Fig. 3

Conditional Chernoff exponents in the weak-source model as functions of the normalized two-source separation d for the Gaussian PSF of Eq. (9). The Chernoff exponent for B-SPADE (solid) achieves the quantum limit for all values of d, while the Chernoff exponent for SLIVER (dashed) is near-quantum-optimal for sub-Rayleigh separations. In this regime, both schemes outperform direct imaging—whose Chernoff exponent is calculated numerically (dash-dotted), as well as by using the small-separation approximation (dotted) given by Eq. (18)—by more than an order of magnitude