quantum mechanics - How is the Hanbury-Brown and Twiss effect used to measure the size of stars?

I understand what an Hanbury Brown and Twiss (HBT) interferometer does, but how can this be used to measure the apparent angular diameter of some object?

What is the mathematical explaination?

Answer

An HBTI works in a very similar manner to a Fizeau / Michelson stellar interferometer. But in an HBTI, a correlation is made between fluctuations of amplitude (intensity) at points across a surface, unlike a Fizeau/Michelson which correlates fluctuations in phase. The timing of these fluctuations is much longer and this leads to a much larger tolerance in path length differences than with phase interferometers.

It can be shown^[1][2] that the visibility $V$ at a baseline $d$ is equal to: $$V^{2}=\gamma^{2}= \frac{\langle I_1 * I_2 \rangle}{\langle I_1 \rangle \langle I_2 \rangle}$$

Where $I_1$ and $I_2$ are the measurements at two separated detectors, and the angle brackets indicate time averages.

^{[1] The Intensity Interferometer, Hanbury Brown.
[2] Optical Stellar Interferometry, Labeyrie.}