## Flow velocity estimation using joint Spectral and Time domain Optical Coherence Tomography

Optics Express, Vol. 16, Issue 9, pp. 6008-6025 (2008)

http://dx.doi.org/10.1364/OE.16.006008

Acrobat PDF (3076 KB)

### Abstract

We propose a modified method of acquisition and analysis of Spectral Optical Coherence Tomography (SOCT) data to provide information about flow velocities. The idea behind this method is to acquire a set of SOCT spectral fringes dependent on time followed by a numerical analysis using two independent Fourier transformations performed in time and optical frequency domains. Therefore, we propose calling this method as joint Spectral and Time domain Optical Coherence Tomography (joint STdOCT). The flow velocities obtained by joint STdOCT are compared with the ones obtained by known, phase-resolved SOCT. We observe that STdOCT estimation is more robust for measurements with low signal to noise ratio (SNR) as well as in conditions of close-to-limit velocity measurements. We also demonstrate that velocity measurement performed with STdOCT method is more sensitive than the one obtained by the phase-resolved SOCT. The method is applied to biomedical imaging, in particular to *in vivo* measurements of retinal blood circulation. The applicability of STdOCT different measurement modes for *in vivo* examinations, including 1, 5 and 40 µs of CCD exposure time, is discussed.

© 2008 Optical Society of America

## 1. Introduction

1. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science **254**, 1178–1181 (1991). [CrossRef] [PubMed]

2. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, “Measurement of Intraocular Distances by Backscattering Spectral Interferometry,” Opt. Commun. **117**, 43–48 (1995). [CrossRef]

3. M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. **7**, 457–463 (2002). [CrossRef] [PubMed]

15. B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express **13**, 3931–3944 (2005). [CrossRef] [PubMed]

12. B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography,” Opt. Express **11**, 3490–3497 (2003). [CrossRef] [PubMed]

16. S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, “Motion artifacts in optical coherence tomography with frequency-domain ranging,” Opt. Express **12**, 2977–2998 (2004). [CrossRef] [PubMed]

*in vivo*. Recently, a novel spectral method has been proposed in order to minimize the influence of phase instabilities so called resonant Doppler imaging [17

17. A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Resonant Doppler flow imaging and optical vivisection of retinal blood vessels,” Opt. Express **15**, 408–422 (2007). [CrossRef] [PubMed]

*et al.*, [18

18. R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, “Three dimensional optical angiography,” Opt. Express **15**, 4083–4097 (2007). [CrossRef] [PubMed]

*et al.*, in 2006 [19

19. Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous BM-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. **45**, 1861–1865 (2006). [CrossRef] [PubMed]

20. Z. Chen, T. E. Milner, D. Dave, and J. S. Nelson, “Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media,” Opt. Lett. **22**, 64–66 (1997). [CrossRef] [PubMed]

21. J. A. Izatt, M. D. Kulkami, S. Yazdanfar, J. K. Barton, and A. J. Welch, “In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Opt. Lett. **22**, 1439–1441 (1997). [CrossRef]

*in vivo*in OCT functional studies.

## 2. Theory

8. R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, “Real-time assessment of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography,” Opt. Express **11**, 3116–3121 (2003). [CrossRef] [PubMed]

15. B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express **13**, 3931–3944 (2005). [CrossRef] [PubMed]

*k*and time

*t*according to the following equation:

*I*(

*k*,

*t*) is the spectral fringe signal,

*I*

_{0}(

*k*) is spectral density of the light source,

*R*and

_{l}*R*denote the reflectivity of the sample and reference mirror, respectively;

_{r}*z*(

_{l}*t*) denotes the optical path difference between the reference mirror and the

*l*-th interface in the sample, which is time dependent due to the movement of the reference mirror and/or due to the displacement of the

*l*-th interface in the sample. The displacement of the interfaces within the sample is usually caused either by a movement of the entire sample itself or by a motion of the specific interface

*z*within the sample. If we assume that both, reference mirror velocity and velocities in the sample are constant during the acquisition of the spectral fringes, Eq. (1), then the time-dependent position of the

_{l}*l*-th interface

*z*(

_{l}*t*) can be expressed as:

