Towards skin polarization characterization using polarimetric technique

Towards skin polarization characterization using polarimetric technique first-author †E-mail:p_ghassemi@modares.ac.irmiranbmh@modares.ac.ir †E-mail:p_ghassemi@modares.ac.irmiranbmh@modares.ac.ir p_ghassemi@modares.ac.ir corresp ‡Corresponding Author ‡Corresponding Author †E-mail:p_ghassemi@modares.ac.irmiranbmh@modares.ac.ir †E-mail:p_ghassemi@modares.ac.irmiranbmh@modares.ac.ir p_ghassemi@modares.ac.ir Biomedical Engineering Group, Department of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-111, Tehran, Iran Biomedical Engineering Group, Department of Electrical and Computer Engineering, Tarbiat Modares University, P.O. Box 14115-111, Tehran, Iran Measurement of optical properties of skin is an expanding and growing field of research. Recent studies have shown that the biological tissue, especially skin, changes the polarization state of the incident light. Using this property will enable the study of abnormalities and diseases that alter not only the light intensity but also its polarization state. In this paper we report an experimental study for measuring changes of polarization state of the light scattered from a phantom similar to a sample model of scattering skin. Using the notation of Stokes vector for the polarized light and Mueller matrix for the sample with its polarization properties, we have shown that some elements of the matrix were particularly sensitive to the changes of the polarization-altering physical properties of the scatterers within the phantom. Polarization Skin Phantom Scattering polarimetry Mueller matrix Stokes vector INTRODUCTION 1 Development of appropriate diagnostic techniques for measuring and monitoring skin abnormalities is currently one of the challenging areas of research (Sidorchuk, 2002 2002 ; Andreassi et al., 2004 2004 ; Matuszak and Radwanska, 2006 2006 ; Beard, 2008 2008 ). Most of diagnostic methods and evaluation methods for measuring the progress of skin disease are based on visual examination by dermatologists (Andreassi et al., 2004 2004 ; Skvara et al., 2005 2005 ; Celebi et al., 2008 2008 ). Therefore, reliability and repeatability of such methods are almost questionable. Skin shows absorption and scattering properties when it is exposed to light. Most of available methods are based on measuring intensity of reflected, scattered or transmitted light. Techniques like microscopy or dermatoscopy are able to only diagnose physical parameters that make changes to the light intensity (Andreassi et al., 2004 2004 ; Beard, 2008 2008 ). Researches have shown that biological tissue can affect the polarization state of the incident light. The main polarization-altering agents of skin are scattering particles like nuclei cells and mitochondria, and collagen fibers that demonstrate birefringent effect (Amos and White, 2003 2003 ). Development of skin abnormalities can also change the polarization state of the scattered light (Baba et al., 2002 2002 ; Cerny et al., 2007 2007 ). Therefore, the progress of such diseases could be measured and monitored by measuring the changes in the polarization state. Polarized light can be represented mathematically by a 4×1 vector known as the Stokes vector (Perry et al., 1978 1978 ; Azzam and Bashara, 1987 1987 ; Bohren and Huffman, 1998 1998 ). By measuring the Stokes vector of the scattered light from an object and comparing its elements with those of the incident light, we can obtain a 4×4 matrix known as the Mueller matrix characterizing the object under study. Each of the 16 elements of the Mueller matrix depends on the polarization-altering features of the object affecting the polarization state of the light. Polarization-altering components of skin could illustrate different polarization properties based on their shape, size, composition, structure, etc. The objective of this paper is to show the sensitivity of some elements of the matrix to the changes of physical properties of scatterers and collagen fibers, using the notation of Stokes vector for the polarized light and Mueller matrix for the skin. We have used a polarimetric experimental setup to measure the elements of the Mueller matrix of a phantom similar to the biologic skin with scattering and polarization properties. Our results have shown that polarimetry is a valuable technique that can be used for measuring the change in scattering and polarization