JP2014128487A

JP2014128487A - Skin evaluation method and skin evaluation system

Info

Publication number: JP2014128487A
Application number: JP2012288957A
Authority: JP
Inventors: Rie Otsuki; 理恵大槻; Shoji Tominaga; 昌二富永
Original assignee: Kao Corp
Current assignee: Kao Corp
Priority date: 2012-12-28
Filing date: 2012-12-28
Publication date: 2014-07-10
Anticipated expiration: 2032-12-28
Also published as: JP6131597B2

Abstract

PROBLEM TO BE SOLVED: To estimate layer thickness and pigment concentration of epidermis and dermis based on the measurement of spectral reflection factor of a skin, and also estimate layer thickness and keratin concentration of a horny layer.SOLUTION: Using an estimation formula of spectral reflection factor of a skin, an estimation value R(λ) of spectral reflection factor of a skin is calculated with concentration of keratin contained in a horny layer, thickness of the horny layer, etc. as parameters. An estimation value R(λ) in which the difference between the estimation value R(λ) and a corresponding measured value R(λ) is smaller than a specified value is acquired, and parameters used for calculating the estimation value R(λ) are acquired.

Description

本発明は、クベルカムンク理論を用いて、表皮、真皮及び角層のそれぞれの層厚や色素濃度を推定する皮膚の評価方法及び皮膚の評価システムに関する。 The present invention relates to a skin evaluation method and a skin evaluation system for estimating layer thicknesses and pigment concentrations of the epidermis, dermis and stratum corneum using Kubelka-Munk theory.

皮膚を表皮、真皮、皮下組織の３層構造ととらえてクベルカムンク理論により皮膚の分光反射率の式をたて、分光反射率の実測から皮膚のメラニン量とヘモグロビン量を推定する方法が知られている（特許文献１参照）。 There is a known method for estimating the skin melanin and hemoglobin levels by measuring the spectral reflectance by measuring the spectral reflectance of the skin using Kubelka-Munk theory, taking the skin as the three-layer structure of the epidermis, dermis, and subcutaneous tissue. (See Patent Document 1).

しかしながら、クベルカムンク理論を用いて表皮や真皮の色素濃度を推定する従来の方法では推定精度が低いので推定値が必ずしも科学的に妥当なものとはいえず、さらに、角層については層厚も色素濃度も把握することができない。 However, the conventional method of estimating the pigment concentration in the epidermis and dermis using Kubelka-Munk theory has a low estimation accuracy, so the estimated value is not necessarily scientifically valid. The concentration cannot be grasped.

一方、角層はケラチン、細胞間脂質、水分で構成されており、これらの濃度はヒトによって異なっているだけでなく、体内外から影響を受け、同じヒトでも大きく変動し、皮膚の見え方に影響を及ぼす。例えば、肌が乾燥して角層に含まれている水分が少ないと、皮膚が不透明に見える。さらに、角層の厚さも皮膚の見え方に影響を及ぼし、特に過剰な角層肥厚はくすみの要因になるとも考えられている。 On the other hand, the stratum corneum is composed of keratin, intercellular lipids, and moisture, and these concentrations are not only different from person to person, but also affected by the outside and inside of the body. affect. For example, when the skin is dry and the moisture contained in the stratum corneum is small, the skin appears opaque. Furthermore, the thickness of the stratum corneum also affects the appearance of the skin, and it is considered that excessive stratum corneum thickening is a factor of dullness.

特開2010-51589号公報JP 2010-51589 A

上述の背景技術に対し、本発明が解決しようとする課題は、皮膚の見え方を客観的に解析するため、皮膚の分光反射率の計測に基づき、表皮や真皮の層厚や色素濃度をより一層精確に推定すると共に、角層の層厚やケラチンの濃度も精確に推定することに関する。 In order to objectively analyze the appearance of the skin, the problem to be solved by the present invention with respect to the above-described background art is that the layer thickness and pigment concentration of the epidermis and dermis are further determined based on the measurement of the spectral reflectance of the skin. It relates to estimating the layer thickness of the stratum corneum and the concentration of keratin more accurately while estimating it more accurately.

本発明者は、クベルカムンク理論を用いて皮膚の分光反射率を推定するにあたり、角層における光の減衰を考慮した特定の光学モデルをたて、角層に含まれるケラチンの濃度と角層の厚み、並びに角層と空気層との境界面における空気層側と角層側の双方の反射率をパラメータとして有する皮膚の分光反射率の推定式を導出した。そして、この推定式を使用することにより、角層、表皮及び真皮のそれぞれの層厚や色素濃度を高い精度で推定できることを確認し、本発明を完成させた。 In estimating the spectral reflectance of the skin using the Kubelka-Munk theory, the present inventor established a specific optical model that takes into account the attenuation of light in the stratum corneum, the concentration of keratin contained in the stratum corneum, and the thickness of the stratum corneum. In addition, an estimation formula for the spectral reflectance of the skin having both the air layer side and the stratum corneum side reflectances at the interface between the stratum corneum and the air layer as parameters is derived. And by using this estimation formula, it confirmed that each layer thickness and pigment | dye density | concentration of a stratum corneum, epidermis, and dermis could be estimated with high precision, and completed this invention.

即ち、第１に、本発明は、皮膚の分光拡散反射率の推定式として、次式(A1)を使用し、 That is, first, the present invention uses the following formula (A1) as an estimation formula of the spectral diffuse reflectance of the skin,

（式中、
λは可視光波長、
ｋ₁は、角層と空気層との境界面で空気層側から入射した光が反射したときの境界面反射率（以下、角層表面の境界面反射率という）、
ｋ₂は、角層と空気層との境界面で角層側から入射した光が再び角層内に反射したときの内部境界面反射率（以下、角層の内部反射率という）、
Ｔ_sc(λ)は、角層の分光透過率であって、ケラチンの濃度及び角層の厚みをパラメータとして有する、
Ｒ’(λ)は、クベルカムンク理論に基づく表皮以下の皮膚組織の分光反射率の推定式であって、皮膚内部色素濃度、表皮の厚み及び真皮の厚みをパラメータとして有する。）
式(A1)において、角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか一つ以上をパラメータとして皮膚の分光反射率の推定値Ｒ_est(λ)を算出し、該推定値Ｒ_est(λ)と、それに対応する皮膚の分光反射率の実測値Ｒ_measure(λ)との差が規定値よりも小さくなる、または差が最小になる推定値Ｒ_est(λ)を求め、そのときの推定値Ｒ_est(λ)の算出に用いたパラメータにより前記パラメータの１つ以上を求める皮膚の評価方法を提供する。 (Where
λ is the visible light wavelength,
k ₁ is the interface reflectivity when light incident from the air layer side is reflected at the interface between the stratum corneum and the air layer (hereinafter referred to as the interface reflectivity of the stratum corneum surface),
k ₂ is the internal interface reflectance when the light incident from the stratum corneum side at the interface between the stratum corneum and the air layer is reflected again into the stratum corneum (hereinafter referred to as the internal reflectivity of the stratum corneum),
T _sc (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )
In formula (A1), the interface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the concentration of pigment in the skin, the thickness of the epidermis and the thickness of the dermis one or more parameters as to calculate the spectral reflectance of the skin estimate R _est (λ), estimated value R _est and (lambda), the measured value of the spectral reflectance of the skin corresponding to R _measure (λ) An estimated value R _est (λ) that makes the difference between the two values smaller than the specified value or the smallest difference is obtained, and one or more of the parameters are determined according to the parameters used to calculate the estimated value R _est (λ) at that time A method for evaluating skin is provided.

