020-2008 Optics Express Szkulmowski

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Flow velocity estimation using joint Spectral and

Time domain Optical Coherence Tomography

Maciej Szkulmowski, Anna Szkulmowska, Tomasz Bajraszewski,

Andrzej Kowalczyk, and Maciej Wojtkowski*

Institute of Physics, Nicolaus Copernicus University, ul. Grudziadzka 5, PL87-100 Torun, Poland*Corresponding author: [email protected]

Abstract: We propose a modified method of acquisition and analysis of

Spectral Optical Coherence Tomography (SOCT) data to provideinformation about flow velocities. The idea behind this method is to acquirea set of SOCT spectral fringes dependent on time followed by a numerical

analysis using two independent Fourier transformations performed in time

and optical frequency domains. Therefore, we propose calling this method

as joint Spectral and Time domain Optical Coherence Tomography (joint

STdOCT). The flow velocities obtained by joint STdOCT are compared

with the ones obtained by known, phase-resolved SOCT. We observe thatSTdOCT estimation is more robust for measurements with low signal to

noise ratio (SNR) as well as in conditions of close-to-limit velocitymeasurements. We also demonstrate that velocity measurement performedwith STdOCT method is more sensitive than the one obtained by the phase-

resolved SOCT. The method is applied to biomedical imaging, in particular

to in vivo measurements of retinal blood circulation. The applicability of

STdOCT different measurement modes for in vivo examinations, including

1, 5 and 40 s of CCD exposure time, is discussed.

2008 Optical Society of America

OCIS codes: (170.4500) Optical coherence tomography; (170.3880) Medical and biological

imaging; (170.4470) Ophthalmology; (280.2490) Flow diagnostics

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#92569 - $15.00 USD Received 7 Feb 2008; revised 7 Apr 2008; accepted 8 Apr 2008; published 14 Apr 2008

(C) 2008 OSA 28 April 2008 / Vol. 16, No. 9 / OPTICS EXPRESS 6008


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1. Introduction

Optical Coherence Tomography (OCT) provides cross-sectional images of internal structure

of objects with micrometer resolution, and can be either performed in time [1] or frequency

domain [2]. The latter is performed by analysis of interferometric modulations of light

intensity versus optical wavelengths (spectral fringe signal). In Spectral OCT known also as

Spectral domain OCT (SOCT/SdOCT) spectral intereferometric fringes are registered by a

spectrometer. This modality is particularly useful for ophthalmic examinations since it offershigh speed of more than 20 000 A-scans per second and detection sensitivity of more than95dB [3-6]. The spectral interferometric fringe signals are collected for each lateral position

of the scanning beam and numerically processed to obtain two-dimensional cross-sectional

images representing the amount of back-reflected light versus depth and lateral positions of

the elements of internal structure of an object.

In addition to morphological imaging, SOCT can provide visualization of physiological

parameters [7-11]. At present the retinal blood flow attracts attention as a potentially

important physical parameter in the functional OCT studies. The measurements of




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bidirectional flow by Spectral OCT have been demonstrated by many groups [8, 12, 13]. In

all of these publications, authors used the phase-resolved technique based on linear

relationship between the phase difference of consecutive spectral fringe signals and the

velocity of the moving sample. This technique is analogous to phase-resolved approach

applied in the OCT methods with the time domain detection [14].Two main factors deteriorate and even preclude velocity recovery in the phase-resolved

OCT techniques: its vulnerability to low signal-to-noise ratio (SNR) [15] and motion artifacts

causing severe phase instabilities [12, 16]. Both problems frequently occur in OCT

measurements of biomedical objects in vivo. Recently, a novel spectral method has been

proposed in order to minimize the influence of phase instabilities so called resonant Doppler

imaging [17], which determines flow velocities on the intensity basis without the need of

extracting the signal phase. Moreover, this method overcomes a phenomenon of blurring ofinterference fringes caused by any sample movement during CCD camera integration time.Another phase independent method was proposed by Wang, et al., [18]. Since this technique

separates the moving and static components within a sample, only blood perfusion imaging is

possible without any flow velocity estimations. This optical angiography relies on introducing

a constant Doppler frequency to modulate the spatial OCT spectral interferograms what was

initially introduced to Spectral OCT by Yasuno, et al., in 2006 [19].

