Photoacoustic Doppler Effect from Flowing Small Light-Absorbing Particles
Hui Fang, Konstantin Maslov, and Lihong V. Wang*
Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University in St. Louis,
One Brookings Dr., St. Louis, Missouri 63130, USA
(Received 22 July 2007; published 29 October 2007)
From the flow of a suspension of micrometer-scale carbon particles, the photoacoustic Doppler shift is
observed. As predicted theoretically, the observed Doppler shift equals half of that in Doppler ultrasound
and does not depend on the direction of laser illumination. This new physical phenomenon provides a
basis for developing photoacoustic Doppler flowmetry, which can potentially be used for detecting fluid
flow in optically scattering media and especially low-speed blood flow of relatively deep microcirculation
in biological tissue.
DOI: 10.1103/PhysRevLett.99.184501 PACS numbers: 47.80.Cb, 47.35.Rs, 47.55.Kf, 87.80.?y
Laser flowmetry and acoustic flowmetry based on the
Doppler effect  have become valuable tools for fluid
coherence optical Doppler tomography  was developed.
They all require the presence of small scattering tracer
particles to provide detectable backscattering signals. In
measurement of tissue blood flow [4,5], red blood cells
work as endogenous scattering tracer particles.
In this Letter, however, we describe the observation of a
new physical phenomenon—the photoacoustic Doppler
(PAD) effect from moving particles—and its application
for flow measurement. Here, small light-absorbing parti-
cles  are used as tracer particles. The term ‘‘photo-
acoustics’’  (or the equivalent ‘‘optoacoustics’’ )
usually refers to the generation of acoustic waves by
modulated or pulsed optical radiation, an effect discovered
by A.G. Bell in 1880. The PAD effect thus deals with the
Doppler frequency shift of the generated acoustic waves.
Previously, the PAD effect due to moving light excitation
was discussed in the research of a moving thermoacoustic
array [9,10]. In those studies, no flow in the medium was
involved. Instead, a laser beam was scanned over an ab-
sorbing liquid. As a result, the Doppler shift was found to
depend on the laser scanning speed.
Comparedto the aforementioned
scattering-based Doppler flowmetry, PAD-based flowme-
try should have much lower background noise. If there are
no other absorbers besides the tracer particles inside the
measured volume, the PAD signal should only come from
the tracer particles. PAD flowmetry can potentially quan-
tify tissue blood flownoninvasively because red blood cells
are dominant endogenous light-absorbing tracer particles
that can absorb light 100 times more than the background
. In contrast, the scattering-based Doppler signal usu-
ally suffers from overwhelming background reflection
from the flow’s surrounding medium [12–14].
Let us first consider theoretically the PAD shift from a
flowing light-absorbing particle. The particle is suspended
in a liquid and flows with the liquid along velocity vector V
(Fig. 1). When the particle is illuminated by an amplitude-
modulated continuous-wave laser beam, an acoustic wave
is generated due to the photoacoustic effect, and the acous-
tic wave can be detected by an ultrasonic transducer. If the
laser beam is modulated at frequency fOwith 100%
modulation depth, its intensity I as a function of time t
can be express as
I ? I0?1 ? cos?2?fOt??=2;
where I0denotes the peak intensity. Such a laser beam can
be treated as a photon density wave with frequency fO. If
the particle is not in motion, the photoacoustic wave has
the same frequency as fO[15,16]. Otherwise, the photo-
acoustic wave is subject to a Doppler shift.
Because photoacoustic pressure amplitude is propor-
tional to the absorbed optical power density, the Doppler
shift depends on the frequency of the intensity fOinstead
of the frequency of the field. The Doppler shift should also
depend on the flow velocity V and the flow direction angles
? and ? as illustrated in Fig. 1, where K
the wave vectors of the photon density and acoustic waves,
respectively. If V is much less than the sound speed, the
Doppler shift can be expressed as ?fO
cos?, where cOand cAdenote the speeds of light and
cOcos? ? fO
FIG. 1 (color online).
shift. The small light-absorbing particle moving along velocity
vector is illuminated by modulated continuous-wave light.
Schematic for photoacoustic Doppler
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© 2007 The American Physical Society
sound, respectively, in the medium. In this expression, the
first term represents the shift in the frequency of the photon
density wave ‘‘seen’’ by the particle as a moving receiver;
the second term represents the shift in the frequency of the
photoacoustic wave ‘‘observed’’ by the ultrasonic trans-
ducer, where the particle works as a moving source.
Because cO=cA? 105and V ? cA, usually only the sec-
ond term is detectable. Therefore, we have
This shift equals half of the shift in pulse-echo Doppler
ultrasound and doesnot depend on the direction ofthe laser
illumination. Unlike the laser Doppler effect, the PAD
effect deals with a photon density wave instead of an
optical wave, and the photon density wave has a much
longer wavelength than the acoustic wave. Therefore, the
Doppler shift of the illumination laser is negligible.
The experimental setup (Fig. 2) we used is based on
continuous-wave (cw) photoacoustic microscopy [17,18].
