2.1.

Measuring Device

In our method, translucency is calculated from reflectances measured using a CM-2600d portable spectral reflectometer (Konica Minolta, Tokyo, Japan). This device has an optical system with diffusion light illumination/8-deg detection [Fig. 1a]. Reflectance can be measured in 10-nm increments across a 360–740-nm spectrum. Specular component excluded (SCE) mode was used in this study.

Fig. 1

(a) Schematic of the measurement device. Light from the light source is diffused by the integrating sphere and illuminates the sample. Part of the reflected light enters the detector and its spectrum is measured. (b) Measurement area when aperture radius exceeds detector viewing radius. The measurement radius is equal to the viewing radius. (c) Measurement area when detector viewing radius exceeds aperture radius. The measurement radius is equal to the aperture radius.

The CM-2600d reflectometer can alternate the detection radius between 4 and 1.5 mm, and the target mask that comes into contact with the sample can be changed. We utilized these features of the device in the present study. For normal measurements, a target mask with a 5.5-mm aperture radius is used when the detection radius is set to 4 mm (MAV mode), and a target mask with a 3-mm aperture radius is used when the detection radius is set to 1.5 mm (SAV mode). However, using a target mask with a different aperture radius allowed the creation of measurement conditions different from those normally used.

Let us consider how varying the aperture radius of the target mask changes the measurement radii when the detector viewing radius of the device is constant. If the viewing radius is smaller than the aperture radius, then the entire viewing area is the sample surface, and the measurement radius is equal to the viewing radius [Fig. 1b]. Conversely, if the viewing radius is larger than the aperture radius, then only the area of the sample within the aperture is exposed within the viewing area and the measurement radius is equal to the aperture radius [Fig. 1c].

2.2.

Formulation of Edge Loss

To optimize the measurement conditions, we modeled reflectance measurement in order to evaluate edge loss for a given measurement conditions and a given PSF. Wavelength is not explicitly stated, but each parameter is in fact a function of wavelength. Using the bidirectional scattering surface reflectance distribution function (BSSRDF) [TeX:] $S\left({\vec x_{\rm i},\vec \omega _{\rm i}; \vec x_{\rm o},\vec \omega _{\rm o} } \right)$ $S\left({\vec{x}}_{\mathrm{i}},{\vec{\omega }}_{\mathrm{i}};{\vec{x}}_{\mathrm{o}},{\vec{\omega }}_{\mathrm{o}}\right)$ , incident radiance [TeX:] $L_{\rm i} \left({\vec x_{\rm i},\vec \omega _{\rm i} } \right)$ $L_{\mathrm{i}}\left({\vec{x}}_{\mathrm{i}},{\vec{\omega }}_{\mathrm{i}}\right)$ from direction [TeX:] $\vec \omega _{\rm i} $ ${\vec{\omega }}_{\mathrm{i}}$ to point [TeX:] $\vec x_{\rm i} $ ${\vec{x}}_{\mathrm{i}}$ and outgoing radiance [TeX:] $L_{\rm o} \left({\vec x_{\rm o},\vec \omega _{\rm o} } \right)$ $L_{\mathrm{o}}\left({\vec{x}}_{\mathrm{o}},{\vec{\omega }}_{\mathrm{o}}\right)$ from point [TeX:] $\vec x_{\rm o} $ ${\vec{x}}_{\mathrm{o}}$ in direction [TeX:] $\vec \omega _{\rm o} $ ${\vec{\omega }}_{\mathrm{o}}$ can be expressed according to the following relationship:^{7, 8}

With further assumptions of isotropy and homogeneity regarding BSSRDF and incident radiance, Eqs. 1, 2, 3, apparent reflectance r can be calculated as follows:

Finally, edge loss is evaluated. When both the illumination radius and measurement radius are finite, apparent reflectance is less than true reflectance due to edge loss. We defined edge loss E quantitatively as this percentage decrease, as follows:

2.3.

