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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?

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up vote 4 down vote accepted

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.

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A good (non mathematical) explanation I found on this is here:

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Welcome to Astronomy! Whilst this may theoretically answer the question, it would be preferable to include the essential parts of the answer here, and provide the link for reference. – Grant Thomas Dec 14 '11 at 16:09

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