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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 10 — Oct. 2, 2009
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Flow velocity estimation by complex ambiguity free joint Spectral and Time domain Optical Coherence Tomography

Maciej Szkulmowski, Ireneusz Grulkowski, Daniel Szlag, Anna Szkulmowska, Andrzej Kowalczyk, and Maciej Wojtkowski  »View Author Affiliations


Optics Express, Vol. 17, Issue 16, pp. 14281-14297 (2009)
http://dx.doi.org/10.1364/OE.17.014281


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Abstract

We show that recently introduced joint Spectral and Time domain Optical Coherence Tomography (STdOCT) can be used for simultaneous complex ambiguity removal and functional Spectral OCT images. This permits to take advantage of higher sensitivity achievable near the zero-path delay. The technique can be used with all Spectral OCT systems that are equipped with an optical delay line (ODL) and provide oversampled scanning patterns. High sensitivity provided by STdOCT allows this technique to be used in Spectral OCT setups with acquisition speed of 100 000 lines/s. We show that different imaging ranges and velocity ranges can be achieved by switching on/off the ODL and a small modification in the processing algorithm. Additionally, the relatively small computational burden of the technique allows for fast computations in the range of less than 5 minutes for 3D data set. We present application of proposed technique to full-range two- and three-dimensional imaging. Morphological and Doppler tomograms of human retina in-vivo are shown. Finally, we identify and discuss artifacts of the technique.

© 2009 OSA

1. Introduction

Another method that exploits Doppler effect to perform velocity measurements is joint Spectral and Time domain OCT (STdOCT) [18

18. M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 16(9), 6008–6025 (2008). [CrossRef] [PubMed]

]. This technique uses only amplitudes of Fourier transformations to estimate the Doppler frequencies and, as compared to phase-resolved Doppler OCT, offers higher sensitivity and better reliability in quantitative velocity estimation in the entire velocity range. Additionally, it provides quantitative velocity values well localized spatially inside the sample and gives good velocity readings for low velocity values. The latter is caused by the fact that it does not use any thresholds that limit the velocity range. What is important, the technique does not require the data to be back Fourier transformed at any stage of the procedure. Consequently, its numerical complexity is only slightly increased compared to standard phase-resolved OCT imaging with A-scans averaging. Therefore, the data processing can be performed with the speeds of thousands lines per second. Recently, we also showed that its high sensitivity makes the technique well suited for segmentation of the vessel network in 3D data acquired at line-rates of 100 kHz [19

19. A. Szkulmowska, M. Szkulmowski, D. Szlag, A. Kowalczyk, and M. Wojtkowski, “Three-dimensional quantitative imaging of retinal and choroidal blood flow velocity using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 17(13), 10584–10598 (2009). [CrossRef] [PubMed]

].

In order to take advantage of the highest sensitivity achievable in Spectral OCT near the zero optical path-delay position, the complex conjugate image (“mirror” image) of the sample should be removed. This would also facilitate imaging of the thick structures such as the retina in the proximity of the optic nerve head, where large retinal veins and arteries can appear simultaneously with choroidal vessels. To get rid of the undesired “mirror” images several techniques such as multi-frame methods [15

15. Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. 45(8), 1861–1865 (2006). [CrossRef] [PubMed]

,20–26

20. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27(16), 1415–1417 (2002). [CrossRef]

] and variants of the BM-mode technique [15

15. Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. 45(8), 1861–1865 (2006). [CrossRef] [PubMed]

,24

24. R. K. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. 90(5), 054103 (2007). [CrossRef]

,27

27. Y. Yasuno, S. Makita, T. Endo, G. Aoki, H. Sumimura, M. Itoh, and T. Yatagai, “One-shot-phase-shifting Fourier domain optical coherence tomography by reference wavefront tilting,” Opt. Express 12(25), 6184–6191 (2004). [CrossRef] [PubMed]

,28

28. S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 microm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express 16(12), 8406–8420 (2008). [CrossRef] [PubMed]

] have been presented to date. Unfortunately, in all of these methods the phase information associated to the sample and its complex counterpart interfere and quantitative velocity estimation is no longer possible.

Information encoded in the phase of spectral fringes is used in both velocity estimation and complex ambiguity removal techniques. These both methods require to use multiple spectral fringe signals to create one line of either structural or functional image. The spectra used in the calculations should be acquired at the same lateral position of the scanning beam in order to obtain well spatially localized phase information. It can be achieved by the lateral scanning either with a discrete step-like or a continuous ramp driving signal. The latter approach is more practical due to strong limitations in the settling time of galvanometric scanners. However, to achieve well defined phase information the continuous lateral scanning has to be performed along with the high sampling density. Additionally, another straightforward advantage of using several spectra to create one line of the tomogram is a sensitivity increase of the structural imaging. This is achieved simply by averaging backscattered intensities of multiple A-scans.

High sampling density is exploited in a modified joint Spectral and Time domain OCT, which we demonstrate in this contribution. The presented technique allows for the complex ambiguity removal simultaneously with quantitative estimation of velocity values in the entire imaging range. The only required modification in the setup is an optical delay line (ODL) in the reference arm that allows for introduction of constant velocity offset during data acquisition. As a result this method is able to work with data acquired with commonly used high density scanning protocols. One of the main advantages of this technique is that the calculation time does not exceed a few seconds for a single cross-sectional image. It has to be noted that doubling the imaging range causes the velocity range to be halved. However, the flexibility of the technique allows for changing from full imaging range to full velocity range by simply switching off the ODL.

We believe that the simplicity of the algorithm, ease of implementation in existing SOCT systems, high sensitivity and numerical efficiency make this new method a practical and reliable tool for retinal flow analysis.

2. Method

In the first step all spectra have to undergo standard SOCT data preprocessing in order to transform them from wavelength domain to wavenumber domain (k domain). Next, uncompensated dispersion is numerically removed and a numerical shaping of the spectral fringes is introduced [29

29. M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4–6), 569–578 (2005). [CrossRef]

]. One of the joint Spectral and Time domain OCT technique variants (described in the following subsections) is applied to the subset of acquired spectra used to create a single line of structural and velocity tomograms. The procedure is applied several times to different sets of spectral fringes until all lines of the tomogram are created. The subsequent subsections describe numerical processing applied to the subset of preprocessed spectra to create a single line of structural and velocity tomograms.

2.1. Standard STdOCT

The spectral fringe signals selected for calculations can be considered as a two-dimensional interferogram and expressed in the following way:

I(k,t)=S(k)(sRs+Rr+2sRsRrcos(2zsk+2νskt)).
(1)

The above signal results from interference between light reflected from a stationary reference mirror (reflectivity coefficient Rr), and backscattered on several interfaces in the sample (reflectivity coefficients Rs). The wavelength dependent spectral envelope is denoted by S (k). The phase of the interferometric signal depends on the positions zs of the scattering interfaces as well as on the projections νs = Vs cos (α) of velocity Vs of the scattering particle in the sample moving in the direction inclined to the probing beam at angle α.

Due to the introduced oversampling, we assume that the lateral distance between consecutive positions of the probing beam is much smaller than the beam diameter. Because of this, in Eq. (1) the spectra can be regarded as having been acquired at the same position of the sample. Therefore, the dependence on the lateral position can be neglected. As a result, the beat frequency ωs = 2νsk that arises for each wavenumber k along the time axis encodes the laterally localized velocity of the s-th interface inside the sample. Simultaneously, the frequency of fringes along the wavenumber axis encodes the axial position of the s-th interface. It needs to be pointed out that the frequency of fringe pattern carries information along both spectral and time axes. The observation that the interferogram can be processed in similar way along both dimensions led to development of the joint Spectral and Time OCT (STdOCT).

In STdOCT two dimensional Fourier transformation is applied to the subset of spectra. Such a two dimensional Fourier transformation converts the data set from wavenumber-time domain (kt domain) to “in-depth position”-“beat frequency” domain ( domain). Two dimensional Fourier transformation can be calculated using two one-dimensional Fourier transformations conducted consecutively along the wavenumber axis and time axis or in opposite order. In order to emphasize this possibility it is useful to plot a STdOCT diagram that shows all possible Fourier transformations that can be applied to a two-dimensional interferogram, as it is presented in Fig. 1.

Fig. 1. STdOCT diagrams. Vertical transitions are accomplished by Fourier transformation along wavenumber axis, horizontal – by Fourier transformation along time axis. Amplitude of the complex signal is displayed for visualization purposes. In the zω-domain complex conjugate images are symmetrical with respect to the central point of the plot (zero position, zero velocity). (a) moving mirror experiment, two points (red arrows) represent two complex conjugate images of the mirror; each of the points gives simultaneously information about position and velocity of the moving mirror with respect to the reference mirror. (b) Laminar flow of Intralipid solution in a glass capillary. Two complex conjugate images of parabolic flow distribution are visible.

In the -domain each moving scattering interface is represented by two signal peaks in well determined in-depth position and beat frequency. The two points are positioned symmetrically with respect to the zero-delay and zero-velocity position due to the complex ambiguity problem. This is clearly visible in the case of SOCT signals coming from a moving mirror Fig. 1(a). The fact that the quantitative distributions of velocity versus depth position can be directly observed in the -domain is even better visualized in an experiment with Intralipid solution flowing in a capillary, Fig. 1(b). Here we can observe the parabolic flow velocity distribution indicating a laminar flow.

Fig. 2. Schematic STdOCT diagrams showing data flow in numerical processing from a subset of raw spectral fringe signals to the final A-scan. Grey areas indicate portions of the data from a given signal space that are used in calculations at each stage of the procedure; (a) standard SOCT data processing; (b) STdOCT data processing.

It has to be noted here that since the Fourier transformation is a linear operation, the sequence of operations transforming data from kt -domain to -domain does not have any importance. However, in structural imaging without complex conjugate removal only a half of the in-depth data carries useful information. This fact is depicted in diagrams in Fig. 2, where grey color marks these parts of signal spaces that are used in further processing. Therefore, it is advantageous to perform the transformation in a sequence starting from the transformation along wavenumber axis as depicted in Fig. 2(b). This allows the transformation along time axis to be performed only on one half of the zt -domain thus reducing the calculation burden by a factor of two.

The possibility of providing information of velocity and morphology simultaneously in one signal space has to be highlighted as an advantage of the STdOCT over other techniques using spatial filtering since it is the sole Fourier based technique that does not require the data to be back transformed at any stage of the procedure. As a result the computation time required for tomogram reconstruction is only a little bit longer than that for the standard SOCT method. However, in order to increase the velocity resolution it is required to perform zero-padding before Fourier transforming the data from zt -domain to the -domain, which impacts on the computation time.

2.2. Complex ambiguity free STdOCT

In this subsection we show that a small modification to the previously described STdOCT technique allows for simultaneous velocity estimation and reconstruction of structural A-scans free from the complex conjugate problem.

Let us now assume that a constant change of optical path difference (OPD) is introduced between the reference and the sample arm of the interferometer. In the case of the OPD changes with the velocity νref the total time-dependent spectral fringe signal I(k,t) can be described by an expression similar to the one shown in Eq. (1):

I(k,t)=S(k)(sRs+Rr+2sRsRrcos(2zsk+2(νs+νref)kt)).
(2)

In the -domain the complex conjugate images are positioned on the opposite sides of both zero-delay line (in case of zs ≠ 0 ) and on opposite sides of zero beat frequency line (in case of νs ≠ 0 ). It is important to note that by the introduction of the additional velocity νref ≠ 0 one shifts the image and its complex conjugate counterpart in opposite directions along the beat frequency axis.

Fig. 3. STdOCT diagrams of Intralipid flow in a glass capillary: (a) without additional velocity; (b) with additional velocity νref (marked by red arrow) introduced in the reference arm of the interferometer.

If the ODL velocity is large enough, the two images together with all the inner velocity components are completely separated along the ω axis. This effect is clearly visualized in Fig. 3(b), which presents data from the same experimental setup as data from Fig. 3(a) but with additionally introduced velocity νref. The conjugate velocity distributions of Intralipid solution are placed on “positive” and “negative” sides of the beat frequency axis.

By analogy to the maximal axial depth-range z ±max = π/2Δk, which depends on the sampling period Δk in the spectral domain, the maximal velocity ν detectable without the 2π ambiguity is determined by the acquisition time of spectral fringe signal Δt:

ν±max=±π2kΔt.
(3)

If the velocity of optical path change is beyond this value it is aliased to the opposite side of the velocity range and gives misleading results. If no velocity offset is introduced in one of the interferometer arms (νref = 0), Eq. (4) determines the maximal velocity detectable inside the sample without the aliasing:

ν±max,sample=ν±max.
(4)

In such a case the sample velocity range is equal to the maximal velocity range. The spatial imaging range is halved in order to avoid an overlap of the complex conjugate images. The entire imaged structure has to fit into one half of the complex space. Conjugate images have to be separated in the way that each of them is placed on opposite side of the zero-path delay position of the imaging range.

The velocity of reference mirror νref ≠ 0 introduced to the system shifts the complex conjugate images along the beat-frequency axis in opposite directions (Fig. 3(b)). If all velocity components of one of the images fit in one half of the velocity range, then the complex conjugate image is placed on the opposite side of the beat-frequency axis. In such a case the beat frequency value ω = 0 separates completely the complex conjugate images in the -domain. The two images do not overlap if the following conditions are fulfilled:

νmax,sample+νref0,
(5)
ν+max,sample+νrefνmax.
(6)

Assuming that maximal and minimal velocities inside the sample have equal modules, the maximal velocity values that can be observed with no ambiguities inside the sample are obtained for νref = νmax/2 and are equal:

ν±max,sample=ν±max2.
(7)

Now in order to reconstruct structural and velocity A-scan only the half of the domain located above or below the ω = 0 should be processed to extract the structural and velocity A-scans. If the expected velocity distribution is asymmetrical, it is necessary to change the velocity offset νref to fulfill the conditions given by formulas (5) and (6).

If the high velocity resolution is necessary, zero-padding along the time axis is performed in both standard and modified STdOCT, before applying the Fourier transformation, Fig. 2(b) and Fig. 4(a). It is therefore advantageous to transform the data from kt -domain to zt -domain first, and perform the second transformation from zt -domain to -domain. In the case of standard STdOCT the latter transformations can be performed only for z ≥ 0, Fig. 2(b), as half of the zt and -domains carries redundant information.

In the similar way redundant information is present in one half of the - and -domains in the case of modified STdOCT processing. Therefore, the total number of Fourier transformations in complex ambiguity free STdOCT can be halved by the proper choice of order of Fourier transformations if no high resolution in velocity is required. In such a case, after transforming data from kt -domain to -domain, the following transition to -domain can be completed for ω ≥ 0 only, Fig. 4(b). This is especially useful for complex ambiguity removal in a real-time tomogram creation for purposes of alignment of the sample. The latter can be also used in the case where no velocity information is required and one is interested only in complex ambiguity removal. This technique has been used by our group for complex ambiguity removal in imaging of whole anterior chamber of the human eye in vivo along with both surfaces of the lens [30

30. I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842–4858 (2009). [CrossRef] [PubMed]

].

Fig. 4. Schematic STdOCT diagram showing data flow in the modified STdOCT algorithm allowing recovery of velocity distribution as a function of depth in the whole imaging range: (a) slower version of the algorithm with high velocity resolution provided by implementation of zero-padding procedure before the t→ω Fourier transformation; (b) faster version of the algorithm without zero-padding.

It is easy to see that both variants of the STdOCT technique differ only by choice of parts of -domain where the procedure of A-scan creation is performed. As a result, the trade-off between velocity range and structural imaging range is different for the regular and the modified technique. Standard STdOCT gives halved structural imaging range but the velocity detection range is full. On the contrary, the complex ambiguity free STdOCT provides full structural imaging range, but the velocity range is halved. In order to separate complex conjugate images in both techniques the images have to be placed on opposite sides of z-axis (in case of standard STdOCT) or ω-axis (in case of modified STdOCT). It has to be noted that if the SOCT setup allows for offsets’ introduction in both z and ω directions, the transition between the two modalities of STdOCT is straightforward, and allows the user to choose the velocity and imaging range according to current needs.