properties of skin and can be developed as a suitable diagnostic tool for measuring skin abnormalities. MATERIALS AND METHODS 1 Theory 2 In scattering polarimetry, a beam of light of arbitrary polarization is represented mathematically by a 4×1 column vector known as the Stokes vector. Its elements, the Stokes parameters, are usually labeled I , Q , U , and V , and defined in terms of electrical field amplitudes parallel E ∥ and perpendicular E ⊥ to the scattering plane (Perry et al., 1978 1978 ; Bohren and Huffman, 1998 1998 ): $$\begin{array}{4}I = \left\langle {{E_{||}}E_{||}^* + {E_ \bot }E_ \bot ^*} \right\rangle = {I_{\rm{H}}} + {I_{\rm{V}}}, \\Q = \left\langle {{E_{||}}E_{||}^* - {E_ \bot }E_ \bot ^*} \right\rangle = {I_{\rm{H}}} - {I_{\rm{V}}}, \\U = \left\langle {{E_{||}}E_ \bot ^* + {E_ \bot }E_{||}^*} \right\rangle = {I_{\rm{P}}} - {I_{\rm{M}}}, \\V = i\left\langle {{E_{||}}E_ \bot ^* - {E_ \bot }E_{||}^*} \right\rangle = {I_{\rm{R}}} - {I_{\rm{L}}}, \\\end{array}$$ where parameters are defined as follows: * , complex conjugate; 〈 〉, time averaging over the interval long compared with the period; E ∥ , amplitude of electric field parallel to the scattering plane; E ⊥ , amplitude of electric field perpendicular to the scattering plane; I , light intensity; H, horizontal state of polarization; V, vertical state of polarization; P, +45° linear state of polarization; M, −45° linear state of polarization; R, right circular state of polarization; L, left circular state of polarization. It can be shown that, in general, I 2 ≥ Q 2 + U 2 + V 2 . The equality holds if the light is strictly monochromatic or completely polarized. For unpolarized light, Q = U = V =0. In general, the degree of polarization (DOP), degree of linear polarization (DOLP) and degree of circular polarization (DOCP) can be calculated from Stokes elements (Azzam and Bashara, 1987 1987 ): $$DOP = \sqrt {{Q^2} + {U^2} + {V^2}} /I,{\text{ }}DOLP = \,\sqrt {{Q^2} + {U^2}} /I,{\text{ }}DOCP = V/I.$$ For a partially polarized beam the sign of V indicates the preferential handedness of the vibration ellipse traced out by the electric field vector (Yao and Wang, 2000 2000 ). In general, the polarization state of a light beam is changed on interaction with a polarization-altering object (for example, polarizer, retarder, reflector, and scatterer). It is possible to represent such an object by a 4×4 matrix known as the Mueller matrix. If the incident beam Stokes vector is denoted by S in and the Mueller matrix of the system by M , the Stokes vector of outgoing beam S out is obtained by (Bohren and Huffman, 1998 1998 ): S out = MS in . The Mueller matrix representing a scattering medium is termed the scattering matrix. The Stokes vectors S in and S out , representing the incident and scattered beams respectively, are then related by the following matrix equation: $$\left[ {\begin{array}{*{20}{c}}{{I_{{\text{out}}}}} \\{{Q_{{\text{out}}}}} \\{{U_{{\text{out}}}}} \\{{V_{{\text{out}}}}} \\\end{array} } \right] = \frac{{\text{1}}}{{{k^{\text{2}}}{r^{\text{2}}}}}\left[ {\begin{array}{*{20}{c}}{{S_{{\text{11}}}}\quad {S_{{\text{12}}}}\quad {S_{{\text{13}}}}\quad {S_{{\text{14}}}}} \\{{S_{{\text{21}}}}\quad {S_{{\text{22}}}}\quad {S_{{\text{23}}}}\quad {S_{{\text{24}}}}} \\{{S_{{\text{31}}}}\quad {S_{{\text{32}}}}\quad {S_{{\text{33}}}}\quad {S_{{\text{34}}}}} \\{{S_{{\text{41}}}}\quad {S_{{\text{42}}}}\quad {S_{{\text{43}}}}\quad {S_{{\text{44}}}}} \\\end{array} } \right]\left[ {\begin{array}{*{20}{c}}{{I_{{\text{in}}}}} \\{{Q_{{\text{in}}}}} \\{{U_{{\text{in}}}}} \\{{V_{{\text{in}}}}} \\\end{array} } \right]{\text{,}}$$ where parameters are defined as follows: S ij , elements of the scattering Mueller matrix; k , wave number of the medium surrounding the particles; r , distance between the observation point and any scatterer in the medium. Each element of the scattering matrix is angle-dependent function of wavelength, size, shape, and composition of the scatterers within the scattering medium. To measure all the 16 elements of the scattering matrix, a combination of a light source, polarizer and retarder in the incident path and a combination of polarizer (analyzer), retarder, and detector in the detecting path are required. A required polarization state can be generated using appropriate selection of the azimuth angle of the polarizer and retarder in the incident path. The polarization state of the beam emerging from