*z*is the depth position of the

_{l}*l*-th interface at the beginning of data acquisition and

*v*is the difference between the velocity of the reference mirror and an axial component of velocity (parallel to the direction of the probing beam propagation) of the

_{l}*l*-th interface. If the

*l*-th interface moves with velocity

*V*at an angle

_{l}*α*to the probing beam and the velocity of the reference mirror is equal to

*v*this can be expressed as:

_{r}*z*of

_{l}*l*-th interface and small additional change of

*δz*, that occurs if the

*l*-th interface is moving. Equation (5) highlights the time-dependence of the interferometric fringes and shows that signal is modulated in time with frequency

*ω*. This beat frequency is caused by a Doppler effect, that arises for each

_{l}*l*-th interface along the time axis. This frequency depends on the velocity

*v*and is different for each wavenumber

_{l}*k*:

### 2.1 Velocity measurement using phase-resolved SOCT

*δz*of

*l*-th interface, that arises during the time Δ

*t*between two consecutive measurements, the velocity

*v*of the

_{l}*l*-th interface can be calculated. Since

*δz*is much smaller than

*z*, the difference between two consecutive measurements appears as a phase change ΔΦ of interferometric fringes:

_{l}*t*is approximately equal to the exposure time of the detector, therefore 1/Δ

*t*is the frame rate of an array detector (or equivalently ‘A-scan’ rate). It is important to ensure that ΔΦ is less than 2

*π*. Since the phase can be unambiguously determined in the range of 2

*π*, and the phase difference is within the range of 4π a procedure of phase wrapping has to be performed to transform the phase differences to the range (-

*π*,

*π*) [12

12. B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography,” Opt. Express **11**, 3490–3497 (2003). [CrossRef] [PubMed]

13. S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express **14**, 7821–7840 (2006). [CrossRef] [PubMed]

*π*, the phase shift it is left as it is, and when

*π*<|ΔΦ|<2

*π*, the phase shift is replaced by ΔΦ-sign(ΔΦ)2

*π*. The phase differences ΔΦ from the range (0,

*π*) are considered positive, while those form (-

*π*,0) negative. Usually more than two measurements are used to estimate the phase differences. Wrapped phase differences ΔΦ are averaged out to increase the sensitivity and accuracy of the velocity estimation [8

8. R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, “Real-time assessment of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography,” Opt. Express **11**, 3116–3121 (2003). [CrossRef] [PubMed]

12. B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography,” Opt. Express **11**, 3490–3497 (2003). [CrossRef] [PubMed]

15. B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express **13**, 3931–3944 (2005). [CrossRef] [PubMed]

*π*(ΔΦ

_{±max}=±

*π*) is:

_{min}is equal to the standard deviation of the estimator of the phase differences

*σ*

_{ΔΦ}and is limited by signal-to-noise ratio (SNR) [15

**13**, 3931–3944 (2005). [CrossRef] [PubMed]

22. S. Yazdanfar, C. H. Yang, M. V. Sarunic, and J. A. Izatt, “Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound,” Opt. Express **13**, 410–416 (2005). [CrossRef] [PubMed]

23. B. Vakoc, S. Yun, J. de Boer, G. Tearney, and B. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express **13**, 5483–5493 (2005). [CrossRef] [PubMed]

_{min}=(

*SNR*)

^{-1/2}[15

**13**, 3931–3944 (2005). [CrossRef] [PubMed]

*et al.*, suggest that retinal blood flow velocities <0.2 mm/s are out of the scope of the standard phase-resolved OCT method in the case of

*in vivo*imaging [23

23. B. Vakoc, S. Yun, J. de Boer, G. Tearney, and B. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express **13**, 5483–5493 (2005). [CrossRef] [PubMed]

### 2.2 Velocity measurement using joint Spectral and Time domain OCT

*M*spectra collected in time increments Δ

*t*at the same transverse location of the probing beam, Eq. (5). As the data are registered and analyzed in wavenumber and time space simultaneously, we called this method joint Spectral and Time domain OCT (STdOCT).

