  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 under
aperiodic convolution. 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. A diffuse point-spread function applied in any
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 point-spread functions can
now be made sufficiently large to span the size of the object under measure.
Such large 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
continuum self-adjoint or Hermitian functions that underpin wave theory and
quantum mechanics.