the scattering medium can be measured by appropriate adjustment of the azimuth angles of the polarizer and retarder and noting the intensity of the detected signal in the detecting path. It can be shown that using the following suggested positions for the polarization elements in the incident and detecting paths, all the elements of the scattering matrix can be calculated (Hariharan, 1992 1992 ; Cameron et al., 1998 1998 ; Roma and Dinescu, 2008 2008 ): $$M = \left[ {\begin{array}{*{20}{c}}{{I_{{\text{HH}}}} + {I_{{\text{HV}}}} + {I_{{\text{VH}}}} + {I_{{\text{VV}}}}\quad {I_{{\text{HH}}}} + {I_{{\text{HV}}}} - {I_{{\text{VH}}}} - {I_{{\text{VV}}}}\quad {I_{{\text{PH}}}} + {I_{{\text{PV}}}} - {I_{{\text{MH}}}} - {I_{{\text{MV}}}}\quad {I_{{\text{RH}}}} + {I_{{\text{RV}}}} - {I_{{\text{LH}}}} - {I_{{\text{LV}}}}} \\{{I_{{\text{HH}}}} - {I_{{\text{HV}}}} + {I_{{\text{VH}}}} - {I_{{\text{VV}}}}\quad {I_{{\text{HH}}}} - {I_{{\text{HV}}}} - {I_{{\text{VH}}}} + {I_{{\text{VV}}}}\quad {I_{{\text{PH}}}} - {I_{{\text{PV}}}} - {I_{{\text{MH}}}} + {I_{{\text{MV}}}}\quad {I_{{\text{RH}}}} - {I_{{\text{RV}}}} - {I_{{\text{LH}}}} + {I_{{\text{LV}}}}} \\{{I_{{\text{HP}}}} + {I_{{\text{HM}}}} - {I_{{\text{VP}}}} - {I_{{\text{VM}}}}\quad {I_{{\text{HP}}}} - {I_{{\text{HM}}}} - {I_{{\text{VP}}}} + {I_{{\text{VM}}}}\quad {I_{{\text{PP}}}} - {I_{{\text{PM}}}} - {I_{{\text{MP}}}} + {I_{{\text{MM}}}}\quad {I_{{\text{RP}}}} - {I_{{\text{RM}}}} - {I_{{\text{LP}}}} + {I_{{\text{LM}}}}} \\{{I_{{\text{HR}}}} - {I_{{\text{HL}}}} + {I_{{\text{VR}}}} - {I_{{\text{VL}}}}\quad {\text{ }}{I_{{\text{HR}}}} - {I_{{\text{HL}}}} - {I_{{\text{VR}}}} + {I_{{\text{VL}}}}\quad {I_{{\text{PR}}}} - {I_{{\text{PL}}}} - {I_{{\text{MR}}}} + {I_{{\text{ML}}}}\quad {I_{{\text{RR}}}} - {I_{{\text{RL}}}} - {I_{{\text{LR}}}} + {I_{{\text{LL}}}}} \\\end{array} } \right].$$ In Eq.( 5 5 ), each element of the matrix is obtained by adding the detected intensities in response to different polarizer and retarder settings in the incident and detecting paths. For example, I HH denotes the detected light intensity in responded to horizontal polarization setting in the incident path and horizontal polarization setting in the detecting path. I HV represents a next experiment by changing the polarizer setting in the detecting path to vertical position. Table 1 1 shows the complete notations. H: horizontal polarization; V: vertical polarization; P: +45° linear polarization; M: −45° linear polarization; R: right circular polarization; L: left circular polarization 2 Detecting path 6 Incident path H V P M R L H I HH I VH I PH I MH I RH I LH V I HV I VV I PV I MV I RV I LV P I HP I VP I PP I MP I RP I LP M I HM I VM I PM I MM I RM I LM R I HR I VR I PR I MR I RR I LR L I HL I VL I PL I ML I RL I LL Preparation of skin phantom 2 In some previously published studies, researchers have made use of water, epoxy resin, polyester, etc. to produce skin-like phantoms. The objective has been to generate a phantom with a homogenous matrix with an acceptable stability (Roma and Dinescu, 2008 2008 ; Gangnus et al., 2004 2004 ). The use of phantoms such as Intralipid in water, titanium dioxide in agar, glass microspheres in epoxy resin, epoxy resin with titanium dioxide, and glass microspheres in polyester has been recommended for optical and polarization study of skin (Gangnus et al., 2004 2004 ; Meglinski and Matcher, 2002 2002 ; Pogue and Patterson, 2006 2006 ). In our study we used epoxy resin with titanium dioxide (TiO 2 ) as a stable phantom for our polarization measurements. The materials that we used were epoxy resin EM-8037 (Epoxiran, Iran), hardener (Epoxiran, Iran) and titanium particles (Kemira, Finland), which were added to epoxy resin to resemble skin scatterers. Experimental setup 2 We set up a laboratory-based scattering polarimetric system using appropriate optical devices such as a laser source (HeNe laser, λ =632.8 nm, 7.5 mW), two wide band polarizer plates, two quarter (1/4) wave plates (retarders), two collimating lenses to focus laser on the sample and to collect the scattered light from the sample, and an optical detector. The block and schematic diagrams of the system are shown in Figs. 1 1 and 2 2 . A photograph of the system is shown in Fig. 3 3 . As shown, the light source, lens, polarizer and retarder form the polarization state generator (PSG) unit. The PSG unit generates the polarized light with arbitrary states of