Content uploaded by Jan Sørensen Dam
Author content
All content in this area was uploaded by Jan Sørensen Dam
Content may be subject to copyright.
Comparison of spatially and temporally resolved
diffuse-reflectance measurement systems for
determination of biomedical optical properties
Johannes Swartling, Jan S. Dam, and Stefan Andersson-Engels
Time-resolved and spatially resolved measurements of the diffuse reflectance from biological tissue are
two well-established techniques for extracting the reduced scattering and absorption coefficients. We
have performed a comparison study of the performance of a spatially resolved and a time-resolved
instrument at wavelengths 660 and 785 nm and also of an integrating-sphere setup at 550–800 nm.
The first system records the diffuse reflectance from a diode laser by means of a fiber bundle probe in
contact with the sample. The time-resolved system utilizes picosecond laser pulses and a single-photon-
counting detection scheme. We extracted the optical properties by calibration using known standards
for the spatially resolved system, by fitting to the diffusion equation for the time-resolved system, and by
using an inverse Monte Carlo model for the integrating sphere. The measurements were performed on
a set of solid epoxy tissue phantoms. The results showed less than 10% difference in the evaluation of
the reduced scattering coefficient among the systems for the phantoms in the range 9–20 cm
⫺1
, and
absolute differences of less than 0.05 cm
⫺1
for the absorption coefficient in the interval 0.05–0.30 cm
⫺1
.
© 2003 Optical Society of America
OCIS codes: 120.3150, 120.5820, 170.3890, 170.1470.
1. Introduction
Measuring the optical properties of biological tissue
has grown into a mature procedure in the field of
biomedical optics. Knowing the light-scattering and
absorption properties of tissue is the basis of a wide
range of both diagnostic and therapeutic applica-
tions. Examples include laser-induced fluorescence
to diagnose malignant tissue
1,2
as well as laser-
induced hyperthermia
3,4
and photodynamic thera-
py
5,6
to treat diseased tissue. Novel techniques for
optical analysis of deep structures, based on so-called
optical tomography, are also being developed.
7,8
The goal of such methods is to obtain spatial maps of
the optical properties of the tissue volume. In the
development of these techniques, for validation pur-
poses it is important to be able to accurately measure
optical properties locally. Small sampling volumes
must then be used in which the tissue can be re-
garded as homogeneous.
A number of techniques to measure the local opti-
cal properties of tissue have been developed. Com-
mon to most methods is measurement of the diffuse
reflectance, and in some cases transmittance, from a
sample of the tissue either in vitro or in vivo. The
data are then related to the optical properties by
means of a suitable inverse algorithm based either on
a theoretical light-propagation model or on calibra-
tion by use of standards with known scattering and
absorption properties. When spatially resolved re-
flectance measurements are performed, the sample is
illuminated by a cw light source in a spot, and the
diffuse reflectance is recorded at different radial
distances.
9–15
Time-resolved measurements, how-
ever, utilize subnanosecond pulses from a laser. Af-
ter a pulse has passed passing through a portion of
the tissue, its time dispersion can be measured.
16–23
Both of these methods are two-parameter techniques;
i.e., the extracted properties are absorption coeffi-
cient
a
⬘and reduced scattering coefficient
s
⬘.
Even though measurements of these two types are
now common in biomedical optics, to our knowledge
no systematic investigation to experimentally com-
pare the performance of various systems seems to
have been made. We have evaluated the perfor-
The authors are with the Department of Physics, Lund Institute
of Technology, P.O. Box 118, SE-22100 Lund, Sweden. J. Swart-
ling’s e-mail address is johannes.swartling@fysik.lth.se
Received 4 November 2002; revised manuscript received 21
April 2003.
0003-6935兾03兾224612-09$15.00兾0
© 2003 Optical Society of America
4612 APPLIED OPTICS 兾Vol. 42, No. 22 兾1 August 2003
mance of a spatially resolved and of a time-resolved
system on the same samples. In addition, we com-
pared the results with those from integrating-sphere
measurements, which are known to give accurate re-
sults for in vitro samples.
5,24–27
When a measure-
ment of the collimated transmittance is added to the
integrating-sphere measurements, this technique be-
comes a three-parameter method and permits the
determination of
a
, scattering coefficient
s
, and
scattering anisotropy factor g. Reduced scattering
coefficient
s
⬘is defined as
s
⬘⫽共1⫺g兲
s
.
Our aim in this study was to compare the results
and investigate the limitations of the three systems.
Inhomogeneous samples are also discussed. In each
of the following three sections, one of the three sys-
tems is briefly described, with references to publica-
tions in which thorough descriptions of the technical
details and the data-evaluation methods may be
found. Next, data from a phantom study and in vivo
measurements are presented.
2. Spatially Resolved Diffuse Reflectance System
A. Fiber-Probe System
The fiber-probe system was extensively described in
Ref. 15. The system was designed with real-time
measurements of the skin surface in a clinical envi-
ronment in mind. It consists of a probe head with a
200-m source fiber in the center surrounded by five
equally spaced concentric rings of 250-m detector
fibers. Light from four replaceable low-power diode
lasers is coupled into the source fiber. The diode
lasers may be selected arbitrarily to suit different
applications. In the research reported in this paper,
diode lasers at wavelengths of 660 and 785 nm 共with
output powers of 2 mW at the probe head兲were used.
