Joint optimal measurement for locating two incoherent optical point sources near the Rayleigh distance

Abstract Simultaneously optimizing the estimation of centroid and separation two incoherent optical point sources is constrained by a tradeoff relation determined an incompatibility coefficient. At Rayleigh distance, coefficient vanishes thus no longer restricts simultaneous optimization measurement for joint estimation. We construct such optimal elaborated analysis on operator algebra symmetric logarithmic derivative. Our work not only confirms existence this specific imaging model, but also gives promising method to characterize condition compatibility general multiparameter problems.