PSF Fitting (for Point-Spread Function Fitting) is the analysis of overlapping Airy Disks to determine the likely scenario that produced them. Through such analysis, stars and other unresolved astronomical objects can be identified beyond what the Rayleigh Criterion for the telescope's Angular Resolution suggests.
The technique is typically carried out by computation using software to process images, creating proposed more-resolved images, using a formula for the point spread function to calculate the image the telescope would produce, and using a Chi-Squared Test or similar statistical test to evaluate them. It works best if a small enough adjustment the proposed image yields a score indicating whether it is closer to the ideal.
The technique is used for resolving stars that are close together in the Celestial Sphere, or similarly close to other objects such as galaxies. It is also used in Direct Imaging of Extra-Solar Planets.