Cross section equivalence between photons and non-relativistic massive particles for targets with complex geometries

The quantum radar cross section (QRCS) is a concept that gives information on the amount of returns (or scattered energy towards the detector) one can expect from a particular target when being illuminated with a small number of photons. This cross section is highly dependent on the target’s geometry, as well as the illumination angle and the scattering angle from the target. The expression for the quantum radar cross section equation has been derived in the context of photon scattering. In this paper, it will be shown that an equivalent cross section expression, including the alternate form written in terms of Fourier transforms, can be derived using quantum scattering theory applied to non-relativistic, massive particles. Both single particle and multiple particle illumination are considered. Although this approach is formulated based upon massive, non-relativistic particle scattering, its equivalence to the expression based upon photon scattering provide many valuable insights of representing and interpreting these equations in the context of quantum radar. This includes an improved algorithm to simulate the QRCS response of an object illuminated with any number of photons desired.