Factors Influencing Normal Perimetric Thresholds Obtained Using the Humphrey Field Analyzer

Transcription

1 Investigative Ophthalmology & Visual Science, Vol. 33, No. 3, March 1992 Copyright Association for Research in Vision and Ophthalmology Factors Influencing Normal Perimetric Thresholds Obtained Using the Humphrey Field Analyzer Peter R. Herse The relationships between dioptric blur, pupil size, retinal eccentricity, and retinal sensitivity were investigated in the central 5 of the visual field in 10 normal subjects using the Humphrey Field Analyzer. Pupil size did not influence the foveal sensitivity or retinal profile in the unblurred condition. The slope of the retinal profile was significantly steeper in the 3 mm pupil size condition ( 0.62 db/degree) than when compared to the 8 mm pupil size condition (-0.34 db/degree), when averaged over all dioptric blur conditions. The depth of focus for the 3 mm pupil size condition (3.86 diopters) was significantly greater than that found for the 8 mm pupil size condition (1.82 D). The retinal threshold doubling eccentricity (E2) was calculated to be similar to that of grating acuity and contrast sensitivity (3.71). The data suggest that while large depth of focus effects in small pupil sizes appear to reduce the need for accurate refractive error corrections in determining perimetric retinal sensitivities, variations in the slope of the retinal profile under conditions of uncontrolled dioptric blur and pupil size may result in the artifactual sensitivity decreases. Therefore, it is recommended that measurement of pupil size and accurate correction of near refractive errors be performed to minimize the possibility of incorrect detection of central visual field defects. Invest Ophthalmol Vis Sci 33: , 1992 The retinal sensitivities measured by perimetry decrease with increasing levels of dioptric blur. 1 " 8 Similarly, the effect of variations in pupil size on retinal sensitivity also has been extensively studied. In cases of extreme change in pupil size, perimetric sensitivities have been shown to decrease with decreases in pupil diameter. 49 " 10 Reduced retinal illumination"" 14 or diffraction effects 15 that occur in the small pupil diameter condition have been proposed as explanations of these findings. Conversely, at the clinical level, numerous reports 16 " 19 have established that perimetric retinal sensitivity is not noticeably influenced over the normal physiological range of pupil sizes. However, previous studies in the literature have implicitly assumed no interaction between pupil size and defocus effects. This apparent separation of the effects of dioptric blur from the effects of pupil size is probably artifactual. Pupil diameters of 2-4 mm diameter tend to minimize the effects of dioptric blur by decreasing the point spread of the retinal image This effect is very familiar to the clinician through the finding of a large depth of focus in a patient with small pupil diameters. From the Department of Optometry, University of Auckland, Auckland, New Zealand. Submitted for publication: January 31, 1991; accepted October 21, Reprint requests: Peter R. Herse, Department of Optometry, University of Auckland, Auckland, New Zealand. A recent study 22 explored the effect of refractive blur and retinal eccentricity on static perimetric thresholds using fully dilated pupils. While useful information was provided regarding the normal visual field profile, the authors admit that the large pupil sizes used in their study may have resulted in an overestimation of the clinical effect of refractive blur and retinal eccentricity. 