The time-honoured Rayleigh criterion specifies the minimum separation between two incoherent sources that may be resolved into distinct objects. It also applies to signals in the time-frequency domain. We revisit this problem by examining the Fisher information required for resolving the two signals. The resulting Cramér–Rao bound gives the minimum error achievable for any unbiased estimator. When only the intensity in the image plane is recorded, this bound diverges as the separation between the sources tends to zero, an effect that has been dubbed the Rayleigh curse. Nonetheless, this curse can be lifted with suitable measurements. We discuss optimal strategies that confirm immunity to the Rayleigh curse and an unprecedented experimental precision.
Paolo Villoresi