Briefly, a cw diode laser (center wavelength: 784 nm;
average power: 120 mW) was amplitude-modulated by a
function generator (‘‘function generator 1’’) with 100%
modulation depth at frequency fO? 2:4550 MHz. The
laser beam was focused onto the flow sample with a spot
of ?1:0 mm in diameter. A narrow band piezoelectric
transducer (center frequency: 2.4550 MHz; numerical ap-
erture NA: 0.85) was aligned to be confocal with the laser
focal spot. The acoustic signal detected by the transducer
was amplified by a narrowband preamplifier and relayed to
the ‘‘signal’’ input of a lock-in detector. Another function
generator (‘‘function generator 2’’) was synchronized with
‘‘function generator 1’’ to provide a ‘‘reference’’ input for
the lock-in detector with frequency fRef? fO. The lock-in
detector uses phase sensitive detection to produce a pair of
quadrature-demodulated outputs ‘‘X’’ and ‘‘Y,’’ where
‘‘X’’ is the low-pass filtered product of the signal and the
reference, and ‘‘Y’’ is the low-pass filtered product of the
signal and the ?90?phase shifted reference. The band-
width of the low-pass filter is determined by the time
constant and was chosen to be 102 Hz in the experiment
(the time constant was set as 1 ms). The lock-in detector
worked at the maximum sampling rate of 512 Hz with a
total sampling points of 15360 (the maximum is 16800).
The digitized ‘‘X’’ and ‘‘Y’’ were then transferred to the
computer and analyzed spectrally. The frequency differ-
ence between the signal and the reference is the Doppler
shift of the signal.
As shown in Fig. 2, the fluid flow was generated by a
syringe pump (BSP-99M,Braintree Scientific) with a 10 cc
syringe (Multifit, Becton, Dickinson & Co.) and a Tygon@
tube (inside diameter: 0.51 mm; outside diameter:
1.53 mm; S-54-HL, Saint-Gobain Performance Plastics).
The tube was formed into a circle and mechanically fixed
inside a water tank. A vertical segment of the circle was
measured at a downstream distance of ?50 cm from the
flow entry connected to the syringe. Through the syringe
pump, the volume flow rate, Q, could be manually set from
0:04 to 39:6 cc=hr with steps of 0:04 cc=hr.
The flow sample was a particle suspension with volume
fraction ? ? 15%,where the particle diameters distributed
from 2 to 12 micrometers (carbon glassy spherical powder,
484164, Sigma-Aldrich). The solution for suspending the
particles was made by dissolving an appropriate amount of
solid sodium polytungstate (Sometu) into distilled water so
that its mass density became about 1:46 g=cm3, which
matched that of the particles. Also, 1% volume of
Tween-20 (Sigma-Aldrich) was added into the solution to
reduce particle aggregation. The absorption coefficient of
the suspension was estimated to be about 1:0 mm?1by a
transmission measurement using the same diode laser.
We first took a set of measurements to study the depen-
dence of the PAD shift on the flow speed. The flow direc-
tion was set toward the transducer. Figure 3 plots the shifts
versus the average flow velocity?VS, which was calculated
by dividing Q by the cross sectional area of the tube. The
square symbols indicate the mean Doppler shifts, and the
error bars indicate the standard deviations, both calculated
from the measured Doppler power spectra. As an example,
the power spectrum for ?VS? 4:4 mm=s is plotted as an
inset in Fig. 3. For comparison with the theory, the mean
shift is predicted from Eq. (2), i.e., fO
where cA? 1500 m=s, and 0?and 60?represent the de-
tection angular range of the ultrasonic transducer due to its
numerical aperture. As can be seen, the measured mean
Doppler shifts agree well with the theoretical predictions,
whereas each standard deviation is about half of the asso-
ciated mean shift. We repeated the same set of measure-
FIG. 2 (color online).
continuous-wave photoacoustic Doppler flow measurement.
Diagram of the experimental setup for
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2 NOVEMBER 2007
ments 10 times, and the results were consistent with those
shown in Fig. 3.
The observed standard deviations were modeled by tak-
ing into account the flow velocity profile, the flow angular
distribution, and the transit time of each particle through
the detection volume . It was found that a parabolic
velocity profile led to standard deviations greater than the
mean shifts, whereas a fully blunted velocity profile (i.e.,
zero at the tube boundary andconstant elsewhere) provided
better agreement with the experimental observation. This
finding suggested that the actual flow was blunted.
Previous studies dealing with a similar type of flow also
demonstrated that the velocity profile deviated from parab-
ola and blunted to a shape that depended on parameters
such as the particle volume concentration, particle size,
flow channel size, flow speed, and downstream distance
As also shown in Fig. 3, the measurable?VSwas in the
range of 0:055–8:8 mm=s. The maximum measurable?VS
was limited by the signal-to-noise ratio. When ?VSin-
creased, the power spectrum broadened linearly with?VS.
At the same time, the spectral amplitude decreased and
eventually approached the noise level. Increasing the laser
power or improving the transducer sensitivity can extend
the maximum. In contrast, the minimum measurable ?VS,
which represents the velocity sensitivity of the system, was
limited by the frequency resolution of the system
(0.033 Hz). Increasing the number of sampling points can
improve the minimum. The theoretical limit of the velocity
sensitivity, estimated from the PAD broadening due to the
Brownian motion of tracer particles, is2?fO
10?7mm=s, where the Boltzmann constant kB? 1:38 ?