22 Therefore, it is the purpose of the present study to establish the effect of refractive blur and retinal eccentricity on static automated perimetric thresholds over a range of pupil sizes. Materials and Methods Macular sensitivities were measured on the right eyes of 10 normal subjects (five male, five female) between the ages of years. All subjects were optometry students and practiced perimetric observers. All subjects had corrected visual acuities of 20/20 or better. No ocular pathology was detected using ophthalmoscopic examination. Visual field testing was performed within the central 5 of the visual field using an automated perimeter (Humphrey Field Analyzer; macular threshold program plus foveal threshold option; stimulus size III). This program assessed retinal sensitivity over a grid of 16 points plus a foveal test (Fig. 1). Two drops of tropicamide 1.0% ophthalmic solution were administered to the right eye of each subject to dilate the pupil and minimize the effects of accommodation. After 5 min, a "cycloplegic" refraction of 611

2 612 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / March 1992 Vol Fig. 1. Spatial distribution of peri metric stimuli locations. All units are in degrees from fixation. the dilated eye was performed. The pupil diameter was measured after completion of the refraction. All subjects had pupil diameters greater than 8 mm at this stage. An 8 mm artificial pupil plus the "cycloplegic" refraction (including a D working distance lens to compensate for the perimeter bowl radius) was placed before the right eye of the subject using the back lens cell of a trial frame. The left eye was occluded. The distance from the cornea to artificial pupil was approximately 10 mm. Macular thresholds (including foveal thresholds) were determined over a randomly presented range of dioptric blurs (0.00 D, D, D, D, D, D) viewing through the 8 mm artificial pupil. At the end of this thresholding cycle, the subjects' pupil diameters were verified still to be greater than 8 mm. The 8 mm artificial pupil was replaced by a 3 mm artificial pupil, and macular thresholds were assessed over the same range of dioptric blurs as previously. Poor accommodative function was verified at the end of each thresholding cycle using a "push-up" test (inability to clearly read N.8 print within arms length). Subject within-test fatigue appeared to be negligible as all subjects were alert and reliable. Only three false positives and no false negatives were recorded in the 120 visual field assessments performed during the study. Completion of the experimental paradigm for each subject required approximately 1.5 hr. Effect of Blur on Foveal Thresholds Foveal thresholds for both pupil sizes were compared over the six levels of dioptric blur. Linear regressions between foveal sensitivity and dioptric blur were derived for both pupil sizes. The mean slopes of the linear regressions for both pupil sizes were compared using analysis of variance (ANOVA). Effect of Blur on Averaged Macular Thresholds All of the 48 sensitivity values (16 locations X 3 threshold estimates) determined by the macular threshold program were averaged for each level of dioptric blur. Linear regressions between macular sensitivity and dioptric blur were derived for both pupil sizes. The slopes of the linear regressions were compared for both pupil diameters using ANOVA. Effect of Increasing Retinal Eccentricity The angular distance of the 16 measured points in the visual field from the fixation point were determined (0.00, 1.41, 3.16, and 4.24 ). The sensitivities of points with equal retinal eccentricities were then averaged, and linear regressions between averaged sensitivity and retinal eccentricity were derived for the six levels of dioptric blur for each of the two pupil diameters. The slopes of the linear regressions within each pupil size group for the six levels of dioptric blur were compared using ANOVA followed by Tukey's multiple comparison test (P = 0.05). Results Effect of Blur on Foveal Thresholds Foveal thresholds were found to decrease in a linear manner (r 2 > 0.90) with increasing dioptric blur for 3 mm and 8 mm pupil diameters (Fig. 2). The rate of decrease in the 8 mm pupil size condition (-2.45 db/ D) was significantly greater (ANOVA; P = 0.001) than in the 3 mm pupil size condition (-1.43 db/d) BLUR (D) Fig. 2. Variation of foveal sensitivity with increasing amounts of dioptric blur (n = 10).

