January 15, 2003 / Vol. 28, No. 2 / OPTICS LETTERS
Bifocal optical coherenc refractometry of turbid media
Sergey A. Alexandrov, Andrei V. Zvyagin, K. K. M. B. Dilusha Silva, and David D. Sampson
Optical+Biomedical Engineering Laboratory, Department of Electrical and Electronic Engineering, The University of Western
Australia, Crawley, WA 6009, Australia
Received August 23, 2002
We propose and demonstrate a novel technique, which we term bifocal optical coherence refractometry, for the
rapid determination of the refractive index of a turbid medium.
creation of two closely spaced confocal gates in a sample.
gates is measured by means of low-coherence interferometry and used to determine the refractive index.
present experimental results for the refractive indices of milk solutions and of human skin in vivo.
axial scan rate determines the acquisition time, which is potentially of the order of tens of milliseconds, the
technique has potential for in vivo refractive-index measurements of turbid biological media under dynamic
conditions.© 2003 Optical Society of America
120.5710, 180.3170, 180.1790, 170.7050, 170.4580.
The technique is based on the simultaneous
The optical path-length difference between the
Detailed knowledge of the refractive index is essential
in the understanding of light–tissue interactions in liv-
Such knowledge is important for in vivo
optical diagnostics and laser treatments.
the reported significance of the refractive index in-
clude the relationship of the refractive index of human
stratum corneum to tissue hydration2and large re-
fractive-index differences between normal and malig-
nant breast tissue3and between normal and calcified
Such differences are not necessarily
observed in samples in vitro, and the results of mea-
surements of samples in vitro and in vivo can differ
significantly.For example, the refractive index of rat
mesenteric tissue in vitro was found to be 1.52, com-
pared with 1.38 in vivo.5
The majority of existing techniques for refractive-
index determination, e.g., the method of critical angle,6
can be applied only in vitro to clear media or superfi-
cial layers.Recently a new technique that is appli-
cable to turbid media has emerged that uses optical
coherence tomography to track the shift in focal length
that results from translating the focus of the objec-
tive along the optical axis within the medium.2,7
refractive index of human skin, adipose tissue, and
muscle has been measured in vivo by this technique2
and by a modified version of it.8
ments made with the technique are inherently slow, as
they rely on an accurate, discrete axial displacement of
In this Letter we propose a new technique for the
direct, rapid measurement of refractive index in a tur-
bid medium, which we term bifocal optical coherence
refractometry.The technique is based on the simulta-
neous creation of two confocal gates and associated fo-
cal points within the sample.
interferometry to determine the optical path length be-
tween the two points from which the refractive index
is determined.The acquisition rate of the measure-
ment is subject to the same scan rate as low-coherence
interferometry, making the method well suited to the
rapid (of the order of milliseconds) measurement of the
refractive indices of turbid media, including biological
tissue in vivo.
The proposed technique, illustrated schematically in
Fig. 1, is based on a scanning Michelson interferome-
One uses low-coherence
ter that employs a linearly polarized broadband source.
For convenience, the optical circuit is illustrated (and
implemented) by use of optical fiber.
arm the beam is collimated, expanded, and split; a
polarizing beam splitter ?PBS1? is used to minimize
loss.One beam passes through a weak lens, Lf, and
the other beam passes through a path-length compen-
sator, C, to equalize the optical path lengths of the
beams.The beams are recombined by a second polar-
izing beam splitter, PBS2, and aligned to the axis of
objective lens Lobj.The weak lens causes one beam to
focus closer to the objective; thus two axially separated
focal points are formed. Light that is backscattered
from the sample is collected by the optical fiber, thus
producing a confocal gate for each beam.
The optical path length between the two focal points
Dlopt is measured by axial scanning of the reference
optical path length.The optical path length in a
homogeneous sample of refractive index n, obtained
by marginal ray-tracing analysis, is given by
In the sample
?fobj2 a??NA2?n22 1? 1 n2?1?2
2?fobj2 a 2 Dl??NA2fobj4?n22 1? 1 ?nfDl?2?1?2
where NA is the numerical aperture of the objective
lens, f and fobjare the focal lengths of the weak lens
and the objective lens, respectively, a is the distance in
Fig. 1.Schematic diagram of the proposed technique.