In this paper we present an alternative method of measuring and processing OCT signalsproviding information on the spatial distribution of flow velocities. We propose joint time and

frequency domain detection of interferometric OCT signals. The information about thevelocity is obtained directly similarly to first velocity estimation techniques in TdOCT [20,21] from the time dependent beating frequency due to the Doppler shift between the

reference and the sample light beams. Since the velocity estimation is not based on explicit

phase information extracted from interferometric fringes, the proposed variant of Doppler

SOCT is significantly less sensitive to undesired phase instabilities present in low SNRconditions. Since it does not require any phase wrapping and averaging procedure, it is

accurate for flows close to the upper limit of measurable velocities. This approach does not

require any modifications in hardware of a standard SOCT instrument. High sensitivity of this

method facilitates flow velocity estimation within the time frame required by the regular OCT

imaging. In many biomedical applications, especially in ophthalmology, there are severelimitations in optical power, which can be delivered to the sample. In such cases a

preservation of high sensitivity requires fixed value of exposure time of the CCD camera

collecting the spectral fringe data. In this case the multi-shot measurements required inSTdOCT can be balanced by reduction of CCD exposure time. And the same it is possible to

keep sensitivity and the optical power delivered to the object at the same levels like in regular

SOCT imaging. In such case the spectral fringe signals can be first processed and then

superimposed giving the structural reconstruction, while time dependent Fourier

transformation will yield information about flow velocities. Comparing to phase-resolvedtechniques our method can operate in conditions of much lower SNR still preserving highaccuracy in the whole velocity range, what is crucial in any quantitative measurements of

biomedical samples in vivo in OCT functional studies.

2. Theory

In Spectral OCT Fourier transformation (FT) of the spectral fringe signal measured by a

single exposure of a CCD camera creates one line of a structural cross-sectional image (A-

scan). In order to asses a velocity of a moving interface most of known methods require atleast two spectral fringes acquired in the same lateral position of a sampling light beam [8] or

almost the same lateral position [15]. The acquired set of spectral interferometric fringes can

be described as a function of wavenumber kand time t according to the following equation:




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( ) ( ) ( )( )

++=

l

lrlr

l

l ktzRRRRkItkI 2cos2, 0 , (1)

where ),( tkI is the spectral fringe signal, )(0 kI is spectral density of the light source, lR and

rR denote the reflectivity of the sample and reference mirror, respectively; ( )tzl denotes the

optical path difference between the reference mirror and the l -th interface in the sample,

which is time dependent due to the movement of the reference mirror and/or due to thedisplacement of the l -th interface in the sample. The displacement of the interfaces within

the sample is usually caused either by a movement of the entire sample itself or by a motion

of the specific interface lz within the sample. If we assume that both, reference mirror

velocity and velocities in the sample are constant during the acquisition of the spectral

fringes, Eq. (1), then the time-dependent position of the l -th interface )(tzl can be expressed

as:

( ) tvztzztz llll +=+= )( (2)

In this relation, lz is the depth position of the l -th interface at the beginning of data

acquisition and lv is the difference between the velocity of the reference mirror and an axial

component of velocity (parallel to the direction of the probing beam propagation) of the l -thinterface. If the l -th interface moves with velocity lV at an angle to the probing beam and

the velocity of the reference mirror is equal to rv this can be expressed as:

rll vVv = cos (3)

Here velocities directed towards a beam-splitter are regarded positive.

One can rewrite Eq. (1) making use of Eqs. (2) and (3).

( ) ( ) ( )( )

+++

=l

ktzl

zrRlRrR

l lRkItkI )(2cos2

0, (4)

( ) ( ) ( )

+++=

l

llrlr

l

l tkzRRRRkItkI 2cos2, 0 (5)

Although the above equations represent the same interference pattern, they emphasize its

different properties. Phase of the oscillatory component visible in Eq. (4) is a function of

wavenumber and its modulation frequency depends on static position lz of l -th interface

and small additional change of z , that occurs if the l -th interface is moving. Equation (5)

highlights the time-dependence of the interferometric fringes and shows that signal is

modulated in time with frequency l . This beat frequency is caused by a Doppler effect, that

arises for each l -th interface along the time axis. This frequency depends on the velocity lv

and is different for each wavenumber k:

kvll 2= (6)

The phase-resolved methods of velocity estimation enables extracting and using the phase of

the signal Eq. (4) while the joint Spectral and Time domain OCT uses the Fourier

transformation to analyze the time-dependent frequency of the signal Eq. (5).




