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Abstract
We developed a method to estimate the reflectance, transmittance, and absorbance of a layer of cosmetic foundation (FD) applied to skin from the reflectance of bare skin and FD applied to skin under two measurement conditions using the translucency of skin. Conversely, using the relationship between the applied amount of FD and the reflectance of the FD layer, the applied amount could be estimated. These values could be measured stably regardless of the similarity of reflectance and color between bare skin and made-up skin. The measured values were taken from actual skin, which satisfies the condition of actual usage.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Among the variety of cosmetic products, cosmetic foundation (FD) is used to give skin a good tone and appearance [1]. By applying FD to skin, the unevenness of skin color can be diminished and skin tone can be improved. However, this can also make the skin texture appear unnatural and can produce an overall bad complexion if the choice of FD or the way it is applied is not appropriate. Also, even if the makeup seems to successfully hide skin trouble in front of a dresser, flaws can show up under different lighting conditions, for example, in sunlight, due to differences in the spectrum, brightness, and directionality of the lighting environment. To avoid such unpleasant consequences and obtain optimal performance of FD, it is helpful to evaluate the interaction between light and skin after FD is applied [2,3]. However, the number of reports about this issue is small relative to its importance. The main source of the difficulty is the similarity of the color of skin and that of made-up skin. By its nature, the color of made-up skin is close to that of skin, which is desirable for achieving a natural appearance; however, it makes the separation of the optical characteristics of FD from those of skin difficult [4].
Thus far, some studies have been conducted to determine the optical characteristics of FD on skin [2–9]. Some used an artificial surface, which is usually optimized using mathematical modeling, to precisely determine the optical characteristics of the FD layer and perform a detailed analysis with high reproducibility. For example, the FD layer can be analyzed quantitatively with measurements based on the Kubelka-Munk theory [5,8]. Typically, a black and white plate is used, by which we can evaluate the ratios of the light intensity reaching the base surface and that not reaching it to the total reflected light intensity, and then transform these values to absorption and scattering coefficients for the FD layer [6]. The method gives good reproducibility because the optical properties of the base surface can be reliably controlled and optimized. However, the surface of the base is different from that of skin in many aspects, some of which influence the optical conditions of FD. For example, some aspects of surface energy, viscoelastic character, and microscopic contour result in differences in the dynamics of application and the condition of the FD coating. Some studies tried to make the surface condition closer to skin by, for example, using colored material [2]. However, they are still different from actual skin, and not adequate to match the coating condition. Some studies have tried to evaluate the optical properties of a FD coating using a numerical simulation approach based on the buildup of elements [9]. However, theoretical models tend to simplify the phenomena, and cannot yet incorporate the full complexity of the optical phenomena involved. In addition, when the phenomenon under study occurs only when skin has contact with FD, application to skin is crucial for evaluation. For example, after the elapse of a certain period after makeup application, discoloration can happen due to sebum and sweat secretion and friction of skin, which are unique phenomena of skin and cannot be reproduced without it [6,7,10]. For this reason, an understanding of the optical properties of FD applied to skin is important.
To overcome these difficulties and achieve precise evaluation of the optical characteristics of FD applied to skin in a typical use environment with high accuracy, we exploited the translucent nature of skin. When light penetrates skin, it is dispersed under the surface and some of it is reflected. As can be expected from the requirement that the FD layer modify the appearance of skin in spite of its thinness, the scattering power of FD should be much higher than that of skin. Therefore, the degree of lateral spread of reflected light from skin with FD applied is lower than that from bare skin. It follows, then, that the degree of spreading depends on the FD’s optical characteristics and the applied amount. We developed a method to extract the optical condition of the FD layer using the variation of the lateral spreading of light inside skin, which is not influenced by how similar the reflectance spectrum of made-up skin is to that of bare skin. When the reflectance of a translucent material like skin is measured, occasionally, edge loss, a phenomenon in which penetrating light is scattered and lost outside of the measurement area, becomes a problem; specifically, edge loss decreases the reflectance [11,12]. Conversely, by measuring the degree of edge loss, the degree of translucency can be evaluated. We applied these ideas to evaluate the condition of a FD layer. Specifically, we used a method that measures and evaluates two types of reflectance under different conditions – paired areas of illumination and measurement [12]. In this method, although the theoretical model is simplified, observed objects have the same condition as under actual usage.
