Cross-correlation scheme for quantum optical coherence tomography based on Michelson interferometer

Quantum optical coherence tomography (QOCT) offers a simple way to cancel dispersion broadening in a sample while also providing twice the resolution compared to classical OCT. However, to achieve these advantages, a bright and broadband source of entangled photon pairs is required. A simple implementation uses collinear spontaneous parametric down-conversion in a Michelson interferometer (MI), yet this autocorrelation scheme suffers from parasitic terms and sensitivity to phase noise. Here, we introduce a cross-correlation MI-based QOCT that overcomes these drawbacks, significantly advancing QOCT toward practical applications.

💡 Research Summary

This paper presents a cross‑correlation scheme for quantum optical coherence tomography (QOCT) implemented in a Michelson interferometer (MI), addressing the major limitations of the previously used auto‑correlation configuration. Classical optical coherence tomography (OCT) suffers from axial resolution limited by the source coherence length and is strongly degraded by group‑velocity dispersion (GVD) in the sample. QOCT, based on Hong‑Ou‑Mandel (HOM) interference of entangled photon pairs generated by spontaneous parametric down‑conversion (SPDC), intrinsically cancels even‑order dispersion and offers twice the axial resolution for the same spectral bandwidth. However, practical QOCT implementations have relied on collinear SPDC sources coupled into an MI and measured coincidences from a single output port (auto‑correlation). In that arrangement the coincidence interferogram contains, besides the desired HOM dip (M₀), two parasitic contributions: a single‑photon Michelson term (M₁) and a narrow‑band pump‑photon term (M₂). The M₁ term is broadband and overlaps with M₀ when a broadband SPDC source is used, reducing the effective resolution and signal‑to‑noise ratio (SNR). Moreover, phase fluctuations in the fiber network broaden the spectral components, making post‑processing cumbersome.

The authors propose to detect coincidences between the two distinct output ports of the MI (cross‑correlation). By projecting onto the state |Ψ(ab)⟩ = â†_out(ω₁) b̂†_out(ω₂) |0⟩, the M₁ term disappears entirely, leaving only the constant background (M_c), the HOM dip (M₀) and the narrow pump term (M₂). In the Fourier domain M₀ appears as a broad Gaussian centered at zero frequency, while M₂ is a sharp peak at the pump frequency ω_p with bandwidth δ ≪ Δ (Δ being the SPDC bandwidth). Consequently, simple Fourier filtering or averaging over a delay interval of 2π/ω_p cleanly isolates M₀ without sacrificing the SPDC bandwidth. Importantly, the amplitude of M₀ in the cross‑correlation interferogram is twice that of the auto‑correlation case and carries a negative sign, i.e., a deeper dip, while the loss associated with the 50/50 beam splitter is avoided. The net effect is a four‑fold increase in coincidence rate compared with the auto‑correlation scheme.

The theoretical model is derived in detail. The MI is described by four input and four output modes (a, b, c, d) linked by the beam‑splitter matrix. The sample is modeled as a single reflective layer with response H(ω)=r e^{iωT}. The SPDC state is expressed as |Ψ⟩ = (1/√2)∫∫F(ω_s,ω_i) â†_in(ω_s) â†_in(ω_i) |0⟩, where |F|² factorizes into a phase‑matching Gaussian (bandwidth Δ) and a pump Gaussian (bandwidth δ). Substituting these into the coincidence probability formula yields the explicit expressions for M_auto(τ) and M_cross(τ). The cross‑correlation interferogram contains only the constant term, the HOM dip (M₀), and the pump term (M₂), confirming the theoretical advantage.

Experimentally, a degenerate collinear SPDC source based on a periodically poled lithium niobate (PPLN) crystal pumped by a continuous‑wave 657 nm laser produces photon pairs centered at 1313 nm with a 50 nm bandwidth. The source is coupled into a polarization‑maintaining single‑mode fiber and injected into an MI built from fiber beam splitters (FBS). A circulator at the input and a second FBS at the output allow simultaneous acquisition of auto‑ and cross‑correlation coincidences using three InGaAs single‑photon detectors (D1, D2, D3) and a time‑tagger. Single‑photon counts from D2+D3 provide a classical OCT reference.

Three experimental demonstrations are reported:

1. Proof‑of‑concept – Using a mirror as the sample, the cross‑correlation interferogram shows a clean HOM dip with a full‑width at half‑maximum (FWHM) corresponding to an axial resolution of 16.6 µm, matching the theoretical c/Δ value. No M₁ peak is observed, confirming the elimination of the parasitic term. The auto‑correlation interferogram, by contrast, exhibits an additional peak that broadens the effective PSF.

2. Dispersion cancellation test – Inserting a 5 mm thick silicon window (high GVD) before the mirror, the classical OCT interferogram broadens dramatically, whereas both auto‑ and cross‑correlation QOCT interferograms remain essentially unchanged. This demonstrates the inherent dispersion cancellation of QOCT, now realized with a bright collinear source.

3. Defectoscopy application – Two silicon windows separated by an air gap are placed in the sample arm. The cross‑correlation QOCT resolves the two interfaces and the thin air layer (≈5 µm) with high contrast, whereas classical OCT cannot distinguish the layers due to dispersion‑induced broadening. This showcases the practical utility of the scheme for high‑resolution, dispersion‑robust imaging of multilayer structures.

The authors also analyze the impact of phase noise in the fiber network. While the single‑photon OCT interferogram’s spectral width is inflated by a factor of ~20 relative to the measured SPDC spectrum, the cross‑correlation QOCT spectrum remains dominated by the narrow pump peak (M₂) and the broad HOM dip (M₀), confirming robustness against phase fluctuations.

In summary, the cross‑correlation MI‑QOCT scheme offers four decisive advantages over the auto‑correlation approach: (i) removal of the broadband parasitic M₁ term, eliminating resolution degradation; (ii) a two‑fold increase in HOM dip amplitude with a sign inversion, yielding a deeper, more easily detectable dip; (iii) a four‑fold improvement in coincidence detection efficiency because the 50 % loss at the beam splitter is avoided; (iv) straightforward separation of the desired signal from the pump‑related term in the Fourier domain, enabling simple post‑processing even with ultra‑broadband SPDC sources. Together with intrinsic dispersion cancellation and enhanced SNR, this method represents a significant step toward practical, high‑speed, high‑resolution quantum OCT systems suitable for biomedical imaging, semiconductor inspection, and other applications where axial resolution and dispersion robustness are critical.