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2.1 Velocity measurement using phase-resolved SOCT

The idea behind the phase-resolved OCT is to determine the phase difference between points

at the same depth in consecutive A-scans. Knowing the change of position z of l -th

interface, that arises during the time t between two consecutive measurements, the velocity

lv of the l -th interface can be calculated. Since z is much smaller than lz , the difference

between two consecutive measurements appears as a phase change of interferometricfringes:

=

=

ttkvl

42. (7)

Here is the phase difference between successively recorded depth profiles at the same

location of the probing beam. The time between successive profiles acquisition t is

approximately equal to the exposure time of the detector, therefore t1 is the frame rate of

an array detector (or equivalently A-scan rate). It is important to ensure that is less than

2 . Since the phase can be unambiguously determined in the range of 2 , and the phase

difference is within the range of 4 a procedure of phase wrapping has to be performed to

transform the phase differences to the range ),( [12, 13]. In the procedure adapted to

recovery of bidirectional flows the following algorithm is used: if 1 the minimum phase difference can be determined as21

min )(= SNR [15]. Vakoc, et al., suggest that retinal blood flow velocities


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constant speed. M measurements of spectral interferometric fringes are performed at the

same lateral location (Eq. 5). Collected spectral fringe signals undergo standard SOCT

preprocessing consisting of background removal and rescaling to wavenumber domain [24].

Then spectral fringes are plotted as rows, so the abscissa corresponds to wavenumber and the

ordinate to time ( tk plane,Fig. 1(a)). A Doppler frequency arising from a movement of l -th interface is visible as a frequency of the signal along the t-axis while the modulation

frequency along k-axis provides information on location of l -th interface. The two-dimensional set of spectral fringes is analyzed by Fourier transformations, that can be appliedin two separate ways. First FT can be performed horizontally thus it converts the STdOCT

data from wavenumber domain to the depth ( tz plane, Fig. 1(b)). The second FT acts

vertically and converts data from time domain to Doppler frequency, that corresponds to

velocity ( k plane, Fig. 1(c)).

Fig. 1. Joint Spectral and Time domain OCT analysis of a mirror moving withconstant velocity; individual images are linked via one- (1D) and two-dimensional(2D) Fourier forward and inverse transformations (FT and IFT, respectively). The

amplitudes of Fourier transforms are plotted in log scale on panels (b), (c) and (d);a. 2D interferogram consisting of 25 spectra recorded in time increments

s40=t ; b. structural image: reconstruction of the axial mirror position; c.

velocity image: Doppler shift for each k is retrieved; d. combined structural and

velocity image representing the Doppler shift distribution in depth; red rectangleindicates the resulting point that simultaneously localizes moving mirror and itsvelocity; e. single line from structural panel, maximum of the peak correspond to theaxial position of the mirror: 0.14mm; f. single line from velocity panel, maximum of

the peak correspond to the mirror velocity: 14.2 kHz, 0.95mm/s.




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Using both Fourier transforms, one after another, 2D spectral fringes are converted to

velocity distribution in depth ( z plane, Fig. 1(d)). Note that panels (b), (c), (d) display

only amplitudes of complex valued functions. The top-right panel (Fig. 1(b)) corresponds to

data processed in standard SOCT, where the structure of the object is reconstructed. Standard

SOCT uses the modules of Fourier transforms of data to create structural A-scans and the

phases to calculate the velocities with phase-resolved method. Here,M

registered spectraresult in M structural A-scans and only structural information is presented with no velocityinformation. Maximal optical path difference between the mirror in the reference arm and the

reflecting interface in the sample arm define imaging range in depth maxz . It is connected

with the sampling interval in wavenumber domain k of recorded spectra:

kz

=

2max

(10)

The variable z , that encodes the position of the sample is chosen to be positive if thesampling arm is longer then the reference arm, and negative in the opposite case. The image

of the objective mirror is visible as a single interface which apparently is fixed in time. This

image is doubled due to the fact that registered interferogram is a real-valued function [25]. In

STdOCT as well as in standard SOCT complex conjugation of the image is consideredunwanted, thus not displayed in resulting cross-sectional images. Therefore, in the practical

applications only positive depths are displayed.The bottom left panel (Fig. 1(c)) corresponds to the one-dimensional distribution of

velocity of moving object with no information about structure of the sample. To increase the

sampling density, zero-padding in time domain is applied. The velocity is recovered from the

Doppler frequency l , according to Eq. (6). For each known k the velocity can be calculated

separately. Therefore, this representation of data can be also used to find exact relationship

between wavenumbers and pixels in an array detector, and the same to calibrate the

spectrometer very accurately. In this particular case the velocity of moving mirror is

measured to be 14.25 kHz (0.95 mm/s) for k=7.5 106

m-1

, Fig. 1(f). The question of velocity

distribution within the object is trivial in the case of a mirror. If the object is more complex,

magnitude and direction of the movement will be known but there would be no informationabout the position of the moving interface. Similar to the phase-resolved OCT, the maximal

value of bidirectional flow velocity maxv is given by the time interval t between

consecutive measurements of the spectral fringes:

tkv

=

2max

(11)

and for us40=t it becomes mm/s2.5max =v .