3 No. 3 FACTORS INFLUENCING AUTOMATED PERIMETRIC THRESHOLDS / Herse 613 Table 1. Variation in the slopes of the retinal sensitivity profile with increasing amounts of dioptric blur for 3-mm and 8-mm pupil size conditions Pupil Blur (D) 0.00 Eccentricity (degrees) Regression slope (db/degree) 3 mm 8 mm ± 0.22 (SD) ± ± ± ± ± 0.22 Mean = ± 0.32 (SD) ± ± ± ± ±0.22 Mean = Effect of Blur on Averaged Macular Thresholds Averaged macular thresholds were found to decrease in a linear manner (r 2 > 0.90) with increasing dioptric blur for 3 mm and 8 mm pupil conditions. The rate of decrease in the 8 mm pupil size condition (-1.84 db/d) was significantly greater (ANOVA; P = 0.001) than in the 3 mm pupil size condition (-1.10 db/d). The rate of decrease of sensitivity in the 3 mm foveal test condition (-1.43 db/d) was not significantly different (paired t-test; P > 0.05) from the 3 mm averaged macular test condition (-1.13 db/d). The rate of decrease of retinal sensitivity in the 8 mm foveal test condition (-2.45 db/d) was significantly different (paired t-test; P < 0.005) from the 8 mm averaged macular test condition (-1.84 db/d). Effect of Increasing Retinal Eccentricity The averaged sensitivity data obtained in this analysis are shown in Table 1. Sensitivity was found to decrease in a linear manner with increasing retinal eccentricity (r 2 > 0.90). The rates of sensitivity decrease with increasing retinal eccentricity, or the retinal profiles, were not significantly different between the various increasing levels of dioptric blur in the 3 mm pupil size condition (ANOVA followed by Tukey's test; P = 0.05). The average slope of the retinal profile over all levels of dioptric blur for the 3 mm pupil size condition was calculated to be db/degree. A similar result was found in the 8 mm pupil size condition. The slopes of the retinal profiles were not significantly different over five of the six levels of dioptric blur measured (ANOVA followed by Tukey's test; P = 0.05). The slope of the retinal profile was found to be significantly steeper (ANOVA followed by Tukey's test; P = 0.05) in the unblurred condition. The average slope of the retinal profile over all levels of dioptric blur for the 8 mm pupil condition was calculated to be db/degree. The average slope of the retinal profile in the 3 mm condition ( 0.62 db/degree) was found to be significantly different (ANOVA followed by Tukey's test; P = 0.05) from the averaged retinal profile slope in the 8 mm condition (-0.34 db/degree). The slope of the retinal profile in the unblurred 3 mm pupil size condition (-0.73 db/degree) was not significantly different (paired t-test; P > 0.10) from that found in the unblurred 8 mm pupil size condition (-0.77 db/degree). Discussion 5 Degrees Versus 30 Degrees It should be emphasized that the data of this investigation apply only to the central 5 of the visual field. Can the information gained from within the central 5 of the visual field be directly related to the more clinically relevant 30 visual field? While this question was not directly addressed in this study, it is useful to compare the slopes of the retinal sensitivity function in the central 5 visual field to that obtained in the central 30 visual field. The slope of the unblurred retinal sensitivity profile for the central 5 of the visual field was found to be about db/degree. This lies within the range of reported slopes for the central 5 visual field (-0.86 db/degree; db/degree; db/degree 23 ). In comparison, the slope of the unblurred retinal sensitivity profile for the central visual field has been reported as almost half as steep (-0.44 db/degree; db/degree; db/degree 23 ). Thus, it appears inappropriate to directly apply the conclusions obtained in

4 614 INVESTIGATIVE OPHTHALMOLOGY & VISUAL SCIENCE / Morch 1992 Vol. 33 this study to data related to the more clinically common 30 visual field. Weber's Law and Decreased Retinal Illumination Automated perimeters operate at relatively low background illumination levels (Humphrey Field Analyzer, 31.6 apostilb; OCTOPUS, 4 asb). A concern has been raised that with small pupil sizes, retinal illumination would drop below that necessary for Weber's law to operate. This theoretically would increase the intensity of the test stimulus needed for threshold detection, and thus would artifactually increase the possibility of detecting visual field depressions. Experimental evidence that supports this proposal is available It should be noted, however, that pupil size was not adequately controlled in these experiments, leading to some doubts about the conclusions of the studies. In the experiment of Klewin and Radius, 13 normal undilated pupils were used while neutral densityfilterswere placed before the test eye. With a more dense filter, the pupil would dilate. Thus retinal illumination was not simply a