JOURNAL OF THE OPTICAL SOCIETY OF AMERICA VOLUME 65, NUMBER 1 JANUARY 1975

Contrast sensitivity and viewing distance* Robert T. Hennessy† and Whitman Richards

Department of Psychology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (Received 3 September 1974)

Index Headings: Vision; Interference; Laser; Polarization.

A number of studies have reported that the size of hu­man visual receptive fields may change with accomoda­tion or convergence distance of the e y e s . 1 - 3 Recently, Cavonius and Hilz4 tested the hypothesis that neural changes in receptive field size a r e responsible for changes of visual acuity with viewing distance. They used a l ase r technique for creating sinusoidal in terfer­ence fringes on the retina, which bypasses the influ­ence of accommodation on the ret inal image. Thei r resu l t s show no changes of contrast sensitivity depen­dent upon the accommodation and convergence distance of sinusoidal targets ranging from 1 to 60 c/deg. The following is a report of a s imi lar study that confirms the findings of Cavonius and Hilz.

Interference fringes were created in the ret ina by use of a laser apparatus s imilar to that described by Camp­bell and Green.5 Beam-splitt ing p r i s m s were used to superimpose the interference pat tern, a uniform field of l a se r light, and the fixation target in the field of view of the subject 's right eye. The fixation target was also seen by the subject 's left eye, through a beam-spli t t ing pr ism identical to that in front of his right eye. The sinusoidal interference pat tern and the uniform field were both produced by light from a Metrologic 2 mW unpolarized He-Ne l a se r . Random interference points or speckle charac ter i s t ics of l ase r light were apparent in both fields. The two laser fields were c ross polar­ized and the relative i r radiances were controlled by a rotating piece of Polaroid sheet.

For each spatial frequency, additional neutral density f i l te rs , a s required, were inserted or removed from the paths of the homogeneous field or the sinusoidal in­terference pattern in order that the threshold de te rmi­nations would be near the middle of the polar izer range. These insert ions or removals were made in such a man­ner as to keep the mean luminance constant at 15 cd/m2 , as measured by a brightness match to an adjacent field previously calibrated with a Macbeth i l luminometer.

The binocular fixation target consisted of a homoge­neous, white annulus of 15 cd/m 2 equivalent luminance. The size of the annulus was adjusted to subtend a visual angle of 3° diameter by 1/6° wide. With proper align­ment, the monocular test field appeared a s a 2° disk lying within the fixation annulus. The remainder of the visual field was dark.

Contrast-sensit ivity measurements were obtained for seven sinusoidal spatial frequencies, 0 .6 , 1.3, 2 .6 , 5.0, 7. 5, 10, and 20 c/deg with fixation target distances of 25 and 175 cm.

Four men and one woman, ages 23-41, served a s subjects. All had 20/20 near and far acuity, with cor ­rection if necessary . Each subject viewed the fixation

target three t imes at both fixation distances for each of the seven spatial frequencies. The sequence of fixation-target distances was alternated in a counterbalanced manner for the five subjects. For each fixation distance and spatial frequency, the subject was instructed to ad­just the angle of a Polaroid sheet, s tar t ing below thresh­old of detection until the sinusoidal pattern became just noticeable. A total of six adjustments was made for each spatial frequency at each viewing distance by each subject.

It was not possible to transform angular settings of the polar izer to accurate values of absolute contrast b e ­cause the average luminance of the sinusoidal pattern was not known exactly. Also, polarization from ref lec­tions within the optics of the apparatus may affect the relationship between polar izer angle and transmit ted light. With our best allowance for such fac tors , we e s ­timate that the best contrast sensitivity obtainable for any observer was approximately 0. 09 for a spatial f re­quency of 10 c/deg. This value i s higher than i s usually reported, probably because the interference technique generates masking pat terns from multiple extraneous sources within the optics of the eye. Determination of the absolute contrast sensitivity of the eye is not our objective, however. Rather , the point of interest is whether the relat ive contrast modulation for the near -and far-fixation distances differ significantly; i . e . , does contrast sensitivity change as a function of fixation d i s ­tance.

FIG. 1. Comparison of sinusoidal contrast sensitivity for near and distant fixation. The transmittance ratio shown on the or­dinate is equal to the contrast ratio at threshold for the two viewing distances. Ratios less than 1. 0 indicate that near fixation has the higher threshold.

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98 L E T T E R S TO THE EDITOR Vol. 65

The angular measures were transformed to a linear variable, transmittance, by use of the formula T = cos2(θ), where T is the transmittance and θ is the angle between the two fixed and one variable Polaroid sheets. The ratio was then computed, Tf/Tn , where Tf and Tn are the threshold transmittances for the far-fixation and near-fixation conditions, respectively. This ratio is equal to the contrast ratio at threshold. The mean transmittance ratios are shown in Fig. 1 as a function of spatial frequency. A repeated-measures analysis of variance (F= 4.67; dƒ = 6,24, p< 0. 05) in­dicated significant differences of transmittance ratios.

Duncan's New Multiple Range Test6 revealed that the transmittance ratio for the 20 c/deg spatial frequency was responsible for the significant F value. It can be seen in Fig. 1 that the transmittance ratio for 20 c/deg is less than 1.0 indicating that, for the near-fixation condition, contrast sensitivity was less than for the far-fixation condition. Fixation condition had no significant effect on contrast sensitivity at the six other spatial frequencies tested; the transmittance ratios are all very nearly 1.0.

Because all but one spatial-frequency condition showed no differences of contrast sensitivity as a function of viewing distance, we conclude that accommodation and convergence do not affect sinusoidal contrast sensitivity, or if they do, they have an effect of less magnitude than observer variability. If we attribute the significant effect at the 20 c/deg spatial frequency to an undeter­mined systematic error in our experimental procedure, then our results are in substantial agreement with those of Cavonius and Hilz.

*Work supported by the AFOSR under Contract F44620-69-C-0108 to WR and by the Sloan Foundation Grant and NIGMS Training Grant No. GM 01064 awarded to Prof. H. -L . Teuber, Dept. of Psychology, M.I. T.

† Now at Human Factors Research, Inc . , Goleta, Calif. 93017. 1 W. Richards, Neuropsychologia 5, 63 (1967). 2 E. Marg and J. E. Adams, Experientia 26, 270 (1970). 3 L. Harvey, Vision Res. 10, 55 (1970). 4 C. R. Cavonius and R. Hilz, J. Opt. Soc. Am. 63, 929 (1973). 5 F . W. Campbell and D. Green, J. Physiol. (Lond) 181, 576

(1965). 6 D. B. Duncan, Biometrics 11, 1 (1955).