The bottom right panel, Fig. 1(d) shows the result of two-dimensional Fourier

transformation of the set of M spectral fringes. Coordinates of displayed signals link

positions of all measured interfaces with corresponding velocities. Each interface zl is

represented by two symmetric points appearing with respect to the zero-path-delay and zero-

velocity. The interpretation of resulting points, shown in Fig.1(d), is following: the mirror

surface localized at um140=z (Fig. 1(e)) moves with the velocity of 14.2 kHz (Fig. 1(f)).

The sign of velocity value indicates forward or backward direction. The point localized at

( ,z )=(-0.14 mm, -14.2 kHz) is its complex conjugate.

The points are in fact fuzzystructures. This is due to the fact that their width along the z axisdepends on the axial resolution and the spread along the - axis is caused by the dependence

of the Doppler frequency on wavenumber, vk2= , Eq. (6). A velocity value for each z

position is calculated from Doppler frequency indicated by the point with maximal amplitude.




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2.3 Conditions of reliable velocity measurement for phase-resolved SOCT and joint Spectral

and Time domain OCT SNR analysis

In order to compare both methods we determine conditions under which each of them fails invelocity estimation. As phase-resolved SOCT operates on phases and STdOCT on signal

amplitudes, we have to analyze how decreasing SNR affects distributions of measured phases

and measured amplitudes.

Since every registered signal can be considered as a deterministic signal and a random noise,we assume that our interferometric fringe signal ),( tkI [Eq. (1)] is a sum of a harmonic

component S and a noise component X.

XStkI +),( (12)

The harmonic component can be expressed by a real-valued function with a given amplitude

kts , frequency kt and the initial phase set to be zero (random variable and its specific value

are denoted by capital and lowercase letter, respectively):

( )ksS zkt cos= . (13)

The noise component in turn, can be expressed as a sum of harmonic components with

random phases n (with uniform distribution) and random amplitudes n :

( )

=N

n

nnX cos , (14)

and its statistical properties can be described by a Gaussian function with a mean value 0=x

and a variance2

kt :

=2

2

2 2exp

2

1

ktkt

xX

. (15)

The distribution of amplitudes n is identical for all frequencies and has a mean value equal

to zero and a variance equal to 2 . The relation between and kt is following:

Nkt222

= . (16)

As SOCT measurements are performed in tk space (Fig. 1(a)), the phaseresolved method

operates in tz space (Fig. 1(b)) and STdOCT in z space (Fig. 1(d)), the amplitudes

kts , zts , zs are coupled via Fourier transformations. If the Fourier transformation is defined

to conserve power of the signal (E[I2] = E[Z

2],Z= FT(I)), the amplitudes are amplified with

respect to a number of points in Fourier transforms N, M :

zztkt sNM

sN

s 22

== , (17)

while the energy of the noise is preserved and equally distributed among the real and

imaginary part of the transform:

2222Im

2Re

2 222 += zztkt . (18)

In order to describe the relation between the signal amplitude and the distribution of the noise

with the same frequency we introduce a parameter :

kt

s= , (19)




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and we define SNR as a quantity that describes parameters of standard structural tomograms

( tz space):

ztzts

SNR

log20log20 == , (20)

and any further comparisons between joint STdOCT and phase-resolved SOCT are based on

above definition of SNR.

Table 1 presents relations between the amplitudes and the variances under condition thatFourier transformation is scaled to preserve signal energy. These results are similar to

analysis performed by Leitgeb, et al. [26]. Comparing the values of signal-to-noise parameter

after one- and two-dimensional Fourier transformation one can see that z (STdOCT) is

2/1M times higher comparing to zt (phase-resolved SOCT).

Table 1. Signal amplitude kts and the noise standard deviation after one- and two-

dimensional Fourier transformation;N, M number of points in the first and the second FT,

respectively.

g g=|FT1D(g)| g=|FT2D(g)|

kts ktzt sN

s 2

= ktz sMN

s 2

=

2

N=

2

N=

kts=

== ztzts

ztz

zM

s

1==

The distributions of phase and amplitude of signal G is based on the formalism presented

by Goodman to describe the phase and amplitude distribution of a sum of a constant known

phasor S and a random phasor X [27].

After Goodman, the probability density function for the phase is given by the following

expression:

( ) ( ) ,

otherwise0

cos2

sinexp

2

cos

2

2222


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Fig. 2. Phase distributions for various values ofzt parameter.

