Daniel G. Green

Depth of focus, eye size and visual acuity

Abstract We develop formulas for calculating the approximate depth of focus of any eye. They show that the magnitude of depth of focus is inversely proportional to the size of the eye and to its visual acuity. One particular implication of these quantitative relations, which is supported by previous data from rats and human infants, is that small eyes with low acuity should have large depths of focus. We show that the observed relation between defocus and contrast sensitivity in rats in predicted by our formulas. We also analyze recent findings in human infants and show that they demonstrate a good correspondence between the improvement in accuracy of the accommodative response with age and the reduction in depth of focus (predicted from our formulas) as acuity and eye size increase over the same age range. Optical factors such as astigmatism, refractive error and chromatic and spherical aberration should have no effect on visual resolution unless they exceed the depth of focus of an eye. Thus, our arguments imply that these factors may be relatively unimportant in small eyes with low acuity.

Regional variations in the visual acuity for interference fringes on the retina

1. The visual acuity of the peripheral retina was measured using both sinusoidal gratings viewed in the usual way and interference fringes formed on the retina directly.

The contrast sensitivity of the colour mechanisms of the human eye

1. To isolate the colour receptive systems of the eye, a sinusoidal grating of one colour was superimposed on a bright background of another colour and the threshold contrast for resolving the grating was determined.

A dissection of the electroretinogram from the isolated rat retina with microelectrodes and drugs

The origins of the a- and b-wave of the ERG were studied using simultaneous recordings made across the receptor layer and the full thickness of a piece of isolated albino rat retina. An inwardly directed current flowing across the rod outer segments was eliminated from the recording when postsynaptic activity was blocked with cobalt or when current source density measurements were made along the length of the outer segments. Rod photovoltages were inferred by removing extraneous field potentials from the recordings made across the photoreceptor layer. The spatial properties of the photovoltage indicates the responses came from an area about 100 microm in diameter. The glutamate analog. APB, which blocks depolarizing bipolar cells, eliminated the b-wave but left the a-wave unaffected. The ERG component due to depolarizing bipolar cells was inferred by subtracting recordings obtained before and after APB. After treatment with APB a slow component remained. This component was completely blocked by barium (200 microM), which blocks potassium channels on Müller cells. Barium had virtually no effect on low-intensity photovoltages but did affect the amplitude and shape of the saturated responses. Barium increased the amplitude of the component of the ERG which underlies the b-wave. It was concluded that the depolarizing bipolar cells directly generate the b-wave of the ERG.

Double-pass measurements of the retinal-image quality with unequal entrance and exit pupil sizes and the reversibility of the eye’s optical system

We have used a modified double-pass apparatus with unequal entrance and exit pupil sizes to measure the optical transfer function in the human eye and have applied the technique to three different problems. First, we confirm that in the eye the double-pass spread function is the cross correlation of the input spread function with the output spread function [J. Opt. Soc. Am. A 12, 195 (1995)]. Consequently, when entrance and exit pupil sizes are equal, phase information is lost from the double-pass images. Second, we show that in double-pass measurements the eye behaves like a reversible optical system. That is, when entrance and exit pupils are equal, the double-pass image results from two passes through an optical system having a transfer function that is the same in both directions. To test for reversibility in the living eye we have used a double-pass apparatus with different exit and entrance pupil sizes (one of them small enough to consider the eye diffraction limited), so that the ingoing and the outgoing transfer functions are different. The measured image quality was unchanged when the pupils were interchanged, i.e., when the first-pass entrance pupil size becomes the second-pass exit pupil size, and vice versa. Third, the technique provides a means for inferring the complete optical transfer function of the eye, including the phase transfer function, and the shape of the point-spread function.

Contrast sensitivity of the human peripheral retina

Abstract Threshold contrasts were measured psychophysically for a sinusoidal grating target centered 12° in the peripheral retina. The relationship between contrast sensitivity, the reciprocal of the threshold contrast, and the spatial frequency of the gratings can be adequately described by the difference of two Gaussian functions. The parameters of the fitted Gaussians are used to describe the effects of varying the mean luminance of the target on the shape of the contrast sensitivity function. With increasing luminance the characteristic radii—parameters which are related to the width of the spread function of the visual system—decrease, while the overall contrast sensitivity of the eye increases.

Sinusoidal flicker characteristics of the color-sensitive mechanisms of the eye

THERE is a body of literature suggesting that temporal factors are of importance in the processing of color information by the visual system. Perhaps most striking, and likewise most difficult to understand in physiological terms, are the illusions of color elicited by flickering achromatic stimuli such as in the well-known Benham’s top illusion. More directly, there is evidence that the temporal integrating properties of the three cone systems of trichromatic color vision are different. IKEDA and BOYNTON (1962) have shown that the spectral sensitivity of the eye depends on flash duration, and KELLY (1962) has similarly demonstrated that frequency of flicker is an important variable in determining the photopic spectral sensitivity of the eye. DE LANGE (1958) reported that when ,red and green stimuli are sinusoidally alternated in exact antiphase, the eye detects a residual brightness flicker that cannot be eliminated by varying the relative intensities of the stimuli. However, if both the relative proportions of the two lights in the mixture and the phase relations between them are varied, this residual flicker can then be eliminated. It has been suggested by WALRA~EN and LEEBFZK (1964) that these findings reflect frequency-dependent differences in the attenuation and phase characteristics of the color-mediating systems. Using techniques developed by STILES (1939, 1949) wherein a test stimulus, that chiefly stimulates one class of cone, is superimposed on a background which favors the other two, it is possible to arrange matters so that the test stimulus excites only a single cone mechanism. The two-color incremental threshold approach and various modifications, in which the dark light of bleached pigment is substituted for a real light background, have been used to determine the spectral sensitivities (Snrss, 1939,1949; BRINDLEY, 1953; WALD, 1964), dark adaptation properties (Du CROZ and RUSHTON, 1965), spatial integrating properties (BRINDLEY, 1954; GREEN, 1968) and after-flash interactions (ALPERX and RUSHTON, 1965) of the separate red, green, and blue mechanisms of color vision. Recently, using on-off blue flicker superimposed on a yellow background, BRINDLEY, Du CROZ and RUSHTON (1965) have shown that the blue cone mechanisms have a greatly depressed critical flicker fusion frequency. The experiments presented here were designed to extend these observations by measuring the flicker thresholds for sinusoidally modulated red, green, and blue stimuli superimposed on bright backgrounds of a complementary color. The object of these experiments was the determination of the temporal frequency response curves, the so-called de Lange characteristics, of the separate cone mechanisms.

Light Adaptation in the Rat Retina: Evidence for Two Receptor Mechanisms

Light adapting the rat retina with transient white flashes too dim to bleach a substantial amount of visual pigment produces a change in electroretinogram spectral sensitivity and an increase in flicker fusion frequency. Increment threshold curves obtained with a long wavelength adapting stimulus and a short wavelength test stimulus show rod saturation.

Testing the Vision of Cataract Patients by Means of Laser-Generated Interference Fringes

In a new technique for measuring the visual acuity of cataract patients the light from a laser is used to form interference patterns of variable fineness on the patients retina. The fineness of the interference pattern that the patient can detect gives an indication of the potential for improved vision. Comparison of this estimate of the potential with the patients vision after cataract extraction shows that this test can indicate the condition of the fovea behind a cataract.

Scotopic and photopic components of the rat electroretinogram

1. Increment thresholds were measured on the albino rat retina using the e.r.g. as an indicator of visual sensitivity.