Estimation of Spatial Scale across the Visual Field Using Sinusoidal Stimuli

Automated perimetry is one of the most widely used clinical psychophysical tests for detecting and monitoring visual defects in patients with a range of eye diseases and is the standard of care for monitoring patients with glaucoma. The most common form in clinical use is conventional automated perimetry (CAP), which assesses the differential light threshold for sharp-edged circular luminance increments presented at 54 to 72 locations within ±30° from fixation using optical systems with shutters and movable mirrors.1 The stimuli used for CAP were based on psychophysical methods and principles of the first half of the 20th century and stimulus design was guided by Weber's law, Ricco's law, and Bloch's law.2 A decade after CAP stimuli were standardized as circular increments, new display systems were used to produce a different type of stimulus: sinusoidal grating stimuli with little or no increment in mean luminance.3 Grating stimuli became widely used in spatial vision research, with both psychophysical and electrophysiological studies using grating stimuli rather than luminance increments. The Fourier transform of the CAP stimulus has a significant DC component (the increment in luminance) but also has components at a range of spatial frequencies (due to the edge), so a wide range of cortical spatial mechanisms could mediate detection.4 Grating stimuli can be used to eliminate the luminance increment and target a single spatial frequency, although the window through which the grating is viewed will add additional spatial frequency components. Several researchers used these stimuli to make systematic measurements at different locations in the visual field, each study extensively examining only two or three subjects.5–7 As spatial vision models became more sophisticated, it became clear that optimal stimuli had two-dimensional windows, such as sinusoidal gratings windowed by two-dimensional Gaussian windows8–10; these have become a standard stimulus in spatial vision and are commonly referred to as “Gabor patches.”11,12 However, to date only a few studies have used Gabor patches for perimetry.11,13–15 The present study used Gabor patches to assess variation in contrast sensitivity across the central visual field. The purpose of the current manuscript is to contribute to further linkage between perimetry and spatial vision by performing perimetry with modern stimuli and applying the method of “spatial scale” to the central visual field tested by CAP. Spatial scale corresponds to magnification or minification of a stimulus required to equate contrast sensitivity at different locations in the visual field. Watson8 noted the advantages of using a fixed spatial bandwidth for Gabor patches when assessing spatial scale, since the window size decreases as spatial frequency increases, so that change in spatial scale will magnify the stimulus as it is moved away from the fovea. Previous studies had potential bias because the stimulus window was varied with eccentricity based on prior assumptions rather than as simple magnification. We used Watson's method as an assumption-free means of assessing the scaling factor. Perimetric sensitivity for CAP declines more slowly with eccentricity than does ganglion cell density16 or cortical magnification,17,18 and for eccentricities from 4° to 30° variation in sensitivity with test location can be accounted for by a change in spatial scale with little or no change in overall sensitivity.19 Our goal was to develop an empirical model for variation in spatial scale across the normal visual field, and use this model to predict perimetric sensitivities for a range of stimuli, based on sensitivity to a single stimulus. A successful model would allow the choice of stimuli for perimetry to be based on predictable effects of stimulus parameters.