Page 1

A digital frequency ramping method for

enhancing Doppler flow imaging in Fourier-

domain optical coherence tomography

Zhijia Yuan1, Z. C. Luo1,3, H. G. Ren1, C. W. Du2,3, Yingtian Pan1,*

1Department of Biomedical Engineering, 2Department of Anesthesiology, Stony Brook University,

NY, Stony Brook, 11794, 3Medical Department, Brookhaven National Laboratory, Upton, NY, 11973

*Corresponding author: Yingtian.Pan@sunysb.edu

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

OCIS codes: (110.4500) Optical coherence tomography; (100.2000) Digital image processing.

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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 ν0 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 ν0 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 ν0 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.

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Received 2 Dec 2008; revised 6 Feb 2009; accepted 11 Feb 2009; published 27 Feb 2009

2 March 2009 / Vol. 17, No. 5 / OPTICS EXPRESS 3953

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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=2π/λ . The interferometric signal with respect to spectral modulation at depth ∆z

within a biological tissue (i.e., 1/2 of the optical pathlength difference between the sample and

reference arms) can be expressed as

∆=∆ ∆ + +

Where Ir is the light intensity in the reference arm and [Is,i(∆z)]1/2 is the backscattering

amplitude from depth of ∆z 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 Nx is the pixel number of the FDOCT image in the transverse

direction. The spectral amplitude term can be simplified by Ai(k, ∆z)=2[IrIs,i(∆z)]1/2S(k). Here,

νs 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 νf refer to the shift caused by the local blood flows that to be detected

from the biological tissue. τ is the duration between each A-scan. Compared with

conventional Doppler OCT that measures the phase difference between adjacent A-scan, i.e.,

(νs+νf )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*

=∆

,

( ,)2( ) ( )cos 2

z S k

(

ν

)

i r s i

I I

sf

I kz k zi

τφν

, (i=1, 2, …, Nx)

+⋅

(1)

i(k, ∆z), is first obtained by a Hilbert transform in k-space,

[

),(

IHzkI

ii

] )

z

,(

*

k

∆

(2)

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

∆=∆

*( ,

i

I k

) ( ,)sin 2(

ν

)

isf

z A kz k z

∆ + +

i

τφν

, (i=1, 2, …, Nx)

+

(3)

with the sine and cosine interferogram pairs in Eq. (1) and Eq. (3), an arbitrary digital Doppler

frequency ν0 can be introduced to form a new spectral interferometric signal Pi(k, ∆z)

∆=∆

(

ν

)(

ν

)

τ

i

τ

izkIzkIzkP

iii

0

*

0

sin),( cos),(),(

∆+

(4)

which gives,

0

( ,) ( ,)cos 2(

ν

)

iisf

P kz A kz k z

∆ + +

i

τφνν

, (i=1, 2, …, Nx)

∆=∆+−⋅

(5)

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Fig. 1. Flow chart of DFRM. The spectral interferometric signal Ii(k) was first combined with

its Hilbert transform I*i(k) to generate a target signal Pi(k) with arbitrary phase shift ν0iτ along

the lateral direction. Thereafter, a lateral Hilbert transform was performed to compute Pi(k)’s

analytic signal Hix(k). By applying iFFT to Hix(k) to reconstruct the image Ri(z), the signal is

separated to positive or negative part of Ri(z) depending on the sign of their lateral phase

modulation frequency.

Apparently, Eq. (5) indicates that the new target function Pi(k, ∆z) allows us to

numerically provide a constant Doppler frequency ν0 or a phase modulation (ν0)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

ν0 is inserted, a Hilbert transform in the transverse direction is applied to obtain the analytic

signal of Pi(k, ∆z) [20]. If ν0 is within the range of (νs, νs+νf ), then the net frequency term

∆νf,0=(νs+νf -ν0 )>0 and that in the surrounding tissue background without flow ∆νb,0=(νs -

ν0)<0, which will allow us to binarize the flow νf above the background νs. As a result, the

analytic signal within the dynamic flow range can be written as,

{

,0

( ,) ( ,) cos 2

iif

Hkz A kz k zi

}

,0

sin 2

x

f

j k z

∆ + +∆

i

τφντφν

, (i=1, …, Nx) (6)

∆=∆ ∆ + +∆+

and that in the surrounding tissue as

{}

,0 ,0

( ,) ( ,) cos 2 sin 2

x

iibb

H kz A kz k z

∆ + +∆

i

τ

j k z

∆ + +∆

i

τφνφν

, (i=1,…, Nx) (7)

∆=∆+

where the flow in Eq. (6) has a positive lateral phase modulation (∆νf,0>0), while background

in Eq. (7) has a negative lateral phase modulation (∆νb,0<0). Thereafter, an inverse FFT along

the axial (z) direction,

∆=

()

(),

x

ii

Rz iFFT Hkz

∆

(8)

will allow for reconstruction of the image Ri(∆z) in which the Doppler flow part distributed in

the positive side (i.e., ∆z ≥ 0), thus can be explicitly differentiated from the noise background

distributed in the negative side (i.e., ∆z ≤ 0) [20].

More importantly, as ν0 is arbitrary, the above procedure can be repeated to ramp ν0 from

-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 ν0 critical to enhancing Doppler flow detection is

always difficult if not impossible. Figure 2 further illustrates how ν0 can be ramped to enable

quantitative flow measurements. To simplify the procedure, we set the A-scan duration τ=1

and system phase noiseνs=0, so that (νs+νf -ν0)τ = (νf -ν0). For a positive flow (e.g., νf1 >0),

Fig. 2(a) shows that, as ν0 (Red curve) is ramped, e.g., ν0(n)=-π+π(2n/N), n=0, 1, …N from –

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