Sharp images from diffuse beams: factorisation of the discrete delta function

Abstract

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.

References in corpus (7)

• Compressive ghost imaging
• Ghost imaging with a single detector
• High Dynamic Range Pixel Array Detector for Scanning Transmission Electron Microscopy
• One mask to rule them all: Writing arbitrary distributions of radiant exposure by scanning a single illuminated spatially-random screen
• Ghost imaging with the human eye
• Wieferich pairs and Barker sequences, II
• Computational Ghost Imaging

Cited by in corpus (4)

• Ghost projection. II. Beam shaping using realistic spatially-random masks
• Families of delta-correlated arrays derived from the Fourier spectra of Huffman sequences
• Extending the known families of scalable Huffman sequences
• Diffuse arrays that autocorrelate and project as delta-like points