Optimization of Measurement Conditions

From Eq. 5, we evaluated the relationship between illumination radius, measurement radius, and edge loss with numerical integration. Here we used a simple function system [Eq. 6] as the function system for the PSF for the purpose of approximation because our objective was simply to evaluate the effect of the relative degree of lateral spread,

With numerical integration, changes in edge loss with the illumination radius d _i and the ratio of the measurement radius to the illumination radius d _o/d _i as parameters are evaluated. A plot of the results is shown in Fig. 2. Edge loss increases with decreasing d _i and increasing d _o/d _i. These results are consistent with findings from previous studies.^{12, 13, 14, 16, 17}

Fig. 2

Magnitude of edge loss for illumination radius (d _i) and measurement radius/illumination radius (d _o/d _i) given in Eq. 6 (μ_eff = 0.8 mm⁻¹) for normalized PSF. Points A–D in the plot show conditions used for reflectance measurement (see Table 1). Edge-loss values at points A–D in the plot were 0.050, 0.118, 0.354, and 0.553, respectively. The combination of A and C was used in Experiment 2.

Using the variation of edge loss under different conditions, the level of translucency of the sample can be evaluated. Selecting combinations so as to maximize the difference in edge loss facilitates detection of even small variations. Taking Fig. 2 as a reference, a good combination of conditions would be large d _i and small d _o/d _i together with small d _i and large d _o/d _i in order to maximize signal-to-noise ratio (S/N). Optimum conditions must be selected from among those possible, taking into account the additional restriction imposed by the device of possible viewing radii of 4 and 1.5 mm. In addition, radii that are too small will cause the measurement to be affected by the reduced amount of light reflected from the sample and by irregularities in skin topography and color unevenness.

Conditions A and C from Table 1 were ultimately selected as standard conditions to combine for calculating translucency index. Conditions B and D were used in experiment 1 for the purposes of comparison. The MAV mode was used for conditions A, C, and D, and the SAV mode was used for condition B. For conditions A and B, the standard target masks for the MAV and SAV modes were used, respectively. For conditions C and D, the aperture size of each target mask was customized by affixing a black sheet with a hole to a target mask for the MAV mode. Edge-loss values E(A), E(B), E(C), and E(D) in Fig. 2 were 0.050, 0.118, 0.354, and 0.553, respectively.

Table 1

Illumination radius (d i) and measurement radius (d o) conditions A–D and the respective geometrical settings.

2.4.

Calculation of Reflectance and Translucency Index

First, sample reflectance was recalculated from the device output values to exclude the reflected component from the target mask from measurement values. Apparent reflectance r _i under condition i is calculated from

Using the pair of apparent reflectances of the sample thus obtained under the combination of conditions i and j to meet E(i) < E(j), the translucency index T _i,j is defined by the following:

2.5.

Experiments

3.1.

Experiment 1: Measurement of Translucent Samples

Reflectances were calculated from output values under each measurement condition using Eq. 7, and Fig. 3a shows translucency indices T _A,C, T _A,B, and T _C,D at a wavelength of 650 nm and the errors calculated from these combinations with Eq. 8. Figure 3b shows the spectrum of translucency index T _A,C as a representative example. The S/N designated in Sec. 2.5 was improved in the order of T _A,B, T _C,D, T _A,C as 11.01, 15.08, 28.29, respectively.

Fig. 3

(a) Translucency indices of prepared translucent samples (various combinations of measurement conditions for calculating translucency index) at a wavelength of 650 nm. The lower the concentration of foundation (measured in weight percent) in the sample, the higher the translucency. (b) T _A,C as a representative example. Error bars are shown for 0.5 and 0.2 wt%. In order of increasing translucency, each line represents 0.50, 0.20, 0.15, 0.10, and 0.05 wt%, respectively.

This result supports the hypothesis set out in Sec. 2.3 that the S/N would improve with increasing change in edge loss. From the given edge loss values for conditions A-D in Fig. 2, changes in edge loss between combinations A-B, C-D, and A-C can be calculated as 0.068, 0.201, and 0.304, respectively, meaning that the ranking orders of changes in edge loss and S/N were consistent.

Looking at the comparative values of translucency indices between samples, for T _A,C and T _A,B the relationship was such that the index increased with increasing translucency across the whole range of sample translucencies. For T _C,D, however, this ranking order did not hold true between samples with higher translucency of ≤0.20 wt%.