0146-9592/03/020117-03$15.00/0© 2003 Optical Society of America
OPTICS LETTERS / Vol. 28, No. 2 / January 15, 2003
air from the principal plane of the objective lens to the
sample interface, and Dl is the distance between
the two focal points in air.
that the group index and the refractive index are
equal, implying negligible dispersion.
the parameters of the system are known, or were
previously determined, the refractive index, averaged
over the axial distance between the two focal points,
can be calculated.
To test the technique we constructed an experi-
mental setup based on a fiber-optic, low-coherence
illuminated with polarized light from a superlumines-
cent diode with a mean wavelength of 815 nm and a
3-dB bandwidth of 22 nm.
line comprised a frequency-domain, folded-grating
lens-and-tilted-mirror configuration operated off axis
and in double pass.9
The grating had 830 lines?mm,
and the lens was a 100-mm focal-length, infrared
achromatic doublet. The mirror was 20 mm in diame-
ter and was angle scanned by means of a galvanometer
at 60 Hz.Polarization controllers were placed in both
the reference and the sample arms, which enabled
the power in each branch of the sample arm to be
adjusted separately. A tilted plane-parallel glass
plate was used as the path-length compensator.
angle of the plate to the optical axis was varied until
the optical path-length difference between the two
beams in the sample arm was equal to the optical
path length between the two focal points.
cal lengths of the weak lens and the objective lens
were 1000 and 10 mm, respectively.
diameter, measured by a scanning slit, was 7 mm.
At the output of the interferometer, the signal was
photodetected and its envelope was determined by use
of a modified phase-locked loop circuit,10displayed
on an oscilloscope, and subsequently transferred to a
We adopted a relatively simple calibration proce-
dure.We determined the axial separation of the focal
points in air by manually stepping a plane mirror
in 10-mm intervals through the two focal points
and recording the axial scan profile for each mirror
location.The maximum values of the signals were
determined for each measured position of the mirror.
The resultant experimental points are plotted in
Fig. 2.The scatter in the experimental points was
due primarily to the imperfect axial alignment of the
mirror and to the uncertainties in the axial position
during manual translation.
tance between the two focal points we least-squares
fitted the points with a fourth-order polynomial (not
shown in Fig. 2), and a peak-finding routine was used.
The distance was thus measured to be 120 6 2 mm.
The theoretical curve shown in Fig. 2 was calculated
from the axial response function of the system11,12and
the estimated fiber, lens, and beam parameters.
spite the limitations of the experimental setup, Fig. 2
shows that there is reasonable agreement between
experiment and theory. We checked the calibration
procedure for consistency by scanning the objective
lens for a fixed mirror position, which gave the same
results to within experimental error.
Equation (1) assumes
The scanning optical delay
To determine the dis-
Experimental measurements were made of commer-
cially available milk (nominal 2% fat content by vol-
ume) at various dilutions.
in a cuvette with a glass window of 150-mm nominal
thickness.The results of a scan through a 20% milk
solution are shown in Fig. 3.
of 256 axial line scans acquired in approximately 2 s.
A fouth-order polynomial was least-squares fitted to
the experimental data.The fitted curves are shown
as thicker curves in Fig. 3.
routine to determine the separation between the
fitted curves. Measurements were made for various
dilutions from 5% to 75%.
of the refractive index was 1.34 6 0.01 ?6s?, which
is consistent with the value reported in Ref. 13 of
1.344 6 0.004 at a wavelength of 633 nm.
experimental error, we did not find any dependence
on dilution, which is consistent with the results of
Differences in the functional forms of the two sets
of peaks are evident in Fig. 3.
the convolution of the source autocorrelation function
S?Dli?, with the axial sample reflectivity R?ls? modi-
fied by the axial response function of the sample-arm
confocal optical system h?ls?, is given by12
Milk solutions were placed
The trace is an average
We used a peak-finding
The resultant mean value
The signal envelope is
and corresponding theoretical axial intensity distribution.
Experimental response to a stepped mirror in air
retical curves fitted to the confocal peaks.
Axial response for a 20% milk solution with theo-
January 15, 2003 / Vol. 28, No. 2 / OPTICS LETTERS
thick skin on the dorsal surface of a human thumb in vivo.
Inset: Optical coherence tomography image of the corre-
sponding skin section.
