## Abstract

A digital frequency ramping method (DFRM) is proposed to improve the signal-to-noise ratio (SNR) of Doppler flow imaging in Fourier -domain optical coherence tomography (FDOCT). To examine the efficacy of DFRM for enhancing flow detection, computer simulation and tissue phantom study were conducted for phase noise reduction and flow quantification. In addition, the utility of this technique was validated in our in vivo clinical bladder imaging with endoscopic FDOCT. The Doppler flow images reconstructed by DFRM were compared with the counterparts by traditional Doppler FDOCT. The results demonstrate that DFRM enables real-time Doppler FDOCT imaging at significantly enhanced sensitivity without hardware modification, thus rendering it uniquely suitable for endoscopic subsurface blood flow imaging and diagnosis.

©2009 Optical Society of America

## 1. Introduction

Optical coherence tomography (OCT) is an optical imaging technique that can provide noninvasive cross-sectional imaging of biological tissue at sub-10μm spatial resolution and intermediate (1-3mm) depths [1, 2]. Recent technological advances include Fourier-domain optical coherence tomography (FDOCT) to enable real-time 2D and even 3D OCT imaging[3], ultrahigh-resolution OCT (uOCT) to permit cellular imaging[4, 5], and endoscopic OCT (EOCT) for *in vivo* high-resolution visualization of internal organs and clinical diagnosis of epithelial tumors[6-9]. In addition, some new imaging approaches have been derived from conventional OCT technique to detect more specific features of biological tissue morphology, physiology, and even functions. For instance, Doppler OCT (DOCT), by extracting the phase change induced by the flowing scatterers (e.g., red blood cells) in the biological tissue, has been reported to permit quantitative imaging of subsurface blood flows at high spatiotemporal resolutions, thus allowing for more specific functional imaging diagnosis[10-14].

High-speed DOCT was first developed in time-domain OCT by subtracting the ‘amplified’ phase difference between two adjacent depth scans, i.e., A-scan based Doppler flow measurement [11, 13, 14]. This technique was largely simplified in FDOCT resulting in drastically improved imaging rate and signal-to-noise ratio (SNR) by virtue of fast Fourier transform (FFT) so that *in vivo* real-time 2D and even 3D DOCT can be permitted [10, 12, 15, 16]. Despite its superior spatiotemporal resolutions for noninvasive subsurface flow imaging, DOCT has suffered a major drawback from excessive phase noise which may originate inherently from dynamic multiple scattering, speckle noise, heterogeneity of biological tissue and the amplitude shot noise of the detected spectral interferometric fringes as well as motion-induced artifacts of *in vivo* regime, in particular, in endoscopic DOCT imaging where handshake often induces substantial phase noise or artifacts. Several approaches have been explored to enhance the SNR for flow detection [17-23], among which optical angiography (OAG), based on B-scan phase modulation thresholding in FDOCT has been recently reported by Wang’s group to effectively suppress phase noise and thus allow for 3D mapping of cerebral microvascular perfusion through intact mouse cranium at unprecedented sensitivity and resolution[20, 24]. In their OAG systems, a constant Doppler frequency shift *v*
_{0} was used to threshold the phase or frequency term in the transverse Hilbert transform to differentiate the dynamic flow signal from static or random, slow-moving noise background. A stable *v*
_{0} was generated by either linearly scanning the reference mirror with a PZT translator or by angularly actuating an off-center servo mirror in the sample arm of an FDOCT system [20, 25].

Based on the principle of B-scan phase modulation thresholding (Hilbert transform in the transverse direction), we further develop a solely numerical approach, i.e., digital frequency ramping method (DFRM), which employs computer generated numerical Doppler frequency to enhance flow detection sensitivity and resolution. As the need for hardware-based Doppler frequency shift implementation is circumvented, this new technique can be applied to conventional FDOCT, thus potentially allowing for 2D and even 3D optical angiography in real time. More importantly, by digitally ramping the Doppler frequency *v*
_{0} from low to high and from positive to negative, this technique enables quantitative flow imaging, which is crucial to a wide variety of physiological and functional imaging studies where quantitative blood flow monitoring is required. To examine the efficacy of DFRM for enhancing flow imaging, computer simulation and tissue phantom study were conducted for phase noise reduction and flow quantification. In addition, initial *in vivo* validation of this new technique was performed in our clinical bladder imaging studies using endoscopic FDOCT.

