OCT Interferogram: Fringe-Resolved Coherence Gating (2D)

Source & Sample

Center wavelength λ₀ 850 nm

Source bandwidth Δλ 50 nm

Lateral scan speed 15 col/s

Tissue sample

Raw interferogram (this column)

Readouts

Axial res. Δz (free space)

— µm

Axial res. Δz (in tissue)

— µm

Carrier fringe period

— nm

B-scan progress

How it works

This is the 2D companion to the 3D OCT B-scan simulator, and it computes a genuinely different part of the instrument: instead of jumping straight to the coherence-gated envelope, it simulates the actual raw interferometer signal — the carrier fringes produced when reference and sample light interfere — and then quadrature-demodulates that fringe signal in real time to recover the same envelope, exactly as the electronics of a real time-domain OCT system do.

Raw interferogram at reference depth z:
  I(z) = Σᵢ √Rᵢ · cos(2k₀(z − zᵢ)) · exp(−4ln2·((z − zᵢ)/Δz)²)
  k₀ = 2π / λ₀         (carrier wavenumber)

Quadrature demodulation (recovers the envelope):
  Iᵢ = ⟨ I(z)·cos(2k₀z) ⟩ₗₚ,  Qᵢ = ⟨ I(z)·sin(2k₀z) ⟩ₗₚ
  envelope(z) = 2·√(Iᵢ² + Qᵢ²)

Coherence length / axial resolution:
  Δz = (2·ln2 / π) · λ₀² / Δλ

Fresnel reflectivity at an index step:
  R = ((n₁ − n₂) / (n₁ + n₂))²

Carrier fringes — every echo isn't just a smooth blob; it's a burst of interference fringes spaced λ₀/2 apart in optical path, visible only within one coherence length of the true boundary. The live trace below shows this directly.
Demodulation — the dashed envelope is not drawn from a formula; it is computed by multiplying the raw fringe signal by reference oscillators at the carrier frequency and low-pass filtering, then reading off the recovered magnitude — the same lock-in technique real OCT detection electronics use.
λ₀ / Δλ — a wider bandwidth shortens the coherence length (sharper axial resolution, fewer visible fringes per echo) but also lowers signal per gate — the same resolution–sensitivity trade-off as the 3D companion.
Real-world relevance: this fringe-and-demodulate pipeline is literally what happens inside a time-domain OCT engine before any B-scan image is ever formed.

Scanning beam Live B-scan image