*M*measurements of spectral interferometric fringes are performed at the same lateral location (Eq. 5). Collected spectral fringe signals undergo standard SOCT preprocessing consisting of background removal and rescaling to wavenumber domain [24

24. M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express **12**, 2404–2422 (2004). [CrossRef] [PubMed]

*k*–

*t*plane, Fig. 1(a)). A Doppler frequency arising from a movement of

*l*-th interface is visible as a frequency of the signal along the

*t*-axis while the modulation frequency along

*k*-axis provides information on location of

*l*-th interface. The two-dimensional set of spectral fringes is analyzed by Fourier transformations, that can be applied in two separate ways. First FT can be performed “horizontally” thus it converts the STdOCT data from wavenumber domain to the depth (

*z*–

*t*plane, Fig. 1(b)). The second FT acts “vertically” and converts data from time domain to Doppler frequency, that corresponds to velocity (

*k*–

*ω*plane, Fig. 1(c)).

*z*–

*ω*plane, Fig. 1(d)). Note that panels (b), (c), (d) display only amplitudes of complex valued functions. The top-right panel (Fig. 1(b)) corresponds to data processed in standard SOCT, where the structure of the object is reconstructed. Standard SOCT uses the modules of Fourier transforms of data to create structural A-scans and the phases to calculate the velocities with phase-resolved method. Here,

*M*registered spectra result in

*M*structural A-scans and only structural information is presented with no velocity information. Maximal optical path difference between the mirror in the reference arm and the reflecting interface in the sample arm define imaging range in depth

*z*

_{±max}. It is connected with the sampling interval in wavenumber domain Δ

*k*of recorded spectra:

*z*, that encodes the position of the sample is chosen to be positive if the sampling arm is longer then the reference arm, and negative in the opposite case. The image of the objective mirror is visible as a single interface which apparently is fixed in time. This image is doubled due to the fact that registered interferogram is a real-valued function [25

25. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. **27**, 1415–1417 (2002). [CrossRef]

*ω*, according to Eq. (6). For each known

_{l}*k*the velocity can be calculated separately. Therefore, this representation of data can be also used to find exact relationship between wavenumbers and pixels in an array detector, and the same to calibrate the spectrometer very accurately. In this particular case the velocity of moving mirror is measured to be 14.25 kHz (0.95 mm/s) for k=7.5·10

^{6}m

^{-1}, Fig. 1(f). The question of velocity distribution within the object is trivial in the case of a mirror. If the object is more complex, magnitude and direction of the movement will be known but there would be no information about the position of the moving interface. Similar to the phase-resolved OCT, the maximal value of bidirectional flow velocity

*v*

_{±max}is given by the time interval Δ

*t*between consecutive measurements of the spectral fringes:

*t*=40us it becomes

*v*

_{±max}=±5.2mm/s.

*M*spectral fringes. Coordinates of displayed signals link positions of all measured interfaces with corresponding velocities. Each interface

*z*is represented by two symmetric points appearing with respect to the zero-path-delay and zerovelocity. The interpretation of resulting points, shown in Fig. 1(d), is following: the mirror surface localized at

_{l}*z*=140um (Fig. 1(e)) moves with the velocity of 14.2 kHz (Fig. 1(f)). The sign of velocity value indicates forward or backward direction. The point localized at (

*z*,

*ω*)=(-0.14 mm, -14.2 kHz) is its complex conjugate.

*ω*– axis is caused by the dependence of the Doppler frequency on wavenumber,

*ω*=2

*vk*, Eq. (6). A velocity value for each

*z*position is calculated from Doppler frequency indicated by the point with maximal amplitude.

### 2.3 Conditions of reliable velocity measurement for phase-resolved SOCT and joint Spectral and Time domain OCT – SNR analysis

*I*(

*k*,

*t*) [Eq. (1)] is a sum of a harmonic component

*S*and a noise component

*X*.