function of the neutral density filter used. Pupil size also was relatively uncontrolled in the experiment of Huer et al, 14 in which the only mention of pupil size indicated that the pupils were fully dilated. A more rigorous experiment, in which pupil size was controlled, has been performed by Wood et al. 19 In this study, retinal sensitivity was assessed over a range of three pupil sizes and two retinal illumination levels. It was found that the mean retinal sensitivity was unaffected by pupil size over a background luminance range of asb. This was interpreted to suggest that Weber's law remained constant over the range of adaptation levels used. This conclusion is supported in the present study, which found no significant difference between the foveal sensitivities or the slopes of the unblurred retinal profiles in the 3 mm and 8 mm pupil size conditions. Thus, based on the apparent conflict in the literature, it remains uncertain whether the previously postulated breakdown of Weber's law occurs in small pupil perimetry. Effect of Dioptric Blur on Retinal Sensitivity Macular sensitivity: It has been reported that the averaged macular sensitivity in eyes with dilated pupils (>4 mm) decreased 1.26 db/d of blur. 22 This result lies between the averaged macular results obtained in the present study for 3 mm (-1.10 db/d) and 8 mm (-1.84 db/d) pupil diameters. Foveal sensitivity: The unblurred foveal sensitivities found in the 3 mm (35.9 ± 1.3 db) and 8 mm (36.6 ± 1.2 db) pupil size conditions were not significantly different (paired t-test: P > 0.10), demonstrating that dilation does not appear to influence foveal sensitivity. This agrees with a similar finding by Lindenmuth et al. 24 Can the decrease in foveal sensitivity found with increasing levels of dioptric blur be explained by the optical modulation transfer function (MTF) of the eye? The ocular MTF decreases with increasing levels of dioptric blur, and the ocular MTF decreases more rapidly with increases in pupil diameter. 25 " 27 It is possible to calculate a rate of decrease in the theoretical ocular MTF per diopter of blur for 3 mm (-1.85 db/ D) and 5 mm (-2.67 db/d) pupil size conditions. 25 These calculated rates agree reasonably with rates of decrease in sensitivity per diopter of blur found in the present study for the 3 mm (-1.45 db/d) and 8 mm (-2.45 db/d) pupil size conditions. The similarity of the calculated data suggests that the decrease in foveal sensitivity occurring with increasing dioptric blur may be explained by the effects of dioptric blur on the optical MTF of the eye. The rate of decrease in foveal sensitivity per diopter of blur is approximately 1.3 times greater than that calculated using the averaged macular sensitivity data. The difference is not thought to be a result of degradation of the optical MTF at 4 eccentricity, because the optical properties of the eye have been shown to remain relatively constant throughout most of the mid-peripheral retina. 28 While the reasons for this effect are uncertain, it is possible that the differences in rates between the fovea and macular areas may be related to decreases in the cone 29 " 31 or ganglion cell 2932 ' 33 spacings with increasing retinal eccentricity. Depth of Focus Effects A number of studies have shown that the depth of focus of the eye depends on pupil size and the spatial frequency components of the target For example, it has been reported 34 that the calculated depth of focus in dilated eyes (8 mm pupil size) increased when the spatial frequency of the target was reduced from 3.5 cycles per degree (2.50 D) to 0.25 cpd (17.00 D). Similarly, the calculated depth of focus for a 3.5 cpd target increased when the pupil size was reduced from 8 mm (2.20 D) to 2 mm (4.50 D). 34 It was suggested that the ability to detect the small contrast modulation decrements produced by dioptric blur was provided by spatial filters tuned to about 4 cpd, close to the peak of the contrast sensitivity function. 34 If the measurement of perimetric sensitivity is based on the output of contrast-sensitive spatial filters tuned to the peak of the contrast sensitivity function, the results obtained in contrast sensitivity studies near 3-5 cpd can be expected to be similar to those obtained using the contrast detection strategies of perim-

