Optical super-resolution for two unequally bright point sources based on the fractional Hilbert transform

We propose to utilize fractional Hilbert transform (FHT) to fulfill the optical super-resolution for two unequally bright point sources. For such an asymmetric case, we compare the FHT scheme with both the direct imaging and conventional Hilbert transform schemes. We calculate the Fisher information about the separation and the relative intensity of two light sources. Based on single and multiple parameter estimation, we demonstrate that the FHT scheme has its unique advantages in estimating the separation of the unequally bright point sources. An unconditional enhancement of the measurement precision can be achieved by the FHT scheme. We believe that the FHT can be a good candidate in fulfilling the optical super-resolution in realistic scenarios.