Quoting from Goodman, the probability density function of the amplitude A of the sum of a

constant phasor and a random phasor is given by a Rician density function:

( ) ,

otherwise0

02

exp202

22

2

>

+

=

aas

Isaa

ap (22)

Where )(0 I is a modified Bessel function of the first kind, zero order. As the length of the

known phasor s increases, the shape of density function )(apA changes from that of a

Rayleigh density to approximately a Gaussian density with mean equal to s .

Joint STdOCT uses the time dependent modulation of the signal, therefore it is successful,

when the amplitude of signal is higher than the maximal amplitude of noise component. This

occurs when the distributions of signal amplitude ( 0z , Eq. (21)) and noise ( 0=z ) are

separated. The minimal value ofz, which almost always meets this requirement is 7=z ,

Fig. 3.

Fig. 3. The probability density functions of amplitude for different value of

parameter z. Black and red curve correspond to the distributions of amplitude of

pure noise ( z=0) and amplitude of signal for critical value of (

z=7) that assurecorrect recovery of velocity in STdOCT.

When z converges to zero, the probability of detecting the correct position of signal

amplitude decrease. Every detection of noise causes indication of random velocity, therefore,




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the distribution of recovered velocity broaden and its mean value converges to the center of

the available velocity range (usually to zero).To determine critical values of SNR below which STdOCT and the phase-resolved

method give false readings, we performed computer simulations based on provided

theoretical model. In order to reconstruct the process of velocity estimation, multiple signals

( 30=M ) were generated with respect to the shape of spectrum and the probability density

function of amplitude (Eq. (22)) and phase (Eq. (21)). The magnitude of change in harmoniccomponent between consecutive signals was set to correspond to 0.35 maxv and 0.75 maxv .

Both methods operates on exactly the same amount of generated signals. The velocity was

recovered for different SNR and the results are shown in Fig. 4.

Fig. 4. Computer simulations of velocity estimations obtained with STdOCT and

phase-resolved SOCT for two different velocities (0.35vmax and 0.75 vmax solid

and dashed curve, respectively) under the conditions of decreasing SNR.

Both methods fail for certain SNR, however STdOCT is more robust under low SNR. Thefailure appears as an underestimate of retrieved velocity values. In joint STdOCT the critical

SNR above which recovered velocity is reliable does not depend on the magnitude of the set

velocity, whereas phase-resolved SOCT fails earlier for higher velocity.

To explain this effect we analyzed the velocity recovery process in the phase-resolvedmethod within the entire theoretical range. Four different velocities: 0.05, 0.35, 0.75 and 0.95

of vmax were chosen and the velocity estimation for each of them was performed. The

dependence of velocity reading on proximity to the theoretical limits of velocity are shown inFig. 5(a). One can see that there is no significant difference in critical values of SNR for

velocities


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Fig. 5. Computer simulations of velocity recovery using phase-resolved method. a.

Retrieved velocity values versus SNR for different assumed values of velocity. b.Retrieved velocity versus assumed values vreal and corresponding phase difference

distributions for v=0.73vmax.

Basing on performed analysis we can determine the conditions under which joint

STdOCT and phase-resolved SOCT fail in velocity measurement. For the phase-resolved

method the critical SNR, that guarantees reliable velocity detection in whole velocity range is

estimated to be >30 dB (Fig. 5), whereas the corresponding value for STdOCT is >6 dB

(Fig. 4). Additionally, since signal amplitude zA used in joint STdOCT to retrieve velocity

value depends on number of spectra registered in time (M ), the critical SNR can be

improved 2/1M times with increasing number of measurements (Table 1.). In phase-resolvedSOCT increasing number of spectra does not improve measurement sensitivity, however it

facilitates detection of mean value of phase difference distribution.

Performed simulations do not take into consideration the washout of interference fringes

[17]. This phenomenon deteriorate SNR, hence in this way it affects velocity recovery.

Because both methods suffer from the blurring of interference fringes in the same degree, the

conducted comparison is still valid.

