Stellar intensity interferometry in the photon-counting regime

TL;DR

The paper surveys stellar intensity interferometry (SII) and explains how intensity correlations encode angular structure via the Siegert relation and the van Cittert–Zernike theorem. It derives and validates SNR expressions for photon-counting detectors, showing that the SNR scales with factors such as spectral flux, throughput, and timing resolution, and discusses alternative derivations and regimes. Experimental and numerical results address spurious correlations, laboratory validation with artificial stars, and on-sky measurements (e.g., Rigel and Vega), quantifying both statistical and systematic uncertainties. It also discusses future directions, notably wavelength multiplexing with high-time-resolution detectors, and analyzes how SII performance depends on coherence, spectral matching, and detector performance to extend reach to fainter stars.

Abstract

Stellar intensity interferometry consists in measuring the correlation of the light intensity fluctuations at two telescopes observing the same star. The amplitude of the correlation is directly related to the luminosity distribution of the star, which would be unresolved by a single telescope. This technique is based on the well-known Hanbury Brown and Twiss effect. After its discovery in the 1950s, it was used in astronomy until the 1970s, and then replaced by direct (``amplitude'') interferometry, which is much more sensitive, but also much more demanding. However, in recent years, intensity interferometry has undergone a revival. In this article, we present a summary of the state-of-the-art, and we discuss in detail the signal-to-noise ratio of intensity interferometry in the framework of photon-counting detection.

Figures (6)

• Figure 1: Pictures of different facilities used for intensity interferometry with large light collectors. Top-left: the Narrabri observatory, with two telescopes set up on railroad tracks to vary the baseline size and orientation HBT:1968. Top-right: the H.E.S.S. site in Namibia with Cherenkov telescopes 3 and 4 specifically used for intensity interferometry Zmija:2023. Bottom: VERITAS array in Arizona with 4 Cherenkov telescopes Abeysekara:2020.
• Figure 2: Intensity interferometry performed by the I2C consortium at Calern Observatory (France). Left: The two telescopes of C2PU, separated by 15 m, used for spatial intensity interferometry. Right: The coupling device connected to the telescope’s Cassegrain port. It spectrally filters the incoming light, separates the two polarization channels, and injects the light into multimode fibers that feed photon detectors deAlmeida:2022.
• Figure 3: Signal-to-noise ratio in the determination of the bunching peak amplitude, as a function of the rms amplitude of the noise, $\sigma_\mathrm{noise}$, in log-log scale. Inset: the same in linear scale for a restricted range. The fitting parameters are the amplitude $C$ (for all), the rms width $\tau_\mathrm{el}$ (for two or more fitting parameters), the center of the peak $t_0$ (three or four fitting parameters), and the offset $y_0$ (only with four fitting parameters). For the integral method, we have computed the integral over many realizations of the noise and plotted the ratio between the mean and the standard deviation.
• Figure 4: (a) Scheme of the setup to measure $g^{(2)}(\tau)$ without spurious correlations. At the entrance of the fibered splitter, we inject light coming from a white-light source, which has been subsequently injected in a single-mode fiber (to ensure maximum spatial coherence), spectrally filtered (with $\lambda=780$ nm and $\Delta\lambda = 1$ nm), and polarized (not shown here, see e.g. Guerin:2017). The 10-m multimode fibers (MMF) between the splitter and the SPADs ensures that the afterglow peaks are well separated from the bunching peak, and the 40-m coaxial cable on one channel ensures that the bunching peak is far away from the TDC cross-talk. Finally, the two SPADs are separated by $\sim 3$ m to avoid radiative cross-talk. (b) Corresponding $g^{(2)}(\tau)$ measurement, with an integration time of 46 h and count rates of $1.6\times 10^6$ counts per second per detector. The afterglow peaks reach 1.02 in amplitude. The range $\tau <-150$ nm is used to normalize the $g^{(2)}(\tau)$ function to one.
• Figure 5: Signal-to-noise ratio measured in the lab with an artificial star, as a function of the number of coincidences in the correlation histogram far from the bunching peak. The dashed line is the expected $S\!N\!R_\mathrm{fit} = \tau_\mathrm{c} \sqrt{N_\mathrm{c}/(2\sqrt{\pi}\tau_\mathrm{el} t_\mathrm{bin})}$ with $t_\mathrm{bin} = 10$ ps. Inset: Bunching peak at the maximum integration time. The binning has been changed to $t_\mathrm{bin} = 60$ ps for graphical improvement. The goodness of fit is $R^2 = 0.93$.