第２に、本発明は、化粧料の適用前後の皮膚について、上述の評価方法で角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか１つ以上を推定し、化粧料の適用前後の推定値の変化に基づいて化粧料の作用を評価する化粧料の評価方法を提供する。 Secondly, according to the present invention, the skin before and after the application of cosmetics is subjected to the above-described evaluation method, the interface surface reflectance of the stratum corneum, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, A cosmetic evaluation method that estimates any one or more of thickness, internal pigment concentration, epidermal thickness, and dermis thickness, and evaluates the action of the cosmetic based on changes in estimated values before and after application of the cosmetic. provide.

第３に、本発明は、被験者の皮膚について、上述の皮膚の評価方法によって求められた角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか１つ以上に基づいて化粧料を被験者に推奨する化粧料の推奨方法を提供する。 Thirdly, according to the present invention, for the skin of a subject, the boundary surface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, and the stratum corneum determined by the skin evaluation method described above. A cosmetic recommending method for recommending a cosmetic to a subject based on any one or more of the thickness of the skin, the pigment concentration in the skin, the thickness of the epidermis and the thickness of the dermis is provided.

第４に、本発明は、皮膚の分光反射率に基づいて、角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか１つ以上を推定する皮膚の評価システムであって、
皮膚の分光反射率の実測値Ｒ_measure(λ)の入力部、及び演算手段を備え、
演算手段が、皮膚の分光反射率の推定式として、拡散反射光の分光反射率を推定する次式(A1)を使用し、 Fourth, the present invention is based on the spectral reflectance of the skin, and the interface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the skin internal pigment A skin evaluation system that estimates any one or more of concentration, epidermal thickness, and dermis thickness,
An input unit for the measured value R _measure (λ) of the spectral reflectance of the skin, and a calculation means;
The calculation means uses the following equation (A1) that estimates the spectral reflectance of diffuse reflected light as the estimation formula of the spectral reflectance of the skin,

（式中、
λは可視光波長、
ｋ₁は、角層表面の境界面反射率、
ｋ₂は、角層の内部反射率、
Ｔ_sc(λ)は、角層の分光透過率であって、ケラチンの濃度及び角層の厚みをパラメータとして有する、
Ｒ’(λ)は、クベルカムンク理論に基づく表皮以下の皮膚組織の分光反射率の推定式であって、皮膚内部色素濃度、表皮の厚み及び真皮の厚みをパラメータとして有する。）
式(A1)において、角層表面の境界面反射率、角層の内部反射率、角層のケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか一つ以上をパラメータとして皮膚の分光反射率の推定値Ｒ_est(λ)を算出し、該推定値Ｒ_est(λ)と、それに対応する皮膚の分光反射率の実測値Ｒ_measure(λ)との差が規定値よりも小さくなる、または差が最小になる推定値Ｒ_est(λ)を求め、そのときの推定値Ｒ_est(λ)の算出に用いたパラメータにより前記パラメータの１つ以上を出力する皮膚の評価システムを提供する。 (Where
λ is the visible light wavelength,
k ₁ is the interface reflectance of the stratum corneum surface,
k ₂ is the internal reflectivity of the stratum corneum,
T _sc (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )
In formula (A1), any one of the interface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin in the stratum corneum, the thickness of the stratum corneum, the concentration of pigment in the skin, the thickness of the epidermis and the thickness of the dermis One or more of the spectral reflectance of the skin estimate R _est a (lambda) is calculated as a parameter, the estimated value R _est (lambda), between the actual measurement value R _{its measure} of the spectral reflectance of the skin corresponding (lambda) _Obtain an estimated value R _est (λ) where the difference is smaller than the specified value or minimize the difference, and output one or more of the parameters according to the parameter used to calculate the estimated value R _est (λ) at that time Provide a skin evaluation system.

第５に、本発明は、上述の皮膚の評価システムにおける演算装置が備えるコンピュータプログラムであって、
皮膚の分光反射率の推定値として、皮膚の拡散反射光の分光反射率の推定値Ｒ_est(λ)を、次式(A1)により、角層表面の境界面反射率、角層の内部反射率、角層のケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか１つ以上をパラメータとして算出する工程、 5thly, this invention is a computer program with which the arithmetic unit in the above-mentioned skin evaluation system is provided,
As an estimated value of the spectral reflectance of the skin, an estimated value R _est (λ) of the diffuse reflected light of the skin is obtained by using the following equation (A1) as a boundary surface reflectance of the stratum corneum surface and an internal reflection of the stratum corneum. Calculating the rate, the keratin layer concentration, the stratum corneum thickness, the skin pigment concentration, the epidermis thickness and the dermis thickness as parameters,

（式中、
λは可視光波長、
ｋ₁は、境界面反射率、
ｋ₂は、角層の内部反射率、
Ｔ_sc(λ)は、角層の分光透過率であって、ケラチンの濃度及び角層の厚みをパラメータとして有する、
Ｒ’(λ)は、クベルカムンク理論に基づく表皮以下の皮膚組織の分光反射率の推定式であって、皮膚内部色素濃度、表皮の厚み及び真皮の厚みをパラメータとして有する。）
上記皮膚の分光反射率の推定値Ｒ_est(λ)と、予め入力された皮膚の分光反射率の実測値Ｒ_measure(λ)との差を算出する工程、
該差が規定値よりも小さくなる、または差が最小になる推定値Ｒ_est(λ)を求める工程、
その推定値Ｒ_est(λ)の算出に用いたパラメータを出力する工程
を含むコンピュータプログラムを提供する。 (Where
λ is the visible light wavelength,
k ₁ is the interface reflectance,
k ₂ is the internal reflectivity of the stratum corneum,
T _sc (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )
Calculating a difference between the estimated value R _est (λ) of the spectral reflectance of the skin and a measured value R _measure (λ) of the spectral reflectance of the skin that is input in advance;
Obtaining an estimated value R _est (λ) in which the difference is smaller than a specified value or the difference is minimized;
A computer program including a step of outputting a parameter used for calculating the estimated value R _est (λ) is provided.

本発明の皮膚の評価方法によれば、クベルカムンク理論を用いて皮膚内部色素濃度を推定するにあたり、クベルカムンク理論を適用する皮膚の光学モデルに角層を含め、皮膚の分光反射率の推定式として、角層と空気層との境界面における空気層側及び角層側の双方の反射率と、角層に含まれるケラチンの濃度及び厚みをパラメータとする角層の分光透過率を含む特定の式を使用するので、科学的に妥当なレベルの推定精度で、皮膚内部色素濃度（例えば、表皮のメラニン、真皮の酸化ヘモグロビン、還元ヘモグロビン、ビリルビン、カロチンなど）や、角層内部のケラチンの濃度を求めることができ、さらに角層、表皮及び真皮の厚み等も求めることができる。そして、この角層内部のケラチンの濃度や角層の厚みに基づき、角層の分光透過率を、より高い精度で推定することができる。 According to the skin evaluation method of the present invention, when estimating the internal pigment concentration using Kubelka-Munk theory, the skin optical model to which Kubelka-Munk theory is applied includes the stratum corneum, A specific formula including the reflectance of both the air layer side and the stratum corneum side at the interface between the stratum corneum and the air layer, and the spectral transmittance of the stratum corneum with the concentration and thickness of keratin contained in the stratum corneum as parameters. Since it is used, the concentration of pigment inside the skin (for example, melanin in the epidermis, oxyhemoglobin in the dermis, reduced hemoglobin, bilirubin, carotene, etc.) and the concentration of keratin in the stratum corneum are obtained with a scientifically reasonable level of accuracy. Furthermore, the thickness of the stratum corneum, epidermis and dermis can be determined. Based on the keratin concentration inside the stratum corneum and the thickness of the stratum corneum, the spectral transmittance of the stratum corneum can be estimated with higher accuracy.