*s*, frequency

_{kt}*ω*and the initial phase set to be zero (random variable and its specific value are denoted by capital and lowercase letter, respectively):

_{kt}*(with uniform distribution) and random amplitudes*

_{n}*α*:

_{n}*x̄*=0 and a variance

*σ*

^{2}

*:*

_{kt}*α*is identical for all frequencies and has a mean value equal to zero and a variance equal to

_{n}*σ*

^{2}

*. The relation between*

_{α}*σ*and

_{α}*σ*is following:

_{kt}*k*–

*t*space (Fig. 1(a)), the phase-resolved method operates in

*z*–

*t*space (Fig. 1(b)) and STdOCT in

*z*–

*ω*space (Fig. 1(d)), the amplitudes

*s*,

_{kt}*s*,

_{zt}*s*

_{zω}are coupled via Fourier transformations. If the Fourier transformation is defined to conserve power of the signal (

*E*[

*I*

^{2}]=

*E*[

*Z*

^{2}],

*Z*=FT(

*I*)), the amplitudes are amplified with respect to a number of points in Fourier transforms

*N*,

*M*:

*z*–

*t*space):

*et al.*[26

26. 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). [CrossRef] [PubMed]

*κ*(STdOCT) is

_{ωz}*M*

^{1/2}times higher comparing to

*κ*(phase-resolved SOCT).

_{zt}*S*and a random phasor

*X*[27].

*κ*the density function becomes more narrow, converging towards a Dirac delta function centered at Φ=0, whereas when the length of the known phasor

_{zt}*s*decreases to zero (

*κ*→0), this distribution converges to uniform distribution, Fig. 2. As the phase-resolved SOCT requires phase subtraction, the width of the final distribution broadens two times. The broader distribution is, the more random wrapped phase differences are detected, and in turn the averaged value of phase differences is closer to zero.

_{zt}*A*of the sum of a constant phasor and a random phasor is given by a Rician density function:

*I*

_{0}(·) is a modified Bessel function of the first kind, zero order. As the length of the known phasor

*s*increases, the shape of density function

*p*(

_{A}*a*) changes from that of a Rayleigh density to approximately a Gaussian density with mean equal to

*s*.

*κ*≠0, Eq. (21)) and noise (

_{zω}*κ*=0) are separated. The minimal value of κ

_{zω}_{zω}, which almost always meets this requirement is

*κ*=7, Fig. 3.

_{zω}*κ*converges to zero, the probability of detecting the correct position of signal amplitude decrease. Every detection of noise causes indication of random velocity, therefore, the distribution of recovered velocity broaden and its mean value converges to the center of the available velocity range (usually to zero).

_{zω}*M*=30) were generated with respect to the shape of spectrum and the probability density function of amplitude (Eq. (22)) and phase (Eq. (21)). The magnitude of change in harmonic component between consecutive signals was set to correspond to 0.35

*ν*

_{max}and 0.75

*ν*

_{max}. Both methods operates on exactly the same amount of generated signals. The velocity was recovered for different SNR and the results are shown in Fig. 4.

_{max}were chosen and the velocity estimation for each of them was performed. The dependence of velocity reading on proximity to the theoretical limits of velocity are shown in Fig. 5(a). One can see that there is no significant difference in critical values of SNR for velocities <0.5 v

_{max}, whereas for higher velocities the critical SNR shifts substantially towards higher values and for 0.95 v

_{max}it is 25dB higher than for 0.05 v

_{max}. In other words, for a given value of SNR the phase-resolved method can give correct velocity readings for lower velocities and underestimated values for higher velocities, for example for 20dB 0.95 v

_{max}is estimated to be 0.75 v

_{max}, whereas lower velocities are correctly recovered. Figure 5(b) shows simulated values of velocity retrieved by the phase-resolved method versus the velocities set in the simulation as real ones. In both cases normalization was applied to display the velocities in respect to the maximum measurable velocity V

_{max}. It is visible that for higher SNRs it is possible to measure correctly higher values of velocity. SNR defines the shape of phase difference distribution. When the width of distribution becomes broad comparing to phase range, the wrapping procedure causes that some of the phase differences are found as positive and the other as negative (Fig. 5(b) right panel). Since the final velocity estimation is based on calculation using several phase differences, its averaged value decreases to zero for the phase difference close to ±

*π*. Hence, the decreased value of averaged phase difference underestimates the value of velocity in the phase resolved OCT.