The fibers of each single ring of detector fibers are
bundled and terminated on a separate silicon photo-
diode for each ring. In addition, three photodiodes
and a temperature sensor are mounted directly near
the perimeter of the probe head. Thus, diffuse re-
flectance R共r兲can be collected at six distances, i.e., r⫽
0.6, 1.2, 1.8, 2.4, 3.0, 7.8 mm. Furthermore, a sep-
arate reference detector monitors the output of the
source fiber at the probe head. Data acquisition and
storage are controlled by a laptop PC connected to a
digital signal processing board. One cycle of four
successive measurements 共i.e., one at each wave-
length兲including dark measurements can be per-
formed in ⬃10 ms; thus the maximum sampling rate
of the system is ⬃100 Hz. To minimize any inter-
ference from background light or drift of the light
source, the dark measurements are subtracted from
the measured reflectance data, after which they are
normalized relative to the source reference. The
digital signal processing board accomplishes this be-
fore the data are analyzed, displayed, and stored by
the PC.
B. Calibration and Prediction Algorithms
Because the unknown numerical apertures of the
fiber-probe light source and detectors were not know
the system was calibrated directly on a set of phan-
toms instead of by use of a mathematical light-
propagation model. The phantoms consisted of
epoxy resin with well-defined quantities of TiO and
absorbing pigment added for scattering and absorp-
tion, respectively. The scattering and absorption
spectra were determined from integrating-sphere
measurements. A set of 72 calibration phantoms
was used, with 8 different scatterer concentrations
and 9 different absorber concentrations. The cali-
bration phantoms were prepared in the same way as
the validation set described below in Section 5. The
ranges of optical properties used in the calibration
phantoms were, at 660 nm, 0.01 ⬍
a
⬍0.5 and 4.5 ⬍
s
⬘⬍25 cm
⫺1
. At 785 nm the ranges were 0.05 ⬍
a
⬍0.5 and 4.0 ⬍
s
⬘⬍20 cm
⫺1
.
In theory,
a
and
s
⬘can be determined by use of
R共r兲data from only two of the six detector distances
of the fiber probe. However, to reduce the influence
of tissue inhomogeneity and of noisy measurement
conditions we included the signals from all source–
detector distances in the analysis. We did this for
each measurement by first applying principal-
component analysis to the data from all six source–
detector distances of the probe system and then using
the resultant weight coefficients for the two main
principal components, P
1
and P
2
, in the analysis.P
1
and P
2
from all phantoms were then fitted to two-
dimensional polynomials by least-squares regression
to create a calibration model to extract
a
and
s
⬘
from the spatially resolved measurements in the
same way as described in Ref. 15 We call this tech-
nique the multiple polynomial regression 共MPR兲
method. The next step was to solve the inverse
problem of determining
a
and
s
⬘from R共r兲mea-
surements of a set of prediction samples. We did
this by employing a two-dimensional Newton–
Raphson algorithm of the two principal components
from each measurement.
3. Time-Resolved System
A. Instrument for Time-Resolved Measurements
Picosecond pulsed diode lasers at 660 and 785 nm
共SEPIA; PicoQuant GmbH, Germany兲were used as
light sources. The light was brought to the sample
by a 50-m-diameter gradient-index optical fiber. A
600-m-diameter fiber was used to collect the dif-
fusely reflected light and guide it to the detector, a
microchannel plate-photomultiplier tube 共R2566U;
Hamamatsu Photonics K. K., Japan兲. A time-
correlated single-photon-counting technique
17
was
employed to record the time-dispersion curves. To
this end, an SPC-300 computer card 共Becker & Hickl
GmbH, Germany兲provided the fast electronics for
this measurement. The whole system fits neatly on
a small cart for portability and to facilitate use in a
clinical environment. The system is controlled from
a flat-panel PC with a touch-sensitive screen. The
system is intended either for surface measurements
of time-resolved reflectance or for invasive measure-
1 August 2003 兾Vol. 42, No. 22 兾APPLIED OPTICS 4613
ments by means of interstitial fibers inserted into the
tissue.
The overall temporal response function of the sys-
tem was approximately 100 ps 共full width at half-
maximum兲when the average power after the fiber
was tuned to approximately 2 mW. Tuning to
higher power resulted in a broader response function.
For tissues, these specifications give an optimal
range of interfiber distances of approximately 1–2
cm. The measurements were performed at an inter-
fiber distance of 15 mm. For each measurement,
100,000 counts were acquired.
B. Data Evaluation
We obtained the absorption and reduced scattering
coefficients by fitting the solution of the diffusion
equation for a semi-infinite homogenous medium,
with the extrapolated boundary condition,
28
to the
measured data. The diffusion coefficient, D, was as-
sumed to be independent of the absorption of the
medium; i.e., D⫽1兾3
s
⬘.
29
The theoretical curve
was convolved with the instrumental transfer func-
tion, as measured with the source and the detector
fiber facing each other, with collimating lenses to
collect the light for the detector fiber. The resultant
curve was fitted to the data over a range starting at
80% of the maximum intensity on the rising flank and
ending at 1% on the trailing flank.
30
We accom-
plished the fit with a Levenberg–Marquardt algo-
rithm
31
by varying
a
and
s
⬘to minimize
2
.