## 2. Methods

#### 2.1. Digital frequency ramping method (DFRM)

As has been reported [3, 26], FDOCT works on spectral radar for optical ranging, the depth-resolved backscattering profile (i.e., A-scan) is encoded on the spectral interferogram at different modulation frequencies and can thus be reconstructed by inverse fast Fourier transform (iFFT) after spectral calibration to convert the measured spectrograph to k-space where *k*=2*π*/*λ*. The interferometric signal with respect to spectral modulation at depth Δz within a biological tissue (i.e., 1/2 of the optical pathlength difference between the sample and reference arms) can be expressed as

Where I_{r} is the light intensity in the reference arm and [I_{s,i}(Δz)]^{1/2} is the backscattering amplitude from depth of Δz in the sample arm which constitutes the structural OCT image. *S*(*k*) is the cross spectrum and *ϕ* is a random phase of the scattering biological tissue. i is the sequential A-scan index and N_{x} is the pixel number of the FDOCT image in the transverse direction. The spectral amplitude term can be simplified by *A _{i}*

*(*

*k*,*Δz*)=2[I_{r}I_{s,i}(Δz)]^{1/2}*S*(

*k*). Here,

*v*refer to the Doppler frequency shifts induced by the relative motion between the sample and reference arms (e.g., motions of the sample probe and of the living biological tissue, and system vibration) and

_{s}*v*refer to the shift caused by the local blood flows that to be detected from the biological tissue.

_{f}*τ*is the duration between each A-scan. Compared with conventional Doppler OCT that measures the phase difference between adjacent A-scan, i.e., (

*v*+

_{s}*v*)

_{f}*τ*, the phase modulation will be further amplified if measured along the transverse direction (i.e., B-mode Doppler OCT).

Figure 1 illustrates the flowchart of DFRM for flow image reconstruction. The first step of DFRM is to introduce a phase shift into the original spectral interferometric signal; this is numerically implemented using Hilbert transform. As shown in Fig. 1, the sinusoidal phase term of Eq. (1), i.e., *I*
^{*}
*i*(*k*, *Δz*), is first obtained by a Hilbert transform in k-space,

where H stands for Hilbert transform operator. The result can be rewritten as,

with the sine and cosine interferogram pairs in Eq. (1) and Eq. (3), an arbitrary digital Doppler frequency *v*
* _{0}* can be introduced to form a new spectral interferometric signal

*P*(

_{i}*k*,

*Δz*)

which gives,

Apparently, Eq. (5) indicates that the new target function *P _{i}*(

*k*,

*Δz*) allows us to numerically provide a constant Doppler frequency

*v*or a phase modulation (

_{0}*v*)

_{0}*iτ*to a standard FDOCT system, thus circumventing the need for hardware implementation by either by scanning reference mirror or actuating an off-center servo mirror in the sample arm. After

*v*is inserted, a Hilbert transform in the transverse direction is applied to obtain the analytic signal of

_{0}*P*(

_{i}*k*,

*Δz*) [20]. If

*v*is within the range of (

_{0}*v*,

_{s}*v*+

_{s}*v*), then the net frequency term Δ

_{f}*v*=(

_{f,0}*v*+

_{s}*v*-

_{f}*v*)>0 and that in the surrounding tissue background without flow Δ

_{0}*v*=(

_{b,0}*v*-

_{s}*v*)<0, which will allow us to binarize the flow

_{0}*v*above the background

_{f}*v*. As a result, the analytic signal within the dynamic flow range can be written as,

_{s}and that in the surrounding tissue as

where the flow in Eq. (6) has a positive lateral phase modulation (Δ*v _{f,0}*>0), while background in Eq. (7) has a negative lateral phase modulation (Δ

*v*<0). Thereafter, an inverse FFT along the axial (z) direction,

_{b,0}will allow for reconstruction of the image *R _{i}*(

*Δz*) in which the Doppler flow part distributed in the positive side (i.e., Δz≥0), thus can be explicitly differentiated from the noise background distributed in the negative side (i.e., Δz≤0) [20].

