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Optical properties of human nails in THz frequency range
Victoria A. Guseva, Sviatoslav I. Gusev*, Petr S. Demchenko, Egor A. Sedykh, and Mikhail K. Khodzitsky
Laboratory of THz Biomedicine, ITMO University, 49 Kronverksky Pr., St.Petersburg 197101, Russian Federation *e-mail: mail@gusev-spb.ru
Abstract. This work is devoted to investigation of optical properties (dispersion of refractive index, permittivity and absorption coefficient) of human nails in THz frequency range. These data were obtained by THz time-domain spectroscopy (TDS) technique in transmission mode. These results may be used to develop non-invasive technique of human pathologies control using nail as a reference sample in reflection mode of THz TDS. © 2016 Journal of Biomedical Photonics & Engineering.
Keywords: spectroscopy, nail, refractive index, permittivity, absorption, penetration depth
Paper #3146 received 2016.11.31; accepted for publication 2016.12.29; published online 2016.12.31. doi: 10.18287/JBPE16.02.040306. [Saratov Fall Meeting 2016 Special Issue].
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1 Introduction
Diabetes mellitus is a group of metabolic diseases characterized by hyperglycemia resulting from defects in insulin secretion, insulin action, or both [1]. The chronic hyperglycemia of diabetes is associated with long-term damage, dysfunction, and failure of various organs, especially the eyes, kidneys, nerves, heart, and blood vessel. Accurate and efficient assessment of blood glucose concentration is critical in clinical management of many pathological conditions in human population. There is a direct relationship between the level of glucose in the blood of patients with diabetes and the probability of developing complications of the disease [2].
Optical properties of whole blood are important parameters in biophysical investigations and medical diagnostics. Variations in cellular and biochemical composition of whole blood markedly affect the values of different optical parameters (absorption, scattering, index of refraction etc.) [3-7].
One of the most important benefit of spectroscopy methods is the possibility of non-invasive analysis of media.8 Transmission mode of spectroscopy is common way for collecting data about easy extractable media [9, 10]. On the one hand transmission mode of medium analysis provides accurate results, but can be unsuitable for completely non-invasive investigation of biological tissues and fluids [11, 12]. On the other hand, reflection mode of spectroscopy cannot be used for direct blood optical measurement due to the location of blood below the surface of the human body [13]. Moreover, THz reflected signal considerably weakened due to the water contained in the skin layer. Despite this, capillar blood located in fingers' nail beds may be investigated through the nails in the reflection mode (see Fig. 1).
Fig. 1 Scheme of non-invasive reflective spectroscopy of the capillar blood inside the nail bed.
At this variant of reflective spectroscopy, it is need to know optical properties of nail plate for analysis of nail bed spectral data. It is not enough papers with detailed data about optical properties of human nails in THz frequency range. For example, in the Ref. [14] it
was shown only refractive index and dispersion of absorption coefficient of nails. This work is dedicated to retrieve optical properties of human nails for purposes of non-invasive glucose measuring technology.
2 Experimental setup
The optical properties of nail plates were studied in the frequency range of 0.1-1 THz using time-domain spectrometer in transmission mode [11, 15]. The scheme of the setup is shown in the Fig. 2.
Fig. 2 Schematic diagram of the set up (FL-1 -femtosecond laser based on potassium-yttrium tungstate crystal activated with ytterbium (Yb: KYW), generating femtosecond pulses; F1, 2 - a set of teflon filters for IR wavelength range cutting off, BS - beamsplitter, DL -optical delay line, M1, 2, 3 - mirrors, Sam - investigated sample, Wol. - Wollaston prism, CdTe - electro optical cadmium-telluric crystal, BD - balanced detector, LA -lock-in amplifier, PC - personal computer, GTP - Glan-Taylor prism, PM1, 2 - parabolic mirrors, Ch - chopper, DAC - digital to analog converter, ADC - analog to digital converter
Broadband pulsed THz radiation is generated using a InAs semiconductor in the magnetic field of 2 T by irradiating it with femtosecond pulses of an Yb: KYW laser (wavelength of 1040 nm, the pulse duration of 120 fs, the pulse repetition frequency of 75MHz, the power of 1 W). THz radiation has the following output characteristics: the spectral range from 0.05 to 2 THz, the average power up to 30 ^W, the pulse duration of 2.7 ps. The main power is concentrated at the frequency range from 0.12 to 1.1 THz. THz radiation passes through a teflon filter (which cuts the wavelengths shorter than 50 цт). After that, the radiation passes through the sample fixed in a focal plane perpendicularly to the beam. THz sample pulse affects on the anisotropy of the electrooptical CdTe crystal. As a result, THz pulse induces birefringence of the probe
beam in the crystal due to the electrooptical effect. The birefringence magnitude is directly proportional to the intensity of terahertz wave electric field in the time point E(t). These data are required to calculating E(w) using Fourier transform.
3 Sample preparation
There are 10 different nails measured at this experiment. The nail samples were taken from hands of man corpse
(Fig 3).
Thicknesses of each nail were measured 10 times with micrometer. This feature helps to decrease error caused by thickness measuring (the most significant error in transmissive TDS of thin structures). Determination of samples thicknesses is shown in Table 1.
Each sample of nail plate was prepared for recording of transmission time-amplitude signal: there were the same zones of nail plates for thickness measuring and signal transmission (Fig. 4). The diameter of the THz pulse spot is 3 mm. Dried nail plates had not any other specific treatment before experiment.