5 No. 3 FACTORS INFLUENCING AUTOMATED PERIMETRIC THRESHOLDS / Herse 615 etry. If this is the case, we also might expect the depth of focus measurements obtained using sine-wave targets of 3-5 cpd to give results similar to those obtained using perimetric targets. What is the depth of focus measured using static perimetry? Depths of focus indices were calculated using the 50% modulation decrease criterion proposed by Legge et al. 34 In this method, depth of focus is denned as the amount of dioptric blur required to reduce observer sensitivity to target modulation by 50% (0.3 log units). The results of these calculations, using stimulus size III targets, are shown in Figure 2. For the 3 mm pupil/foveal viewing condition, the depth of focus was calculated to be 3.86 D. For the 8 mm/foveal viewing condition, the depth of focus was calculated to be 1.82 D. These results agree reasonably with the 3.5 cpd grating results of Legge et al 34 mentioned above, suggesting that perimetric sensitivity and contrast sensitivity at 3.5 cpd may be mediated by similar mechanisms. Thus, while the sharply focussed circular perimetric stimulus is composed of many spatial frequency components, the data argue that the depths of focus found in static perimetry may be explained by modelling the perimetric stimulus as a low spatial frequency target of about 4 cpd. Effect of Retinal Eccentricity Studies on the effects of dioptric blur on perimetric sensitivity have reported that the slope of the retinal profile in dilated eyes remains constant over a wide range of dioptric blur (-0.24 db/degree; db/ degree 22 ). The quoted value for the decrease in retinal profile slope for stimulus size III given by Allergan- Humphrey is about db/degree. 37 The results of this study (-0.34 db/degree) for 8 mm pupil diameters lie between these values. The slopes of the retinal profile in the unblurred 3 mm and 8 mm pupil size conditions were found to be not significantly different (P> 0.10). The foveal sensitivities found in the 3 mm and 8 mm pupil size conditions were found to be not significantly different (P > 0.10). These data suggest that, in the unblurred state, pupil size has little influence on retinal sensitivity. 16 However, it should be noted that the slopes of the retinal profile with increasing levels of dioptric blur are, on average, about 1.8 times steeper in the 3 mm (-0.62 db/degree) pupil size condition than in the 8 mm (-0.34 db/degree) pupil size condition. A number of studies have investigated factors that alter the slope of the retinal profile. Flattening of the retinal profile with increasing pupil size has been reported in the unblurred condition, although only at eccentricities greater than 10, 19 Flattening of the retinal profile also has been reported with an increase in the size of the perimetric target Conversely, a steepening of the retinal profile has been reported with increasing age. 39 However, these studies offer no readily understood explanation as to why the retinal profile should be flatter in the blurred 8 mm pupil size condition. At this time, the reasons for pupil-dependent variations in retinal profile are unclear. 19 The decreased effectiveness of light rays entering through the edge of the dilated pupil (Stiles-Crawford effect), optical modulation transfer effects, and the increased spherical aberration of the eye that occurs in the dilated pupil (resulting in increased intraocular light scatter) may play a role in explaining thesefindings. Further investigation into this area is needed. E2 Factors Grating and vernier acuities have been used to investigate the mechanisms underlying spatial vision. 40 " 45 The retinal eccentricity at which the foveal threshold for a particular form of spatial vision doubles in value has been termed the E2. 40 The E2 for vernier acuity, stereoacuity, and phase discrimination has been reported to be about These values have been correlated to the variation of inverse cortical magnification with increasing eccentricity, suggesting that fine "positional" acuity is mediated by predominantly cortical mechanisms. 29 Conversely, the E2 for grating resolution and contrast sensitivity has been reported to be about This correlates with the rate of decrease into the peripheral retina of cone spacing and beta ganglion cell density, suggesting that grating resolution is predominantly controlled by retinal mechanisms. 29 Regarding perimetric sensitivity, if the averaged data for the unblurred 3 mm and 8 mm pupil size conditions are plotted with the normalized ratio of peripheral to foveal thresholds on the ordinate and retinal eccentricity on the abscissa (Fig. 3), the calculated E2 is found to be This value lies within the reported E2 range for contrast sensitivity and grating resolution (1.5-4 ). The result suggests that the spatial vision mechanisms controlling perimetric sensitivity, like grating resolution, are predominantly retinal in origin. Conclusion This study has four main conclusions. (1) The E2 factor for static perimetry was calculated to be The similarity of this result to values reported for grating resolution and contrast sensitivity suggests that similar mechanisms, such as cone and ganglion cell spacing, are involved in all three types of spatial vision. (2) The averaged slope of the macular sensitivity

