Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound

Open Access Open Access

Abstract

Doppler optical coherence tomography (DOCT) is a technique for simultaneous cross-sectional imaging of tissue structure and blood flow. We derive the fundamental uncertainty limits on frequency estimation precision in DOCT using the Cramer-Rao lower bound in the case of additive (e.g., thermal, shot) noise. Experimental results from a mirror and a scattering phantom are used to verify the theoretical limits. Our results demonstrate that the stochastic nature of frequency noise influences the precision of flow imaging, and that the noise model must be selected judiciously in order to estimate the frequency precision.

©2005 Optical Society of America

Full Article  |  PDF Article
More Like This
Cramer–Rao lower bounds on the estimation of the degree of polarization in coherent imaging systems

Nicolas Roux, François Goudail, and Philippe Réfrégier
J. Opt. Soc. Am. A 22(11) 2532-2541 (2005)

Estimation of parameters of a laser Doppler velocimeter and their Cramer–Rao lower bounds

Jian Zhou and Xingwu Long
Appl. Opt. 50(23) 4594-4603 (2011)

Self-referenced Doppler optical coherence tomography

Siavash Yazdanfar and Joseph A. Izatt
Opt. Lett. 27(23) 2085-2087 (2002)

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1. Fiber-optic, time-domain Michelson interferometer used to measure the frequency precision of Doppler OCT. BPF, band-pass filter; A/D, analog-to-digital converter; I, Q, in-phase and quadrature signal components after demodulation.
Fig. 2.
Fig. 2. Algorithm for calculating frequency precision and signal-to-noise ratio (SNR). The OCT reflectance image of Liposyn is shown on the left, with the arrow indicating the direction of the incident beam. The standard deviation of the noise is calculated in the region of interest (ROI) located outside of the sample. At each axial position, the average signal value across 100 scans is measured and divided by the noise to measure local SNR. At the same depth, the variance of the Doppler frequency (right) is measured and compared to the theoretical frequency precision.
Fig. 3.
Fig. 3. Experimental and theoretical frequency standard deviation (SD) versus SNR for A) additive noise only and B) both additive and multiplicative (speckle) noise. The observation time was different for the two experiments, resulting in different theoretical limits. The inset of A), magnifying lower SNR values on a log-log scale, suggests that the autocorrelation algorithm used to estimate frequency is a maximum likelihood estimator. CRLB, Cramer-Rao lower bound based on the additive model of Eqs. (2) and (5).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

s ( t ) = A ( t ) cos [ 2 π ( f r f s ) t + β ( t ) ] ,
s ( t ) = A ( t ) cos [ 2 π f s t + β ( t ) ] , 0 t t 0
f s min = 1 t 0
Var [ α ̂ ( R ) α ] ( E { [ ln p ( R α ) α ] 2 } ) 1
r ( t ) = s ( t , α ) + n ( t )
σ α ̂ 2 ( 1 N 0 0 t 0 [ s ( t , α ) α ] 2 d t ) 1
σ f ̂ 2 ( 2 π 2 3 A 2 N 0 t 0 2 ) 1
f s min σ 1 t 0 SNR
R ( τ ) = R ( τ ) exp [ i ϕ ( τ ) ] s * ( t ) s ( t + τ )
Ω = 16 ( π λ 0 ) 2 D T [ rad s ]
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved