Physics in Medicine & Biology
`
`Refractive indices of human skin tissues at eight
`wavelengths and estimated dispersion relations
`between 300 and 1600 nm
`To cite this article: Huafeng Ding et al 2006 Phys. Med. Biol. 51 1479
`
`View the article online for updates and enhancements.
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`INSTITUTE OF PHYSICS PUBLISHING
`
`Phys. Med. Biol. 51 (2006) 1479–1489
`
`PHYSICS IN MEDICINE AND BIOLOGY
`
`doi:10.1088/0031-9155/51/6/008
`
`Refractive indices of human skin tissues at eight
`wavelengths and estimated dispersion relations
`between 300 and 1600 nm
`
`Huafeng Ding1, Jun Q Lu1, William A Wooden2, Peter J Kragel3 and
`Xin-Hua Hu1
`
`1 Department of Physics, East Carolina University, Greenville, NC 27858, USA
`2 Department of Surgery, Brody School of Medicine, East Carolina University, Greenville,
`NC 27858, USA
`3 Department of Pathology, Brody School of Medicine, East Carolina University, Greenville,
`NC 27858, USA
`
`E-mail: hux@ecu.edu
`
`Received 7 September 2005, in final form 3 January 2006
`Published 1 March 2006
`Online at stacks.iop.org/PMB/51/1479
`
`Abstract
`The refractive index of human skin tissues is an important parameter in
`characterizing the optical response of the skin. We extended a previously
`developed method of coherent reflectance curve measurement to determine the
`in vitro values of the complex refractive indices of epidermal and dermal tissues
`from fresh human skin samples at eight wavelengths between 325 and 1557 nm.
`Based on these results, dispersion relations of the real refractive index have been
`obtained and compared in the same spectral region.
`
`(Some figures in this article are in colour only in the electronic version)
`
`1. Introduction
`
`Understanding the response of the skin to optical radiation is essential to the dermatological
`applications of photomedicine. Among various skin optical parameters, refractive index is an
`important one. At the microscopic scales ranging from 1 to 10 µm, refractive index variation
`causes light scattering which can be understood by direct solution of the Maxwell equations
`within the framework of classical electrodynamics for simple shaped particles (Bohren and
`Huffman 1983, Ma et al 2003a) and for biological cells (Lu et al 2005). For highly turbid
`tissues of human skin with sizes of 1 mm or larger, modelling of tissue optics based on the
`electrodynamic theory is very difficult, and the real refractive index and scattering parameters
`are often treated as independent parameters within the frameworks of effective medium theory
`and radiative transfer theory, respectively. For example, in the widely used method of Monte
`Carlo simulation of light distribution in biological tissues, photon interaction with an interface
`
`0031-9155/06/061479+11$30.00 © 2006 IOP Publishing Ltd Printed in the UK
`
`1479
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`H Ding et al
`
`between tissue regions of different refractive indices is described according to the Fresnel
`equations which require the index as the key parameter (van Gemert et al 1989, Wang et al
`1995, Lu et al 2000). Furthermore, accurate modelling of measured light signals near a skin
`surface requires the refractive indices of skin tissues to account for the redistribution of light
`due to the index mismatch at the surface (Lu et al 2000, Meglinsky and Matcher 2001, Bartlett
`and Jiang 2001, Maet al 2003b, 2005).
`Determination of the refractive indices of the human skin tissues, however, presents
`challenges because of their highly turbid natures. In transparent or absorbing media such as
`the aqueous solutions with molecular solutes, propagation of light is dominated by its coherent
`component. The reflection and refraction of a light beam, as it passes through an interface
`between two media of different refractive indices, are described with the Fresnel equations
`on the basis of an effective medium theory. In contrast, light propagation in a turbid medium
`produces a scattering component that becomes increasingly dominant as the light penetrates
`into the medium. This feature of interaction often precludes the use of refraction method to
`determine the refractive index of biological tissue samples where uniform and thin samples
`are very difficult to obtain. Recently, we developed an automated reflectometer system for
`determining the refractive index of a turbid sample by measurement of its coherent reflectance
`R versus the incident angle θ without the need to section skin tissues (Ding et al 2005). Here
`we report complex refractive indices of fresh human skin tissues determined by nonlinear
`regression of R(θ) with the Fresnel equations. The complex refractive index has been obtained
`at eight wavelengths between 325 and 1557 nm for both the epidermis and dermis tissues.
`With these data we investigated various dispersion schemes for interpolation of the index data
`at other wavelengths in this spectral region.
`
`2. Methods
`
`Fresh skin tissue patches were obtained from the patients undergoing abdominoplasty
`procedures at the plastic surgery clinic of the Brody School of Medicine, East Carolina
`University (ECU). A study protocol approved by the Institutional Review Board of ECU
`was strictly followed and a consent form was signed by each participating patient before the
`surgery. We obtained one skin tissue patch from each of the 12 female patients with ages
`between 27 and 63 years old; 10 are Caucasian and 2 are African Americans, with the skin
`data compiled in table 1. Each skin patch was stored in a bucket on crushed ice (∼2 ◦C)
`inside a refrigerator immediately after surgery. Samples with sizes of about 1 cm × 1 cm were
`prepared by removing the hair on the skin surface with scissors and subcutaneous fat tissue
`with a razor blade and warming the skin to a room temperature of about 22 ◦C with 0.9%
`saline drops. Care was taken to preserve the stratum corneum layer of the skin epidermis. The
`skin sample was pressed against the base of the prism with a pistol pressurized by a nitrogen
`gas cylinder to maintain good contact between the sample and the prism. The periphery of
`the tissue sample between the pistol and prism base was sealed with plastic tape to prevent
`sample dehydration during the measurement. By pressing either the epidermis or dermis side
`of the skin sample against the prism base, the coherent reflectance curves of skin epidermis or
`dermis were measured, respectively. All reflectance curve measurements were performed at
`the room temperature within 30 h after the abdominoplasty procedure.
`An automated reflectometer system has been designed and constructed to measure the
`coherent reflectance as a function of incident angle. Compared to other approaches of index
`determination based on fibre insertion and OCT (Bolin et al 1989, Tearney et al 1995, Knuttel
`and Boehlau-Godau 2000), this method has the combined benefits of high accuracy, wide
`spectral capability and instrumentation simplicity. The system has been described in detail
`
`3
`
`

`

`Refractive indices of human skin tissues and estimated dispersion relations
`
`1481
`
`PD2
`
`IR
`
`A
`
`prism
`
`θ
`
`n0
`
`n
`
`sample
`
`I0
`
`C
`
`PD1
`
`Figure 1. The schematic of the reflectomer system.
`
`Table 1. The human skin sample data.
`
`ID no.
`
`Age
`
`Race
`
`Tissue location
`
`Skin type Measurement
`
`1
`2
`3
`4
`5
`6
`7
`8a
`9a
`10a
`11a
`12
`
`42
`40
`27
`63
`56
`54
`34
`55
`49
`41
`39
`44
`
`Caucasian
`Caucasian
`African American
`Caucasian
`Caucasian
`Caucasian
`Caucasian
`Caucasian
`Caucasian
`Caucasian
`African American
`Caucasian
`
`Abdomen
`Abdomen
`Abdomen
`Abdomen
`Abdomen
`Arm
`Abdomen
`Abdomen
`Abdomen
`Abdomen
`Abdomen
`Abdomen
`
`III
`I
`V
`II
`II
`II
`II
`I
`III
`II
`V
`III
`
`Pressure dependence
`633 nm, 532 nm
`442 nm
`1064, 850 nm
`325,1550 nm
`1310, 633 nm
`1064, 325 nm
`532,633 nm
`442,1310 nm
`850,1550 nm
`532, diffuse reflection
`Pressure dependence
`
`a The skin structures of the samples from these patients have been examined through histology.
`
`elsewhere (Ding et al 2005). Briefly, a right-angle glass prism was used to interface with a
`skin sample on the prism base and a linear polarized laser beam was propagated through one
`side surface as the incident beam on the prism–sample interface at an incident angle of θ.
`The coherent reflectance R of the laser beam was measured at the angle of specular reflection
`by a photodiode of either Si or GaAs, depending on the light wavelength. Two coherent
`reflectance curves, Rs(θ ) or Rp(θ ), have actually been measured for each sample with either
`s- or p-polarized incident beam, respectively. The incident angle θ can be varied between
`48◦ and 80◦ with a stepsize of 0.125◦ and resolution of 0.006◦. A schematic diagram of the
`optical setup is presented in figure 1. The powers of the incident and reflected beams were
`measured by two identical photodiodes and the effect of the reflection loss at the side surfaces
`of the prism was removed to determine the coherent reflectance (Rs or Rp). To reduce the
`contribution of diffuse reflection to reflection signal, a pinhole of 2 mm diameter was used in
`front of the photodiode, resulting in an angular range of 1.74 × 10−2 rad or about 1.00◦ in
`the measurement. The incident laser beam, modulated at 370 Hz for lock-in detection, was
`produced by one of seven continuous-wave (cw) lasers at one of eight wavelengths: λ = 325,
`442, 532, 633, 850, 1064, 1310 and 1557 nm. The diameter of the beam was set to between 1
`and 2 mm with the incident beam power adjusted to be about 1 µW.
`The measured coherent reflectance curves have been fitted by the calculated values, ˜Rs(θ )
`and ˜Rp(θ ), according to the Fresnel equations. The fitting requires the assumed value of the
`
`4
`
`

`

`1482
`
`H Ding et al
`
`(a)
`
`(b)
`
`θ=45°
`
`θ=70°
`
`Water
`Dermis
`Epidermis
`
`10-2
`
`10-3
`
`10-4
`
`10-5
`
`10-6
`
`10-1
`
`10-2
`
`10-3
`
`10-4
`
`Reflection Signal (a.u.)
`
`-4
`
`-3
`
`-2
`
`-1
`0
`1
`Rotation Angle(°)
`
`2
`
`3
`
`4
`
`Figure 2. The reflection signal versus rotation angle of the detector at the incident angle of
`(a) θ = 45◦; (b) θ = 70◦ with a s-polarized beam at λ = 633 nm for deionized water, the epidermis
`and dermis of one skin sample. The error bars of about ±5% were removed for clear view and the
`two dashed lines indicate the angular acceptance range of the aperture in front of the photodiode.
`
`complex refractive index of the turbid sample, n = nr + ini, and the known refractive index,
`n0, of the prism. Therefore, the index n was inversely determined using an iteration process
`to achieve least-squared difference between the calculated and measured curves (Ding et al
`2005). The consistency between the measured and calculated coherent reflectance curves is
`described by a coefficient of determination, R2, defined as
`R2 = 1 −!N
`i=1 (Ri − ˜Ri )2
`!N
`i=1 (Ri − ¯R)2
`where Ri and ˜Ri denote the measured and calculated reflectances at the ith angle of incidence
`θ i, respectively, and ¯R is the mean value of measured reflectance over N values of θ. The R2
`value ranges between 0 and 1 with R2 = 1 for a perfect fit. The system was calibrated before
`measurements of each sample by comparing the measured real refractive index of deionized
`water with the published value at the wavelength of measurements (Hale and Querry 1973).
`From the water data, the experimental error in determination of the real refractive index nr of
`transparent samples by the reflectometer system was found to be about δnr = ±0.002.
`
`(1)
`
`,
`
`3. Results
`
`To ensure that the reflection signal is dominated by its coherent component, we measured the
`angular distribution of the reflected beam around a specular reflection angle at two positions
`(θ = 45◦ or 75◦) with λ = 633 nm. Similar data with deionized water were used as the
`baseline and all are plotted in figure 2. These results demonstrate that the contribution of the
`diffusely reflected light to the coherent reflectance signal is negligible within the 1◦ angular
`range defined by the photodiode aperture (indicated by the dashed lines in figure 2). Two
`typical sets of coherent reflectance curves from the epidermis and dermis sides of the skin
`
`5
`
`

`

`Refractive indices of human skin tissues and estimated dispersion relations
`
`1483
`
`(a)
`
`(b)
`
`75
`
`80
`
`measured data, skin type: III
`calculated curve
`measured data, skin type: V
`calculated curve
`
`measured data, skin type: III
`calculated curve
`measured data, skin type: V
`calculated curve
`
`50
`
`55
`
`60
`65
`Incident Angle (°)
`
`70
`
`1.0
`
`0.8
`
`0.6
`
`0.4
`
`0.2
`
`0.0
`1.0
`
`0.8
`
`0.6
`
`0.4
`
`0.2
`
`0.0
`
`Reflectance
`
`Figure 3. The typical measured coherent reflectance curves of two skin samples from two patients
`at λ = 442 nm with a s-polarized incident beam: (a) epidermis, (b) dermis. The solid lines
`are calculated curves based on the Fresnel equations with the following values of the complex
`refractive index: (a) n = 1.445 +i1.00 × 10−2 for ID no. 3 (skin type: V) and n = 1.458 +i8.34 ×
`10−3 for ID no. 9 (skin type: III); (b) n = 1.394 +i9.30 × 10−3 for ID no. 3 and n = 1.404 +i9.20
`× 10−3 for ID no. 9.
`
`samples of two patients with different skin types are presented in figure 3 together with the
`fitted curves based on the Fresnel equations. From these results one can see that the agreement
`between the measured and calculated reflectance curves varies from sample to sample and is
`gauged by the coefficient of determination R2. To determine the sensitivity of the refractive
`index on the nonlinear regression, we analysed the relation between R2 and n with selected
`data of the coherent reflection curves and typical results are presented in figure 4. On the basis
`of the standard deviations in the distribution of R2 values, we estimated that the uncertainty in
`obtaining the real and imaginary is about nr = ±0.006 and ni = ±0.005, respectively, for
`the turbid tissues of both the epidermis and dermis.
`To select an appropriate pressure applied to the skin tissue sample for achieving good
`contact between the sample and prism with minimal tissue damage, we determined the complex
`refractive index from two skin samples as a function of the pressure, as shown in figure 5. It
`can be seen from the data that the real index is not sensitive to the air pressure set between
`2 × 105 and 5 × 105 Pa. Signs of damage to the skin samples became visible when the
`pressure was increased to above 4 × 105 Pa, which included the fast dehydration of the tissue
`samples and significant reduction in the dermis layer thickness. On the basis of these results,
`all subsequent measurements of coherent reflectance of skin tissue samples were carried out
`at a fixed pressure of 2.06 × 105 Pa (30 psi or 2.0 atm) to minimize possible structural change
`in the skin tissues.
`At each wavelength, 8 or 12 skin samples were used to measure the coherent reflectance
`curves of Rs(θ ) and Rp(θ ) with 4 from one patient. Half of the samples were measured with the
`epidermis side in contact with the prism base and half with the dermis side. The measurement
`of Rs(θ ) and Rp(θ ) was repeated three times on the same skin sample and thus the data set
`
`6
`
`

`

`1484
`
`H Ding et al
`
`1.380
`
`1.385
`
`1.390
`
`1.395
`
`1.400
`
`1.405
`
`Dermis
`Epidermis
`
`1.430
`
`1.435
`
`1.445
`
`1.450
`
`1.440
`nr
`
`(a)
`
`(b)
`
`1.00
`
`0.99
`
`0.98
`
`R2
`
`0.97
`
`1.00
`
`0.99
`
`0.98
`
`R2
`
`0.97
`
`0.000
`
`0.005
`
`0.010
`
`0.015
`
`0.020
`
`ni
`
`Figure 4. The dependence of the coefficient of determination R2 on different choices of ni for
`a coherent reflectance curve measured from the epidermis and dermis sides of a skin sample
`at λ = 442 nm.
`
`0.024
`
`0.020
`
`ni
`
`0.016
`
`0.012
`
`0.008
`
`nr
`ni
`
`1.41
`
`1.40
`
`1.39
`
`1.38
`
`nr
`
`1.37
`
`1.36
`
`1.35
`
`1.5
`
`2.0
`
`2.5
`
`3.0
`3.5
`4.0
`Pressure (105 Pa)
`
`4.5
`
`5.0
`
`5.5
`
`Figure 5. The average real and imaginary refractive index versus sample pressure determined
`from the dermis of two skin samples.
`
`at each wavelength consists of 12 or 18 curves with an incident beam of s- or p-polarization.
`Nonlinear regression to the coherent reflectance curve data by the Fresnel equations was done
`individually to obtain the complex refractive index from each measurement. The coefficient
`of determination R2 ranges from 0.960 to 0.999 for the data from the measurement of the
`epidermis side and from 0.978 to 0.998 for the dermis side. The mean values and standard
`deviations of the complex refractive index have been calculated at each wavelength from the
`
`7
`
`

`

`Refractive indices of human skin tissues and estimated dispersion relations
`
`1485
`
`Cauchy
`Cornu
`Conrady
`
`(a)
`
`s-polarization
`p-polarization
`
`(b)
`
`400
`
`600
`
`800
`1000
`Wavelength (nm)
`
`1200
`
`1400
`
`1600
`
`1.48
`
`1.44
`
`nr
`
`1.40
`
`0.030
`
`0.025
`
`0.020
`
`0.015
`
`ni
`
`0.010
`
`0.005
`
`0.000
`
`Figure 6. The (a) real and (b) imaginary refractive indices of human skin epidermis versus
`wavelength. Each data point and associated error bar is the mean and standard deviation obtained
`from 12 or 18 measurements of 4 or 6 skin samples. The lines in (a) are based on the dispersion
`equations.
`
`data sets. These results are plotted as a function of wavelength in figure 6 for the epidermis
`and figure 7 for the dermis.
`We investigated various dispersion schemes to identify appropriate ones for calculation
`of real refractive index of human skin tissues at wavelengths between 300 and 1600 nm based
`on our index data at eight wavelengths. Among those reported on the index data of ocular
`tissues (Kroger 1992, Atchison and Smith 2005), we selected three schemes to fit to our data:
`the Cauchy dispersion equation
`
`(2)
`
`(3)
`
`C λ
`
`4 ,
`
`B λ
`
`2 +
`
`nr = A +
`the Cornu equation
`
`B
`nr = A +
`(λ − C)
`and the Conrady equation
`
`+
`
`B λ
`
`C
`nr = A +
`λ3.5 .
`The coefficients of each dispersion scheme determined with the least-squares principle from
`our index data are given in table 2.
`
`(4)
`
`4. Discussion
`
`Refractive index plays an important role in characterization of the biological tissues’ response
`to optical illumination, particularly for tissues of heterogeneous composition such as the
`layered skin tissues (Tuchin 2005). The real refractive index not only influences optical
`
`8
`
`

`

`1486
`
`H Ding et al
`
`Cauchy
`Cornu
`Conrady
`
`(a)
`
`(b)
`
`s-polarization
`p-polarization
`
`400
`
`600
`
`800
`1000
`Wavelength (nm)
`
`1200
`
`1400
`
`1600
`
`1.42
`
`1.40
`
`1.38
`
`nr
`
`1.36
`
`1.34
`0.020
`
`0.015
`
`0.010
`
`0.005
`
`ni
`
`Figure 7. The (a) real and (b) imaginary refractive indices of human skin dermis versus wavelength.
`Each data point and associated error bar is the mean and standard deviation obtained from 12 or
`18 measurements of 4 or 6 skin samples. The lines in (a) are based on the dispersion equations.
`
`Table 2. The coefficients of different dispersion equationsa.
`
`Dispersion equation
`
`A
`
`Cauchy
`Cornu
`Conrady
`
`1.3696
`1.2573
`1.3549
`
`C
`B
`2.5588 × 103
`3.9168 × 103
`2.8745 × 103
`4.5383 × 102
`1.7899 × 10 −3.5938 × 106
`a These coefficients were obtained on the basis of equations (2)–(4) with wavelength in the unit of
`nanometres.
`
`pathlengths of light propagating in tissues that can be determined by the methods of phase
`or time-resolved spectroscopy (Duncan et al 1995, Zhao et al 2002) but also affects the light
`measurement outside the tissues due to the index mismatch at the boundaries (Meglinsky
`and Matcher 2001, Bartlett and Jiang 2001, Ma et al 2003b, 2005). With an automated
`reflectometer system, we have extended the technique of measuring the coherent reflectance
`curve (Meeten and North 1995, Ding et al 2005) to obtain the complex refractive indices of
`fresh human skin tissues. These results, therefore, are of interest to researchers wishing to
`conduct quantitative optical studies involving index-mismatched interfaces in the human skin.
`The measurement of coherent reflectance was validated by confirming the dominance
`of the coherent reflection over the diffused one at the specular reflection angle for both of
`the epidermis and dermis sides of the skin samples, as shown in figure 2. Diffuse reflection
`occurs mainly outside the angular range defined by the aperture of the photodiode PD2 (see
`figure 1) and decreases towards the baseline data of water for large incident angles as θ
`approaches 80◦. The diffusely reflected light originates from two sources: the rough tissue
`surface mismatched optically with the prism glass and the tissue bulk. From the index data
`
`9
`
`