More importantly, as *v _{0}* is arbitrary, the above procedure can be repeated to ramp

*v*from -

_{0}*π*/(

*iτ*) to

*π*/(

*iτ*) to cover the full-range Doppler frequency shift, rendering this numerical approach highly suitable for clinical applications with quantitative measurement capability, where pre-determination of the optimal

*v*critical to enhancing Doppler flow detection is always difficult if not impossible. Figure 2 further illustrates how

_{0}*v*can be ramped to enable quantitative flow measurements. To simplify the procedure, we set the A-scan duration

_{0}*τ*=1 and system phase noise

*v*=0, so that (

_{s}*v*+

_{s}*v*-

_{f}*v*)

_{0}*τ*= (

*v*-

_{f}*v*). For a positive flow (e.g.,

_{0}*v*> 0), Fig. 2(a) shows that, as

_{f1}*v*(Red curve) is ramped, e.g.,

_{0}*v*(

_{0}*n*)=-

*π*+

*π(2n/N)*,

*n*=0, 1, …

*N*from -

*π*to

*π*, the green curve

*Δv*=(

_{f}*v*-

_{f}*v*) changes sign from “+” to “-” at

_{0}*v*(i)=

_{0}*v*. The flow component in the reconstructed image

_{f1}*R*(

_{i}*Δz*) will flip accordingly from “+” to “-”, indicating a positive flow at

*v*. Similarly, Fig. 2(b) shows the sign change of

_{f1}*Δv*for a negative flow at

_{f}*v*(j)=

_{0}*v*. Noteworthily, the dashed arrows indicate the periodic 2π phase ramp of

_{f2}*Δv*in both cases.

_{f}#### 2.2. Experimental setup

DFRM is a numerical approach for flow imaging enhancement; therefore, a standard FDOCT system was used to examine the efficacy of this technique in both tissue phantom study and *in vivo* biological tissue study. As depicted in Fig. 3, a pigtailed high-brightness (18mW) broadband source (BBS) was employed to illuminate a fiberoptic interferometer, whose central wavelength and full-width-half-maximum spectral bandwidth were *λ*=1320nm and Δ*λ*=90nm to provide a source coherence length of L_{c}≈8.5μm. A green diode laser (4mW, 532nm) was coupled via a 95%:5% fiber coupler to visually guide 2D and 3D OCT scans. Light exiting the reference fiber was collimated (ϕ 1.6mm), attenuated and retroreflected by a reference mirror mounted onto a 1D stage to match the path length in the sample arm of the Michelson interferometer. The sample arm was connected to a handheld stereoscope in which light exiting the fiber was collimated (ϕ4.2mm), scanned laterally by a 2D servo mirror, and focused by an achromate (f=40mm) onto the biological tissue under imaging. The sample arm could instead be connected to a MEMS-based OCT endoscope in which light exiting the fiber was collimated (ϕ 1.2mm), scanned laterally by a 1D MEMS mirror, and focused by an achromate (f=10mm) onto the lumen of biological tissue for *in vivo* imaging. The light beams returning from the sample and reference arms were recombined in the detection fiber and connected to a spectral imager in which light was collimated by a fiberoptic achromate (f=55mm), diffracted by a holographic grating G (d= 1200mm^{-1}) and focused by an achromatic lens group (f= 120mm) onto a linear InGaAs array. The detected spectral graph, including spectrally encoded interference fringes from different depth (Δz) within the biological sample, was digitized and streamlined to a workstation via a 2-channel 12bit A/D at 5MHz, allowing for 2D imaging (1024pixel × 1000pixel) at ~8fps. The axial and transverse resolutions of the system were ~9μm and ~12μm, respectively. Because of extensive computation, 2D and 3D DFRM flow images were processed and displayed in post-image mode; however, conventional Doppler FDOCT was displayed at ~5fps for locating subsurface flows.

## 3. Results

#### 3.1 Tissue phantom simulation

In order to evaluate the capability efficacy of DFRM for enhancing the flow detection, we first conducted numerical simulation in which a group of flows with varying sizes and flow velocities were modeled. To do so, we normalized the signal amplitude in Eq. (1), i.e., A_{i}(k, Δz)=1 and added computer-generated 2D random Gaussian phase noise ϕ_{n}(i, Δz) to simulate the phase noise background in a Doppler OCT image, i.e.,

For mathematical simplicity, a circular parabolic profile was used to simulate laminar flows, i.e., v_{f} (*x*, *z*)=*v _{f,max}*

*{l-[(x-x*+

_{0})^{2}*(z-z*

_{0})^{2}*where*

^{1/2}/r}*v*was the vertex at the flow center (

_{f,max}*x*,

_{0}*z*) and r was the radius of the vessel. The A-scan duration was set to

_{0}*τ*=1 so that

*v*=

_{f}τ*v*in Eq. (9). Also, taking into account that the phase term is folded in every [-π, π] period, a flow range normalized to [0, π] would be sufficient to evaluate the SNR characteristics of the flow detection; therefore, two typical flow rates were chosen in our modeling, e.g.,