2. Materials and methods
2.1 Theoretical model
To model the optical characteristics of FD applied to skin, we assumed a simple two-layer model, whose concept is based on the Kubelka-Munk theory [5,8,13], as shown in Fig. 1. First, the reflectance of bare skin is defined as rS (Fig. 1(a)). Then the reflectance and transmittance of the FD layer are defined as rF and tF, respectively (Fig. 1(b)). Here, only the longitudinal direction in the figure is considered as the propagation direction. We also assumed that those values do not depend on whether light transmission is upward or downward, and thus did not discriminate between these directions. We expressed the reflectance of FD applied to skin RS+F with these elements. We assumed that the light exits after transfer back and forth between the layers several times, as in Fig. 1(c), and that RS+F is the integration of the intensity for each corresponding path. If the intensity for each path can be expressed as a multiplication of the respective elements in Fig. 1(a) and 1(b), it will become as shown in Fig. 1(c). Therefore, RS+F, as the integration of those paths, can be expressed as $${R_{S + F}} = {r_F} + t_F^2{r_S} + t_F^2{r_S}({{r_F}{r_S}} )+ t_F^2{r_S}{({{r_F}{r_S}} )^2} + t_F^2{r_S}{({{r_F}{r_S}} )^3} +.$$
Fig. 1. Reflection model. Notation for each component in (a): skin layer and (b): cosmetic foundation layer over skin. (c): Decomposition of light intensity into paths and expression of combinations of components.
Because the right side of the formula is a geometric series except for the first term, it can be re-expressed as [13]
It should be noted that the measured RS and RS+F will vary even for a unique subject if the illuminated area and measured area change, because the light spreads laterally inside the skin and the amount of edge loss varies depending on the selection of those areas. Here, the “measurement condition” is a combination of the illuminated area and measured area. Because the FD layer is very thin and has high scattering power, it is reasonable to consider the lateral spread in the FD layer to be almost zero, which means rF and tF are unique for a single subject, independent of the choice of the measurement condition. Here, we use two measurement conditions, “Condition A” and “Condition B.” We define the respective RS variables as RSA and RSB and the respective RS+F variables as RS+FA and RS+FB. However, we assume that rF and tF do not change with the condition because the lateral spread in the FD layer is almost zero. Then, the measurement condition can be included in a rewritten form of Eq. (1) as
If RSA, RSB, RS+FA, and RS+FB are obtained by measurement, Eq. (2) gives a system of equations of unknown variables rF and tF, which can be solved as
This means that rF and tF can be derived from the reflectance of bare skin and FD applied to skin under two conditions. If the difference between the incoming light and outgoing light (the sum of reflectance and transmittance) is regarded as the absorbance aF, and the values are normalized by the incoming light intensity, aF can be derived by the following formula:
Those formulae indicate that if RS+FA → RSA and RS+FB → RSB, then rF → 0, tF → 1, and aF → 0, which is the limit of zero application and is reasonable.
For better accuracy, the difference between RSA and RSB (and between RS+FA and RS+FB) should be large; if not, a small difference has to be divided by another small difference to derive rF, which results in a poor signal to noise ratio. In other words, the two conditions should be chosen so that edge loss is maximized for one condition and minimized for the other. In this study, Condition A was chosen to minimize edge loss and Condition B to maximize edge loss.
