Content uploaded by Stylianos E. Trevlakis
Author content
All content in this area was uploaded by Stylianos E. Trevlakis on Aug 27, 2021
Content may be subject to copyright.
Pathloss modeling for in-body optical wireless
communications
Stylianos E. Trevlakis, Alexandros-Apostolos A. Boulogeorgos, and Nestor D. Chatzidiamantis
Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece, 54124
Emails: {trevlakis; nestoras}@auth.gr; al.boulogeorgos@ieee.org
Abstract—Optical wireless communications (OWCs) have been
recognized as a candidate enabler of next generation in-body
nano-scale networks and implants. The development of an accu-
rate channel model capable of accommodating the particularities
of different type of tissues is expected to boost the design of
optimized communication protocols for such applications. Moti-
vated by this, this paper focuses on presenting a general pathloss
model for in-body OWCs. In particular, we use experimental
measurements in order to extract analytical expressions for the
absorption coefficients of the five main tissues’ constitutions,
namely oxygenated and de-oxygenated blood, water, fat, and
melanin. Building upon these expressions, we derive a general
formula for the absorption coefficient evaluation of any biological
tissue. To verify the validity of this formula, we compute the
absorption coefficient of complex tissues and compare them
against respective experimental results reported by independent
research works. Interestingly, we observe that the analytical
formula has high accuracy and is capable of modeling the
pathloss and, therefore, the penetration depth in complex tissues.
Index Terms—Absorption coefficient, biomedical engineering,
fitting, machine learning, optical properties.
I. INTRODUCTION
Optical wireless communication (OWC) based in-body
biomedical applications have attracted a significant amount of
attention over the last couple of years, due to the performance
excellency (in terms of reliability, speed, energy efficiency and
latency) that they are expected to achieve [1]–[6]. In order to
optimize the in-body OWC system performance, an accurate
channel model that takes into account the tissue characteristics
needs to be employed.
Scanning the technical literature, it can be observed that
most efforts focus on quantifying the optical characteristics of
specific tissues at certain wavelengths [7]–[17]. Also, in [7]–
[9], the authors performed measurements for the optical prop-
erties of both healthy and cancerous skin in the visible and
near-infrared spectral range. In [10]–[12], experiments were
performed that quantified the optical properties of human fe-
male breast tissues in multiple wavelengths and over different
distances. Furthermore, the authors in [13], [14] evaluated
the light absorption and scattering of bone tissue for various
wavelengths in the visible and near-infrared spectrum. Finally,
in [15]–[17], the optical properties of human brain tissue at
various ages were studied in the visible spectrum. However,
such results are not always useful for other researchers due
to various reasons. Firstly, they may not include the required
wavelengths of interest. Secondly, even if the wavelength
is available, the constitution of a tissue is different enough
between distinct individuals that the results cannot be regarded
as confident. As a result, the need arises for the development of
method that estimates the optical properties of a tissue based
on its constitution.
To this end, specific formulas have been reported for the
pathloss evaluation of a generic tissue that take into account
the variable amounts of its constituents (i.e. blood, water,
fat, melanin), but require their optical properties at the exact
transmission wavelength, which hinders the use of these for-
mulas [18], [19]. Motivated by this, this paper derives a novel
mathematical model, which requires no experimental measure-
ments for the calculation of the pathloss for in-body OWCs.
Based on the aforementioned, the technical contribution of the
this work is summarized as follows:
•We extract analytical expressions for the absorption co-
efficients of the five main tissues’ constitutions, namely
oxygenated and de-oxygenated blood, water, fat, and
melanin.
•Based on the these expressions, we derive a general
formula for the absorption coefficient evaluation of any
biological tissue.
•We present the analytical results for the absorption coef-
ficients of complex human tissues, such as brain, bone,
breast and skin, and compare them with experimental
results reported by independent works that prove the
validity of the presented mathematical framework.
•Finally, we illustrate the pathloss as a function of the
transmission wavelength for different complex tissues and
tissue thickness, and provide discussions that highlight
useful insights for the design of communication proto-
cols.
The rest of this paper is organized as follows. Section II
is devoted in presenting the pathloss model based on the
absorption properties of the constituents of any generic tissue.
Section III presents respective numerical results that verify
the mathematical framework and insightful discussions, which
highlight design guidelines for communication protocols. Fi-
nally, closing remarks are summarized in Section IV.
