Division of Neurobiology, University of California, Berkeley, CA, USA.
Ophthalmic Physiol Opt. 2012 Jul;32(4):271-81. doi: 10.1111/j.1475-1313.2012.00913.x.
In the specification of visual targets and their transmission through the eye's optics to form retinal images, the spatial distribution of energy and its Fourier transform, the spatial-frequency spectrum, are equivalent, so long as linearity constraints are obeyed. The power spectrum, in which phase has been discarded, is an insufficient descriptor; it does not enable the original object to be reconstituted.
Not so well known, and explored here, are joint representations in the space and spatial-frequency dimensions. Their properties are outlined for some sample targets and for transforms of the Gabor, Difference-of-Gaussians and Wigner types. A related approach is one in which other kernel functions, such as the Gaussian or its derivative, are substituted for the cosines in the Fourier transform; here also graphs can be generated which jointly display properties both of the target and of its point-by-point representation in a size-tuned domain.
This kind of study has application in matching the performance characteristics of optical devices to the eye's, in optical superresolution, and in the analysis of the demands placed on neural processing in, for example, visual hyperacuity.
在视觉目标的规范及其通过眼睛的光学器件传输以形成视网膜图像的过程中，只要满足线性约束条件，能量的空间分布及其傅里叶变换，即空间频谱，是等效的。丢弃相位后的功率谱是一个不充分的描述符；它不能使原始物体得以重建。
这里要探讨的是在空间和空间频率维度上的联合表示法，它们还不太为人所知。为一些示例目标以及 Gabor、高斯差分和 Wigner 变换的变换，概述了它们的性质。另一种相关的方法是用其他核函数（如高斯函数或其导数）替代傅里叶变换中的余弦；在这里，也可以生成图形，这些图形联合显示了目标及其在大小调谐域中的逐点表示的性质。
这种研究方法可用于将光学器件的性能特征与眼睛相匹配，用于光学超分辨率，以及用于分析例如在视觉超敏度方面对神经处理的要求。
