Dispelling Rayleigh's Curse

Understand

We devise a systematic method to determine the Fisher information required for resolving two incoherent point sources with a diffraction-limited linear imaging device.

• The resulting Cram\'er-Rao bound gives the lowest variance achievable for an unbiased estimator.
• When only intensity in the image plane is recorded, this bound diverges as the separation between the sources tends to zero, an effect which has been dubbed as Rayleigh's curse.
• However, this curse can be lifted using suitable coherent measurements.