Notations: Unless stated otherwise, in this paper, exp(·)
represents the exponential function, while cos(·)and sin(·)
stand for the cosine and sine functions, respectively.
II. PATHLOSS MO DE L
The pathloss caused by the absorption of biological tissue
can be modeled as
L= exp (µaδ),(1)
where δis the transmission distance and µais the absorption
coefficient, which can be defined as
µa=−1
T
∂T
∂δ ,(2)
with Tdenoting the fraction of residual optical radiation at
δ. Thus, the fractional change of the intensity of the incident
light can be obtained as
T= exp (−µaδ).(3)
The absorption coefficient can be expressed as the sum
of all the tissue’s constituents, namely water, melanin, fat,
oxygenated blood and de-oxygenated blood. Thus, (2) can be
analytically expressed as in [18]
µa=BSµa(oBl)+B(1 −S)µa(dB l)
+W µa(w)+F µa(f)+Mµa(m)
,(4)
where µa(i)represents the absorption coefficient of the i-
th constituent, while B,W,F, and Mrepresent the blood,
water, fat, and melanin volume fractions, respectively. Finally,
Sdenotes the oxygen saturation of hemoglobin.
From (4), it becomes evident that, in order to evaluate
the absorption coefficients and volume fractions of each con-
stituent in order to calculate the complete absorption coeffi-
cient of any tissue. Although the techniques for measuring
optical properties evolve in terms of accuracy and speed,
the fact that tissue’s optical properties must be regarded as
variables between different tissues, people and even times,
hinders their mathematical modeling. These variations, on the
one hand are inherent on the individuality of each person,
while on the other hand they are subject to the measurement
techniques and tissue preparation protocols. However, the
absorption coefficients of the tissue’s constituents have been
measured in existing literature and are mainly dependent on
the wavelength of the transmitted optical radiation.
In this direction, we used the machine learning mechanism
based on non-linear regression, which is presented in Fig.1, to
extract analytical expressions for the absorption coefficients of
oxygenated and de-oxygenated blood, water, fat, and melanin
from on the experimental datasets for each of the constituents
as input [20]. In particular, absorption coefficient datasets
of oxygenated and de-oxygenated blood have been provided
in [21]–[24]. The analytical expressions of the absorption
coefficients of oxygenated and de-oxygenated blood, have
been fitted on the experimental results using the sum of
Gaussian functions and can be expressed as
µa(dBl)(λ) =
4
X
i=1
ai(dBl)exp −λ−bi(dBl)
ci(dBl)2!,(5)
Non-linear regression based fitting
mechanism
Input datasets
Output absorption coefficients
Fig. 1. Machine learning based fitting mechanism.
and
µa(oBl)(λ) =
5
X
i=1
ai(oBl)exp −λ−bi(oBl)
ci(oBl)2!.(6)
Furthermore, the absorption coefficient of water has been eval-
uated in several contributions [25]–[27], which were used to
extract a Fourier series that accurately describes the absorption
coefficient as a function of the transmission wavelength. The
extracted analytical expression of the absorption coefficient of
water can be written as
µa(w)(λ) = a0(w)+
7
X
i=1
ai(w)cos(iwλ) + bi(w)sin(iwλ).
(7)
Moreover, the absorption of fat is highly dependent on the
origin of the fat. For proper measurement of the optical
properties, the fat tissue must be purified and dehydrated.
This necessary preparation may cause inconsistencies between
different published works. However, the results presented
in [28] coincide with other works in the visible spectrum and,
thus, they are selected for extracting the mathematical model
for the absorption coefficient of fat. The analytical expression
was extracted by fitting the experimental measurements with
a sum of Gaussian functions and is given by
µa(f)(λ) =
5
X
i=1
ai(f)exp −λ−bi(f)
ci(f)2!.(8)
It should be highlighted that the parameters of the previously
extracted analytical expressions are provided in Table I. Fi-
nally, the experimental data available in open literature for the
absorption coefficient of melanin are highly consistent for the
visible spectrum [18], [29], [30]. Based on these results, the
analytical expression of the absorption coefficient of melanin
is given as
µa(m)(λ) = µa(m)(550) λ
550−3
,(9)
TABLE I
FITTING PARAMETERS FOR CONSTITUENT’S ABSO RPT IO N COE FFIC IEN T.
