A nonlinear crystal converts a pump photon into a frequency-anticorrelated signal/idler pair (spontaneous parametric down-conversion, ωs+ωi = ωpump). Idler goes to a reference mirror, signal probes the tissue sample, and both recombine on a beamsplitter feeding two detectors that register coincidences.
Coincidence rate: C(τ) = R₀ [1 − V · exp(−τ² / 2σ²)]
Classical width: σ_cl(GDD) = √(σ₀² + (GDD/σ₀)²)
Quantum width: σ_q = σ₀ (even-order dispersion cancels)
Classical visibility: V_cl(GDD) = V₀ / √(1 + (GDD/σ₀²)²)
- Mirror delay τ — scans the reference arm's path length; the coincidence rate dips to a minimum at zero relative delay (a Hong-Ou-Mandel-type dip), giving the depth marker.
- Tissue dispersion (GDD) — group-delay dispersion the sample imprints on the light. For frequency-anticorrelated pairs, the two photons' opposite-sign detunings make their even-order dispersion terms cancel in the joint (coincidence) detection, so the quantum dip stays narrow; a classical (unentangled) measurement has no such cancellation and its interferogram broadens and shallows as GDD grows.
- Source bandwidth σ₀ — sets the transform-limited coherence time and hence the best achievable axial resolution, Δz ≈ c·σ₀·2.355 / (2n).
This dispersion-cancellation effect (Steinberg, Kwiat & Chiao, 1992) underlies quantum-optical coherence tomography: it lets a scan keep micron-scale depth resolution through dispersive biological tissue where a classical OCT interferogram would blur.