角層におけるケラチンの濃度には角層に含まれる水分含量などが反映され、角層の厚みには表皮や角層のターンオーバー（表皮や角層などで起こる細胞の生まれ変わり）が反映され、角層の分光透過率は透明感や肌のくすみに影響を及ぼす。また、表皮および真皮の厚みには、加齢変化や肌の代謝状態が反映される。したがって、本発明は、表皮や角層のターンオーバーの繰り返しとくすみに関する評価、基礎化粧料の美白効果の評価、基礎化粧料の開発、顧客への化粧方法のアドバイス等の美容目的で使用する皮膚もしくは化粧料の評価方法又は評価ツールとして有用となる。 The keratin concentration in the stratum corneum reflects the water content in the stratum corneum, and the stratum corneum thickness reflects the turnover of the epidermis and stratum corneum (reincarnation of cells that occur in the epidermis and stratum corneum). The spectral transmittance of the layer affects the transparency and the dullness of the skin. The thickness of the epidermis and dermis reflects aging changes and the metabolic state of the skin. Therefore, the present invention is intended for use in cosmetic purposes, such as evaluation of repeated turnover and dullness of the epidermis and stratum corneum, evaluation of whitening effect of basic cosmetics, development of basic cosmetics, advice on makeup methods to customers, etc. Alternatively, it is useful as a cosmetic evaluation method or evaluation tool.

図１は、本発明の皮膚の評価方法が基とする皮膚の光学モデルの説明図である。FIG. 1 is an explanatory diagram of an optical model of skin based on the skin evaluation method of the present invention. 図２は、角層における光の減衰を表した光学モデルの説明図である。FIG. 2 is an explanatory diagram of an optical model representing light attenuation in the stratum corneum. 図３は、本発明の一実施例の皮膚の評価方法のフローチャートである。FIG. 3 is a flowchart of a skin evaluation method according to an embodiment of the present invention. 図４は、本発明の一実施例の皮膚の評価システムのブロック図である。FIG. 4 is a block diagram of a skin evaluation system according to an embodiment of the present invention. 図５Ａは、白色アクリル板とその上にのせた角層の実測分光反射率である。FIG. 5A shows the measured spectral reflectance of the white acrylic plate and the stratum corneum placed thereon. 図５Ｂは、黒色アクリル板とその上にのせた角層の実測分光反射率である。FIG. 5B shows the measured spectral reflectance of the black acrylic plate and the stratum corneum placed thereon. 図６は、角層の初期散乱係数と初期吸収係数である。FIG. 6 shows the initial scattering coefficient and initial absorption coefficient of the stratum corneum. 図７は、ケラチンの吸収係数である。FIG. 7 shows the absorption coefficient of keratin. 図８は、実施例１で取得した分光反射率曲線である。FIG. 8 is a spectral reflectance curve obtained in Example 1. 図９は、実施例２で取得した分光反射率曲線である。FIG. 9 is a spectral reflectance curve obtained in Example 2. 図１０は、実施例２で推定した分光透過率と、角層サンプルから逆計算した分光透過率の対比図である。FIG. 10 is a comparison diagram of the spectral transmittance estimated in Example 2 and the spectral transmittance calculated backward from the stratum corneum sample. 図１１は、角層内での多重反射を想定した光学モデルの説明図である。FIG. 11 is an explanatory diagram of an optical model that assumes multiple reflections in the stratum corneum. 多重反射を考慮した光学モデルに基づいて推定した分光反射率と実測分光反射率である。The spectral reflectance estimated based on the optical model considering multiple reflections and the measured spectral reflectance.

以下、図面を参照しつつ、本発明を詳細に説明する。 Hereinafter, the present invention will be described in detail with reference to the drawings.

図１は、クベルカムンク理論を用いて皮膚の分光反射率を推定するにあたり、本発明の皮膚の評価方法が基とする光学モデルの説明図である。 FIG. 1 is an explanatory diagram of an optical model based on the skin evaluation method of the present invention in estimating the spectral reflectance of the skin using Kubelka-Munk theory.

同図に示した皮膚の拡散反射光の分光反射率の推定式Ｒ_est(λ)として、本発明では次式(A1)を使用する。 In the present invention, the following formula (A1) is used as the estimation formula R _est (λ) of the spectral reflectance of the diffuse reflection light of the skin shown in FIG.

（式中、
λは可視光波長、
ｋ₁は、角層表面の境界面反射率、
ｋ₂は、角層の内部反射率、
Ｔ_sc(λ)は、角層の分光透過率であって、ケラチンの濃度及び角層の厚みをパラメータとして有する、
Ｒ’(λ)は、クベルカムンク理論に基づく表皮以下の皮膚組織の分光反射率の推定式であって、皮膚内部色素濃度、表皮の厚み及び真皮の厚みをパラメータとして有する。） (Where
λ is the visible light wavelength,
k ₁ is the interface reflectance of the stratum corneum surface,
k ₂ is the internal reflectivity of the stratum corneum,
T _sc (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )

この式(A1)は、皮膚の光学モデルとクベルカムンク理論に基づいて本発明者が導出した皮膚の拡散反射光の分光反射率の推定式である。なお、拡散反射光の分光反射率には、例えば、光トラップを有する積分球を用いてＳＣＥ条件（ＳＣＥ：Supecular Component Exncluded）で測定される分光反射率がある。光トラップの無い積分球などのＳＣＩ条件（ＳＣＩ：Supecular Component Include）で測定される分光反射率は、正反射光と拡散反射光を含めた分光反射率となる。ＳＣＩ条件で測定される皮膚の分光反射率を推定する場合、上述の式(A1)は次式(A1)’と表される。 This formula (A1) is an estimation formula of the spectral reflectance of the diffusely reflected light of the skin derived by the present inventor based on the optical model of the skin and the Kubelka-Munk theory. Note that the spectral reflectance of diffusely reflected light includes, for example, a spectral reflectance measured under an SCE condition (SCE: Supecular Component Exncluded) using an integrating sphere having an optical trap. Spectral reflectance measured under SCI conditions (SCI: Supecular Component Include) such as an integrating sphere without an optical trap is a spectral reflectance including regular reflection light and diffuse reflection light. When estimating the spectral reflectance of the skin measured under the SCI condition, the above formula (A1) is expressed as the following formula (A1) '.

従来のクベルカムンク理論に基づく皮膚の分光反射率の推定式では、特許文献１に示されているように、角層の影響が考慮されていない。これは、角層が、皮膚構造を構成する表皮や真皮に比して著しく薄く、角層にはメラニン等の皮膚内部色素も含まれていないためと考えられる。 In the estimation formula for the spectral reflectance of the skin based on the conventional Kubelka-Munk theory, as shown in Patent Document 1, the influence of the stratum corneum is not taken into consideration. This is presumably because the stratum corneum is significantly thinner than the epidermis and dermis that make up the skin structure, and the stratum corneum does not contain skin internal pigments such as melanin.