_{f}*v*=0.8π for high-velocity group and

_{f,max}*v*=0.2π for low-velocity group. The mean of the phase noise ϕ

_{f,max}_{n}(i, ϕz) was set to 0 for both groups and the standard deviation was set to 0.02π and 0.08π respectively as 0.1

*v*. In each group, three sizes with radius

_{f,max}*r*descending from 50-, to 35-and 20-pixels were used to simulate large, intermediate and small flows centered at x

_{0}, z

_{0}=100 in an FDOCT image of

*N*,

_{x}*N*=200 pixels. For each of the 6 flow configurations, both DFRM and direct phase subtraction method (PSM) used in ordinary Doppler FDOCT [14] were applied to reconstruct the flow images. In DFRM modeling,

_{z}*v*was set to be 1/10 of the vertex

_{0}*v*, i.e.,

_{f,max}*v*=0.08π and

_{0}*v*=0.02π for the high- and low-velocity flow groups, respectively. The flow profiles reconstructed by DFRM and PSM (in logarithmic scale) and normalized by their peak values were collaterally plotted in Fig. 4, and the results clearly demonstrated the enhancement on flow delectability by DFRM over the PSM.

_{0}Yet it is noteworthy that unlike PSM which provided quantitative assessment of flow velocity by subtracting the phase difference between successive axial lines, DFRM by *v _{0}* thresholding could only provide qualitative assessment (i.e., angiography) which detected the existence of flow rather than its velocity. To enable DFRM for quantitative flow imaging, we linearly ramped

*v*with a relatively small step size of Δ

_{0}*v*, i.e.,

_{0}If the velocity of a flow or part of a flow profile *v _{f}*(

*x*,

*z*) fell within the range of [

*v*,

_{0}(i)*v*

_{0}*(i+1)*], its lateral phase modulation (LPM), Δ

*v*(

_{f}*x*,

*z*;

*i*)=

*v*(

_{f}*x*,

*z*)-

*v*(

_{0}*i*) would change sign when

*v*(i) was increased to

_{0}*v*(i+1). According to Eq. (6) and Eq. (7), the corresponding transverse Hilbert transform would flip the signal from positive to negative to be differentiated by Eq. (8). To further enhance the sensitivity of R

_{0}_{i}(Δz) to differentiate Δ

*v*(

_{f}*x*,

*z*;

*i*), the ratio between the positive and negative images, i.e., R

_{i}(Δz>0)/R

_{i}(Δz<0) was calculated, then a threshold of 1 is set to binarize this ratio image to conclude the sign of R

_{i}(Δz). Therefore, a subtraction of the two binarized ratio images yields the net flow signals within (

*v*,

_{0}(i)*v*); hence, by ramping

_{0}(i+1)*v*from low to high and from negative to positive, the quantified flow velocity profile can be obtained at the resolution of Δ

_{0}*v*. Fig. 5 illustrates the reconstruction procedure for (

_{0}*v*(

_{0}*i*)=0.3,

*v*

_{0}*(i+1)*=0.4) of the flow (

*r*50, 0.8π) simulated in Fig. 4.

To test the feasibility of this quantitative approach, we applied DFRM to this simulated flow (*r*50, 0.8π) using step sizes of Δ*v _{0}*=0.02π and Δ

*v*=0.01π, respectively. The results were plotted in Fig. 6 in which the flow profile computed by PSM was shown for comparison. It is obvious that DFRM was able to recover the flow profile fairly accurately; whereas PSM suffered severely from overwhelming phase noise thus preventing it from effective tracking of the velocity variations along the radial direction. Interestingly, a comparison between the results from Δ

_{0}*v*=0.02π and 0.01π reveals that increasing frequency ramping accuracy did not necessarily yield better quantification results. This suggests that under noisy condition, DFRM may provide limited resolution to threshold or binarize the sign of LPM when Δ

_{0}*v*(

_{f}*x*,

*z*;

*i*)→0 and therefore Δ

*v*should be appropriately chosen to maximize the effort of enhancing the resolution for flow velocity recovery while minimizing the computation load.