2.2 Measuring device
For the measurement, we used a CM-2600d spectral reflectometer (Konica Minolta; Tokyo, Japan), which has an optical system with diffuse illumination and an 8° viewing angle. Measurement modes can be chosen in terms of the treatment of UV light and specular components. In the experiment, the “UV excluded” and “specular component included” modes were used. The reflectance was recorded from 400 nm to 700 nm at intervals of 10 nm.
The CM-2600d reflectometer is capable of accepting different target masks, which contact the subject during measurement and function as an aperture. Changing the target masks controls the measurement conditions. Figure 2 shows the measurement conditions when the aperture size of the target mask is altered. In normal measurement, the size of the aperture is specified to be larger than the field of view of the detector (Fig. 2(a)). In this case, an area larger than the measurement area is illuminated, and all reflected light in the field of view is from the subject. If a target mask with an aperture smaller than the field of view is used, the illuminated subject viewed from the aperture is smaller than the field of view, and a part of the target mask is also in the field of view (Fig. 2(b)). By excluding the component of the target mask in the field of view from the reflectance, the reflectance from only the subject can be extracted.
Fig. 2. Structure of measurement device (CM-2600d spectral reflectometer) and graphical interpretation of field of view, illuminated area, and measurement area for two aperture sizes (target masks). (a): The illuminated area is larger than the measurement area when the aperture is larger than the field of view. (b): The illuminated area is as large as the measurement area when the aperture is smaller than the field of view. Here, the component of reflection from the target mask in the field of view is an error source, which should be removed mathematically later. In reality, the detector is tilted at 8° although it is drawn without any tilt (0°). (a) and (b) correspond to Conditions A and B, respectively.
If reflection just occurs at each incident point, the reflectance will not be affected by the measurement condition. However, when the subject is translucent, the incident light will be scattered and lost inside the subject. If the illuminated area is larger than the measurement area, the light will be compensated to some extent from outside of the measurement area (Fig. 2(a)). However, if the illuminated area and the measurement area are the same, such compensation is suppressed (Fig. 2(b)). In short, the edge loss in Fig. 2(b) is larger than that in Fig. 2(a) because the light from outside of the measurement area is blocked; therefore, the reflectance in Fig. 2(b) is smaller than that in Fig. 2(a). This consideration is supported by Ref. [14], which discusses the relationship between the measurement condition and edge loss in detail. As the aperture size becomes smaller, the amount of edge loss becomes larger; however, if it is too small, the measurement becomes unstable due to the unevenness of skin, and this defines the lower limit of this area.
Under the normal condition for reflectance measurement with the CM-2600d reflectometer, the diameters of the illuminated area and the field of view (i.e., measurement area) are set to 11 mm and 8 mm, respectively, which is the condition that suppresses edge loss; this is defined as Condition A. A customized target mask was prepared with an aperture diameter (i.e., diameter of both the measurement area and illuminated area) of 4.8 mm, and the measurement condition with this mask is defined as Condition B. Here, the apertures of two target masks were concentric circles, making them all measurement areas and illuminated areas. According to a previous study [12], it is confirmed that this choice of the measurement condition is suitable for edge-loss detection for average Japanese skin, that is, Types III and IV on the Fitzpatrick scale [15]. The study of Gevaux et al. [14] also indicates that this choice of diameters is appropriate. Hereafter, if the superscript of R is omitted, the variable represents the value under Condition A.
In our method, the measured reflectance has to be calibrated after measurement to remove the component of the reflection from the wall of the target mask, while the output from the CM-2600d reflectometer directly represents the reflectance in a typical measurement. Data for the calibration were acquired separately from skin measurements with each target mask, and then they were used to calibrate the reflectance. More specifically, under Conditions A and B, we measured a blank (the situation of zero reflection from the aperture) and a Spectralon diffuse reflectance standard (99%) (Edmund Optics; Barrington, NJ, USA), and then the reflectance was linearly transformed so that the value for the blank became zero and the value for the Spectralon standard became one. Moreover, the derived values were transformed to reduce the effect of the interface; details are given in Sec. 2.3. It is worth noting that the calibration is not only for reflectance but also for edge loss in this method, which is discussed in detail in Sec. 5.
