## Abstract

The phase-resolved (PR) method is widely used in optical Doppler tomography (ODT) to estimate flow velocity from sequential axial line (A-line) signals. However, the A-line signal contains clutter components induced by stationary or relative slow moving clutter scatterers such as the blood vessel wall or the overall sample with motion artifacts. The clutter component affects the accuracy in quantifying Doppler flow. In this paper, we present a delay line filter (DLF) to reject the clutter effect and enables moving-scatterer-sensitive ODT (MSS-ODT) imaging of flow. The frequency response of DLFs of different orders is theoretically analyzed and we find that a first-order phase-shifted DLF is effective for clutter rejection and for improving the sensitivity to moving scatterers such as moving blood cells. The proposed MSS-ODT method has been experimentally applied to Doppler flow imaging in a capillary flow phantom and a mouse ear in vivo. The ODT data were acquired using a real-time spectral-domain optical coherence tomography (SD-OCT) system with an A-line acquisition rate of 12.3k/s. Doppler flow images obtained with MSS-ODT and the conventional PR-ODT techniques are compared and MSS-ODT is found to be more sensitive to Doppler flow and more accurate in determining vessel size. Small blood vessels that might be masked by clutter signals in PROCT are successfully recovered by MSS-ODT.

©2006 Optical Society of America

## 1. Introduction

Optical Doppler tomography (ODT) [1–2] or color Doppler optical coherence tomography [3] is a recently developed technique for quantitative flow imaging with a micron-scale spatial resolution. The technique utilizes the principle of optical coherent tomography [4] to achieve high spatial resolution and the Doppler effect to differentiate moving scatterers from the stationary scatterer background. The phase-resolved ODT (PR-ODT) technique implemented with autocorrelation of adjacent axial line (A-line) profiles is widely used to calculate the Doppler frequency shift [5–7]. PR-ODT can potentially image small blood vessels and quantify low blood flow rates; however, we found its sensitivity and accuracy can be limited by the clutter component of the interference fringe signal.

Clutter is the unwanted signal component that arises from stationary (or clutter) scatterers in the coherence sampling volume of the probe beam in the sample arm. When the stationary scatterers coexist with the moving scatterers in the coherence sampling volume, the clutter is mixed with the Doppler signal of the moving scatterers and consequently the sensitivity and accuracy in estimating the Doppler flow of these moving scatterers are reduced, particularly when the clutter is dominant in the fringe signal.

Moving-scatterer-sensitive ODT (MSS-ODT) is a new technique using clutter rejection
filters to attenuate the clutter and improve the sensitivity and accuracy in flow rate
estimation for moving scatterers. Recently, we have demonstrated a simple delay line
filter (DLF) for suppressing the influence of clutter in quantifying Doppler flow rate
and vessel size [8]. In this report, we detail
the principle of delay line filtering and demonstrate a phase-shifted delay line filter
(as opposed to a simple DLF) is a more promising clutter rejection filter in a
high-speed SD-OCT system. To improve the effectiveness of clutter rejection, the
phase-shifted DLF is used to lock its stop band to the Doppler frequency shift of
clutter scatterers which move with respect to the probe beam during lateral scanning.
The phase-shifted DLF was applied to phantom flow and *in vivo* blood
flow imaging. The results were compared with those obtained by the traditional PR-ODT
technique, and it was found that the sensitivity of Doppler flow imaging and accuracy in
blood vessel size estimation were significantly improved in the MSS-ODT technique using
a phase-shifted DLF.

## 2. Principle of clutter rejection and velocity estimation

The objective of clutter rejection techniques is to minimize the influence of clutter to Doppler flow signal and improve the sensitivity of Doppler flow estimation algorithms to moving scatterers. Clutter rejection is usually realized in time domain using a simple delay line filter (DLF) [8]. In MSS-ODT, clutter rejection filtering is first applied to the A-line signals and a conventional velocity estimator based on adjacent A-line autocorrelation can then be used to extract the Doppler frequency shift originated from moving scatterers. This operation is different from PR-ODT which directly employs the autocorrelation velocity estimator without clutter rejection.

#### 2.1 DLF for stationary scatterer suppression

The clutter signal can be separated from the moving scatterer’s Doppler signal based on the difference in their Doppler spectra. The separation can be realized using a single DLF shown in the following diagram,

where the input $\tilde{\Gamma}$ (*jT*) is the complex analytical depth profile
obtained from *j*th A-line fringe, *T* is the A-line
repetition period which is the inverse of the A-line scan rate *f _{r}* of an OCT system, and ∑ denotes a sum operation. The output

*M̃(jT)*of this single DLF is

To demonstrate how the DLF helps separate the Doppler spectra of the flow signal from
the clutter signal, we will analyze the frequency response of the DLF. Let
*t=jT*, then the impulse response of the above DLF can be expressed
as

where *δ(t)* is the delta function. The output *M̃(jT)*
is thus the convolution between the input $\tilde{\Gamma}$ (*t*) and the impulse response
*h _{1}(t)* denoted by

Taking the Fourier transform of the above equation, we find the Doppler spectrum of
the output *M̃(f)* is

where $\tilde{\Gamma}$ (*f*) is the spectrum of the input signal in the
Doppler frequency shift (*f*) domain;
*H _{1}(f)* is the frequency response of the DLF and from
Eq. (2) it yields

Following Eq. (4), the Doppler power
spectrum |*M*̃(*f*)|^{2} can be described
as

Here |*H*
_{1}(*f*)|^{2}=4sin (*πfT*) is the
power transfer function of the DLF which can be obtained from Eq. (5).

It is realized that the above DLF can be cascaded, which is equivalent to applying a
high-order filter to the input signal. To simplify the notation in the following
process of constructing a high-order filter, a new variable *z* is
introduced and *z*=exp(*i2πfT*). Eq. (5) can then be rewritten in the
*z*-domain as

An *n*-order DLF can be constructed by cascading a first-order DLF
n-times as shown in the following diagram:

Using Eq. (7), the frequency response
of an *n*-order DLF yields

where *a _{k}* is the binomial coefficient given by

From Eq. (8) and the property of
*z*-transform, the *n*-order DLF shown in the above
diagram can be reformulated to an equivalent filter structure shown as in the
following diagram [9].

The weight coefficients *a _{k}* in the above filter structure are determined by Eq. (9). It is well known that the
implementation of an

*n*-order DLF is computationally more efficient using the above equivalent filter structure. The power transfer function of the above two types of

*n*-order DLF structures is

Compared to the first-order DLF, the advantage of a high-order DLF is that they can provide a larger bandwidth of the stop bands. When the Doppler bandwidth of the stationary scatterers is wide, a high-order DLF might be required to effectively reject their influence.

In practice, the maximum lateral separation between the A-lines fed into the above
n-order DLF should be less than the transverse beam waist to ensure the fringes
remain correlated. Thus only a few successive A-lines will be considered and
consequently only a low order DLF is necessary for clutter rejection. The weight
coefficients for the first four DLFs are calculated from Eq. (9) and tabulated in Table 1 for quick reference. As indicated by
Eq. (10) multiple stop bands of an
n-order DLF exist and the central frequencies of the stop bands
*f _{stop}* are given by

*f*=

_{stop}*mf*, where

_{r}*m*is an integer and

*f*=1/

_{r}*T*is the A-line scan rate. At these central frequencies, the autocorrelation velocity estimator has zero response; therefore they are the blind frequencies of the MSS-ODT technique. It is also noticed that the Doppler flow estimation in these blind frequencies will be influenced when the flow velocity of moving scatterers is beyond the Doppler flow dynamic range determined by the 2-π phase wrapping effect in the autocorrelation estimator. When the motion of clutter scatterers relative to the lateral scanning probe is so small that the resulted Doppler frequency shift falls within the stop bands of the DLF (e.g., near their central frequencies), the clutter signal component is suppressed and its influence on estimating the Doppler frequency shift of moving scatterers is then greatly reduced.

#### 2.2 The phase-shifted DLF

When the probe beam moves relative to the clutter scatterers with a non-90 degree Doppler angle, the resulted Doppler frequency shift is not zero. To effectively suppress such a clutter signal, a DLF with a phase shift can be used which has the stop band frequencies matching the Doppler frequency shift of the clutter scatterers. The implementation of a phase-shifted DLF is shown in the following diagram

where a phase-shift of 2*πf _{s}T* matches to the Doppler
frequency shift

*f*of the clutter scatterers. Typically

_{s}*f*is a fraction of the A-line scan rate

_{s}*f*. Denoting

_{r}*β*=exp(-

*i2πf*) and using Eq. (8), the frequency response of an

_{s}T*n*-order phase-shifted DLF is given by

and the corresponding power transfer function is

Clearly the stop bands of the DLF are shifted to *f _{s}*+

*mf*.

_{r}#### 2.3 Doppler spectrum of the clutter

The Doppler power spectrum of clutter scatterers can be described by the following Gaussian distribution

where *f _{s}* denotes the central Doppler frequency shift of the clutter scatterers and σ
is their Doppler bandwidth. When the flow rate is higher than the dynamic range of
the system, there will be a 2-π ambiguity in the frequency shift estimation process.
The Doppler power spectrum of the clutter scatterers will then influence the
estimation of the Doppler frequency shift of the moving scatterers near

*f=f*+

_{s}*mf*. The normalized Doppler power spectrum S(

_{r}*f*) of the clutter scatterers and the normalized power transfer functions |

*H(f)*|

^{2}of two representative phase-shifted DLFs (e.g., n=1 and n=4) with

*f*being zero and 0.17

_{s}*f*are shown respectively in Figs. 1(a) and 1(b). The Doppler bandwidth

_{r}*σ*of the clutter is set to 0.1

*f*assuming that temporal correlation window width of the clutter is 10

_{r}*T*.

In Fig. 1(b), the stop bands
*f _{stop}* of the DLFs with a phase shift of 2

*πf*can be described by equation

_{s}T*f*=

_{stop}*mf*+

_{r}*f*. The frequencies of the stop bands are all shifted by

_{s}*f*to match the Doppler frequency shift of the clutter scatterers so that their influence to moving scatterer signals can be suppressed. Therefore the phase-shifted DLF can reject clutter signals even though they have a global Doppler frequency shift.

_{s}## 3. MSS-ODT implemented in an SD-OCT system

The above theoretical analysis of clutter rejection can be implemented in any OCT system
capable of performing conventional PR-ODT (such as a time-domain OCT [5–7], an
SD-OCT [10–17], and a swept source OCT [18–23] system) as long as the complex analytical A-line
fringe signal is available. We experimentally validated the above phase-shifted DLFs for
clutter rejection using an SD-OCT system on a flow phantom and an *in
vivo* mouse model.

#### 3.1 SD-OCT setup

Figure 2 shows the schematic of a fiber-based
SD-OCT system used to demonstrate the MSS-ODT method [8]. The light source is a mode-locked Ti:Sapphire laser with center
wavelength at 825 nm and a FWHM bandwidth of ~150 nm. In the reference arm, a prism
pair is used to balance the dispersion of the two arms of the interferometer and a
variable neutral density filter to adjust the reference light level. A
galvanometer-based handheld probe was used to perform transverse beam scanning. The
spectral interference fringes are detected by an imaging spectrometer consisting of a
collimating lens (f=45 cm), a transmission diffraction grating (1200 lines/mm), an
achromatic focusing lens (f=75 cm) and a fast line-scan CCD camera (2048 pixels,
14×14 µm). The detected spectral fringes are digitized with 12-bit resolution and
transferred to a computer at 12.3k lines per second by a frame grabber card. The time
delay between adjacent A-lines is *T* ~81 µs. The exposure time of the
CCD was experimentally optimized to be 75 µs considering the balance between signal
integration and fringe washout caused by the mechanical instability of the system
[24]. The axial resolution of this system
is 2.5 µm in air and its dynamic range is about 106 dB. The power incident on the
sample surface was about 3 mW.

#### 3.2 Signal processing procedures

The following diagram shows the signal processing procedures we used for MSS-ODT in this study to extract the Doppler flow image from the data collected by the above SD-OCT system:

For traditional PR-ODT, only two major steps are needed to obtain the Doppler flow
information. The first step is to reconstruct the *j*th complex
analytical A-line fringe $\tilde{\Gamma}$
* _{j}*(

*z*) from

*j*th A-line spectral fringe. In this step, the spectrum intensity of the reference arm

*I*obtained before imaging is first subtracted from the spectral interference fringe

_{ref}(λ)*I*to remove the DC term, and the result is re-sampled using a cubic spline interpolation algorithm to yield a uniform spectrum

_{j}(λ)*F*in the spatial frequency (

_{j}(k)*k=2π/λ*) domain. $\tilde{\Gamma}$

*(*

_{j}*z*) is then obtained by taking the inverse Fourier transform of

*F*and eliminating the redundant mirror signal (when z<0). The second step is to retrieve the local Doppler frequency shift using the autocorrelation velocity estimator. For MSS-ODT, a critical extra step is required, i.e. a phase-shifted DLF is applied to $\tilde{\Gamma}$

_{j}(k)*before the velocity estimation process (see Eq. (11) and the corresponding diagram above Eq. (11)). An improved sensitivity in flow detection and a better accuracy in vessel size estimation can be achieved by this extra step based on the clutter rejection analysis discussed in the previous sections. The Doppler frequency shift*

_{j}(z)*f(m, n)*at the pixel (

*m, n*) is calculated from the output

*M̃(z)*of the phase-shifted DLF by the following formula

where *p* and *q* are shift steps along the axial
(*z*) direction and lateral scanning (*jT*)
direction. The above calculation is performed within a two-dimensional window of a
size *S×K* pixels where *S* is the height of the
averaging window along the depth (*z*) direction and
*K* is the number of A-lines that the window spans along the
lateral scanning (*jT*) direction.
*M*̃ _{j+1}(z)* denotes the conjugate of

*M̃*. Considering the tan

_{j+1}(z)^{-1}function only provides a phase angle from -π to π, the unambiguous dynamic range of the Doppler frequency shift is [-1/(2

*T*), 1/(2

*T*)], which is about [-6.2, 6.2] kHz given

*T*=81 µs in our study. Because pixels with low intensity will be considerably sensitive to phase noise and cannot be used to extract a reliable flow rate, the Doppler frequency shift is thus set to zero at any given pixel when its intensity falls below a preset threshold.

## 4. Experiment results and comparison of MSS-ODT with PR-ODT

We compare the Doppler flow images obtained by the MSS-ODT and PR-ODT techniques using
the same intensity threshold and the same averaging window size of 4 µm wide by 2.4 µm
deep (corresponding to *S*=4, *K*=4 in Eq. (15)) with the shift steps set to be
*p*=2 and *q*=2. In this study, a first-order
phase-shifted DLF is used in the MSS-ODT.

#### 4.1 Phantom flow in a capillary tube

We validated the improved accuracy in vessel size measurement and flow imaging in
MSS-ODT by a flow phantom experiment. A phantom composed of gelatin mixed with
TiO_{2} granules (1 mg/ml) was used to provide tissue-like background
scattering. The 2% Intralipid solution was flowing through a capillary tube of an
inner diameter 75 µm buried in the gelatin phantom, and the flow rate was controlled
by a syringe pump. A non-perpendicular Doppler angle was chosen by titling the
capillary tube with respect to the OCT probe beam. The spectral interference fringes
from the SD-OCT system were processed using both the PR-ODT and the MSS-ODT
techniques. The movie of the structural image is shown in Fig. 3(a). The Doppler flow images obtained with PR-ODT and
MSS-ODT are shown in Fig. 3(c) and (d) (along
with movies), respectively. These movies are shown at 6 frames per second, but the
frame rate of Doppler flow imaging (including data transfer, real-time signal
processing, and data saving) can reach 12–18 frames per second in our current system.
In these Doppler images, the Doppler frequency shift (*f*) is shown in
kHz and they can be converted to the flow velocity *V*
by*V*cos*θ=fλ*/2. Comparing Figs. 3(c) and 3(d), we
find that the clutter artifact shown up as the green (false-color) background is
greatly suppressed when using the MSS-ODT method. This can also be seen more
quantitatively from the flow profiles in Fig.
3(b) which are plotted along the horizontal direction through the center of
the capillary tube in Fig. 3(c) and Fig. 3(d). Further analysis of the flow profiles
reveals that the inner diameter of the tube was underestimated by the PR-ODT by about
23%, whereas the MSS-ODT method provides nearly accurate size estimation with only
about 4% underestimation (see the inset plot in Fig.
3(b)). The clutter frequency shift *f _{s}* in the phase-shifted DLF was set to be -0.2

*f*for this experiment and it was empirically chosen to maximize the suppression of the background Doppler signal due to clutters. The

_{r}*f*parameter would be changed for different experiments according to the overall clutter Doppler signal level.

_{s}#### 4.2 In vivo blood flow in a mouse ear

We also compared the performance of MSS-ODT and PR-ODT for imaging blood vessels in a
mouse ear *in vivo*. The OCT imaging beam was laterally scanned on the
mouse ear using a handheld probe. Fig. 4(a)
is the movie of the structural images. Fig.
4(c) and Fig. 4(d) show movies of
Doppler flow images of the mouse ear obtained by the PR-ODT and MSS-ODT methods,
respectively. The flow profiles plotted along the horizontal direction through the
center of the right blood vessel in flow images Fig.
4(c) and Fig. 4(d) are shown in
Fig. 4(b). From the flow profiles, we find
that the vessel size is underestimated by PR-ODT by about 30% compared to that
obtained by MSS-ODT (see the inset plot in Fig.
4(b)). This quantitative comparison result is very similar to the finding
in the control phantom studies where MSS-ODT was proved to be more accurate,
suggesting that MSS-ODT provides more accurate estimation of vessel size in vivo as
well. The clutter frequency shift fs in the phase-shifted DLF was again chosen
empirically, i.e. 0.17*fr* for this experiment, to maximize the
background clutter suppression. The movies of the Doppler flow are again shown at 6
frames per second. The results demonstrate that MSS-ODT can achieve better estimation
of blood vessel size than PR-ODT when a phase-shifted DLF is used for clutter
rejection. In Doppler images obtained by MSS-ODT, we also find the background
artifacts induced by the motion of stationary scatterers with respect to the scanning
probe beam are significantly reduced when a phase-shifted delay line filter is
used.

## 5. Summary

A phase-shifted DLF is demonstrated to reject clutter signals, and this new MSS-ODT signal processing method offers an improvement in Doppler flow imaging and vessel size determination. Flow imaging of a small capillary tube and a mouse ear were performed using a SD-OCT system and the Doppler data were analyzed using the MSS-ODT technique. Compared to the conventional PR-ODT technique, it is found that MSS-ODT can improve the sensitivity and accuracy in Doppler flow imaging and vessel size evaluation of small blood vessels. The results strongly suggest that the reported MSS-ODT with a phased-shifted DLF for clutter rejection can be potentially a very valuable tool for depth-resolved imaging of blood flow in human retina.

## Acknowledgments

The authors thank Daniel J. MacDonald and Tao Sun for their assistance with the imaging system and data acquisition, and Michael J. Cobb for his assistance with the animal experiments. This work was supported in part by the National Institutes of Health and National Science Foundation (Career Award XDL).

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