4. Integrating-Sphere System
A. Optical Setup
The integrating-sphere setup was similar to the one
described in Ref. 26, with a 75-W Xe lamp used as the
light source. The sphere 共Oriel Corporation, Strat-
ford, Conn.兲allows detection of total transmittance T
and total reflectance Rfrom a sample placed at either
the entrance or the exit port. We guided the light to
the sphere by using a 600 m-diameter fiber and
collimated it by using a lens and a pair of apertures.
The light from the sphere was guided by an optical
fiber bundle to a spectrometer 共270M; SPEX Indus-
tries, Inc., Edison, N.J.兲. A cryocooled CCD camera
共OMA-Vision; EG&G PARC, Princeton, N.J.兲was
used for detection. The collimated transmittance
was measured in a separate setup in which a series of
collinear apertures served to suppress the scattered
light such that only the nonscattered light was col-
lected by a fiber bundle guiding the light to the spec-
trometer. Attenuation filters were used to increase
the dynamic range of this measurement, which
yielded total attenuation coefficient
t
⫽
a
⫹
s
from
the Beer–Lambert law. To measure the epoxy
phantoms we prepared 1.0-mm-thick slabs.
B. Determination of Optical Properties
We extracted the optical properties from the mea-
sured values R, T and
t
, using an MPR method
based on Monte Carlo simulations
27
that in principle
was similar to the method used for the fiber-probe
system. A previously computed database of Rand T
spanning the expected range of optical properties
共0⬍
a
⬍0.7 cm
⫺1
,1⬍
s
⬍70 cm
⫺1
, 0.4 ⬍g⬍0.9,
n⫽1.55兲was fitted to a polynomial model. The
properties
a
,
s
, and gwere extracted from the
model by a Newton–Raphson algorithm. Unlike in
the method described in Ref. 27, which used a fixed
value of g, three-dimensional rather than two-
dimensional polynomials were used in the regression.
Because of the limited sizes of the ports of the inte-
grating sphere, there were losses of light at the outer
parts of the sample. This effect was incorporated in
to the Monte Carlo simulations, as otherwise the
losses would have led to an overestimation of the
absorption properties.
32
We accomplished this by
incorporating the sphere entrance and exit port di-
ameters in to the Monte Carlo simulations. For
evaluation of tissue samples a different database was
used 共0⬍
a
⬍0.5 cm
⫺1
,5⬍
s
⬍120 cm
⫺1
, 0.8 ⬍g⬍
0.995, n⫽1.4兲.
5. Test Samples
A. Solid Tissue Phantoms
Twenty-five phantoms were prepared from clear,
solvent-free epoxy resin with an aliphatic amine as
hardener 共NM 500; Nils Malmgren AB, Ytterby, Swe-
den兲, according to the guidelines given by Firbank et
al.
33,34
The epoxy had a pot life of ⬃6 h after the two
components were mixed. TiO powder 共T-8141;
Sigma-Aldrich, St. Louis, Missouri兲was used as a
scatterer. Based on integrating-sphere measure-
ments, TiO was found to give a reduced scattering
coefficient
s
⬘of approximately 6 cm
⫺1
兾共mg兾g兲at 785
nm when it was dispersed in the epoxy, linear to at
least 30 cm
⫺1
. As absorbing pigment, toner from a
copying machine was used; it had a fairly flat absorp-
tion spectrum throughout the visible and near-
infrared regions. The toner also had some
scattering characteristics, which means that the ab-
sorption coefficient is not trivially obtained from spec-
trophotometer readings alone. Again based on
integrating-sphere measurements, the absorption co-
efficient of the toner dispersed in epoxy was found to
be approximately 1 cm
⫺1
兾共mg兾g兲at 785 nm. A stock
solution of hardener and toner 共1.2 mg兾g兲was pre-
pared for preparation of the phantom. The TiO was
weighed directly for each phantom, with 1-mg accu-
racy. The concentrations of TiO and absorbing pig-
ment are shown in Table 1. Cylindrical
polypropylene cups were used as molds, resulting in
phantoms with a diameter of 6.5 cm and a height of
5.5 cm. After hardening for 12 h at room tempera-
ture, the phantoms were hardened at 55 °C for 24 h,
and then their upper surfaces were machined
smooth. For the integrating-sphere measurements,
cuvettes were made from microscope slides into
which ⬃1 mL from each phantom was poured before
the epoxy hardened, yielding 1.0-mm-thick samples,
approximately 3 cm by 3 cm wide.
No settling of the TiO during the curing process
was observed by other groups of researchers,
33
and by
4614 APPLIED OPTICS 兾Vol. 42, No. 22 兾1 August 2003
visual inspection we could not detect any settling.
However, in the slabs prepared for the integrating-
sphere measurements, a weak curtain pattern was
visible as the viscous resin was poured into the cu-
vette chamber. The implications of this pattern are
discussed in Section 7 below.
B. Measurements of Pork Meat
Measurements of bone-free pork chops were made
with all systems. The pork chops were purchased at
the local supermarket on the same day as the mea-
surements were made and were kept wrapped in
plastic at room temperature for 3–4 h before the mea-
surements. For the integrating-sphere measure-
ments the meat was cut into 1.0-mm thick slices and
placed between microscope slides, with pieces of
slides used as spacers, and then clamped together.
C. In vivo Measurements
We also performed measurements on the insides of
the forearms of two of the experimenters, using the
spatially and time-resolved systems. The procedure
was otherwise identical to the measurements of the
phantoms.