dBlood oBlood water fat
a0- - 324.1-
a138.63 14 102.2 33.53
a260.18 13.75 −568 50.09
a325.11 29.69 −126.6 3.66
a42.988 4.317 ×1015 236.8 2.5
a5-−34.3 73 19.86
a6- - −40.53 -
a7- - −12.92 -
b1423.9 419.7 697.9 411.5
b231.57 581.5 121.7 968.7
b3559.3 559.9−395.3 742.9
b4664.7−25880 −107.1 671.2
b5-642.6 115.6 513.8
b6- - 35.46 -
b7- - -8.373 -
c133.06 16.97 -38.38
c2660.8 11.68 -525.9
c359.08 46.71 -80.22
c428.53 4668 -32.97
c5-162.5-119.2
w- - 0.006663 -
where µa(m)(550) denotes the absorption coefficient of
melanin at 550 nm, which is equal to 519 cm−1.
III. RES ULTS & D ISCUSSION
This section focuses not only on the verification of the
mathematical framework presented in Section II via comparing
the experimental data with the analytical expressions derived
from it, but also on the illustration of its accuracy in modeling
complex biological tissues, such as skin, bone, breast, and
brain tissue. Finally, the pathloss is evaluated for each complex
tissue and insightful discussions are provided that illustrates
important design guidelines for communication protocols.
Fig. 2 depicts the experimental data for each constituent’s
absorption coefficient against the analytical results extracted
from (6) through (9). In more detail, the analytical expressions
for the oxygenated and de-oxygenated blood, water, melanin,
and fat are drawn in black, red, green, blue, and purple color,
respectively, while the corresponding experimental data are
represented by square, circle, star, triangle, and cross symbols.
The analytical and experimental results coincide, which proves
the validity of the analytical expressions. Another interesting
observation from this figure is that the absorption coefficient
of blood is higher than the rest constituents between 400 and
600 nm, while it is still among the most influential for higher
wavelength values. This highlights that even with relatively
low volume fraction, blood plays an important role in the
total absorption coefficient of any generic tissue. Furthermore,
it is evident that as λincreases, the absorption coefficient
increases as well, which highlights the importance of carefully
400 500 600 700 800 900 1000
10- 4
10- 3
10- 2
10- 1
100
101
102
103
104
a ( c m - 1 )
A n a l y t i c a l E x p e r i m e n t a l
o B lo o d
d B lo o d
M e la n in
W a te r
F a t
Fig. 2. Absorption coefficients of generic tissue constituents as a function of
the transmission wavelength.
selecting the transmission wavelength used in tissues with
high concentration in water. Moreover, we observe that the
absorption coefficient of fat receives values around 1 cm−1
with very small variations, which constitutes its impact on the
total absorption of generic tissues stable throughout the visible
spectrum. Finally, it becomes evident that the absorption of
melanin is among the highest between the generic tissue
constituents, but the most consistent throughout the visible
spectrum. This illustrates the importance of the concentration
of melanin in the tissue under investigation and, at the same
time, the negligible effect of the transmission wavelength on
the absorption due to melanin.
It should be highlighted that, the volume fraction of any
of the constituents plays a very important role in the final
form of the absorption coefficient. For example, if a tissue
is rich in water, the impact of the absorption coefficient of
water after it is multiplied by the water volume fraction can
affect the total absorption coefficient significantly, even if the
absorption coefficient of water seems insignificant on its own.
On the other hand, the impact of a constituent with high
absorption coefficient, such as melanin, can be diminished if it
has a low volume fraction. As a result, although the absorption
coefficients presented in Fig. 2 are very useful for determining
which constituents can affect the total absorption coefficient
of the generic tissue, it is not an absolute metric and must
be used with caution for making assumptions. In the rest of
this section, we present experimental results from the open
literature for the absorption coefficients of complex human
tissues and compare them to the estimation calculated based
on the mathematical framework that is presented above.
In Fig. 3, the absorption coefficients of complex tissues,
such as skin, bone, brain and breast, are presented as a function
of the transmission wavelength. The analytical expressions
and the experimental results are depicted as continuous lines
and circles, respectively. The experimental parameters for
each tissue are provided in Table II alongside their sources.
TABLE II
TISSUE PARAMETERS RELATED TO OPTICAL ABSORPTION FOR SKIN,
BO NE,BRAIN AND BREAST TISSUE.