3. Experiment

We use laboratory high resolution Spectral OCT system comprising a broadband light source

(Broadlighter, Superlum, nm90= , central wavelength 840 nm), a fiber Michelson

interferometer with fixed reference mirror and custom designed spectrometer with a volume

phase holographic grating DG (1200 grooves/mm) and an achromatic lens focusing spectrum

on 12-bit CCD line-scan camera (Aviiva M2, Atmel), Fig. 6. The experiments were performedfor three different objects: moving mirror, capillary flow and blood flow in human retina. In

measurements of the velocity of moving mirror, a silver mirror was attached to a piezo-

actuator (Physik Instrumente) and it was driven by a triangular voltage signal. The exact

velocity was calculated at the moment of a linear slope of the driving signal from trajectoryregistered by the position sensor mounted inside the actuator. Measurements were performed

with A-scan rate of 40.4 s.To investigate flows in scattering media, we used a water solution of Intralipid flowing

through capillaries. Two 700 m thick glass capillaries with flow in opposite directions weremounted at the angle of 88 deg to the direction of the probing beam (z -axis) and stable,

laminar flow was ensured by a medical drip system. The sets of 40 spectra were collected at

the same transversal position of the light beam. The acquisition time was set to 52 s

including 10 s dead time needed for stabilization of the position of galvo scanner driven by

the stepwise signal. The optical power of the light illuminating the sample was 3.3 mW.




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Fig. 6. Experimental Spectral OCT system : OI optical isolator, FC fiber coupler, PC

polarization controller, DC dispersion compensator, NDF neutral density filter, Xgalvo-scanner, L1 lens, DG volume phase holographic grating, CCD line-scan

camera. Three different objects are measured: moving mirror, capillary flow, bloodflow in human retina.

For all retinal blood flow examination the optical power of light illuminating the cornea

was set to 750 W. In the case of regular exposure time (40 s) the velocity recovery is basedon 20 spectra, each recorded with 43 s of repetition time. In measurements with short

exposure time (5 s and 1 s) 40 spectra were collected for each lateral position of the

scanning beam. Despite such a short exposure times, the repetition time was >41 s due to the

dead time of 40 s between consecutive measurements.The velocity estimations in phase-resolved SOCT and joint STdOCT are always based on

exactly the same registered data in all comparative experiments. This guarantees that thedifferences in velocity recovery are solely caused by the methods themselves, not by

experimental environment or different amount of processed data.

4. Results and discussion

4.1 Moving mirror

In order to validate provided theoretical analyses we performed an experiment with a moving

mirror as an object. To investigate the relation between the velocity estimation and SNR, thelight intensity in objective arm had been reduced by a neutral density filter from 20 dB to -

6 dB (from =10 to =0.5) for two velocities 1.9 mm/s and 3.9 mm/s corresponding to 0.35

and 0.95 of vmax. The sets of 30 spectra were collected and then processed to obtain phase-

resolved and STdOCT velocity estimations. Figures7(a), 7(b) presents achieved velocity

values, which are displayed together with theoretical results demonstrated in Fig. 4.

In the next step we verified the capability of measuring velocities close to the upper limit.The objective mirror was driven with different velocities within the whole theoretical range.

The intensity of the light in objective arm was constant and resulted in SNR=17.5 dB in

structural tomogram. A single velocity value was calculated from 18 spectra. Retrieved values

of velocities were marked in Fig. 7(c) together with theoretical prediction.




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Fig. 7. Experimental and theoretical comparison of velocity estimations obtainedwith STdOCT and phase-resolved SOCT a, b. velocity readings for fixed velocities

equal to 0,75 vmax and 0.35 vmax, respectively, under the conditions of decreasingSNR; c. velocity readings in whole theoretical velocity range for fixed

SNR=17.5 dB.

The experimental results are in good agreement with the theoretical model. Althoughtheoretical ranges for both methods are identical, the phase-resolved SOCT fails earlier than

STdOCT and its correctness depends on the magnitude of measured velocity. STdOCT is able

to detect a velocity for SNR ~30 dB lower than the phase-resolved method. This leads toconclusion that useful velocity range in phase-resolved SOCT is significantly narrower than

in STdOCT.

4.2 Capillary flow

Two experiments were designed, one to verify the method of STdOCT in case of bidirectional

flow in scattering media and the other to compare with phase-resolved SOCT. Figure8

presents STdOCT images achieved as individual steps during velocity recovery (section 2.2).

Fig. 8. Bidirectional flow of Intralipid: a. 2D structural tomogram; arrow indicatesthe direction of incident light b. 2D velocity map, c. Doppler shift distribution in

depth calculated from the single set of 40 spectra corresponding to the green verticalline on panel (b). d. distribution of maximal intensity signals retrieved from panel

(c); e. plot of the transverse distribution of velocity corresponding to the greenhorizontal line on panel (b).