6. Results
A. Solid Tissue Phantoms
A spectral characterization of the phantoms obtained
from the integrating-sphere measurements is pre-
sented in Fig. 1. The spectra evaluated for
s
⬘关Fig.
1共a兲兴,
a
关Fig. 1共b兲兴,
s
关Fig. 1 共c兲兴, and g关Fig. 1 共d兲兴 are
shown as averages of the phantoms with equal
amounts of scattering or absorption agents added.
The absorption spectra 关Fig. 1 共b兲兴 were determined
both by the added toner and by the intrinsic absorp-
tion of the epoxy resin.
34
Figure 2 shows the values of
s
⬘and
a
obtained
from each system for wavelength 660 nm. The re-
sults at 785 nm were similar, although the absolute
values were shifted somewhat 共data not shown兲.
The
s
⬘values generally agreed within 10% among
the systems, except for the row of lowest scattering
共row A according to Table 1兲, where the fiber-probe
and time-resolved data were as much as 35% lower
than for the integrating sphere.
The values of
a
are similar for the time-resolved
and the integrating-sphere systems but are some-
what higher with the fiber-probe system. The
integrating-sphere values are, however, more un-
evenly distributed, and there seems to be a trend
toward lower values of
a
for the phantoms with
lower scattering 共A and B兲, as we discuss in Section 7
below.
B. Pork Meat and In Vivo Measurements
The meat sample was included in the study as an
example of realistic biological tissue. Nine mea-
surements were performed with both the fiber-probe
and the time-resolved systems at three positions,
with the probes moved by ⬃0.5 cm between positions.
For the integrating-sphere experiment, measure-
ments of diffuse transmittance and reflectance were
made on three samples. The results from the mea-
surements are presented in Table 2. The fiber-probe
measurements could vary by as much as a factor of 2
when the probe head was moved only ⬃1 cm, indi-
cating that the sample was not particularly homoge-
neous even though it seemed so by visible inspection.
The time-and spatially resolved systems were
tested on the forearms of two of the experimenters.
Although in vivo measurements of the skin surface
represent an inhomogeneous sampling volume, all
measurements were nevertheless evaluated with the
assumption of homogeneity. Three measurement at
approximately the same position were performed.
The results are presented in Table 3. The discrep-
ancies between the systems are discussed in Section
7 below.
7. Discussion and Conclusion
The integrating-sphere method has a proven record
of producing accurate values of the scattering coeffi-
cient, as verified by tests of polystyrene microspheres
in water suspensions, for which the scattering could
be calculated exactly from Mie theory.
27
The results
from that investigation showed that the relative dif-
ference between the measured values of
s
⬘and the
predicted 共by Mie theory兲values of
s
⬘was on average
1.7%. The method used to extract the optical prop-
erties, the MPR method based on Monte Carlo sim-
ulations, can also be regarded as state of the art in
terms of inverse algorithms for integrating-sphere
measurements.
The slabs designed for the integrating-sphere mea-
surements are a potential source of error compared
with the large phantoms, because the slabs exhibit
slight inhomogeneities. When the slabs were in-
spected closely, weak curtain patterns were visible in
them where the epoxy resin had been running down
the sides of the glass cuvette. In preparing the
phantoms we had taken much care to mix the resin
and the scattering–absorbing agents both mechani-
cally and by use of an ultrasonic bath, so we anticipate
that the phantoms themselves were homogeneous.
Deviations in the integrating-sphere results may
Table 1. Concentrations of TiO and Black Pigment Added to the
Phantoms
Phantom Concentration
Increasing
s
⬘TiO 共mg兾g兲
A 0.79
B 1.20
C 1.61
D 2.02
E 2.42
Increasing
a
Black pigment 共g兾g兲
1 6.4
2 13.8
3 21.1
4 28.5
5 35.9
1 August 2003 兾Vol. 42, No. 22 兾APPLIED OPTICS 4615
thus also be the result of measuring not quite the
same properties as in the bulk phantoms.
As we stated in Subsection 5.A, the toner had some
scattering characteristics. However, they were negli-
gible compared with the scattering from the TiO. No
increase in the scattering coefficient could be observed
when the concentration of toner was increased 共Fig. 2兲,
and it is clear from Table 1 that the concentration of
toner was very low compared with that of TiO. The
evaluation of the gfactor 关Fig. 1共d兲兴 was of little im-
portance for comparison with the other systems.
However, the results may be of interest when one is
discussing the merits of the integrating-sphere tech-
nique itself. In performing the
t
measurement it is
imperative that the amount of scattered light that is
collected by the detector be negligible. The collimated
beam setup was therefore rigorously characterized be-
fore being used, and we determined that attenuation
coefficients of as much as 120 cm
⫺1
could be measured
with the setup, well above the numbers found in this
study.
The absorption coefficients extracted by the
integrating-sphere method deviated more among
phantoms that should have the same properties,
shown in Fig 2共f兲. This result was expected because
the evaluation of
a
is problematic when
a
is low.
Monte Carlo simulations showed that the difference
between no black pigment and the lowest concentra-
tion of pigment corresponds to less than 1% difference
in the measurement of Ror T, and thus the evaluation
is highly susceptible to measurement noise. A prob-
lem with integrating-sphere measurements in this re-
spect is losses of light caused by the finite diameters of
the sphere ports, which translate directly into an over-
Fig. 1. Spectral characteristics of the phantoms as measured with the integrating sphere. 共a兲
s
⬘spectra presented as averages of the
phantoms with the same amount of TiO added, corresponding to A–E in Table 1. 共b兲
a
spectra presented as averages of the 1–5 phantoms
in Table 1. 共c兲
s
spectra for A–E. The anisotropy factor gis presented in 共d兲as an average of all phantoms. Error bars represent one
standard deviation.