*A*used in joint STdOCT to retrieve velocity value depends on number of spectra registered in time (

_{zω}*M*), the critical SNR can be improved

*M*

^{1/2}times with increasing number of measurements (Table 1.). In phase-resolved SOCT increasing number of spectra does not improve measurement sensitivity, however it facilitates detection of mean value of phase difference distribution.

17. A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Resonant Doppler flow imaging and optical vivisection of retinal blood vessels,” Opt. Express **15**, 408–422 (2007). [CrossRef] [PubMed]

## 3. Experiment

*Broadlighter*, Superlum, Δ

*λ*=90nm, central wavelength 840 nm), a fiber Michelson interferometer with fixed reference mirror and custom designed spectrometer with a volume phase holographic grating DG (1200 grooves/mm) and an achromatic lens focusing spectrum on 12-bit CCD line-scan camera (

*Aviiva M2*, Atmel), Fig. 6. The experiments were performed for three different objects: moving mirror, capillary flow and blood flow in human retina. In measurements of the velocity of moving mirror, a silver mirror was attached to a piezo-actuator (Physik Instrumente) and it was driven by a triangular voltage signal. The exact velocity was calculated at the moment of a linear slope of the driving signal from trajectory registered by the position sensor mounted inside the actuator. Measurements were performed with A-scan rate of 40.4 µs.

*z*-axis) and stable, laminar flow was ensured by a medical drip system. The sets of 40 spectra were collected at the same transversal position of the light beam. The acquisition time was set to 52 µs including 10 µs dead time needed for stabilization of the position of galvo scanner driven by the stepwise signal. The optical power of the light illuminating the sample was 3.3 mW.

## 4. Results and discussion

### 4.1 Moving mirror

_{max}. The sets of 30 spectra were collected and then processed to obtain phase-resolved and STdOCT velocity estimations. Figures 7(a), 7(b) presents achieved velocity values, which are displayed together with theoretical results demonstrated in Fig. 4.

### 4.2 Capillary flow

*z*were detected and points that most likely correspond to noise (

*κ*≤2) were removed by thresholding procedure, Fig. 8(d). Images (c) and (d) correspond to a single line in 2D velocity map (Fig. 8(b)), on which the values of velocity are encoded using false colors. Figure 8(e) presents a single 1D velocity distribution along the transversal direction indicated by green horizontal line on the velocity map. All presented velocity distributions have parabolic shapes, what implies that measured flow is laminar.

_{zω}_{max}. (Fig. 9(b)) We can observe that both methods give similar readings to approximately half of the velocity range. For higher velocities phase-resolved method dramatically underestimates the velocity values, and for v

_{max}returns zero. In STdOCT velocities beyond the range are wrapped and found as negative values. The distortions of velocity distributions in phase-resolved method appear when SNR decreases or when velocities are too high (however still in the theoretically achievable range).

### 4.3 Retinal blood flow, in vivo

*in vivo*was performed. Figure 10(a) demonstrates cross-sectional image of human retina scanned through the region of optic disc. Figures 10(b) and 10(c) show two-dimensional maps of the flow velocity distribution obtained with SOCT and STdOCT, respectively.

### 4.4 Retinal blood flow imaging with ultra-short CCD exposure time

## 5. Conclusions

*in vivo*for 5 µs and 1 µs exposure time.

## Acknowledgments

## References and links

1. | D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science |

2. | A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, “Measurement of Intraocular Distances by Backscattering Spectral Interferometry,” Opt. Commun. |

3. | M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, “In vivo human retinal imaging by Fourier domain optical coherence tomography,” J. Biomed. Opt. |

4. | N. Nassif, B. Cense, B. H. Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography,” Opt. Lett. |

5. | M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology |

6. | V. J. Srinivasan, M. Wojtkowski, A. J. Witkin, J. S. Duker, T. H. Ko, M. Carvalho, J. S. Schuman, A. Kowalczyk, and J. G. Fujimoto, “High-definifion and 3-dimensional imaging of macular pathologies with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology |

7. | R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, “Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography,” Opt. Lett. |

8. | R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, “Real-time assessment of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography,” Opt. Express |

9. | Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, “Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography,” Opt. Lett. |

10. | M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, “Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy,” J. Biomed. Opt. |

