Resolving Two Point Targets with Unequal and Unknown Intensities in a FPA

This paper presents a method of determining whether two closely spaced objects observed by an electro-optical (EO) sensor are resolvable. The first goal of this work is to develop the method that will determine whether data from an EO sensor is sufficient to estimate two sets of target parameters or whether a single target is more applicable. The second goal is to quantify the effectiveness of this method theoretically and confirm these assertions via Monte Carlo (MC) simulations. Work has been done previously on extracting measurements of single targets, as well as two targets of possibly dissimilar intensity. The current work extends these works in providing a test to determine which method is best to employ. We consider point targets that deposit energy in the FPA according to a Gaussian point spread function (PSF) with parameter sigma(PSF). The resolution determination method is framed as a hypothesis test, with the null hypothesis representing a single set of target parameters to be estimated and the alternate hypothesis indicating two sets of target parameters can be extracted. We derive the approximate type-I error and power of this test and present this data as a Receiver Operating Characteristic (ROC) for varying degrees of target separation. We also present the resolution probability versus target separation for varying target signal-to-noise ratio (SNR) differentials to compare this test with a commonly used approximation. Our simulated results show good agreement with theoretical derivations and we find that the test can nearly perfectly resolve these targets at separations above 0.8 sigma(PSF) for SNR differentials up to 6dB.