The reason for this was considered to be that a considerable degree of edge loss occurs in condition i of Eq. 9 (condition C in this case). If translucency of the sample increases considerably, E(j) approaches 1 and the variation of E(j) becomes smaller. As a result, E(j) becomes less sensitive than E(i) in terms of translucency. As partially differentiating T _i,j with respect to E(i) in Eq. 9 always results in negative values, T _i,j can be seen to decrease as E(i) increases when E(j) is constant. That is, if E(i) increases significantly, T _i,j will not necessarily increase despite increasing sample translucency. Taking these factors into account, it is particularly important to select condition i in Eq. 9 so that edge loss is minimized, in order to expand the coverage of translucency. This result also indicates that the selected combination, which is adequate for the measurement of skin translucency, may be inappropriate for objects with greater translucency.

3.2.

Experiment 2: Measurement of Human Skin

Experiment 2-1: A/E treatment. Figure 4 shows average values for all subjects for reflectance and translucency index spectra before and after treatment for the areas treated with A/E. Reflectance increased after treatment, but the translucency index decreased. Here, values at a wavelength of 650 nm were extracted from the spectrum to specifically investigate the influence of changes in scattering power alone (Fig. 5). Reflectance and translucency index had changed significantly with a 99% confidence level.

Fig. 4

Comparison before and after A/E treatment: (a) r _A and (b) T _A,C spectrum. Solid lines: before treatment; dashed lines: after treatment. Values represent mean values for all subjects. r _A increased and T _A,C decreased as a result of A/E treatment.

Fig. 5

Values at a wavelength of 650 nm extracted from spectra before and after A/E treatment: (a) r _A and (b) T _A,C. Significance was tested using a t-test (paired, bilateral). **: 99% confidence level.

These changes are reasonable from a qualitative perspective. The increase in the proportion of light reflected by the stratum corneum (where light absorption is weak) is considered to reduce the amount of light that reaches and returns from layers below this (where pigment absorb light), making reflectance increase. At the same time, light returning from shallow locations does not show much diffusion, with light diffusing more widely the deeper it reaches, making the translucency index decrease.

Experiment 2-2: UV-induced erythema. Figure 6 shows average values for all subjects for reflectance and translucency index spectra measured before and one day after treatment. Reflectance and translucency index were both decreased one day after treatment at a wavelength of ∼550 nm compared to before treatment. On the other hand, at ∼650 nm, reflectance was almost the same as before and the translucency index was increased. Figure 7 shows values at 550 and 650 nm extracted from the spectra. At 550 nm, both reflectance and translucency index values decreased significantly (99% confidence level). At 650 nm, reflectance was barely changed, but the translucency index was significantly increased (95% confidence level) after one day compared to before irradiation.

Fig. 6

Comparison of before and one day after UV irradiation: (a) r _A and (b) T _A,C. Solid lines: before irradiation; dashed lines: one day after irradiation. Values represent mean values for all subjects. Both r _A and T _A,C decreased at a wavelength of ∼550 nm after one day compared to before irradiation. On the other hand, T _A,C increased while r _A was barely changed at 650 nm.

Fig. 7

Values at 550 and 650 nm extracted from spectra before and one day after UV irradiation: (a) r _A at 550 nm, (b) T _A,C at 550 nm, (c) r _A at 650 nm, and (d) T _A,C at 650 nm. Significance was tested using a t-test (paired, bilateral). **: 99% confidence level, *: 95% confidence level, N.S.: not significant.

Changes at 550 nm are reasonable from a qualitative perspective. Reflectance decreased at a wavelength of 550 nm after one day as a result of erythema with a peak at 24–48 h.^{21, 22} Decreases in reflectance at a wavelength of 550 nm can be explained by the absorption spectrum of hemoglobin, which has strong peak at around 500–600 nm.^{23, 24} The fact that the translucency index also decreased can be explained by the depth reached by light and the degree to which this light contributes to diffusion. Hemoglobin present at a certain depth selectively absorbs the component of incident light that contributes to diffusion. Therefore, when reflectance decreases as a result of absorption by pigment, the translucency index also simultaneously decreases.

