Bergmann and Helmholtz argued that visual resolution requires at least one relatively unstimulated neuron between two relatively stimulated neurons, and it therefore follows that the highest spatial frequency which a neural array can resolve in theory is determined by the spatial sampling density of visual neurons.

This slide illustrates the consequences of disobeying the Bergmann/Helmholtz Law. As long as the pattern is oversampled, as shown by the top row of receptive fields overlaid on the test pattern, the discrete neural image, shown by the bargraph on the right, provides a veridical representation ot the retinal image.

If the pattern is undersampled, however, as shown in the bottom row, the neural image which results is a false representation of the stimulus. Because of the relatively coarse spacing of the neurons in this case, the spatial features of the stimulus are misrepresented in the neural image.

According to theory, the highest spatial frequency which the neural array can represent faithfully is one-half the sampling frequency. This critical case is shown in the middle row, where every second neuron is turned on and the in-between neurons are turned off. This maximum spatial frequency which can appear in the discrete neural image is called the Nyquist frequency, which is numerically equal to half the sampling frequency of the array. The important point to remember is that no matter how high the spatial frequency might be in the optical image, the nerual image can never exceed the Nyquist frequency, a phenomenon called spatial aliasing.

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WWWaveTM 1996
World Wide Web automated virtual environment TM 1996
Kevin Haggerty, Indiana University.