Limitation of the achievable signal-to-noise ratio in optical coherence tomography due to mismatch of the balanced receiver

Carla Carmelo Rosa; Adrian Gh. Podoleanu

doi:10.1364/AO.43.004802

Limitation of the achievable signal-to-noise ratio in optical coherence tomography due to mismatch of the balanced receiver

Carla Carmelo Rosa and Adrian Gh. Podoleanu

Applied Optics
Vol. 43,
Issue 25,
pp. 4802-4815
(2004)
•https://doi.org/10.1364/AO.43.004802

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Carla Carmelo Rosa and Adrian Gh. Podoleanu, "Limitation of the achievable signal-to-noise ratio in optical coherence tomography due to mismatch of the balanced receiver," Appl. Opt. 43, 4802-4815 (2004)

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Abstract

Owing to the limited spectral response of the fiber directional coupler used in a balanced optical coherence tomography configuration, the spectra are different in the two outputs. This affects unfavorably operation of the balanced photodetector unit. Excess photon noise makes a larger contribution than a directional coupler with a flat spectral response. A theoretical model is developed that shows that an optimum set of parameters may be defined to maximize the achievable signal-to-noise ratio. The model leads to a redefinition of the effective noise bandwidth, which takes into account the nonflat response of the directional coupler used. The model also predicts a limitation on the signal-to-noise ratio even when the stray reflectances in the interferometer are brought to zero.

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Parameter	Description
P, P ₀	Optical power of the source and optical power transmitted to the tissue
ν	Optical frequency
E, E(t)	Electric field in complex notation and its real part, respectively
I, I _i	Irradiance and irradiance at the directional coupler input port i, respectively
G(ν)	Power spectral density of the source
G _i(ν)	Power spectral density at the coupler i input port
O	Reflectivity of the object under test
R	Total reflection due to fiber-end reflections
σ	Attenuation due to launching reference light into the second coupler
γ₁	Power cross-coupling efficiency for first coupler
γ(ν)	Power cross-coupling efficiency for the second coupler
α	Photodetector conversion factor of 〈EE*〉 into photocurrent
κ_B	Boltzmann constant
T	Temperature (K)
R _L	Load resistor of the balanced receiver
B	Electrical bandwidth of the balanced receiver including rectifier
e	Electron charge

Coupler	Cross-Coupling Function (wavelength λ, nm)
N1	γ(λ) = -2.378+ 0.00344λ
	Linear fit with r ² = 0.99405
N2	γ(λ) = 4.3- 0.0135λ+ 1.08× 10^-5 λ²
	Polynomial fit with r ² = 0.99556
B1	$γ (λ) = 0.354 + 0.062 \times exp [- \frac{{(λ - 775.7)}^{2}}{488.1}] + 0.146 \times exp [- \frac{{(λ - 827.4)}^{2}}{1579.6}]$
	Multipeak fit with χ² = 0.00002
B2	$γ (λ) = 0.21 + 0.15 \times exp [- \frac{{(λ - 773)}^{2}}{1352}] + 0.245 \times exp [- \frac{{(λ - 837)}^{2}}{4463}]$
	Multipeak fit with χ² = 0.00004

Parameter	Description
P, P ₀	Optical power of the source and optical power transmitted to the tissue
ν	Optical frequency
E, E(t)	Electric field in complex notation and its real part, respectively
I, I _i	Irradiance and irradiance at the directional coupler input port i, respectively
G(ν)	Power spectral density of the source
G _i(ν)	Power spectral density at the coupler i input port
O	Reflectivity of the object under test
R	Total reflection due to fiber-end reflections
σ	Attenuation due to launching reference light into the second coupler
γ₁	Power cross-coupling efficiency for first coupler
γ(ν)	Power cross-coupling efficiency for the second coupler
α	Photodetector conversion factor of 〈EE*〉 into photocurrent
κ_B	Boltzmann constant
T	Temperature (K)
R _L	Load resistor of the balanced receiver
B	Electrical bandwidth of the balanced receiver including rectifier
e	Electron charge

Coupler	Cross-Coupling Function (wavelength λ, nm)
N1	γ(λ) = -2.378+ 0.00344λ
	Linear fit with r ² = 0.99405
N2	γ(λ) = 4.3- 0.0135λ+ 1.08× 10^-5 λ²
	Polynomial fit with r ² = 0.99556
B1	$γ (λ) = 0.354 + 0.062 \times exp [- \frac{{(λ - 775.7)}^{2}}{488.1}] + 0.146 \times exp [- \frac{{(λ - 827.4)}^{2}}{1579.6}]$
	Multipeak fit with χ² = 0.00002
B2	$γ (λ) = 0.21 + 0.15 \times exp [- \frac{{(λ - 773)}^{2}}{1352}] + 0.245 \times exp [- \frac{{(λ - 837)}^{2}}{4463}]$
	Multipeak fit with χ² = 0.00004

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