Tissue B(%) S(%) W(%) F(%) M(%) Source
Skin 0.41 99.2 26.1 22.5 1.15 [7]–[10]
Breast 0.5 52 50 13 0 [10]–[12]
Bone 0.15 30 30 7 0 [10], [13], [14]
Brain 1.71 58.7 50 20 0 [15]–[17]
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
a ( c m - 1 )
A n a l y t i c a l E x p e r i m e n t a l
S k in
B r e a st
B r a in
B o n e
Fig. 3. Total absorption coefficient of complex tissues as a function of the
transmission wavelength.
From this figure, we observe that the analytical expression
for the total absorption coefficient provides a very close fit
to the experimental data, which verifies the validity of the
extracted expressions and provides proof that the presented
mathematical framework can describe the optical absorption
of generic tissues accurately. Furthermore, it is obvious that
the skin absorption coefficient has the most linear behavior out
of all the plotted tissues. This happens because of the increased
concentration of melanin in the skin, which leads to increased
absorption for higher wavelengths. On the other hand, the
absorption coefficients of other tissues, which have increased
blood and water concentrations, bare a strong resemblance to
the blood absorption coefficient in the region between 400
and 600 nm, while the impact of the absorption coefficient of
water becomes visible after 900 nm. This happens because the
higher blood and water volume fractions result in increased ab-
sorption in the wavelengths where each absorption coefficient
has relatively high values.
Having extracted the accurate absorption coefficients for the
various complex tissues, we can calculate the pathloss. To this
end, Fig. 4 depicts the pathloss as a function of the wavelength
due to absorption in skin tissues with different values of
thickness. By observing this figure, it becomes evident that
the pathloss decreases with the wavelength and increases with
the skin thickness. Thus, the optimal wavelength in the plotted
region is 1000 nm. Furthermore, in the following we assume
400 500 600 700 800 900 1000
10- 1
100
101
102
P a t h l o s s ( d B )
Fig. 4. Pathloss due to skin absorption as a function of the transmission
wavelength for different values of skin thickness.
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
P a t h l o s s ( d B )
Fig. 5. Pathloss due to breast absorption as a function of the transmission
wavelength for different values of breast thickness.
a transmission window to be the spectrum region where
the pathloss does not exceed 6 dB, i.e. the residual optical
signal is at least a quarter of the transmitted one. Thus, for
δ= 1 mm a transmission window exists for wavelength values
higher than 450 nm. However, this transmission windows
shrinks as the transmission distance increases. For example,
for δ= 3 mm it reduces to wavelengths higher than 650 nm,
while for δ= 3 mm it becomes even smaller for wavelengths
higher than 650 nm.
In Fig. 5, the pathloss of breast tissue is presented with
regard to the transmission wavelength for various values of
transmission distance. We observe that, as the δincreases, the
pathloss increases as well. On the contrary, the wavelength
influences the pathloss in a non linear manner. Moreover, a
single transmission window exists for all the plotted values of
δand is located after 550 nm. However, for higher values of
400 500 600 700 800 900 1000
10- 1
100
101
102
P a t h l o s s ( d B )
Fig. 6. Pathloss due to brain absorption as a function of the transmission
wavelength for different values of brain thickness.
400 500 600 700 800 900 1000
10- 2
10- 1
100
101
102
P a t h l o s s ( d B )
Fig. 7. Pathloss due to bone absorption as a function of the transmission
wavelength for different values of bone thickness.
δthis transmission window will be divided in two. Finally the
optimal transmission wavelength for breast tissue is 700 nm.
Fig. 6 illustrates the pathloss as a function of the wavelength
for different values of tissue thickness. As expected, for
higher values of δthe pathloss is also higher, while the
behavior of pathloss for wavelength variations is not linear.
For example, as λincreases from 500 to 550 nm the pathloss
increases, while for the same increase from 550 to 600 nm,
pathloss decreases. Also, the optimal transmission wavelength
is 700 nm. Furthermore, two transmission windows exist for
δ= 1 mm. The first is between 450 and 550 nm, while the
second after 600 nm. However, as the transmission distance
increases, only the second window will be valid.
In Fig. 7, the pathloss is depicted as a function of the
transmission wavelength for various transmission distance
values. Yet again, pathloss increases with tissue thickness,
while its behavior with regard to λchanges depends. The
optimal λfor transmission through bone tissue is 700 nm.
For δequal to 1and 2 mm, only one transmission window
exists for λhigher than 450 nm. On the contrary, for higher
δvalues, there are two transmission windows. For example,
for δ= 5 mm, the two windows are 475 −525 nm, and
600 −950 nm.