`

`Refractive indices of human skin tissues and estimated dispersion relations
`
`(a)
`
`1487
`
`(b)
`
`Figure 8. The microscope images of the histology slides of the skin samples from two patients:
`(a) ID no. 9 (skin type: III); (b) ID no. 11 (skin type: V). Bar = 100 µm.
`
`presented in figures 6 and 7, we note that the index mismatch between the epidermis tissue
`and the BK7 glass of the prism is smaller than that of the dermis. Combining this fact with
`the knowledge of the skin epidermis having larger scattering coefficient than the dermis (van
`Gemert et al 1989), one can conclude that the diffuse reflection of the skin tissues seen in
`figure 2 should be dominated by the light scattering in the tissue bulk. This is consistent with
`our previous results on comparison of the diffuse reflection between the porcine skin tissues
`with rough surfaces and the intralipid solution samples with smooth surface (Ding et al 2005).
`The human skin has a layered structure with two primary layers of epidermis and dermis,
`both are beneath the superficial layer of the epidermis or the stratum corneum (sc). We
`examined the tissue structures by preparing histological slides of the skin tissue samples from
`4 patients (with ID no. from 8 to 11, see table 1) with standard H&E staining. Two examples
`of skin slides are shown in figure 8 with one from a Caucasian and another from an African
`American patient. It can be seen that the sc layer is less than 10 µm in thickness, as expected,
`with the thickness of epidermis ranging from about 30 to 80 µm. We further verified that
`the sc layer has no significant effect on the refractive index determination by comparing the
`index values from samples with and without the sc layer prepared from fresh porcine skin
`tissues. The sc layer was removed from the epidermal side of the porcine tissue samples using
`a tape-stripping method (Beisson et al 2001) without heating the samples. The real refractive
`index nr of the epidermis at the wavelengths of 442 nm and 1064 nm was found to be the
`same within the experimental errors between the samples with and without the sc layer. These
`results demonstrated that the sc layer has no significant effect on the real refractive index of
`the skin epidermis because of its small thickness in comparison with the penetration depth
`(Everett et al 1966, van Gemert et al 1989), see also the discussion below. Another point
`worth noting is the effect of the melanin on the refractive index of the skin tissues. As can
`be seen from figure 8, many basal keratinocytes containing melanin pigment are visible near
`the epidermal–dermal junction in patient no. 11 (skin type: V), while little pigment exists in
`patient no. 9 (skin type III). The high density of melanin in the type V skins appears only to
`affect significantly the imaginary refractive index of epidermis, as shown in figure 3.
`A general model of refractive index for a dense and turbid medium remains an open
`question. But according to the existing models of effective medium for absorbing or dilute
`turbid media (Ballenegger and Weber 1999, Barrera and Garcia-Valenzuela 2003) the refractive
`index determined from a coherent reflectance curve should relate to the medium’s optical
`response from over at least the full depth of penetration of the coherent component of the
`incident wave in the medium. The total attenuation coefficients, as the sum of the scattering
`and absorption coefficients, for both the skin epidermis and dermis are expected to be on the
`
`10
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`

`1488
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`H Ding et al
`
`orders of 1 to 10 mm−1 based on the published data (van Gemert et al 1989, Ma et al 2005) in
`the spectral region from 300 to 1600 nm. Consequently, the penetration depth for the coherent
`component should be about a few hundred micrometres or less. Therefore, one would expect
`the tissue response of the first 100 µm layer to dominate the coherent reflectance and thus the
`value of the real refractive index. This conclusion is supported by the wavelength correlation
`of the real refractive index determined from the epidermis and dermis sides of the skin tissue
`samples. The correlation coefficient of wavelength dependence of the real refractive index
`was found to be rcorr = 0.99 between the index determined with s- and p-polarized beam for
`the epidermis and rcorr = 0.95 for the dermis. The values of rcorr decrease drastically to 0.057
`and 0.065 between the index of epidermis and dermis measured with the s- and p-polarized
`beam, respectively.
`Within the previously discussed uncertainty on the real refractive index, our in vitro results
`of nr at about λ = 1310 nm agree with those determined in vivo from human skin epidermis
`(averaged over the sc and other sub-layers) by the OCT method (Tearney et al 1995, Knuttel
`and Boehlau-Godau 2000). The nr of dermis, however, is smaller than the above reported
`in vivo results: 1.36 versus 1.41 at about λ = 1310 nm. The wavelength dependence is similar
`to the nr of bovine and porcine muscle tissues in the visible region (Bolin et al 1989, Li and Xie
`1996). To extend the use of our real refractive index data on a limited number of wavelengths,
`we have tested different dispersion schemes based on the equations by Cauchy, Cornu and
`Conrady. From figures 6 and 7, it is clear that these relations are close to each other and all fit
`to data fairly well for the dermis and very well for the epidermis. Therefore, these equations
`may be used to estimate the values of the real refractive indices of human skin tissues with the
`coefficients given in table 2 between 300 and 1600 nm. These estimations should be further
`improved as the refractive index becomes available at an increased number of wavelengths in
`this spectral region.
`
`Acknowledgments
`
`JQL and XHH acknowledge partial support by a NIH grant (1R15GM70798-01). Comments
`and correspondence should be sent to X H Hu: hux@mail.ecu.edu.
`
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