The information content of optical intensity interferometry
Optical intensity interferometry (II) can in principle resolve structure on angular scales $\theta\sim \lambda/B$, but it measures only the squared visibility $|{\cal V}|^2$, discarding Fourier phase. We quantify what information can actually be recovered from phase-less $|{\cal V}|^2$ measurements as a function of the aggregate signal-to-noise ratio and array configuration, using score-based diffusion models as non-parametric image priors. We construct an image reconstruction pipeline, and validate it by reconstructing a variety of images, including GRMHD simulations of black hole accretion disks and actual SDO/HMI continuum images of the Sun, from phase-less Fourier amplitudes. Using simulated data, we map the reconstruction fidelity of Sun-like stellar surfaces as a function of noise level, number of $(u,v)$ samples, and maximum baseline $B_{\rm max}$, for surface maps spanning a range of activity levels. We find that fidelity depends on the data only through the total signal to noise ratio (SNR) of the surface features of interest, provided that the $(u,v)$ plane is sampled sufficiently densely. These results show that the SNR levels achieved by next-generation intensity interferometers observing realistic sources are sufficient to image highly complicated stellar surfaces.