しかしながら、本発明者は、角層におけるケラチンの濃度や角層の厚みなどによる角層における光の減衰が皮膚の分光反射率に大きく影響し、皮膚の見え方にも影響すると考えた。ここで、ケラチンの濃度とは、ケラチンの量を角層の体積で除算した値を意味する。そして、本発明者は、クベルカムンク理論に基づいて皮膚の分光反射率を推定する場合に、角層表面の境界面反射率ｋ₁、角層の内部反射率ｋ₂、角層のケラチンの濃度、及び角層の厚みにより角層内での光の減衰を考慮した特定の光学モデルを想定し、上述の皮膚の分光反射率の推定式(A1)、(A1)’を導出した。 However, the present inventor considered that the attenuation of light in the stratum corneum due to the keratin concentration in the stratum corneum and the thickness of the stratum corneum greatly affects the spectral reflectance of the skin, and also affects the appearance of the skin. Here, the concentration of keratin means a value obtained by dividing the amount of keratin by the volume of the stratum corneum. And when this inventor estimates the spectral reflectance of skin based on the Kubelka-Munk theory, the interface reflectance k _{1 of} the stratum corneum surface, the internal reflectance k _{2 of} the stratum corneum, the concentration of keratin in the stratum corneum, Assuming a specific optical model that takes into account the attenuation of light in the stratum corneum according to the thickness of the stratum corneum, the above-described estimation formulas (A1) and (A1) ′ for the spectral reflectance of the skin were derived.

即ち、一般に、境界面反射率ｋ₁は、媒質の屈折率を１、反射する面の屈折率をｎとすると、
ｋ₁＝(ｎ−１)²／(ｎ＋１)²
で表され、角層と空気層との境界面に光が空気層側から入射したときに生じる境界面反射率（即ち、角層表面の境界面反射率ｋ₁）は、角層の屈折率をｎとするとこの式によって変化する。角層と空気層との境界面に、皮下組織で反射した光が戻ってきたことにより、この境界面に角層側から入射する光が角層内部に反射することによって生じる境界面内部反射率（即ち、内部反射率ｋ₂）は、例えばJuddらの報告を引用する。また角層表面の境界面反射率ｋ₁や角層の内部反射率ｋ₂は、角層の表面粗さにも依存する。また、角層の屈折率ｎや角層の分光透過率Ｔ_sc(λ)および表面粗さは、角層内部に含まれるケラチン、水分及び脂質の量や割合によって変動する。そこで、本発明者は角層における光の減衰モデルとして図２に示す光学モデルを考え、皮膚表面の拡散反射光の分光反射率Ｒ_est(λ)の推定式として次式(A2)を導出した。なお、図２に示す光学モデルに代えて、図１１に示すように、角層での多重反射を想定した光学モデルを考えた場合、後述する比較例で示すように、この光学モデルで推定される分光反射率は、実測される分光反射率との適合性が劣る。 That is, in general, the interface reflectivity k ₁ is ₁ when the refractive index of the medium is 1 and the refractive index of the reflecting surface is n.
k ₁ = (n−1) ² / (n + 1) ²
The interface reflectance that is generated when light is incident on the interface between the stratum corneum and the air layer from the air layer side (that is, the interface reflectance k ₁ on the stratum corneum surface) is the refractive index of the stratum corneum. If n is n, it changes according to this equation. The interface internal reflectivity generated by the light reflected from the subcutaneous tissue returning to the interface between the stratum corneum and the air layer is reflected by the light incident on the interface from the stratum corneum side. (For example, the internal reflectance k ₂ ) refers to, for example, a report by Judd et al. Further, the boundary surface reflectance k _{1 of the} stratum corneum surface and the internal reflectance k ₂ of the stratum corneum depend on the surface roughness of the stratum corneum. Further, the refractive index n of the stratum corneum, the spectral transmittance T _sc (λ) of the stratum corneum, and the surface roughness vary depending on the amount and ratio of keratin, moisture, and lipid contained in the stratum corneum. Therefore, the present inventor considered the optical model shown in FIG. 2 as a light attenuation model in the stratum corneum, and derived the following expression (A2) as an estimation expression of the spectral reflectance R _est (λ) of the diffuse reflection light on the skin surface. . In addition, instead of the optical model shown in FIG. 2, when an optical model that assumes multiple reflections in the stratum corneum is considered as shown in FIG. 11, the optical model is estimated as shown in a comparative example described later. The spectral reflectance is inferior in compatibility with the actually measured spectral reflectance.

式中、Ｒ_skin1(λ)は皮下組織に到達した光が真皮と表皮表面まで戻り、さらに角層内で光が減衰し、角層と空気との境界面に入射する光の分光反射率である。このＲ_skin1(λ)は、角層の分光透過率をＴ_SC(λ)とすると、クベルカムンク理論により、次式(A3)で表される。 In the equation, R _skin1 (λ) is the spectral reflectance of light incident on the interface between the stratum corneum and air, as the light that reaches the subcutaneous tissue returns to the dermis and epidermis surfaces and further attenuates in the stratum corneum. is there. This R _skin1 (λ) is expressed by the following equation (A3) according to Kubelka-Munk theory, where T _SC (λ) is the spectral transmittance of the stratum corneum.

したがって、式(A2)と式(A3)から、拡散反射光の分光反射率を推定する前述の式(A1)を得ることができる。同様にして、正反射光と拡散反射光を合わせた分光反射率を推定する場合には、前述の式(A1)'を得ることができる。 Therefore, the above-described equation (A1) for estimating the spectral reflectance of the diffuse reflected light can be obtained from the equations (A2) and (A3). Similarly, when estimating the spectral reflectance obtained by combining the regular reflection light and the diffuse reflection light, the above-described equation (A1) ′ can be obtained.

ここで、式(A3)中の角層の分光透過率Ｔ_SC(λ)のパラメータを検討するにあたり、角層の厚みをＤ_sc、角層内に含まれるケラチンによる光の散乱を考慮した角層の散乱係数（以下、変換散乱係数という）をＳ_sc(λ)’、角層内でのケラチンによる光の吸収を考慮した角層の吸収係数（以下、変換吸収係数という）をＫ_sc(λ)’とすると、角層内の分光透過率Ｔ_SC(λ)は、クベルカムンク理論の一般化関数により次式(A4)で表される。 Here, in examining the parameter of the spectral transmittance T _SC (λ) of the stratum corneum in the formula (A3), the angle considering the thickness of the stratum corneum as D _sc and light scattering by keratin contained in the stratum corneum. The scattering coefficient of the layer (hereinafter referred to as the conversion scattering coefficient) is S _sc (λ) ′, and the absorption coefficient of the stratum corneum considering the absorption of light by keratin in the stratum corneum (hereinafter referred to as the conversion absorption coefficient) is K _sc ( When λ) ′, the spectral transmittance T _SC (λ) in the stratum corneum is expressed by the following equation (A4) by a generalized function of Kubelka-Munk theory.

また、変換散乱係数Ｓ_SC(λ)’、変換吸収係数Ｋ_SC(λ)’は、次式(A5-1)、(A5-2）で表される。 Further, the converted scattering coefficient S _SC (λ) ′ and the converted absorption coefficient K _SC (λ) ′ are expressed by the following equations (A5-1) and (A5-2).