10?23J=K, temperature T ? 300 K, viscosity coefficient
? ? 10?3Pa ? s, and the average particle radius a ?
6??a? 6:0 ?
We then experimentally studied the dependence of the
PAD shift on the flow direction. The flow direction was
reversed by simply switching the two ends of the tube (one
was connected with the syringe and the other was hung in
the container as shown in Fig. 2). Figures 4(a) and 4(b) plot
the ac components of the ‘‘X’’ and ‘‘Y’’ signals in a small
time window for two flows with the same
2:20 mm=s but opposite directions. For clarity, the dc off-
sets, which were different for ‘‘X’’ and ‘‘Y’’ (about
?3:5 mV for ‘‘X’’ and about ?2:0 mV for ‘‘Y’’), were
removed. As can be seen, the ac components of ‘‘X’’ and
‘‘Y’’ are similar in amplitude but different in phase with a
shift of ?=2. However, ‘‘Y’’ lags ‘‘X’’ in Fig. 4(a), whereas
‘‘Y’’ leads ‘‘X’’ in Fig. 4(b).
This observation can be understood from the following
simplified model. We assume that the Doppler shift is
infinitely narrow and takes on the experimentally observed
mean frequency?fPAD. The ‘‘X’’ and ‘‘Y’’ signals, repre-
senting the photoacoustic signals that are quadrature-
demodulated by the lock-in detector, can be expressed as
X ? AOcos O??ADcos?2??fPADt ? D? ? EX
Y ? AOcos? O? ?=2?
??ADcos?2??fPADt ? D? ?=2? ? EY:
Here, AOand Odenote the amplitude and initial phase,
respectively, of the unshifted photoacoustic signal;?ADand
Ddenote the amplitude and initial phase, respectively, of
the PAD-shifted photoacoustic signal; and EXand EY
denote the noises. The dc components in both ‘‘X’’ and
‘‘Y’’should come from the particles near the tube wall that
have zero flow velocity because photoacoustic signals
FIG. 4 (color online).
2:2 mm=s. (a) ac components of ‘‘X’’ and ‘‘Y’’ signals for a
flow toward the transducer. (b) ac components of ‘‘X’’ and ‘‘Y’’
signals for a flow away from the transducer.
Directional discrimination of flow in
signals.AverageDoppler flow velocity:
FIG. 3 (color online).
Doppler frequency shift as a function of average flow velocity.
Square symbol: mean frequency shift; Error bar: standard de-
viation of the shift; solid line: theoretically predicted mean shift
from Eq. (2). The inset plots the power spectrum for the average
flow velocity of 4:4 mm=s. PSD: power spectral density.
Experimentally measured photoacoustic
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come from only the particles. The two ac components are
due to the PAD shift and have a phase difference of ?=2.
For the flow measurement shown in Fig. 4(a),?fPADis
positive; thus, ‘‘Y’’ lags ‘‘X.’’ On the contrary, for the
measurement shown in Fig. 4(b),?fPADis negative; thus,
‘‘Y’’ leads ‘‘X.’’ In addition, the dc components in ‘‘X’’
and ‘‘Y’’ can take on different values, whereas the ac
components share the same amplitude.
In summary, we observed the PAD effect from
micrometer-scale light-absorbing particles and used it to
measure flow at an average flow velocity as low as
0:055 mm=s and as high as 8:8 mm=s. We also observed
the directional dependence of the PAD shift. As was dis-
cussed, the measurable range of average flow velocity
can be extended in both directions through technical
Although the PAD flowmetry is in its infancy, our study
showed its capability for measuring low-speed flow in a
small channel. We expect it to be useful for measuring
blood flow in microcirculation, which has average veloc-
ities from a fraction of mm/s in capillaries to tens of mm/s
in small veins and arterials. The PAD flowmetry should be
able to measure this type of blood flow at tissue depths
beyond a few millimeters with preserved directional infor-
mation, which is still a challenge with existing flowmetry
techniques . Acoustic flowmetry has difficulty measur-
ing slow blood flow because tissue background scattering
(so called ‘‘clutter’’ noise) swamps the Doppler signal at
low frequency . The PAD flowmetry has intrinsically
low background and should have much less clutter noise.
Although laser flowmetry and low-coherence optical
Doppler tomography can measure microcirculation using
the short optical wavelength, the flow directional informa-
tion can get lost, and the detection depth is limited to about
1 mm because of multiple light scattering in tissue. The
PAD flowmetry should be less hindered by multiple light
scattering not only because the PAD shift does not involve
the direction of laser illumination but also because photo-
acoustic imaging hasdemonstrated a greater imaging depth
in tissue [23–25]. We are developing the PAD flowmetry
for measuring blood flow of microcirculation in biological
We would like to thank Geng Ku for experimental
assistance and thank Erich Stein and Roger Zemp for
useful discussion. This project is supported by National
Institutes of Health Grants Nos. R01 EB000712 and R01
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