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Robert Hanbury Brown and Richard Q. Twiss sought angular sizes through correlations of detected light intensities. Their method multiplies detector outputs after detection, whereas a Michelson interferometer combines fields before detection.^[ref]

A monochromatic discharge source illuminated a half-silvered beam splitter and two photodetectors. The averaged current product showed an excess near coincidence. Moving one detector introduced a delay that removed it, supplying a control. Slow response weakened the peak. This photon bunching is compatible with fluctuating classical light intensity.^[ref]

For stationary photodetection, the normalized correlation in second-order optical coherence is $g^{(2)}(\tau )=⟨E^{-}(t)E^{-}(t+\tau )E^{+}(t+\tau )E^{+}(t)⟩/⟨E^{-}{E}^{+}{⟩}^2$. Normal ordering expresses the absorption of two photons. In a single mode,A coherent state has $g^{(2)}(0)=1$. A single-mode thermal field has $g^{(2)}(0)=2$ and bunches, while a number state with $n>0$ gives $1-1/n$; a single-photon state has zero ideal coincidence probability at zero delay. Antibunching, a zero-delay suppression relative to nearby delays, is distinct from simply reporting an intensity variance. Multimode averaging and finite detector response reduce observed contrast.

The Hanbury Brown and Twiss effect is measured by splitting the light onto two detectors and histogramming coincidences versus delay. Background counts, detector timing, dead time and afterpulsing need calibration. Two detectors avoid confusing the single detector's inability to register arbitrarily close counts with real antibunching. First-order interference and second-order correlations contain different information: weak first-order coherence does not imply an absence of intensity bunching.^[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]