2.3 Reduction of the effect of the air gap
Here, we explain how the refractive index mismatch (Fig. 3) is reduced following the methodology of Kubelka [13] again. For simplicity, the refractive indices for both skin [16] and the FD layer [9] were assumed to be 1.5, and the incidence angle was limited to normal (0°). This means that only the air gap should be considered as an interface, and the reflectance and transmittance were independent of the direction, upward or downward. With the expression in Fig. 3, the balance of light intensity can be expressed as
With this notation, the derived reflectance RX where $X \in \{{A,B} \}$ in Sec. 2.2, which includes the effect of the interface, corresponds to I0U / I0D. If we use I1U / I1D instead of RX, the effect of the air gap can be excluded. The equivalences ${R^X} = {{{I_{0U}}} / {{I_{0D}}}}$ and ${R^X}^\prime = {{{I_{1U}}} / {{I_{1D}}}}$ can be used to convert Eq. (6) to
Therefore, ${R^X}^\prime $ was used instead of ${R^X}$ as the input to the calculation in Sec. 2.1. Because we defined the refractive indices of the FD layer and skin as 1.5, rI and tI were 0.04 and 0.96, respectively.
2.4 Translucency index
To estimate the extent to which a measured object was translucent as a whole, the translucency index (TI) was defined as
The formula represents how different the reflectance under Condition A is to that under Condition B. In the experiment, because the edge loss was suppressed under Condition A, the value roughly represents the ratio of the edge loss under Condition B to the total reflection; therefore, the value will increase if the lateral spreading of light under the surface increases. It should be noted that the standard of white in the calibration is not only the standard of white but also the standard of translucency, which means that the IT of the standard is defined as zero.
2.5 Cosmetic foundations
As a liquid FD (LFD), “est The Glowing Cream Makeup OC202” (Kao Corporation; Tokyo, Japan) was used. As a powder FD (PFD), “KATE Skin Cover Filter Foundation 02” (Kanebo Cosmetics Inc.; Tokyo, Japan) was used. These foundations are recognized as typical LFDs and PFDs in terms of optical properties.
3. Experiments
This study was reviewed and approved by the Human Research Ethics Committee of Kao Corporation. The subjects provided written informed consent to participate in this study. The participants were healthy Japanese subjects, one male and eight females, in their 20s to 50s (n = 9 in total; Asian; Types III and IV on the Fitzpatrick scale [15]).
A region of interest (ROI) measuring 8 cm × 4 cm ( = 32 cm2) was set on the inner side of the left forearm of each participant, and the ROI was measured as bare skin. Next, a small amount of LFD was uniformly applied to the ROI and it was measured again. Then, LFD was again applied to the ROI and measured; this was repeated until LFD could no longer be added stably. In this way, data for more than one applied amount were acquired for each person. The applied amount was calculated as the decrement of the sum of the weights of the FD container and application tool before and after each application, which was then divided by the application area (32 cm2). After the LFD measurement sequence was finished, the ROI was cleansed with makeup remover and facial wash, and then the same procedure was performed with PFD. For each FD and participant, FD applied to skin was measured three times, except for one participant, for which the PFD was measured only two times. The applied amount ranged from 1 to 6 mg/cm2 for LFD and 0.1 to 0.7 mg/cm2 for PFD.
Although the reflectance was measured in a range of 400 nm to 700 nm, only 500 nm to 700 nm was used for the analysis, because the R and TI of skin became small at wavelengths smaller than 500 nm. This made the variation between reflectance before and after FD application smaller, which resulted in a poor signal to noise ratio for the derived values. If the value inside the root sign in Eq. (4) is negative, tF becomes indeterminate; therefore, if an indeterminate tF was obtained at any wavelength, the measurement was removed from the analysis. Two LFD measurements met this condition. In contrast, limits were not set on the values of rF, tF, and aF; values smaller than zero or larger than one were used as valid data in the analysis.