4616 APPLIED OPTICS 兾Vol. 42, No. 22 兾1 August 2003
estimation of the absorption.
32
These losses, which
can amount to 5% if the attenuation of the sample is
low, were compensated for in the Monte Carlo model.
In our setup the losses correspond to a detection limit
of
a
of ⬃0.5 cm
⫺1
if no correction is applied. If the
true absorption coefficient is lower than this value, the
losses will become the determining factor, and without
corrections the evaluated value of
a
can never be
lower. However, even with corrections it is difficult to
model the experimental conditions exactly, and the
trend of lower values of
a
for the low-scattering phan-
toms 共A and B兲is most likely an artifact that is due to
Fig. 2. Values of
s
⬘and
a
of the solid phantoms, as determined by the three systems, at 660 nm. The results are presented as functions
of phantoms with the same amounts of TiO or black pigment added, according to Table 1. 共a兲,共d兲
s
⬘and
a
, respectively, from the
fiber-probe system; 共b兲,共e兲corresponding results from the time-resolved system; 共c兲,共f兲corresponding results from the integrating-sphere
system. Error bars represent one standard deviation for repeated measurements. Note that, for the integrating sphere, repeated
measurements were performed only for phantoms A1, A5, C3, E1, and E5.
Table 2. Results of Measurements of the Meat Sample
Property
Fiber-Probe Method
Time-Resolved
Method Integrating-Sphere Method
s
⬘
共cm
⫺1
兲
a
共cm
⫺1
兲
s
⬘
共cm
⫺1
兲
a
共cm
⫺1
兲
s
⬘
共cm
⫺1
兲
a
共cm
⫺1
兲g
s
共cm
⫺1
兲
Mean 6.9 0.043 6.6 0.037 4.9 0.061 0.94 82
Standard deviation 1.4 0.014 0.5 0.008 1.1 0.020 0.006 11
1 August 2003 兾Vol. 42, No. 22 兾APPLIED OPTICS 4617
the fact that the compensation in the Monte Carlo
model was not exact. Nevertheless, the results show
that the integrating-sphere method can produce useful
results even for low-absorption coefficients, provided
that proper compensation for losses is made. In this
study the detection limit for
a
was lowered an order of
magnitude to ⬃0.05 cm
⫺1
.
The time-resolved method, however, produced an
even distribution of
a
for the low-absorption phan-
toms 关Fig. 2共e兲兴. The slope of the trailing flank of the
time-dispersion curve is determined largely by the
absorption coefficient, and for low absorption the fit
with the diffusion equation is fairly robust. Our con-
clusion is that the time-resolved technique is prefer-
able when one is measuring low-absorption
coefficients. Another interpretation is that the path
length of the light is very long for the diffusely prop-
agating light, which makes the measurement sensi-
tive even to small absorption coefficients. The
a
values for the highest concentration of absorber and
the lowest amount of scatterer dip slightly compared
with the rest, a result that can be explained by the
fact that the diffusion approximation is starting to
lose validity for those parameters. The fiber-probe
system gave values of
a
that were more evenly dis-
tributed than the integrating-sphere results 关Fig.
2共d兲兴. The value for phantom E5 is likely an outlier,
probably because of the low signal for this high-
attenuation phantom. In as much as we calibrated
the fiber system by utilizing a regression method,
which tends to smooth irregularities in the calibra-
tion data, it is expected that the results will be more
evenly distributed than the integrating-sphere re-
sults for
a
. The absorption values are consistently
higher for the fiber-probe system than for the other
systems, which may be indicative of slight cross talk
in the evaluation model, because the values of
s
⬘are
at the same time the lowest of the three systems.
As for scattering, the fiber-probe system yielded
values of
s
⬘within 5% of the integrating-sphere re-
sults 关Figs. 2共a兲and 2共c兲兴, except for the row with the
lowest scattering. During the experimental work it
was apparent that the fiber-probe system had prob-
lems with low-scattering 共below 5 cm
⫺1
兲coefficients.
This may be attributed to the fixed detection dis-
tances. For low-scattering coefficients the probe
would have needed to measure at longer distances to
provide data for a robust evaluation. The scattering
results for the time-resolved system look similar 关Fig.
2共b兲兴, and, again, it is apparent that the values of
s
⬘
are underestimated for low-scattering samples. In
this case the reason can be attributed to the limited
validity of the diffusion equation for this combination
of
s
⬘,
a
, and interfiber distance. The determina-
tion of
s
⬘was somewhat sensitive to assumptions
made in the fitting process. We achieved the best fit,
in terms of the lowest value of
2
, by allowing starting
time t
0
of the time-dispersion curve to be a fitting
parameter, together with
s
⬘and
a
. It is reason-
able to be able to improve the fit by increasing the
number of fitting parameters. However, it seems
unphysical to have the starting time as a free param-
eter in the fitting procedure when the actual value of
t
0
is known from the reference pulse in the measure-
ment. Even though the
2
values were slightly
worse for fitting with fixed t
0
, the results obtained were
closer to the integrating-sphere results. The results
presented in this paper were thus obtained with a fixed
value of t
0
. Because it is known that the diffusion
approximation is less accurate for early times, Cu-
beddu et al. used the 80% point of the rising flank of
the curve as the starting point of the fitting and the 1%
point of the trailing flank as the end point.
