Lateral and axial resolution criteria in incoherent and coherent optics and holography, near- and far-field regimes

This work presents an overview of spatial resolution criteria in classical optics, digital optics, and holography. Although the classical Abbe and Rayleigh resolution criteria have been thoroughly discussed in the literature, there are a few issues that still need to be addressed, e.g., the axial resolution criteria for coherent and incoherent radiation (which is a crucial parameter in 3D imaging), the resolution criteria in the Fresnel regime, and the lateral and the axial resolution criteria in digital optics and holography. This work discusses these issues and provides a simple guide on which resolution criteria should be applied for a particular imaging scheme: coherent/incoherent, far- and near-field, lateral and axial resolution. Different resolution criteria such as two-points resolution and the resolution obtained from the image spectrum (diffraction pattern) are compared and demonstrated with simulated examples. It is shown that, for coherent light, the classical Abbe and Rayleigh resolution criteria do not provide accurate estimation of the lateral and axial resolution. The lateral and axial resolution criteria based on the evaluation of the spectrum of the diffracted wave provide more precise estimation of the resolution for coherent and incoherent light. It is also shown that the resolution criteria derived in approximation of the far-field can be applied for the near-field (Fresnel) imaging regime