In principle there is exactly the same SNR advantage for both the standard and complex ambiguity free STdOCT techniques. However, in practice introduction of the constant change of optical path difference (OPD) will cause the fringe wash-out effect, which will decrease the spectral fringe visibility and the same the sensitivity of our technique [31

31. 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(13), 2977–2998 (2004). [CrossRef] [PubMed]

,32

32. 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(2), 408–422 (2007). [CrossRef] [PubMed]

]. We can easily calculate the magnitude of the fringe wash-out in the case of our optical delay line, since it is set to the constant velocity value (Eq. (7)) corresponding to the phase shift of λ/8 between consecutive spectral fringe signals. According to the theoretical analysis presented by Bachmann et al. [32

32. 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(2), 408–422 (2007). [CrossRef] [PubMed]

] the sensitivity drop due to such phase shift is only 1dB.

3. Experimental set-up

3.1. SOCT device

The SOCT system based on fiber-optic Michelson interferometer configuration is shown in Fig. 5.

Fig. 5. SOCT set-up used in experiments: FC – fiber coupler (splitting ratio 90:10); PC – polarization controller; L1–L4 – lenses; NDF – neutral density filter; DC – dispersion compensation; ODL – optical delay line; SM-Z – galvanometer scanner (z-scanning); RM – reference mirror; SM-XY – galvanometer scanners (xy-scanning); DG – holographic volume diffraction grating; CMOS – line-scan camera; FG – frame-grabber; COMP – personal computer; IOC – input-output card.

Measured axial resolution in air is equal to 3 μm what corresponds to 2.3 μm in tissue. Imaging range without the complex ambiguity removal technique equals 1 mm in tissue and is doubled to 2 mm in case the complex ambiguity removal technique is used. All measurements were performed with the power of light incident the cornea equal to 750μW at 810 nm.

3.2. Optical delay line

In order to introduce a velocity offset we equipped the reference arm with a simple optical delay line (ODL) based on galvanometer scanner that deflects the light beam towards the reference mirror (Fig. 6). The axis of rotation of the scanner is shifted from the point hit by the light beam, what causes the optical path length of the reference arm to be dependent on the instantaneous angle of the scanner.

The concept to use the ODL based on a scanner with off-axis illumination has been exploited recently by several groups [33–36

33. A. G. Podoleanu, G. M. Dobre, and D. A. Jackson, “En-face coherence imaging using galvanometer scanner modulation,” Opt. Lett. 23(3), 147–149 (1998). [CrossRef]

], but they placed it in the sample arm and used the laterally scanning mirror to introduce the optical path delay. This idea is very elegant but we deliberately decided not to use it as it couples velocity offset with lateral scanning parameters. When ODL is placed in the reference arm, it is much easier to introduce an arbitrary velocity along with arbitrary lateral scanning protocol. It is also possible to switch the ODL off if necessary. This fact is important because of different trade-offs between velocity and imaging ranges in standard and complex ambiguity free STdOCT as mentioned in the method section. Switching off the delay line brings the velocity offset to zero and enables standard STdOCT to provide full velocity range with limited structural imaging range. With the aid of this ODL such transition is possible at any moment, for example during aiming and aligning of the sample.

Fig. 6. (a) Detailed scheme of the optical delay line introduced in the reference arm of the SOCT set-up used in experiments: L1, L2 – lenses; SM-Z – galvanometric scanner; RM -reference mirror; f – focal length of the lens L2; For clarity the neutral density filter and dispersion compensator are removed from the drawing. (b) Parameters used to calculate the optical path difference: δ – shift between the incoming beam and the axis of rotation of SM-Z; α – tilt angle of SM-Z; z – optical path distance introduced by scanner tilt. The part of the light beam marked in red is responsible for optical path difference between the two positions of the rotating mirror. See text for further details.

When the optical beam is deflected by the mirror attached to the galvanometric scanner SM-Z in the distance δ from the pivot, the optical path difference zδ (α) depends on the angle α between the direction perpendicular to the impinging beam and the surface of the scanner:

zδ(α)=δtan(α).
(8)

Taylor expansion of the above expression around an initial angle α 0 yields:

zδ(α)δ[tan(α0)+1cos2(α0)·(αα0)+12sin(2α0)·(αα0)2+].
(9)

In this expression the quadratic term can be omitted, since it is usually much smaller than the linear part. This allows for calculation of the velocity introduced by the scanner rotating with angular frequency ω SM-Z = /dt:

νref=2ddtzδ(α)=2δcos2(α0)·ωSMZ.
(10)

The factor 2 is a consequence of the fact that the light travels the path (α) twice.

In the configuration used in our experiments, the angle α 0 = 45°, therefore Eq. (10) simplifies to:

νref=4δωSMZ.
(11)

4. Results and discussion

4.1. Extinction ratio and scanning protocols for complex ambiguity free STdOCT

In order to measure the extinction ratio of the complex conjugate removal in STdOCT method, we performed experiment with one static mirror and one moving mirror in the interferometer arms. Measured ratio of the complex conjugate remaining signals to the peak corresponding to the mirror position was -22dB and -30dB for 16 and 32 spectral fringes used for STdOCT analysis.

The SOCT setup operates in two main modes. The preview mode displays two structural tomograms (each of 420 A-scans created from 2172 spectra) acquired perpendicularly to each other in horizontal and vertical directions. These two images are used for alignment of the head of the device (probing beam) with respect to the sample. Fast mode of complex ambiguity free STdOCT, Fig. 4(b), allows for real-time display of images at 5 frames/sec.

Table 1. Scanning protocols used in experiments with complex ambiguity free STdOCT.

table-icon
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The signal driving the galvanometer scanner in the ODL is triangular. The angular frequency of the scanner is set to introduce reference velocity νref = νmax/2, which provides maximal velocity range, according to Eq. (7). The amplitude of the scanner driving signal remains constant. Exactly 543 spectra acquisitions are performed along each monotonic ramp of the signal. The triangular signal is synchronized with the beginning of every B-scan. In all cases one final A-scan is constructed from 16 spectral fringe signals. To create B-scans or velocity maps with a reasonable quality we divided our initial 543 spectral fringes into 105 partially redundant sets of 16 spectral fringes (105 =⌊ (543 -16)/5⌋). Separation between each set of 16 fringes is chosen to be 5, only to optimize the calculation time. This procedure introduces some kind of smoothing or interpolation into the velocity maps. Zero-padding (z-axis) up to 128 data points is performed before applying Fourier transformation, Fig. 2(b) and Fig. 4(a).

The calculations are performed with our software written in C and run on a personal portable computer (HP Compaq 8510w). The average computation time in all the above examples (in high velocity resolution mode) is about 1000 final tomogram lines per second. Total computation time depends on the protocol and is equal 6.7 seconds for the 2D_1 protocol, 9.5 seconds for 2D_2 protocol and 286 seconds (approx. 5 minutes) for 3D_1 protocol.

4.2. Complex ambiguity free STdOCT

In order to show the capability of the complex ambiguity free STdOCT technique to provide mirror free velocity and structural tomograms, we performed experiments of in-vitro flows in glass capillaries as well as in retinal vessels in-vivo.

Fig. 7. STdOCT measurement of two glass capillaries with Intralipid solution. (a) structural cross-sectional image obtained using standard STdOCT processing; (b) velocity map obtained using phase-resolved OCT ν max = 20.2 mm/s ; (c) structural cross-sectional image obtained using complex ambiguity free STdOCT; (d) velocity map obtained using complex ambiguity free STdOCT ν max = 10.1 mm/s.

In the first experiment water solution of Intralipid flowing inside two glass capillaries of 700 μm diameter was imaged. Laminar flow of the fluid was assured by a HPLC (High performance liquid chromatography) pump (Selko Industries, Poland). Scanning protocol 2D_1 described in Table 1 was utilized. Fig. 7(a) shows a cross-sectional image obtained by application of standard STdOCT algorithm with immobilized ODL. Fig. 7(b) depicts velocity tomogram obtained with aid of standard phase-resolved [11

11. A. Szkulmowska, M. Szkulmowski, A. Kowalczyk, and M. Wojtkowski, “Phase-resolved Doppler optical coherence tomography – limitations and improvements,” Opt. Lett. 33(13), 1425–1427 (2008). [CrossRef] [PubMed]

]. Two complex conjugate (mirror) images are visible in both tomograms. Figs. 7(c) and 7(d) present structural and velocity tomograms free from one of the mirror images. The data were obtained with the ODL turned on. In the following experiments data were acquired from human retina in-vivo using scanning protocol 2D_2, Table 1. Results are shown in Fig. 8. Sixteen spectra are used to create a single A-scan of the velocity map and complex ambiguity free cross-sectional image from the lateral range of 5 mm. As a result, the effective lateral resolution drops approximately by 50%, to 30 μm. The complex conjugate image is suppressed in both structural and velocity images.

Fig. 8. High density cross-sectional image of human optic disk in-vivo obtained using complex ambiguity free STdOCT: (a) structural tomogram; (b) velocity tomogram ν max =10.1 mm/s.

Fig. 9. Two cross-sectional images of human retina in-vivo measured in the close proximity of optic nerve head from 3D data set. (a) and (c) structural tomogram obtained using complex ambiguity free STdOCT; (b) and (d) velocity map obtained using complex ambiguity free STdOCT ν max = 10.1 mm/s . Arrows indicate artifacts – remaining mirror images of vessels with high flow velocity.

4.3. Artifacts

Optimal configuration of the complex ambiguity free STdOCT requires setting the additional velocity value to reach level of the maximal velocity divided by 2. The additional velocity of the reference mirror causes the optical path difference (OPD) between consecutive spectral fringe signals of νrefΔt = λ 0/8, where λ 0 is the central wavelength of the light used in the experiments. Therefore, OPD between the two extreme positions of the ODL in case of 543 spectra acquisitions is as large as 55 μm. As a result, tomograms acquired with operating ODL suffer from geometrical distortion caused by the OPD changes during scanning, Fig. 10(a).

Fig. 10. Correction of artifact connected with optical path delay changes during data acquisition. (a) tomogram without correction; (b) tomogram with numerical correction of tomogram lines shifts.

This effect can be easily removed by a small modification in numerical dispersion compensation algorithm that is usually performed in the preprocessing stage of the data processing. Each spectrum in the interferogram, Eq. (2), has to be multiplied by the same phase component equal to exp[-i·2Δz·k], where Δz is the instantaneous OPD introduced by the ODL at the moment of acquisition of the central spectrum from the interferogram. Since the phase element is constant for each A-scan of the tomogram, it can be calculated once and tabularized. Therefore, it can be incorporated in numerical dispersion compensation algorithm at no additional computational cost. The result of the procedure is depicted in Fig. 10(b), where the geometrical distortion is no longer present. This procedure has been applied to all tomograms presented in this paper.

Fig. 11. Artifacts appearing when actual flow velocity exceeds velocity range. (a) Structural tomogram with vessel from the complex conjugate image visible (arrows); (b) velocity tomogram of (a), ν max =10.1 mm/s ; (c) signal in -plane corresponding to the tomogram line (dotted line), parabolic velocity distribution cross the velocity range limit.

5. Conclusions

We showed that the joint Spectral and Time domain OCT is a straightforward and computationally efficient data processing scheme that can take advantage of the ultra-high speed OCT imaging of more than 100 000 lines/s. It can be used with any densely sampled scanning protocols and can be incorporated in standard Spectral OCT setups. Simple modification to the algorithm combined with an optical delay line in the reference arm can provide structural and functional complex ambiguity free cross-sectional images. High flexibility of the algorithm allows for rapid changes between standard STdOCT (full velocity range and halved imaging range) and complex ambiguity free STdOCT (halved velocity range and full imaging range). The computational burden is increased as compared to the standard SOCT processing but still a single tomogram can be calculated in few seconds and a 3D data set in no longer than 5 minutes.

Acknowledgments

Project supported EURYI grant/award funded by the European Heads of Research Councils (EuroHORCs) together with the European Science Foundation (ESF – EURYI 01/2007PL) and by Ventures Programme co-financed by the EU European Regional Development Fund both programs are operated within the Foundation for Polish Science. Maciej Szkulmowski and Anna Szkulmowska acknowledge additional support of Foundation for Polish Science (scholarship START 2009). We would also like to acknowledge FEMTOLASERS Produktions GmbH for their support and Prof. Bogusław Buszewski (Department of Environmental Chemistry and Ecoanalytics; Faculty of Chemistry; Nicolaus Copernicus University, Toruń) for providing the pump.

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 254(5035), 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(1–2), 43–48 (1995). [CrossRef]

3.

G. Hausler and M. W. Lindner, ““Coherence radar” and “spectral radar”-new tools for dermatological diagnosis,” J. Biomed. Opt. 3(1), 21–31 (1998). [CrossRef]

4.

M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003). [CrossRef] [PubMed]

5.

R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003). [CrossRef] [PubMed]

6.

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(11), 2404–2422 (2004). [CrossRef] [PubMed]

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. 25(11), 820–822 (2000). [CrossRef]

8.

R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, “Phase-shifting algorithm to achieve highspeed long-depth-range probing by frequency-domain optical coherence tomography,” Opt. Lett. 28(22), 2201–2203 (2003). [CrossRef] [PubMed]

9.

B. Vakoc, S. Yun, J. de Boer, G. Tearney, and B. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express 13(14), 5483–5493 (2005). [CrossRef] [PubMed]

10.

S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14(17), 7821–7840 (2006). [CrossRef] [PubMed]

11.

A. Szkulmowska, M. Szkulmowski, A. Kowalczyk, and M. Wojtkowski, “Phase-resolved Doppler optical coherence tomography – limitations and improvements,” Opt. Lett. 33(13), 1425–1427 (2008). [CrossRef] [PubMed]

12.

R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, “Three dimensional optical angiography,” Opt. Express 15(7), 4083–4097 (2007). [CrossRef] [PubMed]

13.

L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438–11452 (2008). [CrossRef] [PubMed]

14.

Y. K. Tao, A. M. Davis, and J. A. Izatt, “Single-pass volumetric bidirectional blood flow imaging spectral domain optical coherence tomography using a modified Hilbert transform,” Opt. Express 16(16), 12350–12361 (2008). [CrossRef] [PubMed]

15.

Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. 45(8), 1861–1865 (2006). [CrossRef] [PubMed]

16.

Y. K. Tao, K. M. Kennedy, and J. A. Izatt, “Velocity-resolved 3D retinal microvessel imaging using single-pass flow imaging spectral domain optical coherence tomography,” Opt. Express 17(5), 4177–4188 (2009). [CrossRef] [PubMed]

17.

R. K. Wang and L. An, “Doppler optical micro-angiography for volumetric imaging of vascular perfusion in vivo,” Opt. Express 17(11), 8926–8940 (2009). [CrossRef] [PubMed]

18.

M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 16(9), 6008–6025 (2008). [CrossRef] [PubMed]

19.

A. Szkulmowska, M. Szkulmowski, D. Szlag, A. Kowalczyk, and M. Wojtkowski, “Three-dimensional quantitative imaging of retinal and choroidal blood flow velocity using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 17(13), 10584–10598 (2009). [CrossRef] [PubMed]

20.

M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27(16), 1415–1417 (2002). [CrossRef]

21.

M. A. Choma, C. H. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 × 3 fiber-optic couplers,” Opt. Lett. 28(22), 2162–2164 (2003). [CrossRef] [PubMed]

22.

P. Targowski, W. Gorczynska, M. Szkulmowski, M. Wojtkowski, and A. Kowalczyk, “Improved complex spectral domain OCT for in vivo eye imaging,” Opt. Commun. 249(1–3), 357–362 (2005). [CrossRef]

23.

