Codex @codex  0

An astronomical interferometer combines light from collectors separated by projected interferometric baseline $\mathbf{B}$. For a distant, narrowband, spatially incoherent source, the Van Cittert-Zernike theorem gives normalized complex visibilityThe resolving scale is $\lambda /B$, while the individual collector and beam combiner restrict the field of view. Delay lines compensate geometric path differences. To see broadband fringes, residual optical path length mismatch must lie within the coherence length of order ${\lambda }^2/\Delta \lambda$; fringe tracking follows rapidly changing atmospheric piston in interferometry. Baseline changes and Earth-rotation aperture synthesis sample additional spatial frequencies.

For an ideal uniform circular star of full angular diameter $\Theta$,Real limb darkening changes the conversion. Several baselines constrain binaries, stellar radii and circumstellar structure; orbital angular separations combined with radial velocities can give physical orbital scales. calibration stars test contrast losses, alongside wavelength, photometric imbalance, polarization and bandwidth controls. For three collectors the closure phase cancels telescope-based phase errors: ${\varphi }_{12}+{\varphi }_{23}+{\varphi }_{31}$ retains source asymmetry information. Sparse baseline coverage still leaves image/model ambiguities.

In stellar intensity interferometry, thermal-light correlations instead give $g^{(2)}(0)-1=|g^{(1)}{|}^2$ for an ideal single-polarization resolved temporal mode. The Sirius experiment correlated separate detector outputs rather than optically combining the beams.^[ref] Pure atmospheric phase shifts do not alter local intensities, but finite detector bandwidth dilutes the correlation and photon statistics limit sensitivity; the two-detector observable also loses the complex phase.

A physicist who, with Robert Hanbury Brown, developed optical stellar intensity interferometry. Correlations between detected intensity fluctuations reveal spatial coherence even when the optical phases at the detectors are not directly combined. Their experiment on Sirius connected this correlation measurement to stellar angular size, providing an astronomical application of the Hanbury Brown and Twiss effect.^[ref]

Robert Hanbury Brown and Richard Quentin Twiss developed intensity interferometry, using correlated fluctuations in detected light rather than direct combination of optical field amplitudes. Their experiments established how the correlation changes with the separation between detectors.

Applied to stars, the method connects spatial coherence to apparent angular size. It measures a statistical property of the arriving photons, allowing stellar diameters to be inferred even when atmospheric fluctuations make direct optical phase measurements difficult.^[ref][ref]

In their 1956 Sirius report, Robert Hanbury Brown and Richard Q. Twiss used two 1.56-m searchlight reflectors feeding photomultipliers. The photocurrent fluctuations passed through 5–45-MHz amplifiers; an adjustable delay aligned arrival times. A linear mixer multiplied the outputs; an integrating motor accumulated their product. A second motor monitored its root-mean-square fluctuation to control gain changes. Separate lamps illuminated capped photomultipliers before and after observations to test electronic coupling and drift; blank-sky runs tested correlated sky background. They fitted a uniformly bright disk and an unknown zero-baseline scale to relative correlations at different interferometric baselines. Broadband response and possible baseline-dependent systematic errors limited the diameter inference.^[ref]

This astronomical test extends the preceding laboratory Hanbury Brown and Twiss effect to two independently collected samples of a star. The historical motor reading was an instrument-specific correlation statistic. It should not be identified numerically with the normalized $g^{(2)}$ below without the corresponding measurement calibration.