6 616 INVESTIGATIVE OPHTHALMOLOGY 6 VISUAL SCIENCE / Morch 1992 Vol. 33 Acknowledgments I thank Steve McConnell (Allergan-Humphrey New Zealand) for his technical advise, and Graeme Smith and Andrew Sui for their help in running the SAS analysis procedure. I also thank The University of Auckland Optometry Clinic for providing the Humphrey Field Analyzer used in this project. y o x R A 2 = < ECCENTRICITY (degrees) Fig. 3. Variation in normalized perimetric sensitivity with increasing retinal eccentricity (n = 10). The calculated E2 is 3.71 degrees. The error bars represent ±1SD. decrease with increasing levels of dioptric blur was significantly steeper in the 8 mm pupil size condition compared to the 3 mm pupil size condition. This difference may be explained by the effect of pupil size on the optical MTF. (3) Smaller pupils have a greater depth of focus than larger pupils. A 3 db reduction in foveal sensitivity was found to occur with 3.86 D of blur for a 3 mm pupil diameter and with 1.82 D of blur for an 8 mm pupil diameter. This conclusion agrees with previous studies that suggest the use of dilated pupils may overestimate the clinical importance of dioptric blur on perimetric sensitivity. 20 (4) The retinal profile with increasing eccentricity, under conditions of dioptric blur, was found to depend on pupil size. The slope of the retinal profile was significantly steeper in the averaged blur-3 mm pupil size condition compared to the averaged blur/8 mm pupil size condition. The data suggest that while large depth of focus effects in small pupil sizes appear to reduce the need for accurate refractive error corrections in determining perimetric retinal sensitivities, variations in the slope of the retinal profile under conditions of uncontrolled dioptric blur and pupil size may result in artifactual sensitivity decreases. Therefore, measurement of pupil size and accurate correction of near refractive errors should be performed to minimize the possibility of incorrect detection of central visual field defects. Key words: visualfield,blur, pupil size, retinal eccentricity, Humphrey Field Analyzer References 1. Harms H: Entwicklungsmoglichkeiten der perimetrie. Albrecht V Graefes Arch Ophthalmol 150:28, Sloan LL: Area and luminance of test object as variables in examination of the visual field by projection perimetry. Vision Res 1:121, Bedwell CH: Visual Fields: A Basis for Efficient Investigation. London, Butterworths Scientific, 1982, pp Haley MJ: The Field Analyzer Primer, 2nd ed. San Leandro, Allergan Humphrey, 1987, pp Fankhauser F and Enoch JM: The effects of blur upon perimetric thresholds. A method for determining a quantitative estimate of retinal contour. Arch Ophthalmol 68:240, Anderson DR: Testing the Field of Vision. St. Louis, C. V. Mosby, 1982, pp Goldstick BI and Weinreb RN: The effect of refractive error on Octopus Global analysis program G-l. Invest Ophthalmol Vis Sci 28:(suppl)270, Benedetto MD and Cyrlin MN: The effect of blur upon static perimetric thresholds. In Proceedings of 6th International Visual Field Symposium, Heijl A and Greve EL, editors. Dordrecht, The Netherlands, Dr. W. Junk Publishers, 1985, pp Harrington DO: The Visual Fields, 4th ed. St. Louis, C. V. Mosby, 1976, pp Greve EL: Single and multiple stimulus static perimetry in glaucoma: The two phases of perimetry. Doc Ophthalmol 36:1, Engel S: Influence of a constricted pupil on the field in glaucoma. Arch Ophthalmol 27:1184, Forbes M: Influence of miotics on visual fields in glaucoma. Invest Ophthalmol 5:139, Klewin KM and Radius RL: Background illumination and automated perimetry. Arch Ophthalmol 104:395, Heuer DK, Anderson DR, Feuer WJ, and Gressel MG: The influence of decreased retinal illumination on automated perimetric threshold measurements. Am J Ophthalmol 108:643, McCluskey DJ, Douglas JP, O'Connor PS, Story K, Ivy LM, and Harvey JS: The effect of pilocarpine on the visual field in normals. Ophthalmology 93:843, Brenton RS and Phelps CD: The normal visual field on the Humphrey Field Analyser. Ophthalmologica 193:56, Aspinall PA: Variables affecting the retinal threshold gradient in static perimetry, thesis. Department of Psychology, University of Edinburgh, Williams TD: Aging and the central visual field area. Am J Optom Physiol Opt 60:888, Wood JM, Wild JM, and Bullimore MA, Gilmartin B: Factors affecting the normal perimetric profile derived by automated static threshold LED perimetry. I. Pupil size. Ophthalmic Physiol Opt 8:26, Emsley HH: Visual Optics, 5th ed. London, Butterworths, 1977, vol. 1, p Campbell FW and Green DG: Optical and retinal factors affecting visual resolution. J Physiol 181:576, Weinreb RN and Perlman JP: The effects of refractive correction on automated perimetric thresholds. Am J Ophthalmol 101:706, Goldstick and Weinreb RN: The effect of refractive error on automated global analysis program G-l. Am J Ophthalmol 104:229, 1987.