M. V. Sarunic, B. E. Applegate, and J. A. Izatt, “Spectral domain second-harmonic optical coherence tomography,” Opt. Lett. 30(18), 2391–2393 (2005). [CrossRef] [PubMed]

24.

R. K. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. 90(5), 054103 (2007). [CrossRef]

25.

Y. K. Tao, M. Zhao, and J. A. Izatt, “High-speed complex conjugate resolved retinal spectral domain optical coherence tomography using sinusoidal phase modulation,” Opt. Lett. 32(20), 2918–2920 (2007). [CrossRef] [PubMed]

26.

E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005). [CrossRef] [PubMed]

27.

Y. Yasuno, S. Makita, T. Endo, G. Aoki, H. Sumimura, M. Itoh, and T. Yatagai, “One-shot-phase-shifting Fourier domain optical coherence tomography by reference wavefront tilting,” Opt. Express 12(25), 6184–6191 (2004). [CrossRef] [PubMed]

28.

S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 microm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express 16(12), 8406–8420 (2008). [CrossRef] [PubMed]

29.

M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4–6), 569–578 (2005). [CrossRef]

30.

I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842–4858 (2009). [CrossRef] [PubMed]

31.

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(13), 2977–2998 (2004). [CrossRef] [PubMed]

32.

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(2), 408–422 (2007). [CrossRef] [PubMed]

33.

A. G. Podoleanu, G. M. Dobre, and D. A. Jackson, “En-face coherence imaging using galvanometer scanner modulation,” Opt. Lett. 23(3), 147–149 (1998). [CrossRef]

34.

R. A. Leitgeb, R. Michaely, T. Lasser, and S. C. Sekhar, “Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning,” Opt. Lett. 32(23), 3453–3455 (2007). [CrossRef] [PubMed]

35.

L. An and R. K. Wang, “Use of a scanner to modulate spatial interferograms for in vivo full-range Fourier-domain optical coherence tomography,” Opt. Lett. 32(23), 3423–3425 (2007). [CrossRef] [PubMed]

36.

B. Baumann, M. Pircher, E. Götzinger, and C. K. Hitzenberger, “Full range complex spectral domain optical coherence tomography without additional phase shifters,” Opt. Express 15(20), 13375–13387 (2007). [CrossRef] [PubMed]

37.

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 microm,” Opt. Express 13(11), 3931–3944 (2005). [CrossRef] [PubMed]

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: May 22, 2009
Revised Manuscript: July 22, 2009
Manuscript Accepted: July 24, 2009
Published: July 31, 2009

Virtual Issues
Vol. 4, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Maciej Szkulmowski, Ireneusz Grulkowski, Daniel Szlag, Anna Szkulmowska, Andrzej Kowalczyk, and Maciej Wojtkowski, "Flow velocity estimation by complex ambiguity free joint Spectral and Time domain Optical Coherence Tomography," Opt. Express 17, 14281-14297 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-16-14281


