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Interferometric methods have been recently investigated to achievesub-Rayleigh imaging and precision measurements of faint incoherent sources upto the ultimate quantum limit. Here we consider single-photon imaging of twopoint-like emitters of unequal intensity. This is motivated by the fact thatpairs of natural emitters will typically have unequal brightness, as forexample binary star systems and exoplanets. We address the problems ofestimating the transverse separation $d$ and the relative intensity $\epsilon$.Our theoretical analysis shows that the associated statistical errors arequalitatively different from the case of equal intensity. We employ multi-planelight conversion technology to experimentally implement Hermite-Gaussian (HG)spatial-mode demultiplexing (SPADE), and demonstrate sub-Rayleigh measurementof two emitters with Gaussian point-spread function. The experimental errorsare comparable with the theoretical bounds. The latter are benchmarked againstdirect imaging, yielding a $\epsilon^{-1/2}$ improvement in the signal-to-noiseratio, which may be significant when the primary source is much brighter thanthe secondary one, as for example for imaging of exoplanets. However, achievingthis improved scaling requires low noise in the implementation of SPADE, whichis typically affected by crosstalk between HG modes.

Single-photon sub-Rayleigh precision measurements of a pair of incoherent sources of unequal intensity