Although scattering power might also be changed in accordance with changes in thickness under conditions of erythema, the decrease in translucency index at 550 nm hardly seems to be explained by variations in scattering power. Vascular dilation under conditions of erythema²² can cause thickening of the skin and variations in scattering power. If we consider the fact that translucency was increased at 650 nm, at which the extinction coefficient of oxyhemoglobin is two orders of magnitude smaller²³ than the value at 550 nm and hemoglobin density has less effect on translucency than at 550 nm, scattering power should be changed in the direction of increasing translucency.

The order of the translucency index of skin and translucent samples using the proposed method are consistent with the order of μ_eff by VRM. From the results of Experiment 2, in which translucency index of skin was ∼0.3 at 650 nm [Figs. 5b, 7d], and the result of Experiment 1, we can say that forearm skin in Japanese individuals shows a translucency between 0.20 and 0.50 wt%. The order of translucency is thus consistent with the order from VRM mentioned in Sec. 2.5.

Lastly, as an evaluation of the possibilities of the proposed method, absorption coefficients (μ_a) and effective scattering coefficients ( [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ ) were roughly estimated from the reflectances (r _A) and translucency indices (T _A,C) of the result in Experiment 2. Given PSF as a function of the parameters μ_a and [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ , and given specific values of each parameter, we can derive reflectance and translucency index with Eqs. 4, 8, substituting PSF into [TeX:] $R \cdot p\left({\left| {\vec x_{\rm o} - \vec x_{\rm i} } \right|} \right)$ $R·p\left(\left|{\vec{x}}_{\mathrm{o}}-{\vec{x}}_{\mathrm{i}}\right|\right)$ . Inversely, μ_a and [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ can be derived from reflectance and the translucency index as an optimization problem. The formula proposed by Farrel ² was used as the PSF, as a function of μ_a, [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ , refractive index, and the distance from the incident point. The refractive index was set at 1.3, as used by Jensen ⁸ The parameters μ_a and [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ were calculated from r _A and T _A,C, using the “fminsearch” function in MATLAB software (Mathworks, Natick, Massachusetts), in which the Nelder–Mead simplex method is implemented, to solve the optimization problem.

The specific values of the results in Experiment 2 and the derived values of μ_a and [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ from these results are shown in Table 2. The large increases seen in [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ after A/E treatment (from 2.80 to 3.88) and in μ_a after UV-induced erythema (from 0.49 to 0.81) can be anticipated as natural results from changes in the skin. Each calculated μ_a and [TeX:] $\mu^\prime_{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ at “before” at 650 nm and at 550 nm is generally larger (but not exceeding a tenfold increase) than the respective values at the red channel (for 650 nm) and green channel (for 550 nm) according to Jensen ⁸ The differences are supposed to come not only from differences between subjects, but also from inadequate handling of standard white and surface reflection. We think that more appropriate treatment of these issues will increase the reliability of the derived optical properties.

Table 2

Estimated values of μa and $\mu^\prime_{\rm s}$ μs′ from the results (r A, T A,C) in Experiment 2.

3.3.

Limitations of this Measurement Method

The limitations that we have identified thus far are as follows:

First, this method cannot deal with the anisotropy of translucency. Although a previous study showed that skin translucency is anisotropic,¹⁰ the translucency index that this method derived represents the average over all directions. This method cannot deal with anisotropy due to the isotropic shape of the aperture.

A second issue is that the translucency of the standard white plate influences the translucency index values. In the proposed method, the standard white plate is not only the standard for white, but is also the standard for opacity. When calculating reflectance according to Eq. 7, reflectance of the standard white plate is assumed to be constant even under different conditions. If the standard white plate is not completely opaque, however, reflectance will not be constant in the same way as for other translucent samples. If we want to obtain translucency indices of samples as absolute values or to compare indices of different instrument, then the opacity of the standard for white should be corrected.

The third point to consider is that surface reflection is not completely excluded in measurements. When gauging the internal condition of the skin, it is desirable to separate reflected light from the skin into surface reflection and inner reflection, and to calculate the degree of diffusion of inner reflection. Eliminating surface reflection would require adoption of a method such as polarization analysis.^{25, 26}