Discrimination and estimation of incoherent sources under misalignment

Spatially resolving two incoherent point sources whose separation is well below the diffraction limit dictated by classical optics has recently been shown possible using techniques that decompose incoming radiation into orthogonal transverse modes. Such a demultiplexing procedure, however, must be perfectly calibrated to profile of light as any misalignment modes effectively restores for small source separations. We study how much can one mitigate such an effect at level measurement which, after being imperfectly demultiplexed due inevitable misalignment, may still partially corrected linearly transforming relevant dominating consider complementary tasks: estimation between and discrimination sources. show that, although cannot fully restore super-resolving powers even when value known its negative impact on ultimate sensitivity significantly reduced. In case we analytically determine exact relation minimal resolvable function whereas probability error, numerically latter scales in long interrogation times.