December 15, 2008 / Vol. 33, No. 24 / OPTICS LETTERS 2967

Bidirectional Doppler Fourier-domain opticalcoherence tomography for measurement of absolute

flow velocities in human retinal vessels

René M. Werkmeister,1 Nikolaus Dragostinoff,1 Michael Pircher,1 Erich Götzinger,1

Christoph K. Hitzenberger,1 Rainer A. Leitgeb,1 and Leopold Schmetterer1,2,*1Center for Biomedical Engineering and Physics, Medical University of Vienna, Waehringer Strasse 13,

A-1090 Vienna, Austria2Department of Clinical Pharmacology, Medical University of Vienna, Waehringer Guertel 19-20,

A-1090 Vienna, Austria*Corresponding author: leopold.schmetterer@meduniwien.ac.at

Received August 26, 2008; revised October 31, 2008; accepted November 2, 2008;posted November 10, 2008 (Doc. ID 100660); published December 8, 2008

We describe a bidirectional color Doppler Fourier-domain optical coherence tomography system capable ofmeasuring absolute velocities of moving scatterers by illuminating the sample with two linearly and or-thogonally polarized beams, incident at a known angle on the sample. The velocity calculation is indepen-dent of the exact orientation of the velocity vector in the detection plane. First measurements were per-formed on a rotating disk driven at well-defined velocities and tilted by various small angles. Our resultsindicate a high correlation between preset and calculated velocities (correlation coefficient 0.999) and theindependency of these velocities from the tilting angle of the disk. We demonstrate that bidirectional colorDoppler optical coherence tomography allows for the measurement of absolute blood flow values in vivo inhuman retinal vessels. © 2008 Optical Society of America

OCIS codes: 170.3880, 170.4500.

Ocular perfusion abnormalities have been implicatedin a number of sight-threatening diseases includingprimary open angle glaucoma, age-related maculardegeneration, and diabetic retinopathy [1–3]. LaserDoppler velocimetry (LDV) is a technique capable ofmeasuring blood velocities in retinal arteries andveins [4,5]. Combining these measurements withfundus-camera-based measurements of retinal vesseldiameters allows for the calculation of total retinalblood flow [6,7]. Several approaches have been pro-posed to gain depth resolution in LDV by using shortcoherent light. These include variation of the sourcecoherence length [8], use of time-domain optical co-herence tomography (OCT) [9,10], and use of Fourier-domain (FD) OCT (FDOCT) [11–13]. Employing thistechnique in vivo does, however, not allow one tomeasure absolute blood velocities, because the anglebetween the incident laser beam and the movingerythrocytes is unknown. In conventional LDV thisproblem can be overcome by using different anglesfor detection or illumination. Illuminating the eyewith one laser beam and detecting in two distinct di-rections the absolute center line velocity within theretinal vessel �Vmax� is proportional to ��f /��. In thisequation � is the wavelength; �f= f1− f2 is the differ-ence of the Doppler frequency shifts at the two direc-tions, respectively; and ��� is the extraocular anglebetween the two directions of light detection [6]. Withthis technique Vmax can be determined in absoluteunits independently of the direction at which thebeam impinges on the red blood cells. Within DopplerOCT technology several attempts have been made toovercome the problem of the unknown orientation ofthe velocity vector. Davé and Milner illuminated theprobe with two orthogonally polarized beams [14],

while Pederson and co-workers used a glass plate to

0146-9592/08/242967-3/$15.00 ©

introduce different path delays and Doppler angles[15]. Recently Iftimia et al. introduced a dual-beamFD optical Doppler tomography system for applica-tion in the zebrafish heart. This approach includedtwo separate reference arms for each of the illumi-nating beams [16].

In this Letter a bidirectional FDOCT system allow-ing for the measurement of absolute velocities inde-pendent of the Doppler angle � between the incidentlight and the flow velocity vector is presented usingone reference arm only [see Fig. 1(a) for measure-ment geometry]. For this purpose the sample is illu-minated by two beams. The angle �� between thesetwo beams is in vitro determined by the focal lengthof the objective lens, whereas at the ocular fundus it

Fig. 1. (a) Experimental setup: SLD, super luminescentdiode; PC, polarization controller; FC, fiber couplers; M,mirror; L1 and L2, relay lenses; BD, beam displacer; ND,neutral density filter; BS, beam splitter cube; PBS, polariz-ing beam splitter cube; DG, diffraction grating; CL, camera

lens. (b) Geometry of bidirectional velocity measurement.

2008 Optical Society of America

2968 OPTICS LETTERS / Vol. 33, No. 24 / December 15, 2008

is defined by the refraction power of the eye. For ve-locity measurements one needs to calculate the phasedifference � at the same point between two adjacentA lines after Fourier transform. In the two directionsthe phase differences are given by

�1 = 2K� 1v��, �2 = 2K� 2v��, �1�

where K� 1 and K� 2 are the wave vectors of the incidentlaser beams; v� is the velocity vector of the moving ob-ject; and � is the time span between two subsequentrecordings, equaling the illumination time. Followingthe trigonometric derivation of Riva et al. [6], the dif-ference between �1 and �2 can then easily be calcu-lated as

�� = �1 − �2 =4�nv��� cos �

�, �2�

where n is the refractive index of the medium, v isthe absolute velocity, and � is the angle between v�and the plane spanned by K� 1 and K� 2. Accordingly, vcan be calculated independently of the angle of inci-dence as long as this angle is close to � /2.