4. Results
Figure 4 shows the R and TI spectra of bare skin and FD applied to skin of a single representative subject, and the plots of R and TI for all subjects at 700 nm against the applied amount. For reference, the spectra of bulk FDs are also shown in Fig. 4(a) and 4(e), whose exact values at 700 nm were 0.603 for LFD and 0.622 for PFD. In Fig. 4(c), 4(d), 4(g), and 4(h), the plots at the zero point of the horizontal axis are those for bare skin. As an overall trend, as the applied amount increased, the closer the R values moved to the values of bulk FDs; however, the variations from bare skin were small. In contrast, TI varied clearly in response to the applied amount of each FD.
Fig. 4. Data for skin with (a)-(d): LFD applied and (e)-(h): PFD applied. Spectra of (a), (e): R and (b), (f): TI from a series of measurements for one participant. Plots of (c), (g): R and (d), (h) TI at 700 nm from measurements for all participants. As a reference, the reflectance spectra of bulk LFD and PFD are overlaid on the spectra in (a) and (e), respectively. In (c), (d), (g), and (h), the solid line is a regression line, the broken line denotes the 95% confidence interval, and the dotted line denotes the 95% prediction interval. The data for bare skin were excluded from the regression analyses. In (c), (d), (g), (h), the same symbol represents data for the same participant.
The rF, tF, and aF spectra for LFD derived using Eqs. (3)–(5) are shown in Fig. 5(a)-(c). According to the results of regression analyses of those values against the applied amount, the absolute values of the correlation coefficients became larger at longer wavelengths, peaking at 700 nm. The plots at 700 nm are shown in Fig. 5(d)-(f). The relationship between the LFD applied amount and rF is plotted in Fig. 6(a), and the data points are fitted using a quadratic function with a zero constant term. In the same manner, the rF, tF, and aF spectra for PFD are shown in Fig. 5(g)-(i), and the plots at 700 nm are shown in Fig. 5(j)-(l). As with LFD, the correlation coefficients become larger at longer wavelengths and largest at 700 nm for PFD. The relationship between the amount of PFD applied and rF was fitted using a linear function with a zero constant term as shown in Fig. 6(b). For PFD, a linear function was used because the significance level of the second term was p > 0.05 when the quadratic function was applied.
Fig. 5. Data for FD layer with (a)-(f): LFD applied and (g)-(l): PFD applied. Spectra of (a), (g): rF; (b), (h): tF; and (c), (i): aF for skin with (a)-(c): LFD applied and (g)-(i): PFD applied. Plots of (d), (j): rF; (e), (k): tF; and (f), (l): aF at 700 nm for skin with (d)-(f): LFD applied and (j)-(l): PFD applied. The applied amount is indicated as (a)-(c): red, 2 mg/cm2; green, 4 mg/cm2; and blue, 6 mg/cm2; for (g)-(i): red, 0.2 mg/cm2; green, 0.4 mg/cm2; and blue, 0.6 mg/cm2. In (d)-(f) and (j)-(l): the solid line is the regression line, the broken line is the 95% confidence interval, and the dotted line is the 95% prediction interval. In (a)-(c), (g)-(i), the error bars represent the 95% confidence interval. In (d)-(f) and (j)-(l), the same symbol represents data for the same participant.
Fig. 6. Plots of the applied FD amount against rF at 700 nm for (a): LFD and (b): PFD. The function used for fitting is (a): second order and (b): first order (linear), where the constant terms were set to zero. For PFD, the first order was used because the significance level of the second order was p > 0.05. The specific functions are (a): y = 7.607 × x + 24.638 × x2 and (b): y = 3.291 × x.