30
This
approach was practiced in the study reported here too.
A general trend for the time-resolved data is that
s
⬘is slightly higher and
a
slightly lower than for
the other systems. The reason for this systematic
trend can probably be found in higher-order effects
that are not accounted for by the diffusion approxi-
mation, i.e., most notably that the model is not accu-
rate for early times. It has also been suggested that
the radiative lifetimes 共of the order of 100 fs兲of the
scattering events may have to be taken into account,
which could explain the deviation trends in
s
⬘and
a
.
35
The absolute accuracy of the fiber-probe system can
be traced to the accuracy of the integrating-sphere
measurements of the calibration set. The errors in
the calibration set are comparable to the errors in the
validation set measured with the integrating sphere,
because the calibration set was made in an identical
manner. However, the final calibration for the fiber-
probe system is more accurate than the individual
calibration points; this is a result of using the regres-
sion technique.
15
The variation in the measurements of the meat
sample is indicative of the heterogeneity of the sam-
ple and also reflects the different sampling volumes of
the systems. The sampling depth depends critically
on the interfiber distance between source and detec-
tor fiber.
36
The time-resolved system has the largest
sampling volume and tends to average small varia-
tions. This phenomenon can be seen from Table 2,
where the time-resolved system can be seen to exhibit
the lowest standard deviations. The two other sys-
tems sample in millimeter-sized regions, and the re-
sults are thus more sensitive to small inhomogeneties,
such as small streaks of fat or connective tissue. For
the fiber probe the evaluation of the reduced scattering
coefficient is especially sensitive to small inhomogene-
ities, as the scattering coefficient is determined pri-
marily by the reflectance at the closest distance.
15
One way to reduce sensitivity to small inhomoge-
neities and to noise in the detected signals when the
Table 3. Results of Measurements of Forearms of the Experimenters
a
Person
Fiber-Probe Method
s
⬘
Time-Resolved Method
s
⬘共cm
⫺1
兲
1 10.6 2.5
2 11.8 5.0
a
For both persons, the fiber-probe method measured
a
as 0.19
cm, and the time-resolved method measured
a
as 0.20 cm.
4618 APPLIED OPTICS 兾Vol. 42, No. 22 兾1 August 2003
fiber-probe system is used was to use the signals from
all detector distances rather than just two, as was
done in previous studies. In principle,
a
and
s
⬘
may be determined by use of R共r兲data from only two
of the six detector distances of the fiber probe. A
previous paper
15
reported application of the MPR
technique to create a calibration model and subse-
quently to extract
a
and
s
⬘from R共r兲measurements
at r
1
⫽0.6 mm and at r
2
⫽7.8 mm. As only two
optical properties were extracted, i.e.,
a
and
s
⬘, the
MPR method implies exactly two input variables as
well, i.e., R共r
1
兲and R共r
2
兲. In the research reported in
this paper, all source–detector distances from the
measurements were used. The number of indepen-
dent signals was then reduced to two by application of
principal-component analysis as a dimension reduc-
tion method.
As was pointed out above, the sampling volume in
the in vivo skin measurements is inherently inhomo-
geneous, because the skin and the underlying tissues
are a layered structure. This inhomogeneity would
pose no problem in a comparison of the systems if the
sampling volumes were the same, because the inho-
mogeneities would average out. Such is not the case
here, however, as is obvious when one compares the
measurement geometry of the time-and the spatially
resolved systems. The 15-mm fiber spacing for the
time-resolved system means that the detected light
will have traveled along a deeper path than the de-
tected light in the spatially resolved system.
36
For
the spatially resolved system, the sampling depths
will be different for the various radial distances.
Also, as this system measures the diffuse reflectance
for distances up to 7.8 mm from the source only, this
method samples tissue layers at smaller depths than
the time-resolved system. Most of the information
about the scattering is, as mentioned above, collected
at the first detector distance, at 0.6 mm, which means
a very shallow sampling depth. In as much as skin
and subcutaneous layers scatter more than muscle
tissue, the spatially resolved systems consequently
yielded higher values of
s
⬘than the time-resolved
systems 共Table 2兲.
We included the meat sample and the in vivo mea-
surements in our report as presented here to illus-
trate the performance of the systems in more-realistic
measurement situations. Even in the relatively ho-
mogeneous meat sample, the results could vary by a
factor of 2 for the fiber-probe system. The time-
resolved method is the most robust in this respect, as
small heterogeneities tend to average out. The dis-
crepancies in the results point to one important ob-
servation, namely, that quantitative measurements
of optical properties are sometimes impossible to per-
form if the assumption of homogeneous tissue is
made. Only when the tissue can certainly be as-
sumed to be homogeneous are such measurements
useful. In other cases, either relative measure-
ments, which may be system dependent, will have to
suffice or one will have to utilize more-sophisticated
inverse models based on assumptions of inhomoge-
neous tissue. Nevertheless, we have shown that
when the requirement of a homogeneous medium is
fulfilled, the three methods produce results for re-
duced scattering coefficient
s
⬘that coincide with in
10% of one another over most of the relevant param-
eter space for biological soft tissue. The results for
absorption are more complicated in terms of the rel-
ative errors, because the absorption coefficient in
some tissues can be quite low. However, the differ-
ences in the evaluated absolute values for
a
were
within 0.05 cm
⫺1
for the three measurement tech-
niques.