A schematic of the bidirectional Doppler FDOCTsystem is shown in Fig. 1(b). The light source is asuperluminescent diode (Superlum, Russia, SLD-37-HP1) with �=839 nm and a FWHM of 54 nm corre-sponding to a coherence length of 5.75 �m in air. Acalcite beam displacer (Thorlabs BD27) splits the lin-early polarized light into its two orthogonal compo-nents and displaces them parallel by 2.7 mm. In thesample arm the light passes the X–Y galvo scanningstage and illuminates the eye via lenses L1 and L2.For in vitro measurements L2 was removed, andlight was directly focused onto the probe. It is as-sumed that the incident and scattered wave vectorsare collinear. In the detection unit at the exit of theMichelson interferometer the two polarization statesare separated by a polarizing beam splitter andguided into two identical spectrometers, consisting ofa holographic diffraction grating (Wasatch Photonics,

Fig. 2. (Color online) (a) Estimation of disk velocity usingslope. (b) Estimated velocity for three different disk velocitie

velocities).

1200 lines/mm), an achromatic lens �f=200 mm�,and a 2048 element line scan CCD camera (AtmelAVIIVA M2 CL2014) with a pixel size of 1414 �m.This configuration allows for a maximum probingdepth range of 3.1 mm. The same spectrometer setupis necessary to obtain the phase information from thesame depth position for both polarization states, re-ferred to as ch0 and ch1. The system is operated atan A-scan rate of 18,000 lines/s. Using an integra-tion time of 50 �s and a power of 700 �W on thesample the sensitivity of the system close to the zerodelay is 92 dB (equal for both polarization channels).The sensitivity decay due to the finite spectrometerresolution is 8 dB to a depth of 1 mm and 14 dB to adepth of 2.8 mm. The maximum detectable velocityin vivo obtained from Eq. (2) is 56 mm/s (��=2� un-der the condition �=0). The phase noise is measuredto be 0.04 rad for each channel; thus the minimumdetectable absolute velocity is �0.54 mm/s.

Experiments to evaluate the precision of bidirec-tional velocity measurements were performed usingpaper glued on a rotating plastic disk. The disk wasmounted on a rotation stage and oriented in an angleof � /2 with respect to the optical axis of the system.With the chosen objective lens �� was 3.2°. To keepthe velocity vector within the K� 1K� 2 plane the incidentbeams were focused on a point vertical below the ro-tation axis of the disk, i.e., angle � was equal to zero.First the linearity between preset disk velocities andthe velocity extracted from Eq. (2) was examined.Measurements were performed at 23 different veloci-ties in a range from 0.6 to 37 mm/s. 40 A-scans atthe same point were recorded and averaged. The re-sults are plotted in Fig. 2. The velocities measured bythe phase difference in the two detection arms are invery good agreement with the preset velocities andshow a highly linear correlation. The correlation co-efficient for the data set was calculated to be 0.9999.

In a next step we examined the influence of theangle of incidence on the measured phase difference�� between both channels by tilting the disk in steps

ual-beam technique. Solid line, line fit. Dashed line, unityd incident angle between −5° and +5° (dashed lines, preset

the ds an

December 15, 2008 / Vol. 33, No. 24 / OPTICS LETTERS 2969

of 1°. The tilting axis was set into the focal point ofthe incident beams and orthogonal to the planespanned by both beams. Figure 2 shows the velocitiescalculated with Eq. (2) for three different preset ve-locities. For small angles the velocity determined byour method is independent of the orientation of thevelocity vector. The spreading of the measured datais due to the stochastic nature of Doppler signalsfrom strongly scattering media, where the detectedlight is the sum of scattering events from randomlydistributed scatterers [17]. Additional in vitro experi-ments with birefringent media inserted into thesample arm have shown that the error in the mea-sured velocity caused by the cross talk between thetwo channels induced by birefringence of the corneaand retinal nerve fiber layer are of the order of thevelocity resolution of the system and can therefore beneglected. This is due to the geometric separation ofthe two beams.

The capability of measuring absolute flow veloci-ties in vivo was demonstrated by imaging the in-traocular flow in retinal vessels of healthy humanvolunteers. In these measurements the flow directionwas parallel to the detection plane. Figures 3(a) and3(b) show the phase tomograms for the two polariza-tion channels ch0 and ch1. The different angle of in-cidence of the two probe beams leads to contraryphase shifts for the same vessel in the channels ch0

Fig. 3. (Color online) Phase tomograms of human retina invivo, (a) ch0 and (b) ch1. Average data of five vessel centerprofiles of the (c) left and the (d) right vessels and calcu-lated velocities for (e), (f) both vessels. Dashed curves, par-able fit.

and ch1, as can be seen clearly in the tomograms. InFigs. 3(c) and 3(d) average vessel center profiles offive frames at a frame rate of 18 frames/s are plotted.Estimated phase shifts �� between ch0 and ch1 are−2.52 rad for the left vessel [Fig. 3(c)] and 3.43 radfor the right vessel [Fig. 3(d)]. Calculations from Eq.(2) yield maximum flow velocities of 2.2 and 3.1 cm/s,respectively. Owing to the measured velocities,the vessel diameters and the pulsatile behavior thatcould be observed in a time sequence of thetomograms the right vessel is an artery, while the leftone is a vein. Our values are in the same range asthose measured in retinal arteries and veins by Rivaet al. [5].

In conclusion, we have presented a new method forbidirectional FDOCT capable of measuring absolutevelocities of moving scatterers. Previously presentedsystems require exact knowledge of the orientation ofthe velocity vector. By contrast our method is inde-pendent of the direction of this vector in the detectionplane, when the angle of the incident light is close to� /2, which is fulfilled in measurements on vessels atthe posterior pole of the eye.

We acknowledge financial support from the Aus-trian Science Foundation (Fonds zur Förderung derWissenschaftlichen Forschung), grant 15970P.

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