_{0}Figure 7 further compares the SNR between PSM and DFRM for quantitative reconstruction of flows at different velocities, e.g., *v _{f,max}*, from 0.1π to 0.9π. In the modeling, the calculated velocity noise

*v*was defined as the difference between the reconstructed velocity

_{n}*v*and the input noise-free velocity

_{r}*v*, i.e.,

_{f}*v*=

_{n}*v*-

_{r}*v*; then, the SNR was according defined as the ratio between

_{f}*v*and the standard deviation of

_{f,max}*v*, i.e, SNR=

_{n}*v*/

_{f,max}*σ*. The DFRM step size was set to 0.02

_{n}*v*. The results clearly indicate that DFRM provides superior SNR (~25) over PSM (~7) for quantitative flow imaging. Interestingly, in the low flow range (e.g.,

_{f,max}*v*=0.1π to 0.3π), the SNR increases dramatically from 15 to 25 whereas PSM shows no significant difference.

_{f,max}Figure 8 further shows the result of DFRM to extend the dynamic range of flow measurement beyond the [-π, π] limit to 10π high flow velocity. As a result of enhanced SNR, DFRM was to provide high-contrast concentric rings that reflected the 2π phase wrapping effect so that the high flow velocity could be computed by summing up the ring numbers. In comparison, PSM could barely resolve the rings due to excessive phase noise background. It is noteworthy that for proof of principle, this simplified flow model did not simulate the phase washout effect, a high complex issue in the presence of fast flow which may lead to fringe washout of the spectral interferometric signals if recorded in finite acquisition time. This undesirable effect could potentially affect the accuracy of high flow recovery using DFRM.

#### 3.2 Experimental validations

Figure 9 shows the result of flow validation study using tissue phantom, in which the cross section of a controlled flow consisting of 1% intralipid solution (μ_{s}≈2.4cm^{-1}) in a ϕ0.50mm translucent conduit was imaged by FDOCT at a tilting angle of θ=12°. Both DFRM and PSM were able to quantify the flow profile. However, in consistence with the simulation results in Fig. 6, DFRM suppressed the phase noise around the non-flow area more effectively (e.g., the noise level or the background variation decreased 75%) so that the reconstructed velocity profile was smoother, i.e., more accurately quantified.

Following successful simulation and tissue flow phantom calibration studies, we further validated the technique *in vivo* in our ongoing clinical study for bladder cancer diagnosis. Detection of abnormal angiogenesis in bladder wall is of great clinical significance for both cancer diagnosis and for analysis and assessment of other pathological and physiological diseases in the bladder. For instance, angiogenesis into bladder epithelium is deterministic of bladder carcinogenesis; therefore, detection of angiogenesis in bladder epithelium by Doppler OCT can potentially provide crucial diagnosis of bladder cancer, thereby further improving the diagnostic sensitivity and specificity. However, the excessive phase noise has been found to impose a major challenge leading to limited dynamic range of flow detection in endoscopic Doppler OCT. Results of our in vivo clinical study revealed that the excessive phase noise induced by bladder motion and handshaking compromised the detectability of subsurface blood flows in bladder wall; therefore, enhancing the sensitivity of endoscopic Doppler OCT is of high clinical relevance. For the purpose of bladder cancer diagnosis, angiography instead of quantitative Doppler flow imaging is sufficient. Figure 10 compared the results of MEMS-based cystoscopic FDOCT reconstructed by DFRM versus PSM. Panel a) showed the morphological image of a normal human bladder in which the urothelium (U), lamina propria (LP) and upper muscularis were clearly delineated based on their backscattering differences. Panels b) and c) showed the corresponding Doppler COCT images reconstructed by PSM and DFRM based on a single frequency thresholding (in order to suppress the vibration noise caused by handshake, a relatively high threshold at 0.2π was applied, i.e., *v _{0}*=0.2π). Because of high phase noise, only a large, high-velocity flow BV1 was affirmatively identified and the phase noise

*v*induced by bladder motion and handshake was obvious as indicated by the blue arrows (vertical stripes) in panel B). In comparison, 7 more blood flows were uncovered among which BV1-BV5 were affirmatively identified and BVs 6–7 were likely smaller vessels but artifacts could not be ruled out. Interestingly, motion-induced vertical stripes were effectively reduced by taking advantage of the high SNR of the DFRM method.

