Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function for convolution under aperiodic boundary conditions. These arrays spread the energy of a sharp probe beam to simultaneously sample multiple points across the volume of a large object, without losing image sharpness. Applying these point-spread functions in any computational imaging system can reveal the underlying structure of objects less intrusively and with equal or better signal-to-noise ratio. These multi-dimensional arrays are related to previously known, but relatively rarely employed, one-dimensional integer Huffman sequences. Practical probes can now be made that are larger than the object under measure. Such arrays can be applied to ghost imaging, which has demonstrated potential to greatly improve signal-to-noise ratios and reduce the total dose required for tomographic imaging. The discrete arrays built here parallel the self-adjoint or Hermitian functions of the continuum that underpin classical wave theory and quantum mechanics.

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来自漫射光束的清晰计算图像：离散 delta 函数的分解

离散 delta 函数定义了所有成像系统可达到的空间分辨率的限制。在这里，我们构建了广泛的、多维的离散函数，它们紧密地复制了狄拉克 delta 函数在非周期性边界条件下卷积的作用。这些阵列传播尖锐探测光束的能量，以同时对大物体体积内的多个点进行采样，而不会损失图像清晰度。在任何计算成像系统中应用这些点扩展函数可以更少侵入性地揭示物体的底层结构，并且具有相同或更好的信噪比。这些多维数组与先前已知但相对很少使用的一维整数霍夫曼序列有关。现在可以制作比被测物体更大的实用探针。这种阵列可以应用于鬼影成像，这已被证明有可能大大提高信噪比并减少断层成像所需的总剂量。这里构建的离散阵列与支撑经典波动理论和量子力学的连续体的自伴随或厄米函数平行。