Which Eye Sees the Most?

The performance of the eyes is ultimately limited by the physical nature of light. The diameter of the aperture that admits light to the eye sets an upper limit to the spatial frequencies that can be imaged behind the aperture. Diffraction, which is responsible for this limitation, is caused by the wave nature of light. The array of sampling stations the eye uses to detect the image is instead limited by the quantum nature of light. Each sampling station can only sample a finite number of quanta, and any such count is associated with a standard deviation being the square root of the true mean. Effectively, this limits the ability to detect differences in luminance (contrasts) across the image. Diffraction and quantum noise together sets an upper physical limit to the performance of an eye. If the eye's quantum efficiency, integration time, and thermal noise are constants, it is possible to find the optimum sampling frequency that maximises spatial resolution of a stationary image. This optimum depends on eye size and luminance, and differs from the ‘camera type eye’, the ‘pinhole eye’, and the various optical types of compound eye.

We have calculated the maximum detectable spatial frequency for a number of simple and compound types of eye, and plotted the results against luminance and eye size to produce a unique ‘performance surface’ for each type of eye. These performance surfaces allow a comprehensive graphical comparison of the efficiency of the various optical types of eye.