Investigations of optical aberration on quantum diamond microscopy toward high spatial resolution and sensitivity

Quantum diamond microscopy (QDM), which employs nitrogen-vacancy (NV) center ensembles, is a promising approach to quantitatively imaging magnetic fields with both high resolution that approaches the diffraction limit and a wide field of view. The commonly adopted setups of QDM capture the photoluminescence through transparent diamonds, which inevitably entail aberrations -- optical errors that degrade the optical resolution and contrast of the obtainable image. In this study, we delve into the impact of optical aberrations, focusing on their dependence on diamond thickness. We first introduce a rigorous model [Richards et al., Braat et al.] of diffraction that incorporates aberrations, producing the NV center optical image. We confirm that this model accurately reproduces the confocal images of single NV centers obtained at various depths in diamonds. Extending this model to a wide-field microscope, we find that the model also accurately reproduces the USAF 1951 resolution test chart obtained through diamonds of various thicknesses. Based on these investigations, we quantitatively assess the consequent resolution constraints and propose thinning the diamond as a viable solution. We present a robust method to quantitatively ascertain resolution in optical systems influenced by aberrations caused by ray transmission through diamonds. For instance, for a typical microscope with an objective lens of NA = 0.7, the diffraction limit is achievable through diamonds that are 30 $\mu$m thick, and a resolution of 1 $\mu$m is obtained through diamonds that are 100 $\mu$m thick. Those results opens up avenues for enhanced performance in QDM. The Julia package used to calculate the vectorial PSFs is available at ${\texttt VectorPSFs.jl}$.