IV. CONCLUSION
In this paper, we first extracted analytical expressions for the
absorption coefficient of the major generic tissue constituents
based on published experimental measurements. These ex-
pressions enable the estimation of the absorption coefficient
of each constituent at any given wavelength. Based on them,
we formulate the mathematical framework for calculating the
absorption coefficient of any generic tissue with regard to the
transmission wavelength. Finally, we present the analytical
results for the absorption coefficients of complex human
tissues, compare them with experimental results from the open
literature that prove the validity of the presented mathematical
framework. Finally, we illustrate the pathloss as a function of
the transmission wavelength for different complex tissues and
tissue thickness, and provide insightful discussions.
AKN OWL ED GE ME NT
This research is co-financed by Greece and the European
Union (European Social Fund-ESF) through the Operational
Programme “Human Resources Development, Education and
Lifelong Learning 2014-2020” in the context of the project
“IRIDA-Optical wireless communications for in-body and
transdermal biomedical applications” (MIS 5047929).
REFERENCES
[1] S. E. Trevlakis, A.-A. A. Boulogeorgos, and G. K. Karagiannidis,
“On the impact of misalignment fading in transdermal optical wireless
communications,” in 7th International Conference on Modern Circuits
and Systems Technologies (MOCAST), May 2018.
[2] S. Trevlakis, A.-A. A. Boulogeorgos, and G. Karagiannidis, “Signal
quality assessment for transdermal optical wireless communications
under pointing errors,” Technologies, vol. 6, no. 4, p. 109, Nov. 2018.
[3] S. E. Trevlakis, A.-A. A. Boulogeorgos, and G. K. Karagiannidis, “Out-
age performance of transdermal optical wireless links in the presence
of pointing errors,” in IEEE 19th International Workshop on Signal
Processing Advances in Wireless Communications (SPAWC), Jun. 2018.
[4] S. E. Trevlakis, A.-A. A. Boulogeorgos, P. C. Sofotasios, S. Muhaidat,
and G. K. Karagiannidis, “Optical wireless cochlear implants,” Biomed-
ical Optics Express, vol. 10, no. 2, p. 707, Jan. 2019.
[5] S. E. Trevlakis, A.-A. A. Boulogeorgos, N. D. Chatzidiamantis, and
G. K. Karagiannidis, “All-optical cochlear implants,” IEEE Trans. Mol.
Biol. Multi-Scale Commun., vol. 6, no. 1, pp. 13–24, Jun. 2020.
[6] A.-A. A. Boulogeorgos, S. E. Trevlakis, and N. D. Chatzidiamantis, “Op-
tical wireless communications for in-body and transdermal biomedical
applications,” IEEE Commun. Mag., Jan. 2021.
[7] T.-Y. Tseng, C.-Y. Chen, Y.-S. Li, and K.-B. Sung, “Quantification of
the optical properties of two-layered turbid media by simultaneously
analyzing the spectral and spatial information of steady-state diffuse
reflectance spectroscopy,” Biomed. Opt. Express, vol. 2, no. 4, p. 901,
Mar. 2011.
[8] E. Salomatina, B. Jiang, J. Novak, and A. N. Yaroslavsky, “Optical
properties of normal and cancerous human skin in the visible and near-
infrared spectral range,” J. Biomed. Opt., vol. 11, no. 6, p. 064026, Nov.
2006.
[9] Y. Shimojo, T. Nishimura, H. Hazama, T. Ozawa, and K. Awazu,
“Measurement of absorption and reduced scattering coefficients in asian
human epidermis, dermis, and subcutaneous fat tissues in the 400- to
1100-nm wavelength range for optical penetration depth and energy
deposition analysis,” J. Biomed. Opt., vol. 25, no. 04, p. 1, Apr. 2020.
[10] J. L. Sandell and T. C. Zhu, “A review of in-vivo optical properties
of human tissues and its impact on PDT,” J. Biophotonics, vol. 4, no.
11-12, pp. 773–787, Oct. 2011.
[11] A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi,
S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved
diffuse reflectance and transmittance measurements of the female breast
at different interfiber distances,” J. Biomed. Opt., vol. 9, no. 6, p. 1143,
Nov. 2004.
[12] L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, G. M. Danesini, and
R. Cubeddu, “Bulk optical properties and tissue components in the fe-
male breast from multiwavelength time-resolved optical mammography,”
J. Biomed. Opt., vol. 9, no. 6, p. 1137, Nov. 2004.
[13] A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin,
“Optical properties of human cranial bone in the spectral range from
800 to 2000 nm,” in Saratov Fall Meeting 2005: Optical Technologies
in Biophysics and Medicine VII, V. V. Tuchin, Ed. SPIE, Aug. 2006.
