Abstract

We describe how the simple phase difference averaging causes a systematic bias in the velocity estimation obtained by phase-resolved Fourier domain optical coherence tomography (FdOCT). The magnitude of this bias depends on the signal-to-noise ratio as well as proximity of the measured velocity to the limits of the velocity range. We demonstrate the proper way of data processing, which enables obtaining velocity values free of this error. We validate the improved technique by measurements of flow velocity in glass capillaries, in human retinal vessels, and we compare the results with those obtained by standard phase-resolved FdOCT.

© 2008 Optical Society of America

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References

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2008

2006

2005

2003

1995

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, Opt. Commun. 117, 43 (1995).
[CrossRef]

Bajraszewski, T.

Bouma, B.

de Boer, J.

Drexler, W.

Elzaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, Opt. Commun. 117, 43 (1995).
[CrossRef]

Fercher, A. F.

Fujimoto, J.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 2004).

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, Opt. Commun. 117, 43 (1995).
[CrossRef]

Hong, Y.

Hsu, K.

Huber, R.

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, Opt. Commun. 117, 43 (1995).
[CrossRef]

Kowalczyk, A.

Leitgeb, R. A.

Makita, S.

Schmetterer, L.

Szkulmowska, A.

Szkulmowski, M.

Taira, K.

Tearney, G.

Vakoc, B.

Wojtkowski, M.

Yamanari, M.

Yasuno, Y.

Yatagai, T.

Yun, S.

Zawadzki, R. J.

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Figures (4)

Fig. 1
Fig. 1

Phase distributions analyzed for the phase-resolved FdOCT procedure; κ = 3 . a,e,i, two phase distributions of individual Φ m separated by 0.35 π and 0.75 π , respectively; b,f,j, distributions of phase difference Δ Φ m ; c,g,k, distributions of wrapped phase difference Δ Φ m ; d,h,l, distributions of the mean value of phase differences Δ Φ (each an average of 29 Δ Φ m ). Vertical lines, positions of the expected values of averaged phase difference.

Fig. 2
Fig. 2

Pictorial representation of phase distribution: a, phase distribution on the circle; b, phase distribution in the complex plain.

Fig. 3
Fig. 3

Values of flow velocities retrieved by standard (solid curves) and modified (dashed curves) phase-resolved FdOCT as a function of the SNR for different velocities; M = 30 .

Fig. 4
Fig. 4

Measurements of flow velocity in a capillary (top) and in retinal vessels (bottom), M = 30 . a,e, Structural cross-sectional images. b,f, Velocity maps—standard phase-resolved FdOCT; and c,g, velocity maps—modified phase-resolved FdOCT; black lines indicate the origin of velocity distributions displayed in the last column. d,h, Comparison of both methods for 1D velocity distributions extracted from velocity maps.

Equations (6)

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I ( k , t ) = S ( k ) ( l R l + R r + 2 l R l R r cos ( 2 k z l + 2 v l t k ) ) .
Δ Φ m = { Δ Φ m Δ Φ m π Δ Φ m 2 π sgn ( Δ Φ m ) Δ Φ m > π } .
Δ Φ = 1 M 1 m = 0 M 2 Δ Φ m .
v = Δ Φ 2 k Δ t = λ 4 Δ t Δ Φ π .
p ( Φ ) = { e κ 2 2 2 π + κ cos Φ 2 π exp [ κ 2 sin 2 Φ 2 ] Ω ( κ cos Φ ) π < Φ π 0 otherwise } ,
Δ Φ = arctan ( Im [ m = 0 M 2 exp ( i Δ Φ m ) ] Re [ m = 0 M 2 exp ( i Δ Φ m ) ] ) .

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