian appearing blurred while perpendicular cnturs remain clear. 1,2 Differential effects wuld be predicted fr grid patterns riented parallel t, r perpendicular t, the axis f astigmatism. The fact that defcusing affects primarily the high spatial frequencies has been realized since the riginal study f Campbell and Green. 3 Thus, we wuld predict that astigmatism wuld prduce decrements in cntrast sensitivity fr vertically riented sine waves Received December 4, 1979; revisin received February 11, * Research Psychlgist, Ph.D. nly at high spatial frequencies (the specific frequencies depending upn the amunt f astigmatism) and that the decrements wuld be maximal fr astigmatism with the pwer meridian hrizntal. Furthermre, accrding t the multiple channel thery f cntrast sensitivity, differential effects n the respnses t sine waves and square waves shuld ccur if the effects f astigmatism are sufficiently large t eliminate the higher rder harmnics frm participating in the respnse t square waves f lw spatial frequency. This study gives an empirical test f these predictins by measuring cntrast threshlds fr vertical sine and square waves with subjects in whm 2 D f astigmatism was induced in different meridians. METHODS Sinusidal and square-wave gratings, in a vertical dimensin, were generated n a Hewlett-Packard 1311A CRT with a P31 phsphr by cnventinal techniques. 4 The 372

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3 June 1980 Effect f Astigmatism n Grating Visibility Kinney 373 mean luminance f the scillscpe was 4.5 cd/m 2, and its angular subtense was 10.5 X 13.5 degrees at a viewing distance f 114 cm. The surrund was dimly illuminated at 0.1 cd/m 2. Five spatial frequencies, 0.2, 0.5, 2, 5, and 10 cycles/degree (cpd), were chsen t sample adequately visual sensitivity t different spatial frequencies. Fur subjects using bincular visin were emplyed. All were first crrected fr the bserving distance f 114 cm, by adding lenses f D t their nrmal crrectin fr infinity. This crrectin is hereafter referred t as the "n astigmatism" cnditin. Fr the ther cnditins, astigmatism was induced in each eye by the additin f a cylindrical lens f +2 D. The astigmatism was induced at varius meridians by rienting the cylinder axes at 90, 135, and 180 degrees, fr use with the sine waves. Only the extreme cnditins f n astigmatism and a cylinder axis f 090 degrees were emplyed with the square waves. Five levels f mdulatin were selected fr each spatial frequency t range frm zer t an easily perceptible grating. Each level was presented twice in a given sessin. All five levels at all five spatial frequencies were cmbined and randmized fr a ttal f 50 judgments per sessin. The subject's task n each presentatin was simply t state whether r nt stripes were perceived. There were n tempral cnstraints; the stimulus cntinued t be visible until the subject respnded. Tw sessins were run fr each cnditin f astigmatism s that final limens fr each spatial frequency were based upn 20 judgments. RESULTS The mean data fr the fur subjects viewing sinusidal gratings are given in Fig. 1. MEAN 4 St SINE WAVES N Astigmatism 2 diptsr» f Astigmatism t A 4 t.c in t O _L J_ J_.2 t cycles per degree FIG. 1. Cntrast threshlds fr sine-wave gratings with subjects fully crrected r with 2 D f astigmatism at different meridians. The numbers refer t the axis f the cylinders. Mean f fur subjects, with vertical bars indicating ±1 SD fr n astigmatism (]) and fr astigmatism axis 90 degrees ([).

4 374 AM J OPTOM & PHYSIOL OPflCS The shapes f the curves fr all fur individuals were the same, as were the c.ifferential effects f the axis f astigmatism. When fully crrected, cntrast threshlds fr all subjects are best at 2 cpd and rise rapidly in either directin; the curve is in agreement with many in the literatu-e fr these experimental cnditins. 577 With the 2 D cylinder at an axis f 180 degrees (that is, with the pwer meridian parallel t the rientatin f the stripes), there is n change in cntrast threshlds at any spatial frequency. With the cylinder at an axis f 90 degrees, threshlds fr lw spatisl frequencies are unaffected whereas thse fr high spatial frequencies are prer by almst a lg unit. With an intermediate rientatin f the stripes, the lss f sensitivity is intermediate. The vertical bars shw ± ne standard deviatin arund the means fr the n astigmatism and the axis 90-degree astigma- Vl. 57, N. 6 tism cnditins; there is cmplete verlap f standard deviatins at the lw spatial frequencies and nne at high. Standard deviatins fr the ther cnditins, nt shwn t simplify the figure, were f cmparable size. Cmparable data fr the same fur subjects, fr square waves, are shwn in Fig. 2 fr the emmetrpic cnditin and the wrst rientatin f induced astigmatism. Fr the astigmatic cnditin, cntrast threshlds at frequencies f 2 cpd and higher are cnsiderably prer, whereas there is virtually n difference at 0.5 cpd; these results are thus cmparable t thse fr sine waves. Hwever, at 0.2 cpd, there is an apparent change: in cntrast with the data fr sine waves, astigmatism has prduced a reductin in sensitivity resulting in a higher threshld fr this lw spatial frequency. The standard deviatins arund the means at 0.2 cpd barely verlap. I.0 MEAN 4 Ss Square Waves N Astigmatism X 13 at cycles per degree FIG. 2. Cntrast threshlds fr square w«i tr the same fur subjects, either crrected r with 2 D f astigmatism at axis 90 degrees. Vertical bars are ± 1 SD. 10