[14] N. Ugryumova, S. J. Matcher, and D. P. Attenburrow, “Measurement
of bone mineral density via light scattering,” Phys. Med. Biol., vol. 49,
no. 3, pp. 469–483, Jan. 2004.
[15] J. Zhao, H. S. Ding, X. L. Hou, C. L. Zhou, and B. Chance, “In vivo
determination of the optical properties of infant brain using frequency-
domain near-infrared spectroscopy,” J. Biomed. Opt., vol. 10, no. 2, p.
024028, Mar. 2005.
[16] A. N. Yaroslavsky, P. C. Schulze, I. V. Yaroslavsky, R. Schober, F. Ulrich,
and H.-J. Schwarzmaier, “Optical properties of selected native and
coagulated human brain tissues in vitro in the visible and near infrared
spectral range,” Phys. Med. Biol., vol. 47, no. 12, pp. 2059–2073, Jun.
2002.
[17] P. van der Zee, M. Essenpreis, and D. T. Delpy, “Optical properties of
brain tissue,” in Photon Migration and Imaging in Random Media and
Tissues, B. Chance and R. R. Alfano, Eds. SPIE, Sep. 1993.
[18] S. L. Jacques, “Optical properties of biological tissues: a review,” Phys.
Med. Biol., vol. 58, no. 11, pp. R37–R61, May 2013.
[19] S. E. Trevlakis, A. A. A. Boulogeorgos, N. D. Chatzidiamantis, G. K.
Karagiannidis, and X. Lei, “Electrical vs optical cell stimulation: A
communication perspective,” vol. 8, pp. 192 259–192 269.
[20] A.-A. A. Boulogeorgos, S. E. Trevlakis, S. A. Tegos, V. K. Papanikolaou,
and G. K. Karagiannidis, “Machine learning in nano-scale biomedical
engineering.”
[21] S. Takatani and M. D. Graham, “Theoretical analysis of diffuse re-
flectance from a two-layer tissue model,” IEEE. Trans. Biomed. Eng.,
vol. BME-26, no. 12, pp. 656–664, Dec. 1979.
[22] M. K. Moaveni, A multiple scattering field-theory applied to whole
blood. Univ. of Washington, 1970.
[23] J. Schmitt, Optical Measurement of Blood Oxygen by Implantable
Telemetry. Stanford University, 1986. [Online]. Available:
https://books.google.gr/books?id=jIgPIQAACAAJ
[24] Y. Zhao, L. Qiu, Y. Sun, C. Huang, and T. Li, “Optimal hemoglobin
extinction coefficient data set for near-infrared spectroscopy,” Biomed.
Opt. Express, vol. 8, no. 11, p. 5151, Oct. 2017.
[25] G. M. Hale and M. R. Querry, “Optical constants of water in the 200-nm
to 200-µm wavelength region,” Appl. Opt., vol. 12, no. 3, p. 555, Mar.
1973.
[26] V. M. Zolotarev, B. A. Mikhailov, L. I. Alperovich, and S. I. Popov,
“Dispersion and Absorption of Liquid Water in the Infrared and Radio
Regions of the Spectrum,” Opt. Spectrosc., vol. 27, p. 430, Nov. 1969.
[27] D. J. Segelstein, “The complex refractive index of water,” Ph.D. disser-
tation, University of Missouri–Kansas City, 1981.
[28] A. N. Bashkatov, “Optical properties of the subcutaneous adipose tissue
in the spectral range 400–2500 nm,” Opt. Spectrosc., vol. 99, no. 5, p.
836, Nov. 2005.
[29] S. L. Jacques and D. J. McAuliffe, “The melanosome: threshold tem-
perature for explosive vaporization and internal absorption coefficient
during pulsed laser irradiation.” Photochem. Photobiol., vol. 53, no. 6,
pp. 769–775, Jun. 1991.
[30] G. Zonios, A. Dimou, I. Bassukas, D. Galaris, A. Tsolakidis, and
E. Kaxiras, “Melanin absorption spectroscopy: new method for non-
invasive skin investigation and melanoma detection,” J. Biomed. Opt.,
vol. 13, no. 1, p. 014017, Jan. 2008.