Axial response for the stratum corneum of the
where h?ls? ? h1?ls2 lc1? 1 h2?ls2 lc2?, h1and h2are
the axial response functions of the two confocal gates,
lc1and lc2are positions of the peak values of h1and
h2, respectively, Dli? lr2 lsis the optical path-length
difference, and lr and ls are the lengths of the refer-
ence and the sample arms, respectively.
surfaces of the cuvette window are planar scatterers
and are located far from the focal points; hence the sig-
nal that arises from them is given by
I?lr? ? S?Dli?.
The peaks that are due to the glass, located at the
left side in Fig. 3, are described by Eq. (3) and are nar-
rower and with steeper decay than peaks that arise
from the milk sample, which are modified by the con-
focal response function as described by Eq. (2).
To measure the refractive index of human skin
in vivo we exchanged the objective lens for one with
a focal distance of 8 mm, for which the distance
between the focal points in air was measured to be
75 6 2 mm.The dorsal surface of the thumb of a
human volunteer was placed against a glass coverslip,
and the stratum corneum was scanned.
are shown in Fig. 4.The trace in Fig. 4 is an average
of 1024 axial line scans, representing an acquisition
time of approximately 8.5 s.
an image of the corresponding skin section acquired
with a 980-nm optical coherence tomography system
This image confirms that the
thickness of the stratum corneum was sufficient to
encompass the two focal points.
shown in Fig. 4, we measured the refractive index to
be 1.50 6 0.02.The error was assessed by multiple
measurements at the same site.
to the result reported in Ref. 2, i.e., 1.51 6 0.02, which
was obtained in vivo at a wavelength of 1300 nm.
A unique advantage of our technique is the provi-
sion of a direct measurement without the requirement
The inset in Fig. 4 is
Based on the results
Our result is similar
for motion in the sample or the sample arm.
particular implementation demonstrated here is not
unique, and configurations in which the distance
between the focal points can be controlled are of
particular interest. In our implementation the two
foci were formed with orthogonal linear polarization
states; hence any anisotropy of the medium would have
affected the measurement.
configurations are also possible.
the measurement is to first order independent of the
refractive index of the medium between the objective
lens and the two beam foci.
acquisition time was limited by the low optical power
at the surface of the skin, which was approximately
0.1 mW for each beam. With power of the order of
milliwatts, the refractive index could be measured
from the average of a few colocated or adjacently
located axial scans, limited primarily by speckle
noise, making an acquisition time of some tens of
In conclusion, we have proposed and demonstrated
bifocal optical coherence refractometry for the rapid
determination of the refractive index of a turbid
medium. The results of experiments with milk solu-
tions and with human skin in vivo are consistent with
published data.High-speed acquisition would make
the technique suitable for a range of applications and
particularly attractive for in vivo refractive-index
measurements of living biological media under dy-
The accuracy of
In our experiments, the
S. A. Alexandrov’s e-mail address is sergey@ee.
1. V. Tuchin, ed., Handbook of Optical Biomedical Diag-
nostics (SPIE Press, Bellingham, Wash., 2002).
2. G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E.
Bouma, M. R. Hee, and J. G. Fujimoto, Opt. Lett. 20,
3. B. B. Das, F. Liu, and R. Alfano, Rep. Prog. Phys. 60,
4. G. Miller and A. Rogan, eds., Laser-Induced Interstitial
Thermotherapy (SPIE Press, Bellingham, Wash., 1995).
5. F. A. Duck, Physical Properties of Tissue:
hensive Reference Book (Academic, London, 1990).
6. D. Tentori, J. Camacho, and C. Lopez-Famozo, Opt.
Commun. 103, 15 (1993).
7. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H.
Maruyama, and M. Hashimoto, Opt. Lett. 23, 966
8. A. Knuttel and M. Boehlau-Godau, J. Biomed. Opt. 5,
9. K. K. M. B. D. Silva, A. V. Zvyagin, and D. D. Sampson,
Electron. Lett. 35, 1404 (1999).
10. A. V. Zvyagin, J. B. FitzGerald, K. K. M. B. D. Silva,
and D. D. Sampson, Opt. Lett. 25, 1645 (2000).
11. M. Gu, C. J. R. Sheppard, and X. Gan, J. Opt. Soc. Am.
A 8, 1755 (1991).
12. J. A. Izatt, M. D. Kulkarni, H. W. Wang, K. Kobayashi,
and M. V. Sivak, J. Sel. Top. Quantum Electron. 2,
13. A. Jaaskelainen, K.-E. Peiponen, and J. A. Raty,
J. Dairy Sci. 84, 38 (2001).