Low Coherence Interferometry

Time-domain OCT: interferogram of a reflector, fringe visibility, axial resolution, Doppler carrier 2v/λ, scan times and the shot-noise SNR.

Model: Textbook approximation

Centre wavelength λ₀ (nm)Bandwidth Δλ, FWHM (nm)Group index of the sample nReference mirror travel (mm)Mirror speed v (mm/s)A-scans per B-scanReference reflectivity R_rSample reflectivity R_sSource power P₀ (mW)Detector responsivity ρ (A/W)

Results

Axial resolution in air9.322 µm

Axial resolution in the sample6.658 µm

Coherence length l_c (path difference)18.64 µm

Fringe visibility V0.1327

Carrier (Doppler) frequency 2v/λ₀76.92 kHz

Signal bandwidth, FWHM 2vΔλ/λ₀²4.734 kHz

Depth range in the sample1.429 mm

A-scan time (one way)40.00 ms

B-scan time20.00 s

Shot-noise SNR97.2 dB

SNR = ρ P_s/(2e B) (Choma 2003, eq. 9) with P_s = R_s·P₀/2, R_s times the power on the sample behind a 50/50 coupler (the detector receives half of it), and B = 2 × the signal FWHM = 9.47 kHz; it assumes R_r ≫ R_s and a shot-noise-limited reference. Spectral width Δλ/λ₀ = 0.062.

Interferogram of a single reflector

Fringe visibility against sample reflectivity

Model

I(d) = I_r + I_s + 2√(I_r I_s) |γ(d)| cos(2πd/λ₀), |γ(d)| = exp(−(πΔλ d/λ₀²)²/(4 ln 2)), d = path difference

V = 2√(R_r R_s)/(R_r + R_s), Δz = (2 ln 2/π) λ₀²/(n Δλ)

f = 2v/λ₀, Δf = 2vΔλ/λ₀², SNR = ρ P_s/(2e B)

Time-domain OCT: a reference mirror moving at constant speed v scans the coherence gate through the sample, so a reflector gives a burst of fringes at the Doppler frequency 2v/λ₀ under the coherence envelope. Gaussian source, Δλ ≪ λ₀, matched dispersion, no flyback time. The SNR is the shot-noise limit of Choma et al. (2003, eq. 9), with their detection bandwidth 2Δk v/π = 4vΔλ/λ₀².

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Michelson interferometer with a Gaussian source (Δλ ≪ λ₀), matched dispersion, a 50/50 coupler and a reference mirror at constant speed with no flyback. The SNR is the shot-noise limit with a strong reference arm; excess intensity noise is not included.

Fercher A. F., Drexler W., Hitzenberger C. K., Lasser T. (2003). Optical coherence tomography — principles and applications. Rep. Prog. Phys. 66, 239–303. Axial resolution (2 ln 2/π) λ₀²/Δλ. doi:10.1088/0034-4885/66/2/204
Choma M. A., Sarunic M. V., Yang C., Izatt J. A. (2003). Sensitivity advantage of swept source and Fourier domain optical coherence tomography. Opt. Express 11, 2183–2189. Time-domain SNR ρP_s/(2eB), eq. 9, with B = 2Δk v/π. doi:10.1364/OE.11.002183

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