Performance of fourier domain vs. time domain optical coherence tomography

R. Leitgeb; C. K. Hitzenberger; A. F. Fercher

doi:10.1364/OE.11.000889

Optics Express
Vol. 11,
Issue 8,
pp. 889-894
(2003)
•https://doi.org/10.1364/OE.11.000889

Performance of fourier domain vs. time domain optical coherence tomography

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher

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R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, "Performance of fourier domain vs. time domain optical coherence tomography," Opt. Express 11, 889-894 (2003)

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Abstract

In this article we present a detailed discussion of noise sources in Fourier Domain Optical Coherence Tomography (FDOCT) setups. The performance of FDOCT with charge coupled device (CCD) cameras is compared to current standard time domain OCT systems. We describe how to measure sensitivity in the case of FDOCT and confirm the theoretically obtained values. It is shown that FDOCT systems have a large sensitivity advantage and allow for sensitivities well above 80dB, even in situations with low light levels and high speed detection.

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Fig. 1. FDOCT Signal amplitudes for various optical depths after Fourier transform.

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Fig. 2. Different OCT setups, with Optical Delay Line ODL, light source LD, photodiode PD, sample S, detector array DA. a) FDOCT, b) TDOCT.

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Fig. 3. a) FDOCT signal of a mirror and filter D=2 in the sample arm. b) The same signal with reference arm signal subtraction. The remaining DC peak in the center is due to the sample arm DC power.

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Fig. 4. The red line shows the theoretical sensitivity for FDOCT according to Eq. (6) with γ_r=0.15, γ_s=0.07, ρ=0.19, η =0.4, P₀=175µW,τ=1ms, σ_CCD=250e^-(at room temperature), FWC=400 ke^- The blue line is the TDOCT sensitivity for an unbalanced configuration, with γ_r=γ_s=0.25, B=113 kHz, NEC=0,5pA/√Hz. The squared dots are the actual measured system sensitivities for our FDOCT system.

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Tables (1)

Table 1. Detector signals and noise sources for FD and TDOCT systems.

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Equations (8)

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K (n) = \frac{ρ η τ}{h v_{n}} \cdot P (v_{n}) [γ_{s} R_{s} + γ_{r} R_{r} + 2 \sqrt{γ_{r} γ_{s} R_{r} R_{s}} \cos (\frac{4 π v_{n} Δ z}{c + φ})], n = 0, \dots, N - 1,

P (v_{n}) = P (v_{0}) \exp [- {(\frac{2 \sqrt{\ln 2} (v_{n} - v_{0})}{Δ v_{FWHM}})}^{2}] .

P (v_{0}) \overset{DFT}{\to} S {(τ)}_{Peak} = \sqrt{\frac{π}{4 \ln 2}} \frac{Δ v_{FWHM}^{(n)}}{2 N} P (v_{0}) = \frac{P_{0}}{2 N},

Δ v_{FWHM}^{(n)} \overset{DFT}{\to} Δ τ_{FWHM}^{(h)} = \frac{4 \ln 2}{π} \frac{N}{Δ v_{FWMN}^{(n)}} .

{S (τ)}^{Peak}_{FDOCT} = \frac{ρ η τ}{h v_{0}} \frac{P_{0}}{N} \sqrt{γ_{r} γ_{s} R_{r} R_{s}} .

\sum_{FDOCT} = \frac{\frac{1}{N} {(\frac{ρ η τ}{h v_{0}} P_{0})}^{2} γ_{s} γ_{r} R_{r}}{\frac{ρ η τ}{h v_{0}} \cdot \frac{P_{0}}{N} γ_{r} R_{r} [1 + \frac{(1 + Π^{2})}{2} \frac{ρ η}{{h v}_{0}} \cdot \frac{P_{0}}{N} γ_{r} R_{r} \frac{N}{Δ v_{eff}}] + σ_{receiver}^{2}} .

\sum_{TDOCT} = \frac{1}{B} \frac{2 S^{2} γ_{s} γ_{r} P_{0}^{2} R_{R}}{S P_{0} γ_{r} R_{R} (2 q + {S P}_{0} γ_{r} R_{R} \frac{1 + Π^{2}}{Δ v_{eff}}) + {(NEC)}^{2}} .

B = \frac{2 v_{g}}{l_{c}} = \frac{2}{l_{c}} \frac{(scanning range)}{τ} = \frac{N}{Δ τ_{FWHM}^{(h)}} \frac{1}{2 τ} = \frac{π}{4 \ln 4} \frac{N}{m} \frac{1}{τ},

	Fourier Domain (FD)5	Time Domain (TD)6,7,8
Interference signal	$S {(v_{0})}_{FDOCT} = \frac{ρ η τ}{h v_{0}} 2 P (v_{0}) \sqrt{γ_{r} γ_{s} R_{r} R_{s}}$	〈 $S_{TDOCT}^{2}$ 〉=2S ² $p_{0}^{2}$ γ _r γ _sR_rR_s
DC signal S_DC	$\frac{ρ η τ}{h v_{0}} \frac{P_{0}}{N} (γ_{s} R_{s} + γ_{r} R_{r})$	SP₀(γ _SR_S +γ _rR_r )
$σ_{shot}^{2}$	$\frac{ρ η τ}{h v_{0}} \frac{P_{0}}{N} (γ_{s} R_{s} + γ_{r} R_{r})$	2q_eSP ₀(γ _sR_S +γ _rR_r )B
$σ_{excess}^{2}$	$\frac{(1 + Π^{2})}{2} {(\frac{ρ η}{h v_{0}})}^{2} τ \cdot \frac{P_{0}^{2}}{N^{2}} {(γ_{s} R_{s} + γ_{r} R_{r})}^{2} \frac{N}{Δ v_{eff}}$	$\frac{(1 + Π^{2})}{Δ v_{eff}} S^{2} \cdot P_{0}^{2} {(γ_{s} R_{s} + γ_{r} R_{r})}^{2} B$
$σ_{receiver}^{2}$	$σ_{read}^{2}$ + $σ_{dark}^{2}$	NEC² B

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Equations (8)

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