11. | F. Rothenberg, A. M. Davis, and J. A. Izatt, “Non-invasive investigations of early embryonic cardiac blood flow with optical coherence tomography,” FASEB J. |

12. | B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, “In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography,” Opt. Express |

13. | S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express |

14. | Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. F. de Boer, and J. S. Nelson, “Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity,” Opt. Lett. |

15. | B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, “Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm,” Opt. Express |

16. | S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, “Motion artifacts in optical coherence tomography with frequency-domain ranging,” Opt. Express |

17. | A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, “Resonant Doppler flow imaging and optical vivisection of retinal blood vessels,” Opt. Express |

18. | R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, “Three dimensional optical angiography,” Opt. Express |

19. | Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous BM-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. |

20. | Z. Chen, T. E. Milner, D. Dave, and J. S. Nelson, “Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media,” Opt. Lett. |

21. | J. A. Izatt, M. D. Kulkami, S. Yazdanfar, J. K. Barton, and A. J. Welch, “In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography,” Opt. Lett. |

22. | S. Yazdanfar, C. H. Yang, M. V. Sarunic, and J. A. Izatt, “Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound,” Opt. Express |

23. | B. Vakoc, S. Yun, J. de Boer, G. Tearney, and B. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express |

24. | M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation,” Opt. Express |

25. | M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. |

26. | R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of Fourier domain vs. time domain optical coherence tomography,” Opt. Express |

27. | J. W. Goodman, |

**OCIS Codes**

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.4470) Medical optics and biotechnology : Ophthalmology

(170.4500) Medical optics and biotechnology : Optical coherence tomography

(280.2490) Remote sensing and sensors : Flow diagnostics

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: February 7, 2008

Revised Manuscript: April 7, 2008

Manuscript Accepted: April 8, 2008

Published: April 14, 2008

**Virtual Issues**

Vol. 3, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Maciej Szkulmowski, Anna Szkulmowska, Tomasz Bajraszewski, Andrzej Kowalczyk, and Maciej Wojtkowski, "Flow velocity estimation using joint Spectral and Time domain Optical Coherence Tomography," Opt. Express **16**, 6008-6025 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-9-6008