式中、ｗ_SCSとｗ_SCKは、角層中のケラチン濃度であり、
Ｓ_SC(λ)は単位濃度で規格化した光の散乱量を示し（以下、初期散乱係数という）、ｗ_SCSが0のとき角層内でのケラチンによる散乱が無い係数が計算され、
Ｋ_SC(λ)は単位濃度で規格化した光の吸収量を示し（以下、初期吸収係数という）、ｗ_SCKが0のとき角層内でのケラチンによる吸収が無い係数が計算される。 _Where w _SCS and w _SCK are keratin concentrations in the stratum corneum,
S _SC (λ) indicates the amount of light scattering normalized by the unit concentration (hereinafter referred to as the initial scattering coefficient). When w _SCS is 0, a coefficient free from keratin scattering in the stratum corneum is calculated.
K _SC (λ) indicates the amount of light absorption normalized by the unit concentration (hereinafter referred to as the initial absorption coefficient). When w _SCK is 0, a coefficient without absorption by keratin in the stratum corneum is calculated.

角層は一般的にケラチン、水分、脂質で構成され、乾燥や保湿によってこれらの量が変化する。これらの濃度は、物質または質量を角層の体積で除算することで変換できる。例えば角層が乾燥した肌では、乾燥前に比べて角層に含まれる水分量が減り、角層の主成分であるケラチンの濃度が高くなると考えられる。これより、これらの角層成分特に主成分のケラチンの濃度変化が角層の散乱係数と吸収係数を変化させると考えられる。本発明では、散乱係数と吸収係数を変化させる濃度は、角層の主成分であるケラチンの濃度とする。なお、ｗ_SCS＝ｗ_SCKとすることが望ましいが、角層厚が十分に厚い場合はｗ_SCSとｗ_SCKに別々の値を与えても問題ない。 The stratum corneum is generally composed of keratin, moisture, and lipid, and these amounts change depending on drying and moisture retention. These concentrations can be converted by dividing the substance or mass by the volume of the stratum corneum. For example, in the skin where the stratum corneum is dry, it is considered that the amount of water contained in the stratum corneum is reduced compared with that before drying, and the concentration of keratin, which is the main component of the stratum corneum, is increased. From this, it is considered that the change in the concentration of these stratum corneum components, particularly keratin as the main component, changes the scattering coefficient and absorption coefficient of the stratum corneum. In the present invention, the concentration for changing the scattering coefficient and the absorption coefficient is the concentration of keratin, which is the main component of the stratum corneum. Although it is desirable to set w _SCS = w _SCK , there is no problem even if different values are given to w _SCS and w _SCK when the stratum corneum is sufficiently thick.

このように、前述の分光反射率の推定式(A1)、(A1)’は分光透過率Ｔ_SC(λ)をパラメータとして表され、分光透過率Ｔ_SC(λ)は、角層中のケラチンの濃度ｗ_SCSとｗ_SCKと角層の厚みをＤ_scをパラメータとして表されるから、分光反射率の推定式(A1)、(A1)’も角層のケラチンの濃度ｗ_SCと角層の厚みＤ_SCをパラメータとして表されることがわかる。角層の厚みＤ_SCやケラチンの濃度ｗ_SCSとｗ_SCKは、角層における水分や脂質の保持状態や、ターンオーバーが上手く行われているか否かによって異なる。また、角層表面の境界面反射率ｋ₁や角層の内部反射率ｋ₂も被験者ごとに異なる。したがって、これらを分光反射率Ｒ_est(λ)の推定式(A1)又は(A1)’に含む本発明によれば、皮膚の性状を精確に評価することが可能となる。 Thus, the above-described spectral reflectance estimation formulas (A1) and (A1) ′ are expressed using the spectral transmittance T _SC (λ) as a parameter, and the spectral transmittance T _SC (λ) is expressed by keratin in the stratum corneum. Since the concentrations w _SCS and w _SCK and the thickness of the stratum corneum are expressed as D _sc as parameters, the spectral reflectance estimation formulas (A1) and (A1) ′ are also used for the keratin concentration w _SC and the stratum corneum It can be seen that the thickness _DSC is expressed as a parameter. The stratum corneum thickness _DSC and keratin concentrations w _SCS and w _SCK vary depending on the moisture and lipid retention conditions in the stratum corneum and whether turnover is successful. Moreover, the boundary surface reflectance k _{1 of the} stratum corneum surface and the internal reflectance k _{2 of the} stratum corneum vary from subject to subject. Therefore, according to the present invention including these in the estimation formula (A1) or (A1) ′ of the spectral reflectance R _est (λ), it is possible to accurately evaluate the skin properties.

なお、角層に含まれている水分と脂質が増加し、ケラチンの濃度が低下すると、角層の吸収特性が低下して散乱特性が増加する。さらに、例えば、入浴で指がふやけた場合のように、角層に水分量が増加すると、角層の厚みが増加して角層の光学的特性が強散乱になることも起こりえる。このように散乱特性が強い場合には、上述の式(A4)を、次式(A4)’で近似してもよい。 In addition, when the water | moisture content and lipid contained in a stratum corneum increase and the density | concentration of keratin falls, the absorption characteristic of a stratum corneum will fall and a scattering characteristic will increase. Further, for example, when the amount of water increases in the stratum corneum, such as when a finger is swollen during bathing, the thickness of the stratum corneum increases, and the optical properties of the stratum corneum may be strongly scattered. When the scattering characteristic is strong as described above, the above equation (A4) may be approximated by the following equation (A4) ′.

一方、分光反射率Ｒ_est(λ)の推定式(A1)、(A1)’において、Ｒ’(λ)は、クベルカムンク理論に基づく表皮以下の皮膚組織の分光反射率の推定式であり、例えば、表皮以下の皮膚組織として、表皮、真皮及び皮下組織の３層の積層構造を考えるとき、Ｒ’(λ)は次式(1)で表される。なお、表皮以下の皮膚の光学モデルとして、表皮及び真皮の２層の積層構造を考えるときもこれに準じてＲ’(λ)を定めることができるが、皮膚の内部色素を推定する際に重要な分光反射率の再現精度を向上させる点から、表皮、真皮及び皮下組織の３層の積層構造を考えることが好ましい。 On the other hand, in the estimation formulas (A1) and (A1) ′ of the spectral reflectance R _est (λ), R ′ (λ) is an estimation formula of the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory. When considering a three-layer structure of epidermis, dermis and subcutaneous tissue as the skin tissue below the epidermis, R ′ (λ) is represented by the following formula (1). As an optical model of the skin below the epidermis, R '(λ) can be determined in accordance with the two-layer structure of the epidermis and dermis, but it is important when estimating the internal pigment of the skin. From the viewpoint of improving the reproducibility of the spectral reflectance, it is preferable to consider a three-layer laminated structure of the epidermis, dermis and subcutaneous tissue.

