Object frequency characteristics of visual acuity.

The size of letter optotypes on standard visual acuity (VA) charts is typically specified as the logarithm of the minimum angle of resolution (logMAR). A fundamental assumption of the MAR metric is that scale invariance holds for VA. That is, the MAR scale assumes that individuals use the same information to identify letters at the acuity limit, regardless of their VA. In particular, the MAR scale assumes that letter identification is based on the stroke width of the letter at all VA levels. The stroke width of standard Sloan optotypes corresponds to an object frequency of 2.5 cycles per letter (cpl), given that there are five strokes in each letter and two strokes (one light bar and one dark bar) per cycle. If VA is based on stroke width, then the MAR value of a letter can readily be equated to retinal spatial frequency (cycles per degree or cpd) based on the angular subtense of the stroke width. For example, a letter with an MAR of 1 (0 logMAR or 20/20 Snellen equivalent) would correspond to a retinal spatial frequency of 30 cpd, because one cycle would subtend 2 arcmin. However, evidence indicates that VA for letter optotypes, which are broadband in object frequency content, may not be based on object frequencies near 2.5 cpl. For example, object frequencies less than approximately 1.25 cpl were found to mediate VA in the normal periphery for a task that involved discrimination between letter pairs.1 A study of the Fourier components of the Landolt C and tumbling E concluded that, whereas VA for the tumbling E could be based on object frequencies near 2.5 cpl, VA for the Landolt C was most likely based on object frequencies in the range of 1.3 cpl.2 This proposal for the Landolt C was verified experimentally using band-limited targets in a study of the effect of crowding on VA.3 VA measurements using low- and high-pass–filtered tumbling E's showed that the VA for this target in the normal visual field periphery is based on object frequencies lower than the 2.5 cpl proposed previously.4 The finding that VA for broadband targets may be governed by object frequencies lower than 2.5 cpl would not be an issue if scale invariance holds for VA. That is, if individuals with different levels of VA all use the same low object frequencies to identify letters at the acuity limit, then the equivalent retinal frequency would simply be a scalar transform of the nominal retinal frequency that is derived from stroke width. However, there is evidence from studies of contrast sensitivity that the object frequencies used for letter identification vary with letter size.5–7 Specifically, there is a linear relationship between log object frequency and log angular subtense of the letter that has a slope of approximately ⅓, such that contrast sensitivity is mediated by low object frequencies for letters of small angular subtense but higher object frequencies for larger letters. Given that individuals with decreased VA require larger-than-normal letters at the acuity limit, it is possible that they may use higher object frequencies than normally sighted individuals, and scale invariance would not hold for VA. The present study evaluated the extent to which VA is scale invariant by determining whether the same object frequencies mediate VA for individuals who have different VAs. A novel approach was used, in which the high-frequency cutoff of the object frequency region mediating VA was derived by using an equivalent intrinsic blur paradigm. With this approach, the target is successively blurred with Gaussian low-pass filters until VA is affected, under the assumption that, if the removal of specific high object frequencies impairs VA, then those frequencies must be necessary for the task. Gaussian filters were used in the present study because they are the basis for models of equivalent intrinsic blur8–10 and have also been used in studies of the object frequencies mediating contrast sensitivity for letter optotypes.11,12 The amount of Gaussian blur necessary to reduce VA by a factor of √2 was used to estimate the high-frequency cutoff of the object frequencies mediating VA. This degree of Gaussian blur has been termed “equivalent intrinsic blur” and is assumed to be an estimate of the amount of blur within an individual's visual system.8,9 In the present study, the VA of both normally sighted individuals and patients with VA loss due to eye disease was measured with a tumbling E. The patients were included to broaden the range of VA. Equivalent intrinsic blur was measured in the spatial domain (in minutes of arc) and converted to the frequency domain (cpd) to estimate the high-frequency cutoff of the band of retinal frequencies mediating VA. The corresponding high-frequency cutoff of the band of object frequencies mediating VA was obtained by converting the cpd estimate to cpl to establish whether the same object frequencies mediate performance at the acuity limit for individuals with different VA levels.