Retinal ganglion cells (RGCs) are highly sensitive to changes in contrast, which is crucial for the detection of edges in a visual scene. However, in the natural environment, edges do not just vary in contrast, but edges also vary in the degree of blur, which can be caused by distance from the plane of fixation, motion, and shadows. Hence, blur is as much a characteristic of an edge as luminance contrast, yet its effects on the responses of RGCs are largely unexplored.

We examined the responses of rabbit RGCs to sharp edges varying by contrast and also to high-contrast edges varying by blur. The width of the blur profile ranged from 0.73 to 13.05 deg of visual angle. For most RGCs, blurring a high-contrast edge produced the same pattern of reduction of response strength and increase in latency as decreasing the contrast of a sharp edge. In support of this, we found a significant correlation between the amount of blur required to reduce the response by 50% and the size of the receptive fields, suggesting that blur may operate by reducing the range of luminance values within the receptive field. These RGCs cannot individually encode for blur, and blur could only be estimated by comparing the responses of populations of neurons with different receptive field sizes. However, some RGCs showed a different pattern of changes in latency and magnitude with changes in contrast and blur; these neurons could encode blur directly.

We also tested whether the response of a RGC to a blurred edge was linear, that is, whether the response of a neuron to a sharp edge was equal to the response to a blurred edge plus the response to the missing spatial components that were the difference between a sharp and blurred edge. Brisk-sustained cells were more linear; however, brisk-transient cells exhibited both linear and nonlinear behavior.

The chicken has been extensively studied as an animal model for myopia because its eye growth is tightly controlled by visual experience. It has been found that the retina controls the axial eye growth rates depending on the amount and the sign of defocus imposed in the projected image. Glucagonergic amacrine cells were discovered that appear to encode for the sign of imposed defocus. It is not clear whether the downstream neurons, the retinal ganglion cells, still have access to this information—and whether it ultimately reaches the brain. We have analyzed the spike rates of chicken retinal ganglion cells in vitro using a microelectrode array. For this purpose, we initially defined spatial resolution and contrast sensitivity in vitro. Two classes of chicken retinal ganglions were found, depending on the linearity of their responses with increasing contrast. Responses generally declined with increasing defocus of the visual stimulus. These responses were well predicted by the modulation transfer function for a diffraction-limited defocused optical system, the first Bessel function. Thus, the studied retinal ganglion cells did not distinguish between a loss of contrast at a given spatial frequency due to reduced contrast of the stimulus pattern or because the pattern was presented out of focus. Furthermore, there was no indication that the retinal ganglion cells responded differently to defocus of either sign, at least for the cells that were recorded in this study.

The relation between image resolution and information transfer is explored. It is shown that the existence of higher frequency transfer in the image is just a necessary but not sufficient condition for the achievement of higher resolution. Adopting a two-point resolution criterion, we suggest that a 10% contrast level between two features in an image should be used as a practical definition of resolution. In the context of scanning transmission electron microscopy, it is shown that the channeling effect does not have a direct connection with image resolution because sharp channeling peaks do not move with the scanning probe. Through a quantitative comparison between experimental image and simulation, a Fourier-space approach is proposed to estimate defocus and sample thickness. The effective atom size in Z-contrast imaging depends on the annular detector's inner angle. Therefore, an optimum angle exists for the highest resolution as a trade-off between reduced atom size and reduced signal with limited information transfer due to noise.

Motivated by applications in digital image processing, we discuss information-theoretic bounds to the amount of detail that can be recovered from a defocused, noisy signal. Mathematical models are constructed for test-pattern, defocusing and noise. Using these models, upper bounds are derived for the amount of detail that can be recovered from the degraded signal, using any method of image restoration. The bounds are used to assess the performance of the class of linear restorative procedures. Certain members of the class are shown to be optimal, in the sense that they attain the bounds, while others are shown to be sub-optimal. The effect of smoothness of point-spread function on the amount of resolvable detail is discussed concisely.