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### References

- D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical coherence tomography," Science 254, 1178-1181 (1991). [CrossRef] [PubMed]
- A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. Elzaiat, "Measurement of Intraocular Distances by Backscattering Spectral Interferometry," Opt. Commun. 117, 43-48 (1995). [CrossRef]
- M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A. F. Fercher, "In vivo human retinal imaging by Fourier domain optical coherence tomography," J. Biomed. Opt. 7, 457-463 (2002). [CrossRef] [PubMed]
- N. Nassif, B. Cense, B. H. Park, S. H. Yun, T. C. Chen, B. E. Bouma, G. J. Tearney, and J. F. de Boer, "In vivo human retinal imaging by ultrahigh-speed spectral domain optical coherence tomography," Opt. Lett. 29, 480-482 (2004). [CrossRef] [PubMed]
- M. Wojtkowski, V. Srinivasan, J. G. Fujimoto, T. Ko, J. S. Schuman, A. Kowalczyk, and J. S. Duker, "Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography," Ophthalmology 112, 1734-1746 (2005). [CrossRef] [PubMed]
- V. J. Srinivasan, M. Wojtkowski, A. J. Witkin, J. S. Duker, T. H. Ko, M. Carvalho, J. S. Schuman, A. Kowalczyk, and J. G. Fujimoto, "High-definifion and 3-dimensional imaging of macular pathologies with high-speed ultrahigh-resolution optical coherence tomography," Ophthalmology 113, 2054-2065 (2006). [CrossRef] [PubMed]
- R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C. K. Hitzenberger, M. Sticker, and A. F. Fercher, "Spectral measurement of absorption by spectroscopic frequency-domain optical coherence tomography," Opt. Lett. 25, 820-822 (2000). [CrossRef]
- R. A. Leitgeb, L. Schmetterer, W. Drexler, A. F. Fercher, R. J. Zawadzki, and T. Bajraszewski, "Real-time assessment of retinal blood flow with ultrafast acquisition by color Doppler Fourier domain optical coherence tomography," Opt. Express 11, 3116-3121 (2003). [CrossRef] [PubMed]
- Y. Yasuno, S. Makita, Y. Sutoh, M. Itoh, and T. Yatagai, "Birefringence imaging of human skin by polarization-sensitive spectral interferometric optical coherence tomography," Opt. Lett. 27, 1803-1805 (2002). [CrossRef]
- M. A. Choma, A. K. Ellerbee, S. Yazdanfar, and J. A. Izatt, "Doppler flow imaging of cytoplasmic streaming using spectral domain phase microscopy," J. Biomed. Opt. 11 (2006). [CrossRef] [PubMed]
- F. Rothenberg, A. M. Davis, and J. A. Izatt, "Non-invasive investigations of early embryonic cardiac blood flow with optical coherence tomography," FASEB J. 20, A451-A451 (2006).
- B. R. White, M. C. Pierce, N. Nassif, B. Cense, B. H. Park, G. J. Tearney, B. E. Bouma, T. C. Chen, and J. F. de Boer, "In vivo dynamic human retinal blood flow imaging using ultra-high-speed spectral domain optical Doppler tomography," Opt. Express 11, 3490-3497 (2003). [CrossRef] [PubMed]
- S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, "Optical coherence angiography," Opt. Express 14, 7821-7840 (2006). [CrossRef] [PubMed]
- Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J. F. de Boer, and J. S. Nelson, "Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity," Opt. Lett. 25, 114-116 (2000). [CrossRef]
- B. H. Park, M. C. Pierce, B. Cense, S. H. Yun, M. Mujat, G. Tearney, B. Bouma, and J. de Boer, "Real-time fiber-based multi-functional spectral-domain optical coherence tomography at 1.3 µm," Opt. Express 13, 3931-3944 (2005). [CrossRef] [PubMed]
- S. H. Yun, G. J. Tearney, J. F. de Boer, and B. E. Bouma, "Motion artifacts in optical coherence tomography with frequency-domain ranging," Opt. Express 12, 2977-2998 (2004). [CrossRef] [PubMed]
- A. H. Bachmann, M. L. Villiger, C. Blatter, T. Lasser, and R. A. Leitgeb, "Resonant Doppler flow imaging and optical vivisection of retinal blood vessels," Opt. Express 15, 408-422 (2007). [CrossRef] [PubMed]
- R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, "Three dimensional optical angiography," Opt. Express 15, 4083-4097 (2007). [CrossRef] [PubMed]
- Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, "Simultaneous BM-mode scanning method for real-time full-range Fourier domain optical coherence tomography," Appl. Opt. 45, 1861-1865 (2006). [CrossRef] [PubMed]
- Z. Chen, T. E. Milner, D. Dave, and J. S. Nelson, "Optical Doppler tomographic imaging of fluid flow velocity in highly scattering media," Opt. Lett. 22, 64-66 (1997). [CrossRef] [PubMed]
- J. A. Izatt, M. D. Kulkami, S. Yazdanfar, J. K. Barton, and A. J. Welch, "In vivo bidirectional color Doppler flow imaging of picoliter blood volumes using optical coherence tomography," Opt. Lett. 22, 1439-1441 (1997). [CrossRef]
- S. Yazdanfar, C. H. Yang, M. V. Sarunic, and J. A. Izatt, "Frequency estimation precision in Doppler optical coherence tomography using the Cramer-Rao lower bound," Opt. Express 13, 410-416 (2005). [CrossRef] [PubMed]
- B. Vakoc, S. Yun, J. de Boer, G. Tearney, and B. Bouma, "Phase-resolved optical frequency domain imaging," Opt. Express 13, 5483-5493 (2005). [CrossRef] [PubMed]
- M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, "Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and methods for dispersion compensation," Opt. Express 12, 2404-2422 (2004). [CrossRef] [PubMed]
- M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, "Full range complex spectral optical coherence tomography technique in eye imaging," Opt. Lett. 27, 1415-1417 (2002). [CrossRef]
- 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). [CrossRef] [PubMed]
- J. W. Goodman, Statistical Optics (John Wiley & Sons, Inc., New York, 2000).

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