7 No. 3 FACTORS INFLUENCING AUTOMATED PEPJMETPJC THRESHOLDS / Herse Lindenmuth KA, Skuta GL, Rabbani R, Musch DC, and Bergstrom TJ: Effects of pupillary dilation on automated perimetry in normal subjects. Ophthalmology 97:367, Tucker J and Charman WN: Effect of target content at higher spatial frequencies on the accuracy of the accommodative response. Ophthalmic Physiol Opt 7:137, Smith G: Ocular defocus, spurious resolution and contrast reversal. Ophthalmic Physiol Opt 2:5, Charman WN: Effect of refractive error in visual tests with sinusoidal gratings. British Journal of Physiological Optics 32:10, Jennings JAM and Charman WN: Off-axis image quality in the human eye. Vision Res 21:445, Wilson HR, Levi D, Maffei L, Rovamo J, and De Valois R: The perception of form: Retina to striate cortex. In Visual Perception. The Neurophysiological Foundations, Spillman L and Werner JS, editors. New York, Academic Press, 1990, pp Curcio CA, Sloan KR, Packer O, Hendrickson AE, and Kalina RE: Distribution of cones in human and monkey retina: Individual variability and radial symmetry. Science 236:579, Osterberg G: Topography of the layer of rods and cones in the human retina. Acta Ophthalmol 6(suppl):l, Perry VH and Cowey A: The ganglion cell and cone distributions in the monkey's retina: Implications for central magnification factors. Vision Res 25:1795, Schein SJ and De Monasterio FM: The mapping of retinal and geniculate neurones onto striate cortex of the macaque. J Neurosci 7:996, Legge GE, Mullen KT, Woo GC, and Campbell FW: Tolerance to visual defocus. J Opt Soc Am [A] 4:851, Green DG and Campbell FW: The effect of focus on the visual response to a sinusoidally modulated spatial stimulus. J Opt Soc Am [A] 55:1154, Huer DK, Anderson DR, Feuer WJ, and Gressel MG: The influence of refraction accuracy on automated perimetric threshold measurements. Ophthalmology 94:1550, Humphrey Field Analyser Operator's Manual (Models 620 and 630). Allergan-Humphrey Inc, San Leandro, CA, 1986, pp Wood JM, Wild JM, Drasdo N, and Crews SJ: Perimetric profiles and cortical representation. Ophthalmic Res 18:301, Jaffe GJ, Alvarado JA, and Juster RP: Age-related changes of the normal visualfield.arch Ophthalmol 104:1021, Levi D, Klein SA, and Aitsebaomo AP: Vernier acuity, crowding and cortical magnification. Vision Res 25:963, Levi DM and Klein SA: Vernier acuity, crowding and amblyopia. Vision Res 25:979, Westheimer G: The spatial sense of the eye. Invest Ophthalmol VisSci 18:893, Westheimer G: The spatial grain of the perifoveal visual field. Vision Res 22:157, Rovamo J, Virsu V, and Nasanen R: Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision. Nature 271:54, Rovamo J and Virsu V: An estimation and application of the human cortical magnification factor. Exp Brain Res 37:495, 1979.