5. Discussion
As shown in Fig. 5(a)-(c) and Fig. 5(g)-(i), the optical properties rF, tF, and aF for the FD layer could be estimated as spectra. They show reasonable trends that followed the increased application amounts, where rF and aF increased and tF decreased (Fig. 5(d)-(f) and Fig. 5(j)-(l)). Generally, the plots show convergence of rF and aF to zero, and convergence of tF to one under the limit of zero application, which also are reasonable. At 700 nm, the plots of each parameter against the amount of application show high correlation, and the plots are on a unique line with little relevance to the variation between participants. This indicates that the estimated values could be clearly isolated from the effect of skin color and other characteristics of individual skin, while there was a certain degree of individual difference in skin reflectance, as can be seen by the variation at the zero point of the horizontal axis in Fig. 4(c), (g). As shown in Fig. 6, the applied amount can be estimated from rF once the relationship is derived. If the amount increases sufficiently, rF will reach a certain value, and therefore the relationship is basically nonlinear. Actually, the relationship for LFD was nonlinear, as shown in Fig. 6(a). For PFD, it was almost linear (Fig. 6(b)) in the range of this experiment.
The measurability of rF, tF, and aF basically comes from the fact that the degradation of translucency associated with FD application was incorporated into the variation of TI. Primarily, the spectra of made-up skin were close to those of bare skin, which means the reflectance variation before and after FD application was expected to be small (Fig. 4(a), (e)). Therefore, R is unsuitable for FD evaluation. Although the spectra of bulk FD seem different from those of skin, the spectra of skin were insensitive to the amount of FD and the variation was small (Fig. 4(a), (e)), presumably because the applied FD was too thin to change the reflectance to enable precise FD evaluation. In contrast, TI clearly decreased as the FD amount increased in the range of actual application. Moreover, the data points were almost on the same line for all subjects (Fig. 4(d) for LFD and Fig. 4(h) for PFD). This means that the effect of FD on TI is sufficiently larger than individual variations in TI. This led to the strong relationship between the optical characteristics of the FD layer and the amount of FD applied, which indicates that these characteristics are well extracted.
In the experiment, we defined the range of the applied amount as large as possible toward the upper limit; however, the lower limit left room for reconsideration. While the actual amount depends on the individual and product, there are some studies on the applied amount. Although the specific values depend on the conditions in each study, one of them used 0.7 mg/cm2 for LFD and 0.5 mg/cm2 for PFD [17], which is a reasonable match according to our knowledge. The reported value is in the middle of the range in the experiment for PFD; however, it is smaller than the range for LFD. If we accept the discrepancy, the correlation between rF and the applied amount could also be linear for LFD in the actual application range. Additionally, for LFD, the accuracy may decrease in the range of actual usage for LFD; presumably it will become comparable to that for PFD.
The dispersion of measured values increased with decreasing wavelength (Fig. 5(a)-(c), (g)-(i)), and then it became prominent at wavelengths shorter than 500 nm; therefore, only wavelengths larger than 500 nm were used for analysis in the experiment. The excessive dispersion at shorter wavelengths was primarily because the signal to noise ratio became worse due to the decrease in reflectance and a consequent decrease in the difference between the two conditions. As another factor, blood volume variation can be significant, and it can occur very quickly. The difference in blood volume between measurements of bare skin and made-up skin can cause a systematic error. In each spectrum for 0.2 mg/cm2 in Fig. 5(g)-(i), we can see a double bottom in rF and a double peak in tF for PFD between 500 nm and 600 nm, which is the distinctive profile of oxygenated hemoglobin [18]; therefore, this indicates the influence of blood volume variation between the measurements. FD application includes the action of rubbing skin, which can cause an increase in blood flow. In contrast, at longer wavelengths, especially above 600 nm, the absorbance of hemoglobin becomes drastically smaller, and the influence of blood volume variation also becomes small. In the scatter plots in Fig. 4 and Fig. 5 that show data at 700 nm, the influence of blood volume variation may be very small. In addition, the edge loss under Condition B at longer wavelengths is larger than that under shorter wavelengths because the scattering and absorption coefficients become small in skin [18], which is favorable for a high signal to noise ratio. This is the reason that the values at longer wavelengths were more stable than those at shorter ones. However, it is a future subject to determine whether our method is still applicable to infrared wavelengths or whether any limitations exist. The main concern is that the edge loss will increase even in Condition A and become significant, increasing the wavelength further; as a consequence, the reflection under Condition A will decrease and be close to that under Condition B, which results in a bad signal to noise ratio. Once the optimal wavelength is found, in terms of instruments for estimation of the amount of FD, the light source can be replaced with a monochromatic light at one wavelength, for example, for downsizing.
