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

## TL;DR

This paper reviews and compares various spatial resolution criteria in optics and holography, emphasizing the importance of appropriate criteria for different regimes and introducing spectrum-based resolution estimates for improved accuracy.

## Contribution

It provides a comprehensive overview of resolution criteria in classical, digital, and holographic optics, proposing spectrum-based methods for better resolution estimation in various regimes.

## Key findings

- Classical Abbe and Rayleigh criteria are insufficient for coherent light resolution estimation.
- Spectrum-based resolution criteria offer more accurate estimates for both coherent and incoherent imaging.
- Far-field derived criteria can be applied to near-field (Fresnel) regimes.

## Abstract

This work presents an overview of the 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 still several issues which still need to be addressed, for example the axial resolution criterion for coherent and incoherent radiation, which is a crucial parameter of three-dimensional (3D) imaging, the resolution criteria in the Fresnel regime, and the lateral and axial resolution criteria in digital optics and holography. This work discusses these issues and provides a simple guide for which resolution criteria should be applied in each particular imaging scheme: coherent/incoherent, far- and near-field, lateral and axial resolution. Different resolution criteria such as two-point resolution and the resolution obtained from the image spectrum (diffraction pattern) are compared and demonstrated with simulated examples. Resolution criteria for spatial lateral and axial resolution are derived, and their application in imaging with coherent and incoherent (noncoherent) waves is considered. It is shown that for coherent light, the classical Abbe and Rayleigh resolution criteria do not provide an accurate estimation of the lateral and axial resolution. Lateral and axial resolution criteria based on an evaluation of the spectrum of the diffracted wave provide a more precise estimation of the resolution for coherent and incoherent light. It is also shown that resolution criteria derived in approximation of the far-field imaging regime can be applied for the near-field (Fresnel) regime.

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Source: https://tomesphere.com/paper/1905.02774