Nail plate
Fig. 4 Scheme of recording time-amplitude signal.
Fig. 3 Investigated nail samples.
Table 1 Measured thickness values of nails, used in experiment.
Thickness of sample №x, ^m
1 2 3 4 5 6 7 8 9 10
1 450 420 450 410 420 460 410 430 430 360
2 460 410 420 440 410 490 370 450 460 390
3 520 460 410 390 450 470 480 410 470 390
4 430 450 430 410 380 490 460 420 460 410
5 490 440 410 400 390 490 460 430 440 430
6 510 450 480 450 420 490 400 390 430 380
7 490 420 420 420 440 470 400 390 450 430
8 460 460 430 400 450 470 410 430 460 330
9 480 450 420 400 410 490 400 400 450 440
10 540 450 420 410 420 480 390 420 440 430
Average 483±27 441±15 429±15 413±14 419±17 480±10 418±29 417±16 449±11 399±29
4 Data acquisition
For each sample, a time-amplitude transmission waveform was taken 100 times and averaged for each timepoint. Also it was taken reference transmission waveform of air. All the acquired reference and sample waveforms were converted by Fourier transformation into Eref(w) and Esam(w), respectively. Then the THz electric field is:
=
J2n
//w
e~iMtdt = Е0(ш)е
-i^(to)
(1)
where f(t) is the time-amplitude waveform, ю is the angular frequency, Ec(ra) is the amplitude data, ф(ю) is phase data.
The real part of refractive index nreal calculated as:
nreal(f) = 1 +
C((Psam(f)-9ref(f))
2 nlf
(2)
where c is the speed of light in vacuum, l is the thickness of medium, f is the frequency.
The absorption coefficient a is calculated using the amplitude data:
1
ОЭ
1 (E° refif) a(f) = - In'
I \Eo sam (/)
(3)
Both parts of the complex permittivity £ use both parts of the refractive index n:
The penetration depth L is reverse function to the absorption coefficient «.
The imaginary part of the refractive index nimag(f) requires data about the absorption coefficient «:
^real CO ^real CO ^imaq CO
^imaa 2 ^real ^imaa (f>)
(5)
(6)
^imaa (f>)
КО с
All of these optical properties available as results of Spectrina software [11].
a)
b)
e)
f)
Fig. 5 Frequency dispersions of optical propreties of: a) real part of refractive index nreaL(f), b) imaginary part of refractive index nimag (f), c) absorption coefficient n(f), d) penetration depth L(f), e) real part of permittivity £reai (f), f) imaginary part of permittivity £imag (f).
r
5 Results and Discussions
Based on 10 samples, we investigated the frequency dispersions of nreai, n^ag, «, L, e^i, £toag in the frequency range of 0.2 to 1.0 THz (see Fig. 5).
Enough amount of samples and measurements provides the result with a low level of error. The real part of refractive index has stable value of 1.70 ± 0.03 in the frequency range of 0.2 - 1.0 THz. The imaginary part of refractive index has inverse ratio on frequency in the frequency ranges of 0.2 - 0.5 THz (from 0.22 ± 0.03 to 0.11 ± 0.01) and of 0.9 - 1.0 THz (from 0.11 ± 0.01 to 0.10 ± 0.01), but has fixed value of 0.11 ± 0.01 at the frequency range of 0.5 - 0.9 THz. The absorption coefficient has direct ratio on frequency in the frequency range of 0.2 - 0.9 THz (from 18 ± 3 cm-1 to 40 ± 4 cm-1). The penetration depth has inverse correlation with frequency in the frequency range of 0.2 - 0.9 THz (from 0.055 ± 0.008 cm to 0.025 ± 0.002 cm). The real part of permittivity has stable value of 2.89 ± 0.08 in the frequency range of 0.2 - 1.0 THz. The imaginary part of permittivity has inverse ratio on frequency in the frequency ranges of 0.2 - 0.5 THz (from 0.76 ± 0.10 to 0.39 ± 0.02) and 0.9 - 1.0 THz (0.36 ± 0.03 to 0.32 ± 0.04) and fixed value of 0.38 ± 0.02 in the frequency range of 0.5 - 0.9 THz.
These results are dispersions, but not constants. At the same time, some frequency ranges with stable value are suitable for using nail as reference medium. Moreover, all 10 measured nail plates have same optical properties within the margin of error. The absorption coefficient of nail plates increases with the frequency increasing. Therefore, using of low frequency of THz range is more efficient for measuring glucose levels.
In the Ref. [14] it was shown only the refractive index and the dispersion of the absorption coefficient obtained using reflection THz TDS in the frequency range of 0.25 - 2.0 THz. It this paper we obtained all optical properties as dispersions such as the complex refractive index n(f), the absorption coefficient a(f), the penetration depth L(f), the complex permittivity e(f).
6 Conclusion
The dispersions of nail plates optical properties (the complex refractive index n(f), the absorption coefficient a(f) , the penetration depth L(f) , the complex permittivity e(f)) were obtained in the frequency range of 0.2 - 1 THz by THz TDS. These data will be helpful for development of the reflective non-invasive spectroscopic method of blood glucose measuring technique. Due to the radiation penetration depth is more than the nail plate thickness in the frequency range of 0.2 - 0.5 THz, that the radiation of this range can be used for nail bed investigation. Nail could be used as reference layer for investigation of capillar blood by reflection THz TDS.
Acknowledgments
This work was financially supported by the Government of Russian Federation, Grant 074-U01.