We thank Antonio Pifferi 共Department of Physics,
Politecnicio di Milano, Milan, Italy兲for the software
used for the evaluation of the data recorded by the
time-resolved system. In addition, we thank Claes
af Klinteberg, Magnus Andersson, and Anders Nils-
son for aiding us with the time-resolved measure-
ments. We greatly appreciate help from Carsten
Pedersen 共Bang & Olufsen Medicom a兾s, Struer,
Denmark兲in repairing the fiber probe system. This
study was financially supported by European Com-
mission grants QLG1-2000-00690 and QLG1-2000-
01464 and by the Swedish Research Council.
References
1. R. Richards-Kortum and E. Sevick-Muraca, “Quantitative op-
tical spectroscopy for tissue diagnosis,” Annu. Rev. Phys.
Chem. 47, 555–606 共1996兲.
2. G. A. Wagnie`res, W. M. Star, and B. C. Wilson, “In vivo fluo-
rescence spectroscopy and imaging for oncological applica-
tions,” Photochem. Photobiol. 68, 603–632 共1998兲.
3. G. J. Mu¨ ller and A. Roggan, eds., Laser-Induced Interstitial
Thermotherapy 共SPIE Press, Bellingham, Wash., 1995兲.
4. K. Ivarsson, J. Olsrud, C. Sturesson, P. H. Mo¨ller, B. R. Pers-
son, and K.-G. Tranberg, “Feedback interstitial diode laser
共805 nm兲thermotherapy system: ex vivo evaluation and
mathematical modeling with one and four fibers,” Lasers Surg.
Med. 22, 86–96 共1998兲.
5. A. M. K. Nilsson, R. Berg, and S. Andersson-Engels, “Measure-
ments of the optical properties of tissue in conjunction with
photodynamic therapy,” Appl. Opt. 34, 4609–4619 共1995兲.
6. T. Johansson, M. S. Thompson, M. Stenberg, C. af Klinteberg,
S. Andersson-Engels, S. Svanberg, and K. Svanberg, “Feasi-
bility study of a novel system for combined light dosimetry and
interstitial photodynamic treatment of massive tumors,” Appl.
Opt. 41, 1462–1468 共2002兲.
7. J. C. Hebden, H. Veenstra, H. Dehghani, E. M. C. Hillman, M.
Schweiger, S. R. Arridge, and D. T. Delpy, “Three-dimensional
time-resolved optical tomography of a conical breast phantom,”
Appl. Opt. 40, 3278–3287 共2001兲.
8. C. H. Schmitz, M. Locker, J. M. Lasker, A. H. Hielscher, and
R. L. Barbour, “Instrumentation for fast functional optical to-
mography,” Rev. Sci. Instrum. 73, 429–439 共2002兲.
9. T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion
theory model of spatially resolved, steady-state diffuse reflec-
tance for noninvasive determination of tissue optical proper-
ties in vivo,” Med. Phys. 19, 879–888 共1992兲.
10. S. L. Jacques, A. Gutsche, J. Schwartz, L. Wang, and F. Tittel,
“Video reflectometry to specify optical properties of tissue in
vivo,” in Medical Optical Tomography: Functional Imaging
and Monitoring,G.J.Mu¨ ller, B. Chance, R. R. Alfano, S. R.
Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S.
Svanberg, and P. van der Zee, eds. Vol. IS11 of SPIE Institute
Series 共SPIE Press, Bellingham, Wash. 1993兲, pp. 211–226.
11. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner, and
1 August 2003 兾Vol. 42, No. 22 兾APPLIED OPTICS 4619
B. C. Wilson, “Spatially resolved absolute diffuse reflectance
measurements for noninvasive determination of the optical
scattering and absorption coefficients of biological tissue,”
Appl. Opt. 35, 2304–2314 共1996兲.
12. R. Bays, G. Wagnie`res, D. Robert, D. Braichotte, J. F. Savary,
P. Monnier, and H. van den Bergh, “Clinical determination of
tissue optical properties by endoscopic spatially resolved ref-
lectometry,” Appl. Opt. 35, 1756–1766 共1996兲.
13. R. M. P. Doornbos, R. Lang, M. C. Aalders, F. W. Cross, and
H. J. C. M. Sterenborg, “The determination of in vivo human
tissue optical properties and absolute chromophore concentra-
tions using spatially resolved steady-state diffuse reflectance
spectroscopy,” Phys. Med. Biol. 44, 967–981 共1999兲.
14. T. H. Pham, F. Bevilacqua, T. Spott, J. S. Dam, B. J. Tromberg,
and S. Andersson-Engels, “Quantifying the absorption and
reduced scattering coefficients of tissue-like turbid media over
a broad spectral range using a non-contact Fourier interfero-
metric, hyperspectral imaging system,” Appl. Opt. 39, 6487–
6497 共2000兲.
15. J. S. Dam, C. B. Pedersen, T. Dalgaard, P. E. Fabricius, P.
Aruna, and S. Andersson-Engels, “Fiber-optic probe for non-
invasive real-time determination of tissue optical properties at
multiple wavelengths,” Appl. Opt. 40, 1155–1164 共2001兲.