polarization. After interaction with the sample (skin-mimicking phantom), the scattered light is received by the polarization state detector (PSD) unit that consists of lens, retarder, polarizer, and optical detector. The scattering angle for measurements was set to 90°. By making comparison between polarization states of the incident light and scattered light, we can extract the polarization ellipse of the scattered light and elements of the Mueller matrix of the scattering phantom. In our experiment we used a commercially available PSD module from Thorlabs (Thorlabs PA500, UK) to measure the polarization state of light being scattered from the sample. A number of different phantoms were prepared and used for the measurements. These included epoxy resins with and without the TiO 2 particles. We used two different quality types of TiO 2 scatterers. The first type of TiO 2 particles had non-spherical shape and the second type was near-spherical as observed by a scanning electron microscope (Philips XL30, Holland). The objective of using the above particles was to study the presence of the scatterers resembling nuclei cells and mitochondria, and also check on the sensitivity of the technique to the change in shape of the scatterers. In order to study the birefringence properties of skin, in the next step, we prepared phantom of epoxy resin with TiO 2 spherical scatterers but added fiber glass threads to resemble collagen fibers in the skin. It is worth mentioning that during the formation process, the fiber glass is subjected to a high mechanical tension. Under such stress, the fiber material will become birefringent (Gupta, 1988 1988 ; Onofri et al., 2003 2003 ). According to Eq.( 5 5 ), it is necessary to make the 16 independent measurements for calculating the elements of the Mueller matrix. So, we had to make 4 individual polarimetric measurements with 4 different incident polarized light states (vertical, horizontal, +45°, and right circular). RESULTS 1 Initially, we carried out some calibration tests to evaluate the performance of the system. We used a polarizer and retarder, with known polarimetric properties, in place of the sample, and measured their Mueller matrices. The calibration tests were repeated and adjustments were made until we obtained their Mueller matrices in agreement with the references (Bohren and Huffman, 1998 1998 ; Azzam and Bashara, 1987 1987 ) within the instrumentation accuracy (±1.0%). As we mentioned before, we used a commercially available PSD module, which has its own calibration file provided by the manufacturer. The measurements for the prepared phantoms were repeated 10 times to check the repeatability of the results. The results of the polarimetric measurements for obtaining the Mueller matrices of epoxy resins with and without near-spherical TiO 2 particles are shown in Table 2 2 . All elements of the Mueller matrix are normalized to the first elements S 11 . The comparison between the results of these two samples is shown in Fig. 4 4 . i , j =1~4. ER1: epoxy resin without scatterers; ER2: epoxy resin with near-spherical TiO 2 particles. The values of whole elements have been normalized to the values of S 11 2 M resin 2 S i 1 2 S i 2 2 S i 3 2 S i 4 ER1 ER2 ER1 ER2 ER1 ER2 ER1 ER2 S 1 j 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 S 2 j −0.20 −0.17 0.30 0.23 0.66 −0.03 −0.09 −0.13 S 3 j 0.20 0.02 −0.02 −0.02 0.50 0.15 0.17 0.00 S 4 j 0.00 0.00 0.00 0.00 0.26 0.03 0.07 0.01 From Table 2 2 , S 23 , S 31 , S 33 , S 34 , S 43 , and S 44 show considerable sensitivity to the presence of the scatterers. It is clear from Fig. 4 4 that S 23 shows the highest sensitivity to the presence of scattering particles. The results of the polarimetric measurements of epoxy resin with non-spherical TiO 2 particles compared with those of epoxy resin with near-spherical TiO 2 particles are shown in Table 3 3 . A comparison between results is shown in Table 3 3 and Fig. 5 5 . i , j =1~4. ER2: epoxy resin with near-spherical TiO 2 particles; ER3: epoxy resin with non-spherical TiO 2 particles. The values of whole elements have been normalized to the values of S 11 2 M resin 2 S i 1 2 S i 2 2 S i 3 2 S i 4 ER2 ER3 ER2 ER3 ER2 ER3 ER2 ER3 S 1 j 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 S 2 j −0.17 −0.21 0.23 0.29 −0.03 −0.90 −0.13 −0.01 S 3 j 0.02 0.02 −0.02 0.01 0.15 0.18 0.00 −0.01 S 4 j 0.00 0.00 0.00 0.00 0.03 0.03 0.01 0.23 From Table 3 3 , S 23 , S 24 , and S 44 show considerable sensitivity to the change in shape between the two types of scatterers. Also from Fig. 5 5 it is evident that S 23 is the most sensitive marker for the shape of the scatterers. Table 4 4 shows the results of the polarimetric measurements for obtaining the Mueller matrices of epoxy resin with near-spherical TiO 2 particles compared with the same type of scatterers but with added fiber glass threads to create birefringence property. i , j =1~4. ER2: epoxy resin with near-spherical TiO 2 particles; ER4: epoxy resin of the same type with added fiberglass threads. The values of whole elements have been normalized to the values of S 11 2 M resin 2 S i 1 2 S i 2 2 S i 3 2 S i 4 ER2 ER4 ER2 ER4 ER2 ER4 ER2 ER4 S 1 j 1.00 1.00 0.00 0.00 0.00 0.00 0.00 0.00 S 2 j −0.17 −0.12 0.23 0.02 −0.03 0.02 −0.13 0.26 S 3 j 0.02 0.09 −0.02 0.26 0.15 0.01 0.00 0.12 S 4 j 0.00 0.00 0.00 0.00 0.03 0.00 0.01 0.05 From the Table 4 4 , S 22 , S 24 , S 32 , S 33 , and S 34 show considerable sensitivity to the presence of fiber glass threads. From Fig. 6 6 we can say that S 24 is the most sensitive marker for the presence of fiberglass threads or birefringent activity of the phantom. DISCUSSION AND CONCLUSION 1 In this paper, we presented the potential application of polarimetric technique for measuring polarization properties of skin. We carried out measurements of elements of the Mueller matrices of epoxy resin samples with TiO 2 scatterers with and without birefringent fiber glass threads, resembling skin with scattering and birefringent properties. The results presented are in good agreement with the theory that each element of the scattering matrix is dependent on the polarization-altering properties of the particulate medium including the presence of the scatterers, their size and shape, and the birefringence property. As mentioned, the sensitivity of elements is due to the orientation of the electrical field vector with respect to the assumed scattering plane within the particulate medium. Any change to such scattering medium will change the orientation of the electrical field vector. Also, the results presented are in good agreement with experimental results from previously published studies (Yang et al., 2003 2003 ; Viktin et al., 2002 2002 ; Ishimaru et al., 2001 2001 ; Firdous and Ikram, 2005 2005 ). The results show that some elements of the matrix were particularly sensitive to the presence of scatterers and their shape. Also, the results demonstrate the sensitivity of some particular elements to the birefringent effect of the sample. It is evident that S 24 is particularly sensitive to the birefringence property of skin phantom. Also S 23 shows the maximum sensitivity to the presence and change in shape of the scatterers. The choice of the scattering angle of 90° has been arbitrary. As mentioned earlier, the elements of the matrix are angle-dependent functions of the polarization-altering properties of the particulate medium. This means that other angles could be selected. However, the sensitive elements could vary in their sensitivity to the particular polarization-altering property. For example, instead of S 23 , another element may have emerged with highest sensitivity to the presence of the scatterers within the medium. The choice of 90° scattering angle provides a practical setup with view of the development of a future compact system for skin measurement. Although the introduction of fiber glass threads was meant to produce birefringence effect to the particulate medium, it is worth mentioning that the changes in elements of the Mueller scattering matrix, though highly dependent on the birefringence effect, can be due to the introduction of scattering by cylindrical fiber glass threads. This requires a future investigation, using appropriate experimental setup, to differentiate the effect of birefringence and scattering by cylindrical particles. The choice of a scattering angle can play a vital role in such an investigation. It is recommended to do such investigation over a number of scattering angles and use the theory, to find the appropriate angle that can differentiate these two effects. The above results show the applicability of the polarimetric technique that can be developed by designing an appropriate system for measuring polarization properties of skin in a clinical laboratory. 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