## Abstract

The subject of this paper is the nature of the sampling operation performed by the human visual sense, restricted to black and white, nonstereoscopic, photopic vision. The hypothesis is presented that the human visual sense samples the spatial “power” spectrum (The term spatial power spectrum is used throughout to describe the absolute value of the square of the Fourier spatial transform of the image, although it is recognized that the word “power” is, strictly, a misnomer in this context. It is to be particularly noted that the word spectrum does not, here, refer to the electromagnetic frequency spectrum of the radiation associated with the image but to the spatial frequency spectrum of the pattern structure of the image.) of the input image, just as the aural sense samples the temporal power spectrum of the input sound. The justification for this hypothesis is the fact that the sensitivity of the retina (except at the fovea) to form, or pattern, in the input image is very much poorer than is suggested by the corresponding upper cutoff spatial frequency of the retina. This property is characteristic of power-spectrum sensitive devices. A physical model retina is described that could perform the hypothesized spectral-sampling operation.

© 1965 Optical Society of America

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### Equations (6)

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(1)
$$\begin{array}{l}I=[M({\xi}_{i},{\eta}_{j};{t}_{\text{k}})]\\ =[R({\xi}_{i}{\eta}_{j})b({X}_{\text{k}}+\xi ,{Y}_{\text{k}}+\eta ;{t}_{\text{k}})],\\ i=1,2,3\cdots \mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j=1,2,3\cdots \mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{k}=1,2,3\cdots ,\end{array}$$
(2)
$$\begin{array}{l}I=[M({\xi}_{i},{\eta}_{j})]\\ =[R({\xi}_{i},{\eta}_{j})b(X+\xi ,Y+\eta )],\end{array}$$
(3)
$$\text{I}=\left[\underset{\rho ({\xi}_{i}{\eta}_{j})}{\int \int}b(X+\xi ,Y+\eta )d\xi d\eta \right]\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}i=1,2,3\cdots ,\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}j=1,2,3\cdots ,$$
(4)
$$I=[M({\xi}_{i},{\eta}_{j})]=[F({\xi}_{i}{\eta}_{j})B(u,v;{\xi}_{i},{\eta}_{j})],$$
(5)
$$B(u,v;{\xi}_{i}{\eta}_{j})={\left|\underset{W({\xi}_{i}{\eta}_{j})}{\int \int}b(X+\xi ,Y+\eta ){e}^{-i(u\xi +v\eta )}d\xi d\eta \right|}^{2}.$$
(6)
$$F({\xi}_{i},{\eta}_{j})B(u,v;{\xi}_{i}{\eta}_{j})={\int}_{0}^{\mathrm{\Omega}}{\int}_{0}^{\mathrm{\Omega}}B(u,v;{\xi}_{i}{\eta}_{j}){K}_{p}(u,v)dudv,$$