## 5 Conclusions  
Our study reveals the significant impact that PSF modeling and RL deconvolution can have on the analysis of _NuSTAR_ observations of X-ray point sources by enhancing the spatial resolution and enabling the detection of multiple sources in close proximity (\(\gtrsim\)10''). In a case study of pulsars SXP 15.3 and SXP 305, we tested these tools in an investigation of a faint crowded X-ray field in the sky. This approach, not only improves our understanding of specific astrophysical objects but also contributes to the broader capability of X-ray astronomy to explore the very high-energy universe with greater precision and clarity.  
Future work should explore the integration of spatially varying PSFs directly into deconvolution algorithms, allowing for the continuous and seamless incorporation of off-axis signal variations. Bayesian deconvolution and machine learning approaches may offer alternative ways to handle complex PSF attributes and noise characteristics. Furthermore, applying this methodology to a broader set of observations carried out at different wavelengths and targeting more densely populated fields can help assess the effectiveness of the procedure and identify telescope-specific requirements.  
Conceptualization, project administration, resources, and supervision, S.G.T.L.; investigation, methodology formal analysis, and software, S.B., D.M.C. and S.G.T.L.; writing--original draft, S.B.; writing--review and editing, S.B., D.M.C. and S.G.T.L. All authors have read and agreed to the published version of the manuscript.  
NSF-AAG, grant 2109004; NASA Astrophysics Data Analysis Program (ADAP), grant nos. NNX14 AF77G and 80 NSSC18K0430.  
The raw _NuSTAR_ data are publicly available at the HEASoft archive, URL: [[https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/](https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/)]([https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/](https://heasarc.gsfc.nasa.gov/docs/nustar/analysis/)) (accessed on 26 October 2024). The reduced images will be provided by the corresponding author upon request.  
This research project was facilitated in part by the following funding agencies and programs: NSF-AAG, grant 2109004; NASA Astrophysics Data Analysis Program (ADAP), grant nos. NNX14 AF77G and 80 NSSC18K0430; and the Lowell Center for Space Science and Technology (LoCSST) of the University of Massachusetts Lowell.  
The authors declare no conflicts of interest.  
The following acronyms are used in this manuscript:  
\begin{tabular}{l l} CALDB & calibration database \\ DOAJ & Directory of Open Access Journals \\ FPMA & focal plane module A \\ FPMB & focal plane module B \\ HEASARC & High Energy Astrophysics Science Archive Research Center \\ HEASoft & High Energy Astrophysics Software \\ HMXB & high-mass X-ray binary \\ HPD & half-power diameter \\ LD & linear dichroism \\ NS & neutron star \\ _NuSTAR_ & Nuclear Spectroscopic Telescope Array \\ NuSTARDAS & _NuSTAR_ data analysis software \\ PSF & point spread function \\ RL & Richardson-Lucy \\ SMC & Small Magellanic Cloud \\ S/N & signal-to-noise \\ SXP & SMC X-ray pulsar \\ TLA & three-letter acronym \\ XIS & X-ray imaging spectrometer \\ XMM & X-ray multi-mirror mission \\ XRB & X-ray binary pulsar \\ \end{tabular}