Any parameter can be a candidate for estimating the applied amount, but rF is the most appropriate. At first, the absolute value of the correlation coefficient for rF became larger than tF and aF. According to the sequence of calculation, rF is primarily derived, and then tF and aF are secondarily derived from rF, which could be the reason for the higher correlation of rF. In addition, tF and aF can be indeterminate values when errors make the value inside the root of tF become negative. Conversely, rF can always be derived as a real number.
As an error source, the optical characteristics of the diffuse reflectance standard are also conceivable. In the measurement, the standard is not only that for reflectance, but also that for no translucence (a condition in which no lateral spread occurs). According to the calculation procedure, if the TI for a certain subject is zero, this mathematically means that the translucence of the subject is equal to that of the standard. If the standard is not perfectly translucent, no subject has a TI lower than zero; however, the value can be negative if the subject is less translucent than the standard. This is more likely for skin with FD applied than for bare skin, because the former is less translucent than the latter. In this case, RS+FA < RS+FB, which is equivalent to the outcome “TI is negative,” while RSA > RSB, which is the normal magnitude relationship. However, according to Eq. (1), because rF and tF are real numbers, the magnitude relationship for skin with applied FD and that for bare skin must be consistent regardless of the measurement conditions, or tF becomes indeterminate. In fact, for some measurements, TI was negative at shorter wavelengths, which resulted in an indeterminate tF. As a practical issue, the target mask has contact with FD applied to skin during measurement, as it does with the standard during calibration, which can contaminate the standard with FD. In contrast, if there is a gap between the target mask and the subject during measurement to eliminate contamination, this changes the reflectance toward increasing edge loss, which has a significant impact on the measurement in Condition B. Control of contamination and prevention of the gap are competing objectives. Preparation of a replicable substitute to the standard may be a solution for this issue. If the reflectance of the substitute is defined in advance, it can be used for calibration. It is important to minimize the translucency of the substitute. Copier paper, which is thin and has a high scattering coefficient in general, is close to ideal among the materials that we examined.
We should also consider how well the computational model agrees with real phenomena. In the model, only two directions are considered for light travel, which is a common approach and can explain phenomena well considering the simplicity of the model; however, it is also known that there are certain differences from actual phenomena [19]. In addition, the inhomogeneity of the FD layer, the asperity of the skin surface, and the effect of the refractive indices are not considered.
In the experiment, all participants belonged to Types III and IV on the Fitzpatrick scale, and the applicability to other skin types is an issue for the future. Especially, in the case of darker skin, the lateral spreading of light under the surface, which is the key phenomenon exploited by our method, is expected to be suppressed, and further improvement of the method could be necessary to extend its applicability.
6. Conclusion
We developed a method to estimate the reflectance, transmittance, and absorbance of a FD layer applied to skin by comparing the reflectance of bare skin and FD applied to skin under two measurement conditions. Conversely, using the relationship between the amount of FD and the reflectance of the FD layer, the amount of applied FD was estimated. The measured values are those for actual skin, which are precisely what we want to measure.
Disclosures
The authors declare no competing financial interest.
Data availability
The data used to obtain the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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