The structural tomogram of the capillaries and the velocity map that indicates bidirectional

flow are shown in Figs. 8(a), 8(b). Single lines in structural and velocity image are obtainedfrom a set of 40 A-scans. As a first step in velocity recovery, the procedure of zero-padding to

128 points in time space was applied. The signal underwent 2D Fourier transformation and

formed the Doppler shift distribution in depth as shown in Fig . 8(c). The positions of maximal

intensities for each depth z were detected and points that most likely correspond to noise( 2z ) were removed by thresholding procedure, Fig. 8(d). Images (c) and (d) correspond




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to a single line in 2D velocity map (Fig. 8(b)), on which the values of velocity are encoded

using false colors. Figure8(e) presents a single 1D velocity distribution along the transversal

direction indicated by green horizontal line on the velocity map. All presented velocity

distributions have parabolic shapes, what implies that measured flow is laminar.

To compare the STdOCT and phase-resolved flow velocity estimation in scattering media,the flow measurements for different concentrations of Intralipid solution and different flow

rates were performed. Concentration of scattering medium affects signal intensity and its

change yields different characteristics of SNR decrease in depth. The acquisition parameters

of OCT data were unchanged. To take full advantage from recording multiple spectra, we

averaged all single A-scans and they were displayed as a single line in structural tomograms.

The results of both methods of flow estimation are presented in Fig. 9. The experiment was

performed under three different flow conditions. In the first case, Fig. 9(a), the concentrationof the Intralipid solution was chosen in such a way that the SNR changes significantlybetween front and back side of the capillary. The flow velocity was set to approximately 0.75

of maximal velocity. Both methods return a parabolic distribution of flow velocity, however

phase-resolved method exhibits a slight asymmetry, which increases with depth. Then the

Intralipid concentration was changed to maximize SNR at the back side of capillary and the

flow velocity was increased to exceed vmax. (Fig. 9(b)) We can observe that both methodsgive similar readings to approximately half of the velocity range. For higher velocities phase-

resolved method dramatically underestimates the velocity values, and for vmax returns zero. In

STdOCT velocities beyond the range are wrapped and found as negative values. Thedistortions of velocity distributions in phase-resolved method appear when SNR decreases orwhen velocities are too high (however still in the theoretically achievable range).

Fig. 9. Velocity measurements of Intralipid flow in capillaries for different flowrates and concentration of the scattering medium. Each panel consists of 4 images: i.

structural tomogram of the inside of capillary; arrow indicates the direction of lightand green line marks the position of 1D velocity distributions presented on the last

image in the row, ii., iii. velocity maps reconstructed by phase-resolved SOCT and

STdOCT, respectively, iv. comparison of 1D velocity distributions retrieved fromboth velocity maps: green phase-resolved, red - STdOCT; arrow indicates thedirection of light; a. high concentration of Intralipid, flow velocity set to be 0.75

vmax, b. lower concentration of Intralipid, flow velocity slightly higher than vmax, c.high concentration of Intralipid and flow velocity reaches the upper limit, vmax.




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The result of velocity estimation in conditions when both effects occur is shown in Fig. 9(c).

It is evident that for the illuminated side of the capillary, the SNR is sufficient to return

accurate velocity values for both methods. With decreasing SNR and increasing velocity

phase-resolved method starts failing, while STdOCT remains unaffected. These results are in

a good agreement with theoretical predictions and with experiments performed with movingmirror as an object.

4.3 Retinal blood flow, in vivo

As a final test of joint STdOCT and phase-resolved SOCT capabilities in velocity estimations,

the measurement of blood flow in human retina in vivo was performed. Figure10(a)

demonstrates cross-sectional image of human retina scanned through the region of optic disc.

Figures 10(b) and 10(c) show two-dimensional maps of the flow velocity distributionobtained with SOCT and STdOCT, respectively.

Fig. 10. Measurement of blood flow velocity in human retina in the region of optic

disc; a. cross-sectional image of the retina performed in close proximity to opticdisc, b., c. velocity maps based on phase-resolved SOCT and STdOCT methods

respectively.

The velocity distributions inside the vessel indicated by green lines in Fig . 10 are

presented in Fig. 11. Although blood flow in large vessels is evident in both methods, the

quantitative velocity estimations differ significantly. The magnitude of the blood velocity in

the center of the vessel is 1mm/s for the phase-resolved method and 4mm/s for STdOCT. The

recovered shapes of velocity distribution also differ greatly. In the phase-resolved method we

observe distortion in the center of the vessel, what may cause a misinterpretation of nature of

flow.

Fig. 11. Comparison of two velocity estimations: green points indicate phase-resolved SOCT and the red one STdOCT. Diagrams are based on information

extracted from data presented in Fig. 10 (green lines).