[式(1)中、
Ｒ_epi(λ)は表皮の分光反射率で次式(2)で表され、 [In Formula (1),
R _epi (λ) is the spectral reflectance of the epidermis expressed by the following equation (2):

Ｔ_epi(λ)は表皮の分光透過率で次式(3)で表され、 T _epi (λ) is the spectral transmittance of the epidermis, expressed by the following equation (3),

Ｒ_dh(λ)は真皮と皮下組織の２層分の分光反射率で次式(4)で表され、 R _dh (λ) is the spectral reflectance of the two layers of the dermis and subcutaneous tissue and is expressed by the following equation (4):

Ｒ_dermis(λ)は真皮の分光反射率で次式(5)で表され、 R _dermis (lambda) is represented by the spectral reflectance of the dermis by the following formula (5),

Ｔ_dermis(λ)は真皮の分光透過率で次式(6)で表され、 T _dermis (lambda) is represented by the spectral transmittance of the dermis by the following equation (6),

（ただし、
ａ_d(λ)＝(Ｓ_d(λ)＋Ｋ_d(λ))／Ｓ_d(λ)、
ａ_e(λ)＝(Ｓ_e (λ)＋Ｋ_e (λ))／Ｓ_e(λ)、
ｂ_d(λ)＝(ａ_d(λ)²−1)^1/2、
ｂ_e(λ)＝(ａ_e(λ)²−1)^1/2、
Ｄ_eは、表皮厚み、
Ｄ_dは、真皮厚み、
Ｋ_d(λ)は、真皮吸収係数、
Ｋ_e(λ)は、表皮吸収係数、
Ｓ_d(λ)は、真皮散乱係数、
Ｓ_e(λ)は、表皮散乱係数である。）
Ｒ_h(λ)は皮下組織の分光反射率である。] (However,
a _d (λ) = (S _d (λ) + K _d (λ)) / S _d (λ),
a _e (λ) = (S _e (λ) + K _e (λ)) / S _e (λ),
b _d (λ) = (a _d (λ) ² −1) ^1/2 ,
b _e (λ) = (a _e (λ) ² −1) ^1/2 ,
_De is the skin thickness,
D _d is the dermis thickness,
K _d (λ) is the dermal absorption coefficient,
K _e (λ) is the skin absorption coefficient,
S _d (λ) is the dermal scattering coefficient,
S _e (λ) is the skin scattering coefficient. )
R _h (λ) is the spectral reflectance of the subcutaneous tissue. ]

なお、皮下組織に含まれている色素の影響は小さいので、式を簡単にする点でＲ_h(λ)＝1.0とすることができる。 In addition, since the influence of the pigment contained in the subcutaneous tissue is small, R _h (λ) can be set to 1.0 in order to simplify the equation.

これらの式(1)〜式(6)の基となった式はP.Kubelka, Journal of the Optical Society of America, vol. 38, no. 5, pp. 448-457,1948に記載されている。 The formulas based on these formulas (1) to (6) are described in P. Kubelka, Journal of the Optical Society of America, vol. 38, no. 5, pp. 448-457, 1948. .

また、上述の式(2)、(3)中の
ａ_e(λ)＝(Ｓ_e(λ)＋Ｋ_e(λ))／Ｓ_e(λ)
のパラメータとなっている表皮吸収係数Ｋ_e (λ)は、表皮に含まれるメラニン等の色素の吸収によるもので、次式(7)で表わされる。 Further, a _e (λ) = (S _e (λ) + K _e (λ)) / S _e (λ) in the above formulas (2) and (3).
The skin absorption coefficient K _e (λ), which is the parameter of, is due to the absorption of pigments such as melanin contained in the skin, and is expressed by the following equation (7).

（式中(7)、ε_s1(λ)は、表皮に存在する第１の皮膚内部色素のモル吸光係数で、ｗ_s1は、その皮膚内部色素のモル濃度であり、ε_s2(λ)は第２の皮膚内部色素のモル吸光係数で、ｗ_s2は、その皮膚内部色素のモル濃度であり、表皮にさらに異なる色素が存在する場合、同様に式(7)にモル吸光係数とモル濃度の積が加算される。） ( _Where ε _s1 (λ) is the molar extinction coefficient of the first skin internal pigment present in the epidermis, w _s1 is the molar concentration of the skin internal pigment, and ε _s2 (λ) is The molar extinction coefficient of the second skin internal pigment, w _s2 is the molar concentration of the internal skin pigment, and when there is a different pigment in the epidermis, the molar extinction coefficient and the molar concentration are similarly _expressed in Equation (7). The product is added.)

上述の式(5)、(6)中の
ａ_d(λ)＝(Ｓ_d(λ)＋Ｋ_d(λ))／Ｓ_d(λ)
のパラメータとなっている真皮吸収係数Ｋ_d(λ)は、真皮中に含まれる酸化ヘモグロビン、還元ヘモグロビン、ビリルビン、カロチン等の色素の吸収によるもので、次式(8)で表わされる。 A _d (λ) = (S _d (λ) + K _d (λ)) / S _d (λ) in the above formulas (5) and (6)
The dermal absorption coefficient K _d (λ), which is a parameter of, is due to absorption of pigments such as oxidized hemoglobin, reduced hemoglobin, bilirubin, and carotene contained in the dermis, and is expressed by the following equation (8).

（式(8)中、ε_p1(λ)は、真皮に存在する第１の皮膚内部色素のモル吸光係数で、ｗ_p1は、その皮膚内部色素のモル濃度であり、ε_p2(λ)は第２の皮膚内部色素のモル吸光係数で、ｗ_p2は、その皮膚内部色素のモル濃度であり、真皮にさらに異なる色素が存在する場合、同様に式(8)にモル吸光係数とモル濃度の積が加算される。) (In formula (8), ε _p1 (λ) is the molar extinction coefficient of the first skin internal pigment present in the dermis, w _p1 is the molar concentration of the skin internal pigment, and ε _p2 (λ) is The molar extinction coefficient of the second skin internal pigment, w _p2 is the molar concentration of the internal skin pigment, and when there is a further different pigment in the dermis, the molar extinction coefficient and molar concentration are similarly expressed in Equation (8). The product is added.)

なお、分子量が既知の皮膚内部色素では、モル濃度に分子量を掛けて、質量濃度に変換することができるため、質量濃度から適宜モル濃度に変換することで、表皮吸収係数Ｋ_e(λ)、真皮吸収係数Ｋ_d(λ)を求めることもできる。従って、質量濃度等のモル濃度に変換可能なものであれば、表皮吸収係数Ｋ_e(λ)、真皮吸収係数Ｋ_d(λ)を求めることができるため、モル濃度に変換可能な濃度を、以下、単に「濃度」と記載する。 In addition, in the skin internal pigment having a known molecular weight, the molar concentration can be multiplied by the molecular weight to be converted into the mass concentration. Therefore, the epidermal absorption coefficient K _e (λ), The dermal absorption coefficient K _d (λ) can also be obtained. Accordingly, if it can be converted into a molar concentration such as mass concentration, the skin absorption coefficient K _e (λ) and the dermal absorption coefficient K _d (λ) can be obtained. Hereinafter, it is simply referred to as “concentration”.

本発明の皮膚の評価方法においては、上述の式(A1)、(A1)’又はこれらの式において角層の分光透過率Ｔ_SC(λ)を前述の式(A4)で表した場合において、式中の角層表面の境界面反射率ｋ₁、角層の内部反射率ｋ₂、角層に含まれるケラチンの濃度ｗ_scsとｗ_sck、角層の厚みＤ_sc、皮膚内部色素濃度、表皮の厚みＤ_e及び真皮の厚みＤ_dのいずれか一つ以上をパラメータとして皮膚の分光反射率の推定値Ｒ_est(λ)を算出し、該推定値Ｒ_est(λ)と皮膚の分光反射率の実測値Ｒ_measure(λ)との差が規定値よりも小さくなる、または差が最小となるパラメータとして前記パラメータの１つ以上を求め、そうして得られた角層の厚みＤ_scなどのパラメータから皮膚を評価する。 In the skin evaluation method of the present invention, when the spectral transmittance T _SC (λ) of the stratum corneum in the above formulas (A1), (A1) ′ or these formulas is expressed by the above formula (A4), The interfacial reflectance k _{1 of} the stratum corneum surface, the internal reflectance k _{2 of} the stratum corneum, the keratin concentrations w _scs and w _sck , the stratum corneum thickness D _sc , the skin internal pigment concentration, the epidermis The estimated value R _est (λ) of the skin spectral reflectance is calculated using one or more of the thickness D _e of the skin and the thickness D _d of the dermis as parameters, and the estimated value R _est (λ) and the spectral reflectance of the skin are calculated. One or more of the above parameters is obtained as a parameter in which the difference from the actual measurement value R _measure (λ) is smaller than the specified value or the difference is minimized, and the thickness D _{sc of the} stratum corneum thus obtained is determined. Evaluate skin from parameters.