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References

  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(5035), 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(1–2), 43–48 (1995). [CrossRef]
  3. G. Hausler and M. W. Lindner, ““Coherence radar” and “spectral radar”-new tools for dermatological diagnosis,” J. Biomed. Opt. 3(1), 21–31 (1998). [CrossRef]
  4. M. A. Choma, M. V. Sarunic, C. H. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003). [CrossRef] [PubMed]
  5. R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express 11(8), 889–894 (2003). [CrossRef] [PubMed]
  6. 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(11), 2404–2422 (2004). [CrossRef] [PubMed]
  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. 25(11), 820–822 (2000). [CrossRef]
  8. R. A. Leitgeb, C. K. Hitzenberger, A. F. Fercher, and T. Bajraszewski, “Phase-shifting algorithm to achieve high-speed long-depth-range probing by frequency-domain optical coherence tomography,” Opt. Lett. 28(22), 2201–2203 (2003). [CrossRef] [PubMed]
  9. B. Vakoc, S. Yun, J. de Boer, G. Tearney, and B. Bouma, “Phase-resolved optical frequency domain imaging,” Opt. Express 13(14), 5483–5493 (2005). [CrossRef] [PubMed]
  10. S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, “Optical coherence angiography,” Opt. Express 14(17), 7821–7840 (2006). [CrossRef] [PubMed]
  11. A. Szkulmowska, M. Szkulmowski, A. Kowalczyk, and M. Wojtkowski, “Phase-resolved Doppler optical coherence tomography - limitations and improvements,” Opt. Lett. 33(13), 1425–1427 (2008). [CrossRef] [PubMed]
  12. R. K. Wang, S. L. Jacques, Z. Ma, S. Hurst, S. R. Hanson, and A. Gruber, “Three dimensional optical angiography,” Opt. Express 15(7), 4083–4097 (2007). [CrossRef] [PubMed]
  13. L. An and R. K. Wang, “In vivo volumetric imaging of vascular perfusion within human retina and choroids with optical micro-angiography,” Opt. Express 16(15), 11438–11452 (2008). [CrossRef] [PubMed]
  14. Y. K. Tao, A. M. Davis, and J. A. Izatt, “Single-pass volumetric bidirectional blood flow imaging spectral domain optical coherence tomography using a modified Hilbert transform,” Opt. Express 16(16), 12350–12361 (2008). [CrossRef] [PubMed]
  15. Y. Yasuno, S. Makita, T. Endo, G. Aoki, M. Itoh, and T. Yatagai, “Simultaneous B-M-mode scanning method for real-time full-range Fourier domain optical coherence tomography,” Appl. Opt. 45(8), 1861–1865 (2006). [CrossRef] [PubMed]
  16. Y. K. Tao, K. M. Kennedy, and J. A. Izatt, “Velocity-resolved 3D retinal microvessel imaging using single-pass flow imaging spectral domain optical coherence tomography,” Opt. Express 17(5), 4177–4188 (2009). [CrossRef] [PubMed]
  17. R. K. Wang and L. An, “Doppler optical micro-angiography for volumetric imaging of vascular perfusion in vivo,” Opt. Express 17(11), 8926–8940 (2009). [CrossRef] [PubMed]
  18. M. Szkulmowski, A. Szkulmowska, T. Bajraszewski, A. Kowalczyk, and M. Wojtkowski, “Flow velocity estimation using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 16(9), 6008–6025 (2008). [CrossRef] [PubMed]
  19. A. Szkulmowska, M. Szkulmowski, D. Szlag, A. Kowalczyk, and M. Wojtkowski, “Three-dimensional quantitative imaging of retinal and choroidal blood flow velocity using joint Spectral and Time domain Optical Coherence Tomography,” Opt. Express 17(13), 10584–10598 (2009). [CrossRef] [PubMed]
  20. M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A. F. Fercher, “Full range complex spectral optical coherence tomography technique in eye imaging,” Opt. Lett. 27(16), 1415–1417 (2002). [CrossRef]
  21. M. A. Choma, C. H. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3 x 3 fiber-optic couplers,” Opt. Lett. 28(22), 2162–2164 (2003). [CrossRef] [PubMed]
  22. P. Targowski, W. Gorczynska, M. Szkulmowski, M. Wojtkowski, and A. Kowalczyk, “Improved complex spectral domain OCT for in vivo eye imaging,” Opt. Commun. 249(1–3), 357–362 (2005). [CrossRef]
  23. M. V. Sarunic, B. E. Applegate, and J. A. Izatt, “Spectral domain second-harmonic optical coherence tomography,” Opt. Lett. 30(18), 2391–2393 (2005). [CrossRef] [PubMed]
  24. R. K. K. Wang, “In vivo full range complex Fourier domain optical coherence tomography,” Appl. Phys. Lett. 90(5), 054103 (2007). [CrossRef]
  25. Y. K. Tao, M. Zhao, and J. A. Izatt, “High-speed complex conjugate resolved retinal spectral domain optical coherence tomography using sinusoidal phase modulation,” Opt. Lett. 32(20), 2918–2920 (2007). [CrossRef] [PubMed]
  26. E. Götzinger, M. Pircher, and C. K. Hitzenberger, “High speed spectral domain polarization sensitive optical coherence tomography of the human retina,” Opt. Express 13(25), 10217–10229 (2005). [CrossRef] [PubMed]
  27. Y. Yasuno, S. Makita, T. Endo, G. Aoki, H. Sumimura, M. Itoh, and T. Yatagai, “One-shot-phase-shifting Fourier domain optical coherence tomography by reference wavefront tilting,” Opt. Express 12(25), 6184–6191 (2004). [CrossRef] [PubMed]
  28. S. Makita, T. Fabritius, and Y. Yasuno, “Full-range, high-speed, high-resolution 1 microm spectral-domain optical coherence tomography using BM-scan for volumetric imaging of the human posterior eye,” Opt. Express 16(12), 8406–8420 (2008). [CrossRef] [PubMed]
  29. M. Szkulmowski, A. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, W. Wasilewski, A. Kowalczyk, and C. Radzewicz, “Quality improvement for high resolution in vivo images by spectral domain optical coherence tomography with supercontinuum source,” Opt. Commun. 246(4–6), 569–578 (2005). [CrossRef]
  30. I. Grulkowski, M. Gora, M. Szkulmowski, I. Gorczynska, D. Szlag, S. Marcos, A. Kowalczyk, and M. Wojtkowski, “Anterior segment imaging with Spectral OCT system using a high-speed CMOS camera,” Opt. Express 17(6), 4842–4858 (2009). [CrossRef] [PubMed]
  31. 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(13), 2977–2998 (2004). [CrossRef] [PubMed]
  32. 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(2), 408–422 (2007). [CrossRef] [PubMed]
  33. A. G. Podoleanu, G. M. Dobre, and D. A. Jackson, “En-face coherence imaging using galvanometer scanner modulation,” Opt. Lett. 23(3), 147–149 (1998). [CrossRef]
  34. R. A. Leitgeb, R. Michaely, T. Lasser, and S. C. Sekhar, “Complex ambiguity-free Fourier domain optical coherence tomography through transverse scanning,” Opt. Lett. 32(23), 3453–3455 (2007). [CrossRef] [PubMed]
  35. L. An and R. K. Wang, “Use of a scanner to modulate spatial interferograms for in vivo full-range Fourier-domain optical coherence tomography,” Opt. Lett. 32(23), 3423–3425 (2007). [CrossRef] [PubMed]
  36. B. Baumann, M. Pircher, E. Götzinger, and C. K. Hitzenberger, “Full range complex spectral domain optical coherence tomography without additional phase shifters,” Opt. Express 15(20), 13375–13387 (2007). [CrossRef] [PubMed]
  37. 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 microm,” Opt. Express 13(11), 3931–3944 (2005). [CrossRef] [PubMed]

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