The underestimate in phase-resolved SOCT arises from getting out of the useful velocityrange. Beyond the useful range, velocity estimators became progressively underestimated

with decreasing signal and finally decayed to zero. The useful range in STdOCT is wider, but

of course also limited. Another difference is that in STdOCT decreasing signal does not

influence the accuracy of velocity estimation but only the probability of its detection. It gives

confidence that if signal is distinguished from noise and measured velocity does not exceed




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the upper limit, measured velocity is correct. This feature is especially valuable in biomedical

imaging, where diagnoses are based on measured functional parameters.

4.4 Retinal blood flow imaging with ultra-short CCD exposure time

Joint STdOCT comparing to phase-resolved SOCT requires more data to be collected to

estimate velocity value. This experiment is performed to give the proof of concept of time

effective STdOCT. To compensate longer scanning protocols shorter CCD exposure time is

proposed. We assume that higher sensitivity offered by this technique enables measuring the

velocity without any time extension comparing to regular imaging. The capability of

STdOCT to estimate the flow velocity in human retina with extremely short CCD exposure

time of 5 and1 s is presented in Fig. 12.

Fig. 12. Velocity estimation of retinal blood flow with extremely short CCD

exposure time: 5 s and 1 s for top and bottom line, respectively; ellipses markblood vessels a., d. cross-sectional images of human retina in the area of optic disc;maps of the velocity distribution: b., e. Phase-resolved SOCT method, c., f. Joint

STdOCT method.

The maps in the top line (5 s) present spatial distribution of the blood flow velocities only inthe larger vessels. The velocity underestimation in the phase-resolved method results in

vanishing of the middle-size vessels in the flow image. STdOCT results obtained for 1 sexposure time enable reconstructing one large and three smaller vessels. The map based onthe phase-resolved method shows only faded velocity image of the large vessel.

Unfortunately, the present state-of-the-art of CCD technique does not allow taking fulladvantage of extremely short exposure time because the relatively long dead time of the CCD

camera limits the duty ratio to 0.025. In general in OCT studies, there is a pressing need to

collect more data in examination time acceptable for patients. However, in many cases optical

power delivered to the object has to be limited either by the safety regulations or by the power

limitations of the light sources and/or optical components. Recent developments in CCD and

CMOS technologies probably will be soon completed with ultra-fast line scan cameras. This

experiment shows that, in contrast to the phase-resolved method STdOCT is able to benefitfrom these improvements. Phase-resolved SOCT requires higher SNR than it is possible to




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achieve with ultra-short exposure time in CCD technique, whereas STdOCT can still operate

reliably in these conditions.

5. Conclusions

We demonstrate the potential of Joint Spectral and Time domain OCT to estimate flow

velocities accurately. In this approach, SOCT measurements are repeated in one position of

scanning beam to register interferogram, that simultaneously depends on optical frequencies

and time. Intensity modulation along axis of optical frequencies encodes information about

structure and the modulation along time axis contains information on velocity.

We analyze known phase-resolved SOCT method under low SNR conditions. It appears that

retrieved velocities are dramatically underestimated and have tendency to decay to zero. This

strong dependence on SNR is especially adverse in the case of measurements of highlyscattering media, where the contribution of noise increases with depth. This may lead to

considerable corruption of the velocity profile for points located deeper. Another cause of

distortion may occur if the velocity is close to the maximal limit of velocity measurable by

the phase-resolved method. Since velocity estimation in STdOCT is based on Doppler shifts,

it is significantly less vulnerable to both effects and is more reliable for any qualitative and

quantitative analysis as it is demonstrated using the same sets of OCT data. The possibility to

unequivocal assessment of blood circulation in human retina renders STdOCT especially

valuable.

Additionally, STdOCT is more sensitive and it is able to detect a correct value of velocityfor SNR lower at ~30 dB than the phase-resolved method. This unique feature can be used to

compensate longer scanning procedure by shortening CCD exposure time. The proof of

concept of time effective STdOCT is ascertained by presented measurements of blood flow in

human retina in vivo for 5 s and 1 s exposure time.

Acknowledgments

This work was supported by EURYI grant/award funded by the European Heads of ResearchCouncils (EuroHORCs) and the European Science Foundation (ESF). Maciej Wojtkowski

acknowledges additional support of Foundation for Polish Science (Homing project and

EURYI) and Rector of NCU for the scientific grant 504-F. Maciej Szkulmowski

acknowledges support of Polish Ministry of Science, grants for years 2005/2008. Anna

Szkulmowska acknowledges support of Polish Science Foundation FNP2008 scholarship for

young researchers.



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020-2008 Optics Express Szkulmowski