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 jth 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 h₁(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; H₁(f) is the frequency response of the DLF and from Eq. (2) it yields

Following Eq. (4), the Doppler power spectrum |M̃(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.

Table 1. Weight Coefficients of the First Four Delay Line Filters

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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_r, where m is an integer and f_r=1/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 2πf_sT matches to the Doppler frequency shift f_s of the clutter scatterers. Typically f_s is a fraction of the A-line scan rate f_r. Denoting β=exp(-i2πf_sT) and using Eq. (8), the frequency response of an 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_r. The normalized Doppler power spectrum S(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_s being zero and 0.17f_r are shown respectively in Figs. 1(a) and 1(b). The Doppler bandwidth σ of the clutter is set to 0.1f_r assuming that temporal correlation window width of the clutter is 10T.

 

Fig. 1. The normalized Doppler power spectrum S(f) of the clutter, and the normalized power transfer function |H(f)|² of two representative DLFs (e.g., n=1 and n-4) without (a) and with (b) phase shifted. The Doppler bandwidth σf of the clutter scatterers is set to be 0.1 fr and their frequency shift is set to be 0 and 0.17 fr in (a) and (b), respectively.

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In Fig. 1(b), the stop bands f_stop of the DLFs with a phase shift of 2πf_sT can be described by equation f_stop=mf_r+f_s. The frequencies of the stop bands are all shifted by f_s 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.

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.

 

Fig. 2. Schematic of the fiber-based SD-OCT system. PC: polarization controller; L1, L2: lenses; P: prism pair; NDF: neutral density filter for attenuation; M: mirror; DG: transmission diffraction grating; CL: cameral lens; LSCCD: linescan CCD; FG: function generator; Sync: galvanometer scanner drive synchronization.

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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 jth complex analytical A-line fringe $\tilde{\Gamma }$ _j(z) from jth A-line spectral fringe. In this step, the spectrum intensity of the reference arm I_ref(λ) obtained before imaging is first subtracted from the spectral interference fringe I_j(λ) to remove the DC term, and the result is re-sampled using a cubic spline interpolation algorithm to yield a uniform spectrum F_j(k) in the spatial frequency (k=2π/λ) domain. $\tilde{\Gamma }$ _j(z) is then obtained by taking the inverse Fourier transform of F_j(k) 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(z) 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 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_j+1(z). Considering the tan^-1 function only provides a phase angle from -π to π, the unambiguous dynamic range of the Doppler frequency shift is [-1/(2T), 1/(2T)], 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 TiO₂ 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 byVcosθ=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 -0.2f_rfor this experiment and it was empirically chosen to maximize the suppression of the background Doppler signal due to clutters. The f_s parameter would be changed for different experiments according to the overall clutter Doppler signal level.

 

Fig. 3. Movies of the structural image (a) (0.9MB), and Doppler flow images of the 2% intralipid flow in a capillary tube of an ID 75 µm obtained by the PR-ODT (c) (0.8MB) and the MSS-ODT (d) (0.7MB) methods. The image size of both images is 0.80×0.52 mm (transverse x depth) (without rescaling by the refractive index). The pixel size of the images is 492×320. The flow profiles along the horizontal direction through the center of the capillary tube in image (c) and (d) are shown in (b).

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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. 0.17fr 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.

 

Fig. 4. Movies of the structural image (a) (1.1MB), and Doppler flow images obtained by the PR-ODT (c) (0.7MB) and MSS-ODT (d) (0.6MB) methods on a mouse ear in vivo. All the images have a size of 1.16×0.75mm (transverse x depth) (before rescaling by the refractive index), and the image size in terms of pixels is 492×320 (transverse x depth). The flow profiles plotted along the horizontal direction through the center of the right blood vessel in image (c) and (d) are shown in (b).

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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.