以下、本発明の皮膚の評価方法の具体的な処理の流れを、本発明の一つの実施例のフローチャート（図３）、及びこれを実施する皮膚の評価システムのブロック図（図４）を参照して説明する。 Hereinafter, the specific processing flow of the skin evaluation method of the present invention is described with reference to a flowchart (FIG. 3) of one embodiment of the present invention and a block diagram (FIG. 4) of a skin evaluation system for implementing the same. To explain.

この評価システム１は、皮膚の分光反射率の実測値の入力部２、及び演算手段３を備え、演算手段３は記憶部３Ａと計算部３Ｂを有する。なお、入力部２に入力される皮膚の分光反射率は、ＳＣＥ条件で計測される皮膚の拡散反射光の分光反射率でもよく、ＳＣＩ条件で計測される皮膚の正反射光と拡散反射光を含めた分光反射率の実測値でもよい。いずれの実測値が入力されるかに応じて、演算手段３で使用する分光反射率の推定式として前述の式(A1)又は式(A1)’を使用する。以下の説明では、一例として、ＳＣＥ条件で計測される皮膚の拡散反射光を使用する場合について述べる。 The evaluation system 1 includes an input unit 2 for an actual measurement value of spectral reflectance of the skin and a calculation unit 3, and the calculation unit 3 includes a storage unit 3A and a calculation unit 3B. Note that the spectral reflectance of the skin input to the input unit 2 may be the spectral reflectance of the diffuse reflection light of the skin measured under the SCE condition, and the regular reflection light and the diffuse reflection light of the skin measured under the SCI condition. The measured value of the spectral reflectance included may be used. Depending on which actual measurement value is input, the above-described formula (A1) or formula (A1) ′ is used as the spectral reflectance estimation formula used in the calculation means 3. In the following description, as an example, a case where diffuse reflected light of skin measured under SCE conditions is used will be described.

入力部２には、光トラップを有する積分球を備えたＳＣＥ方式の分光測色計、非接触の分光放射輝度計、マルチバンドカメラ等の分光反射率の実測を可能とする分光反射率測定装置が接続される。あるいは、文献などにより既知となっている分光反射率のデータ入力を可能とする入力端子が設けられる。 The input unit 2 includes a spectral reflectance measuring device that enables actual measurement of spectral reflectance, such as an SCE spectrocolorimeter equipped with an integrating sphere having an optical trap, a non-contact spectral radiance meter, and a multiband camera. Is connected. Alternatively, an input terminal is provided that enables data input of spectral reflectance known from literatures and the like.

演算手段３の記憶部３Ａは、皮膚の分光反射率の推定式(A1)、皮膚の分光反射率の実測値又はその入力値、及び各パラメータの入力値又は算出値等を記憶する。 The storage unit 3A of the calculation means 3 stores an estimation formula (A1) of the spectral reflectance of the skin, an actual measurement value or input value of the spectral reflectance of the skin, and an input value or a calculated value of each parameter.

また、演算手段３の計算部３Ｂとしては、パーソナルコンピュータに、市販の関数演算ソフトを組み込んだものを使用することができる。この計算部３Ｂには、皮膚の分光反射率の推定式(A1)を使用し、皮膚の分光反射率の推定値Ｒ_est(λ)を、角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか１つ以上をパラメータとして算出する工程、
上記皮膚の分光反射率の推定値Ｒ_est(λ)と、予め入力された皮膚の分光反射率の実測値Ｒ_measure(λ)との差を算出する工程、
該差が規定値よりも小さくなる、または差が最小となる推定値Ｒ_est(λ)を求める工程、
該差が規定値よりも小さくなる、または差が最小となる推定値Ｒ_est(λ)を算出するために用いたパラメータを出力する工程
を備えたプログラムが組み込まれており、このプログラムにより皮膚の分光反射率の実測値Ｒ_measure(λ)と皮膚の分光反射率の推定値Ｒ_est(λ)との差が規定値よりも小さくなる、または差が最小となるパラメータを出力する。 Further, as the calculation unit 3B of the calculation means 3, a personal computer incorporating commercial function calculation software can be used. This calculation unit 3B uses the estimation formula (A1) of the spectral reflectance of the skin, calculates the estimated value R _est (λ) of the spectral reflectance of the skin, the boundary surface reflectance of the stratum corneum surface, and the inside of the stratum corneum. A step of calculating one or more of reflectance, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the skin internal pigment concentration, the thickness of the epidermis and the thickness of the dermis, as parameters,
Calculating a difference between the estimated value R _est (λ) of the spectral reflectance of the skin and a measured value R _measure (λ) of the spectral reflectance of the skin that is input in advance;
Obtaining an estimated value R _est (λ) in which the difference is smaller than a prescribed value or the difference is minimized;
A step of outputting a parameter used for calculating an estimated value R _est (λ) in which the difference is smaller than a specified value or the difference is minimized.
Is incorporated, and by this program, the difference between the measured value R _measure (λ) of the skin spectral reflectance and the estimated value R _est (λ) of the skin spectral reflectance becomes smaller than the specified value. Or the parameter with the smallest difference is output.

また、この計算部３Ｂで皮膚の分光反射率の推定式(A1)を計算するにあたり、式(A1)中の角層の分光透過率Ｔ_sc(λ)は、上述の式(A4)で表され、角層の変換散乱係数Ｓ_sc(λ)’と変換吸収係数Ｋ_sc(λ)’はそれぞれ上述の式(A5-1)、(A5-2)で表されるとする。また、式(A1)中のＲ’(λ)が、表皮、真皮及び皮下組織の３層の積層構造の分光反射率を推定する上述の式(1)で表され、式(A1)中の表皮の分光反射率Ｒ_epi(λ)が上述の式(2)で表され、式(1)中の表皮の分光透過率Ｔ_epi(λ)が上述の式(3)で表され、式(1)中の真皮と皮下組織の２層分の分光反射率Ｒ_dh(λ)が上述の式(4)で表され、式(4)中の真皮の分光反射率Ｒ_dermis(λ)が上述の式(5)で表され、式(4)中の真皮の分光透過率Ｔ_dermis(λ)が上述の式(6)で表されるとする。 Further, when calculating the estimation formula (A1) of the spectral reflectance of the skin by the calculation unit 3B, the spectral transmittance T _sc (λ) of the stratum corneum in the formula (A1) is expressed by the above formula (A4). The converted scattering coefficient S _sc (λ) ′ and the converted absorption coefficient K _sc (λ) ′ of the stratum corneum are expressed by the above-described equations (A5-1) and (A5-2), respectively. Further, R ′ (λ) in the formula (A1) is expressed by the above formula (1) for estimating the spectral reflectance of the three-layer laminated structure of the epidermis, dermis and subcutaneous tissue, and in the formula (A1) The spectral reflectance R _epi (λ) of the epidermis is expressed by the above formula (2), and the spectral transmittance T _epi (λ) of the epidermis in the formula (1) is expressed by the above formula (3). 1) The spectral reflectance R _dh (λ) of the two layers of the dermis and subcutaneous tissue is expressed by the above equation (4), and the spectral reflectance R _dermis (λ) of the dermis in equation (4) is the above. It is _{assumed that} the spectral transmittance T _dermis (λ) of the dermis in the formula (4) is represented by the above formula (6).