_{s}(x)## 4. Discussion and conclusion

Doppler OCT, in both time-domain and Fourier-domain, has been developed over the past several years to permit subsurface flow imaging in biological tissue quantitatively and at high spatiotemporal resolutions. It is particular interesting for FDOCT technique because both structural and Doppler flow images can be acquired and overlapped in real time and with no or minimal system modification. Yet, the majority of DOCT techniques published so far are based on direct measurement of Doppler flow induced phase changes between successive axial lines or A-scans of a 2D or 3D OCT image [11-19]. This approach, however, is prone to excessive noise due to phase instability induced by the complications such as speckle noise, sample heterogeneity, dynamic multiple scattering of living tissue, and system vibration. Optical angiography (OAG) [20, 25] is a newly developed technique which OAG utilizes hardware implementation (e.g., by either moving the reference mirror with a PZT translator or scanning an off-center servo mirror at sample arm) to generate a proper threshold frequency modulation to separate moving elements from noisy static background. Although not yet quantitative, this technique has been shown to substantially increase the sensitivity and resolution for detecting subsurface flow distribution, including minute arteriolar flows which conventional DOCT based on direct PSM failed to detect.

In this article, we proposed a numerical approach (DFRM) to effectively enhance flow imaging capability of standard FDOCT technique with no further hardware modification. As derived in Eq. (5), this technique allows for numerical introduction of an arbitrary phase modulation to the interference spectrograph measured by FDOCT, thus circumventing the need for phase modulation by mechanical scanning. Simulation of various flows in noisy background presented in Fig. 4 indicates that DFRM was able to effectively offset and thus separate the flow signal from noise background, thus greatly enhancing the sensitivity and SNR for flow detection. As a software-based approach, this method can lift the potential complications of the hardware counterpart in terms of imaging rate, calibration (i.e., preselection) of threshold frequency *v _{0}*, drift of

*v*caused by nonlinearity and instability of mechanical scanning. More importantly, by digital ramping of

_{0}*v*using Eq. (10) which can be computed post FDOCT imaging, DFRM enables quantitative Doppler flow imaging with increased SNR as shown in flow simulation (Fig. 6–7) and flow phantom (Fig. 9) studies. Such quantitative flow imaging capability can be very useful for applications in quantitative analyses of the spatiotemporal hemodynamics of functional brain activations and responses to behavioral, cognitive, and pharmaceutical paradigms. In addition, the phase noise induced by tissue motion, in particular, by handshaking in endoscopic DOCT can be numerically compensated by DFRM, thus rendering a promising method for clinical diagnosis, such as angiogenesis associated with carcinogenesis.

_{0}Despite dramatic improvement provided by OAG and DFRM, Doppler flow imaging is inherently prone to ambient noise deterioration. Unlike structural OCT, a high-velocity flow does not necessarily result in equivalently enhanced SNR due to the fact that the flow signals fold every 2π. Although our high-velocity flow model in Fig. 8 demonstrated the potential DFRM for unwrapping the phase folding induced by fast flows, it is noteworthy that the simulation did not considered other complications in real imaging scenario, e.g., phase washout, sample heterogeneity, amplitude noise and so on. Therefore, our future work will improve current DFRM algorithm to more effectively suppress the background noise and to examine its performances in various experimental conditions and in animal and clinical applications. It is also noteworthy that DFRM, especially quantitative DFRM is exclusively computation intensive which involves multi-dimensional Hilbert transform and FFT. For a 1024pixel × 1000pixel flow image, a 50-step quantitative DFRM reconstruction takes ~60s on a 3.2GHz PC with a custom MATLAB program whereas PAM only takes ~3s; thus, parallel computing or fast computation unit, e.g., exquisite digital signal processing (DSP) with optimized algorithms is required to facilitate instantaneous 2D and even 3D flow display, which is of high clinical relevance for on-site endoscopic OCT/ DOCT diagnosis.

In conclusion, a phase ramping technique termed DFRM is reported to effectively enhance the flow imaging capability of conventional FDOCT. Results of theoretical modeling, tissue flow phantom validation and preliminary endoscopic FDOCT demonstrate the potential of DFRM to significantly enhance the sensitivity and SNR of FDOCT for quantitative subsurface flow imaging at high spatiotemporal resolutions. As a numerical approach, DFRM involves no additional hardware modification to standard FDOCT technique, thus rendering it highly suitable for real-time 2D and 3D flow imaging.

## Acknowledgments

This work was supported in part by NIH Grants 2R01-DK059265 (YP), K25-DA021200 (CD) and Fusion Award (YP). Correspondence can be addressed to yingtian.pan@sunysb.edu.

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