16. S. L. Jacques, “Time-resolved reflectance spectroscopy in tur-
bid tissues,” IEEE Trans. Biomed. Eng. 36, 1155–1161 共1989兲.
17. S. Andersson-Engels, R. Berg, O. Jarlman, and S. Svanberg,
“Time-resolved transillumination for medical diagnostics,”
Opt. Lett. 15, 1179–1181 共1990兲.
18. M. Ferrari, Q. Wei, L. Carraresi, R. A. De Blasi, and G. Zac-
canti, “Time-resolved spectroscopy of the human forearm,” J.
Photochem. Photobiol. B 16, 141–153 共1992兲.
19. S. J. Madsen, B. C. Wilson, M. S. Patterson, Y. D. Park, S. L.
Jacques, and Y. Hefetz, “Experimental tests of a simple diffu-
sion model for the estimation of scattering and absorption
coefficients of turbid media from time-resolved diffuse reflec-
tance measure,” Appl. Opt. 31, 3509–3517 共1992兲.
20. K. Suzuki, Y. Yamashita, K. Ohta, and B. Chance, “Quantita-
tive measurement of optical parameters in the breast using
time-resolved spectroscopy. Phantom and preliminary in vivo
results,” Invest. Radiol. 29, 410–414 共1994兲.
21. J. Ko¨lzer, G. Mitic, J. Otto, and W. Zinth, “Measurements of
the optical properties of breast tissue using time-resolved tran-
sillumination,” in Photon Transport in Highly Scattering Tis-
sue, S. Avrillier, B. Chance, G. J. Mu¨ller, A. V. Priezzhev, and
V. V. Tuchin, eds., Proc. SPIE 2326, 143–152 共1995兲.
22. X. Liang, L. Wang, P. P. Ho, and R. R. Alfano, “True scattering
coefficients of turbid media,” in Optical Tomography, Photon
Migration and Spectroscopy of Tissue and Model Media: The-
ory, Human Studies, and Instrumentation, B. Chance and
R. R. Alfano, eds., Proc. SPIE 2389, 571–574 共1995兲.
23. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valen-
tini, “Noninvasive absorption and scattering spectroscopy of
bulk diffusive media: an application to the optical character-
ization of human breast,” Appl. Phys. Lett. 74, 874–876
共1999兲.
24. J. W. Pickering, S. A. Prahl, N. van Wieringen, J. F. Beek,
H. J. C. M. Sterenborg, and M. J. C. van Gemert, “Double-
integrating-sphere system for measuring the optical properties
of tissue,” Appl. Opt. 32, 399–410 共1993兲.
25. A. Roggan, H. J. Albrecht, K. Do¨ rschel, O. Minet, and G. J.
Mu¨ller, “Experimental set-up and Monte-Carlo model for the
determination of optical tissue properties in the wavelength
range 330–1100 nm,” in Laser Interaction with Hard and Soft
Tissue II, H. J. Albrecht, G. P. Delacretaz, T. H. Meier, R. W.
Steiner, L. O. Svaasand, and M. J. van Gemert, eds., Proc.
SPIE 2323, 21–46 共1995兲.
26. A. M. K. Nilsson, C. Sturesson, D. L. Liu, and S. Andersson-
Engels, “Changes in spectral shape of tissue optical properties
in conjunction with laser-induced thermotherapy,” Appl. Opt.
37, 1256–1267 共1998兲.
27. J. S. Dam, T. Dalgaard, P. E. Fabricius, and S. Andersson-
Engels, “Multiple polynomial regression method for determi-
nation of biomedical optical properties from integrating sphere
measurements,” Appl. Opt. 39, 1202–1209 共2000兲.
28. R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S.
McAdams, and B. J. Tromberg, “Boundary conditions for the
diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11,
2727–2741 共1994兲.
29. K. Furutsu and Y. Yamada, “Diffusion approximation for a
dissipative random medium and the applications,” Phys. Rev.
E50, 3634–3640 共1994兲.
30. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valen-
tini, “Experimental test of theoretical models for time-resolved
reflectance,” Med. Phys. 23, 1625–1633 共1996兲.
31. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P.
Flannery, Numerical Recipes in C: The Art of Scientific Com-
puting 共Cambridge U. Press, New York, 1992兲.
32. G. de Vries, J. F. Beek, G. W. Lucassen, and M. J. C. van
Gemert, “The effect of light losses in double integrating
spheres on optical properties estimation,” IEEE J. Sel. Top.
Quantum Electron. 5, 944–947 共1999兲.
33. M. Firbank and D. T. Delpy, “A design for a stable and repro-
ducible phantom for use in near infra-red imaging and spec-
troscopy,” Phys. Med. Biol. 38, 847–853 共1993兲.
34. M. Firbank, M. Oda, and D. T. Delpy, “An improved design for
a stable and reproducable phantom material for use in near-
infrared spectroscopy and imaging,” Phys. Med. Biol. 40, 955–
961 共1995兲.
35. I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H.-J.
Schwarzmaier, “Effect of the scattering delay on time-
dependent photon migration in turbid media,” Appl. Opt. 36,
6529–6538 共1997兲.
36. M. S. Patterson, S. Andersson-Engels, B. C. Wilson, and E. K.
Osei, “Absorption spectroscopy in tissue-simulating materials:
a theoretical and experimental study of photon paths,” Appl.
Opt. 34, 22–30 共1995兲.
4620 APPLIED OPTICS 兾Vol. 42, No. 22 兾1 August 2003
