= Stellar intensity interferometry
<Stellar intensity interferometry> measures a <star>'s <angular diameter> by comparing fluctuations of detected <light intensity> at separated collectors. Each collector has its own <photodetector>; an <analog multiplier> or a digital correlator compares the electrical outputs. Changing the <interferometric baseline> changes the sampled <spatial optical coherence>. An unresolved <star> produces correlated fluctuations; a resolved extended source supplies different mixtures of emission directions, reducing their correlation.
This makes a useful telescope out of a surprising observable: the fluctuations discarded by an ordinary average-brightness measurement. Optical beams need not travel to a common combiner. A relative <wave phase> perturbation $E_2\mapsto e^{i\phi}E_2$ leaves $|E_2|^2$ unchanged, so pure phase errors do not directly change the local <light intensity>. Electronic delay alignment remains necessary; intensity changes from <atmospheric scintillation>, collection losses, and instrumental noise still require controls.
Let $\mathbf b$ join the collectors and let $\mathbf s_0$ be the unit <line of sight> toward the <star>. The relevant <interferometric baseline> is its projection onto the <plane of the sky>:
$$
\mathbf b_\perp=\mathbf b-(\mathbf b\cdot\mathbf s_0)\mathbf s_0,
\qquad B=|\mathbf b_\perp|.
$$
The reference arrival-time difference has magnitude $|\mathbf b\cdot\mathbf s_0|/c$, with <speed of light> $c$. Correct that delay, with a sign fixed by channel order, before averaging the residual correlation at $\tau=0$. The physical collector separation equals $B$ only when it is perpendicular to $\mathbf s_0$; tracking a <star> can change the projection even for fixed collectors.
\Image[/stellar-intensity-interferometer-geometry.png]
{title=Functional geometry of <stellar intensity interferometry>: separate optical detection followed by electrical correlation}
{description=Original schematic with the reference direction normal to the baseline. Matched optical selection feeds independent detectors; mean removal, response and delay alignment precede multiplication and averaging. This is not a scale drawing of the historical apparatus.}
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