5 June 1980 Effect f Astigmatism n Grating Visibility Kinney 375 This difference is further illustrated in Fig. 3 which shws the rati f square wave t sine-wave sensitivity fr individual subjects with and withut astigmatism. The data are very similar t the riginal cmparisn by Campbell and Rbsn 8 and d nt deviate systematically frm the theretical predictin f 1.27 at frequencies f 0.5 cpd and higher. At 0.2 cpd, hwever, there is a large increase in the sensitivity rati, which averages 7.4 withut astigmatism and 4.4 with it. The effect f astigmatism n this sensitivity rati is much mre apparent in the data f sme subjects than tners. At ne extreme, the sensitivity rati fr SML is reduced frm 8.8 t 3.7 by 2 D f astigmatism, whereas the cmparable decrease fr AR is nly frm 4.5 t 3.9 DISCUSSION The effects f astigmatism n cntrast sensitivity t sine and square waves are, in general, well predicted by thery and in gd agreement with the data accumulated ver the past 15 years f study f cntrast sensitivity. Thus, the fact that astigmatism affects the high spatial frequencies stems frm the defcusing f the image and ccurs in all ptical systems. The amunt f deteriratin depends, f curse, n the amunt f blurring. These data n astigmatism fit well, quantitatively, with data in the literature fr blurring by spherical lenses. Fr example, Campbell et al. 9 reprt 0.35 lg unit at all frequencies abve 5 cpd fr 0.5 D f blur. Regan's 10 measures shw 0.6 lg unit fr 1 D f defcusing, and these data RATIO f SENSITIVITY SQUARE/SINE WAVES WITH a WITHOUT ASTIGMATISM pen symbls - withut clsed symbls-with < SML > AR A JK v CM 01 CO (!) > 10 0> I * w- 3 <» CO *- & Tfi i. $* < 1.27 r cycles per degree FIG. 3. Rati f empirical sensitivity f square waves t sine waves fr individual subjects. Open symbls refer t the fully crrected cnditin; clsed, t the astigmatic. The ratis in the square are theretical ratis as described in the text.

6 376 AM J OPTOM & PHYSIOL OPTICS reveal a maximum f nearly 1.0 lg unit fr the 2 D f astigmatism in the wrst mend ian. Mrever, the cmparisn f sensithjity t square waves and sine waves f the same spatial frequency is in general agreement with the riginal cmparisn f Campbell and Rbsn. 8 With the subjects apprpriately crrected, the difference between sensitivity t square waves and sine waves is as predicted frm the thery. Thus, at 0.5 cpd and higher spatial frequencies, there are n differences between the tw curves ther than that f amplitude, and the factr f 1.27 adequately describes the data. This implies that there are n harmnics invlved in the sensitivity t square waves, nr shuld there be any. At the lwest spatial frequency, 0.2 cpd, hwever, there is a large increase in squjirewave sensitivity ver that f sine waves. This increase, an average rati f 7 is greater than that reprted by Campbell and Rbsn 8 r by Furchner et al. 11 fr square waves f 0.25 cpd. A likely explanatin is the inclusin f respnses by channels sensitive t higher rder harmnics in the respnse t the square wave. Indeed, Fig. 1 shws that many f the higher rder harmnics have the necessary sensitivity t be included in the respnse f square waves at 0.2 cpd* with the greatest sensitivity shwn fr the first harmnic at 0.6 cpd. The ::act that many higher rder harmnics have the requisite sensitivity can be attributed t the specific experimental cnditins emplyed which depress sensitivity t lw spatial frequencies. Bth the use f a lng duratin stimulus and a finite target size have this effect. 12 Theretical sensitivity t square waves, derived frm the thery f prbability summatin amng independent channels, 13,14 is cmpared t the empirical data in the bx " Furier analysis (Nachmias' 5 ) f a square wave at a given spatial frequency yields 1.27 times the amplitude (A) f the fundamental, f (the sine wave at the same frequency), plus dd-numbered harmnics at regularly decreasing amplitudes: l k A(3f) + ^A(5f) + WA(7f), etc. Thus, fr a given harmnic t be invlved in the sensitivity t a specific square wave, the sensitivity t it must be prprtinally increased. At: if fr example, sinusidal sensitivity must be 3 times as areat as at f t prduce equal cntributins. Vl. 57, N. 6 in Fig. 3. The new ratis in this bx were calculated fr each individual, using the hypthetical sine-wave respnse (f Va the sine-wave sensitivity t 0.6 cpd), either alne r tgether with V& the sensitivity t 1.0 cpd) cmpared t the empirical squarewave data. The ratis fr emmetrpic visin emply prbability summatin between channels at 0.6 and 1.0 cpd. b Since astigmatism reduced the hypthetical sensitivity t 1.0 well belw that f 0.6 cpd, fr all subjects, nly ne channel was emplyed in these ratis. This prcedure eliminates bth the large square-sine wave ratis at 0.2 cpd and the differences between the emmetrpic and astigmatic cnditins. Thus, cncrete supprt is given t bth the general thery f prbability summatin amng independent channels and t the suggestin that astigmatism reduces sensitivity t lw frequency square waves by remving the cntributin f higher rder harmnics. Nnetheless, all eight ratis are slightly abve the theretical value f 1.27, implying sme additinal factr is invlved. This result is in general agreement with Furchner et al. 11 wh fund that patterns cmpsed f very lw spatial frequencies were mre visible than predicted by prbability summatin. The practical implicatins f this study are that astigmatism is detrimental t visin nly fr small targets (high spatial frequencies) r fr the recgnitin f frms whse frequency cmpsitin requires gd visin fr high spatial frequencies. Thus, the astigmatic, individual shuld see as well as the emmetrpe if he is clse enugh t the target s that it is cmpsed f nly lw spatial frequencies. This implicatin has recently been tested and fund t be crrect in accunting fr the visin f astigmatic periscpe peratrs using different amunts f magnificatin. 17 ACKNOWLEDGMENTS Wrk perfrmed under Naval Medical Research and Develpment Cmmand Wrk Unit ZF b Quick's methd 16 fr calculating the effects f prbability summatin fr independent channels was emplyed t determine the sensitivity predicted frm the use f all pssible harmnics, but n further increase was btained.

7 June 1980 Effect f Astigmatism n Grating Visibility Kinney 377 REFERENCES 1. Brish, I. M., Clinical Refractin, 3rd ed., Chicag, Prfessinal Press, Inc., Mitchell, D. E., R. D. Freeman, M. Milldt, and G. Haegerstrm, Meridinal amblypia: Evidence fr mdificatin f the human visual system by early visual experience, Visin Res., 13: , Campbell, F. W., and D. G. Green, Optical and retinal factrs affecting visual reslutin, J. Physil. (Lnd.), 181: , Schade, O. H., Optical and phtelectric analg f the eye, J. Opt. Sc. Am., 46: , Van Meeteren, A., and J. J. Vs, Reslutin and cntrast sensitivity at lw luminances, Visin Res., 12: , Carlsn, C. R., R. W. Chen, and I. Grg, Visual prcessing f simple tw-dimensinal sine-wave luminance gratings, Visin Res., 17: , Van Ness, F. L., and M. A. Buman, Spatial mdulatin transfer in the human eye, J. Opt. Sc. Am., 57: , Campbell, F. W,, and J. G. Rbsn, Applicatin f Furier analysis t the visibility f gratings, J. Physil. (Lnd.), 197: , Campbell, F. W., J. Kulikwski, and J. Levinsn, The effect f rientatin n the visual reslutin f gratings, J. Physil. (Lnd.), 187: , Regan, D., Visual evked ptentials and visual perceptin in multiple sclersis, in Prceedings f the San Dieg Bimedical Sympsium 1977, ed- ited by J. I. Martin, Vl. 16, New Yrk, Academic Press, 1977, pp Furchner, C. S., J. P. Thmas, and F. W. Campbell, Detectin and discriminatin f single and cmplex patterns at lw spatial frequencies, Visin Res., 17: , Kelly, D. H., Visual cntrast sensitivity, Opt. Acts, 24: , Graham, N., and J. Nachmias, Detectin f grating patterns cntaining tw spatial frequencies: A cmparisn f single-channel and multiple-channel mdels, Visin Res., 11: , Sachs, M. B., J. Nachmias, and J. G. Rbsn, Spatial-frequency channels in human visin, J. Opt. Sc. Am,, 61: , Nachmias, J., Effect f expsure duratin n visual cntrast sensitivity with square-wave gratings, J. Opt. Sc. Am., 57: , Qucik, R. F., A vectr-magnitude mdel f cntrast detectin, Kybernetik, 16: 65-67, Luria, S. M., J. A. S. Kinney, C. L. Schlichting, and A. P. Ryan, The limiting effects f astigmatism n visual perfrmance thrugh periscpes. Naval Submarine Medical Research Labratry, Grtn, CT, NSMRL Rep. 905 September AUTHOR'S ADDRESS: J Ann S. Kinney Naval Submarine Medical Research Labratry Naval Submarine Base New Lndn Grtn, Cnnecticut 06340

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