また、表皮中の内部色素としてメラニンを仮定し、真皮中の内部色素として、酸化ヘモグロビン、還元ヘモグロビン、ビリルビン、カロチンを仮定する。 Also, melanin is assumed as an internal pigment in the epidermis, and oxygenated hemoglobin, reduced hemoglobin, bilirubin, and carotene are assumed as internal pigments in the dermis.

そこで、式(A1)中のパラメータとして、次のP0〜P10を考え、これらを演算手段３にパラメータとして登録する。 Therefore, the following P0 to P10 are considered as parameters in the formula (A1), and these are registered in the computing means 3 as parameters.

P0：真皮に含まれる酸化ヘモグロビンの濃度（ｗ_hemo）( 式(8) )
P1：真皮に含まれる還元ヘモグロビンの濃度（ｗ_dhemo）( 式(8) )
P2：真皮に含まれるビリルビンの濃度（ｗ_bill）( 式(8) )
P3：真皮に含まれるカロチンの濃度（ｗ_caro ）( 式(8) )
P4：表皮に含まれるメラニンの濃度（ｗ_mela ）( 式(7) )
P5：真皮の厚み（Ｄ_d ）( 式(5)、(6) )
P6：表皮の厚み（Ｄ_e ）( 式(3)、(2) )
P7：角層の厚み（Ｄ_sc）( 式(A4) )
P8：角層に含まれるケラチンの濃度ｗ_scsとｗ_sck（式(A5-1)、(A5-2））
P9：角層表面の境界面反射率（k₁）( 式(A1) )
P10：角層の内部反射率（k₂）( 式(A1) ) P0: Concentration of oxidized hemoglobin in the dermis (w _hemo ) (Equation (8))
P1: Concentration of reduced hemoglobin in the dermis (w _dhemo ) (equation (8))
P2: Concentration of bilirubin in the dermis (w _bill ) (Equation (8))
P3: Carotene concentration in the dermis (w _caro ) (equation (8))
P4: Concentration of melanin in the epidermis (w _mela ) (Equation (7))
P5: Thickness of the dermis (D _d ) (Equations (5), (6))
P6: Skin thickness (D _e ) (Equations (3), (2))
P7: Thickness of stratum corneum (D _sc ) (formula (A4))
P8: Concentration of keratin contained in the stratum corneum w _scs and w _sck (formula (A5-1), (A5-2))
P9: Interfacial reflectance of stratum corneum surface (k ₁ ) (Formula (A1))
P10: Internal reflectance of stratum corneum (k ₂ ) (Formula (A1))

なお、角層の分光透過率Ｔ_SC(λ)は、角層の厚み（Ｄ_sc）と角層に含まれるケラチンの濃度（ｗ_scsとｗ_sck）がわかると、前述の式(A4)、(A5-1)、(A5-2）から推定される。 Note that the spectral transmittance T _SC (λ) of the stratum corneum can be obtained by determining the thickness of the stratum corneum (D _sc ) and the concentration of keratin contained in the stratum corneum (w _scs and w _sck ), Estimated from (A5-1) and (A5-2).

また、本実施例においては、以下の内部色素のモル吸光係数、真皮の散乱係数Ｓ_d(λ)及び表皮の散乱係数Ｓ_e(λ)として文献値を採用し、これらの数値を演算手段３に入力しておく。皮膚内部色素のモル吸光係数の文献値としては、例えばOregon Medical Centerが公開しているデータを使用することができる。 In this example, literature values are adopted as the molar absorption coefficient of the internal dye, the dermis scattering coefficient S _d (λ) and the epidermis scattering coefficient S _e (λ), and these numerical values are calculated by the calculation means 3. Enter in. As the literature value of the molar extinction coefficient of the skin internal pigment, for example, data published by Oregon Medical Center can be used.

内部色素のモル吸光係数
ε_mela(λ)：メラニンのモル吸光係数
ε_hemo(λ)：酸化ヘモグロビンのモル吸光係数
ε_dhemo(λ)：還元ヘモグロビンのモル吸光係数
ε_bill(λ)：ビリルビンのモル吸光係数
ε_caro(λ)：カロチンのモル吸光係数 Molar extinction coefficient of internal dye ε _mela (λ): molar extinction coefficient of melanin ε _hemo (λ): molar extinction coefficient of oxidized hemoglobin ε _dhemo (λ): molar extinction coefficient of reduced hemoglobin ε _bill (λ): mol of bilirubin Absorption coefficient ε _caro (λ): molar absorption coefficient of carotene

演算手段３に入力しておく角層の初期散乱係数Ｓ_sc(λ)（式A5-1）と角層の初期吸収係数Ｋ_sc(λ)（式A5-2）としては、文献値を使用してもよいが、後述する実施例のように角層サンプルの分光反射率の測定から算出したものを使用してもよい。また、角層の吸収係数はケラチン又は他の色素に由来しているので、式(A5-2）において、角層の初期吸収係数Ｋ_sc(λ)に代えてケラチンのモル吸光係数ε_SC(λ)を使用し、角層の変換吸収係数Ｋ_sc(λ)’を次式(A5-2）’で表しても良い。さらに、ε_SC(λ)は角層の光吸収を支配する色素のモル吸光係数に置き換えても良い。 Reference values are used for the initial stratum corneum scattering coefficient S _sc (λ) (formula A5-1) and the stratum corneum initial absorption coefficient K _sc (λ) (formula A5-2) that are input to the calculation means 3. However, it is also possible to use the one calculated from the measurement of the spectral reflectance of the stratum corneum sample as in the examples described later. Also, since the absorption coefficient of the stratum corneum is derived from keratin or other pigments, in the formula (A5-2), instead of the initial absorption coefficient K _sc (λ) of the stratum corneum, the molar extinction coefficient ε _SC ( λ) may be used, and the converted absorption coefficient K _sc (λ) ′ of the stratum corneum may be expressed by the following equation (A5-2) ′. Furthermore, ε _SC (λ) may be replaced with the molar extinction coefficient of the dye that governs the light absorption of the stratum corneum.

図３に示した皮膚の評価方法の流れの概略としては、まず、被験者の皮膚の分光反射率の実測値Ｒ_measure(λ)を取得する（第１工程）と共に、式(A1)において、上述のパラメータP0〜P10を演算手段３に適宜入力して皮膚の分光反射率の推定値Ｒ_est(λ)を算出する（第２工程）。この場合、各パラメータP0〜P10の入力値を変え、それぞれについて皮膚の分光反射率の推定値Ｒ_est(λ)を算出する。第３工程では、皮膚の分光反射率の実測値Ｒ_measure(λ)と推定値Ｒ_est(λ)との差を算出し、これが規定値よりも小さくなる、または最小となるパラメータP0〜P10を求め、そうして得られたパラメータP0〜P10の数値を、被験者の皮膚におけるパラメータP0〜P10の数値であると決定し、その数値に基づいて皮膚を評価する。 As an outline of the flow of the skin evaluation method shown in FIG. 3, first, an actual measurement value R _measure (λ) of the spectral reflectance of the subject's skin is acquired (first step), and in the equation (A1), The parameters P0 to P10 are appropriately input to the calculation means 3 to calculate the estimated value R _est (λ) of the spectral reflectance of the skin (second step). In this case, the input values of the parameters P0 to P10 are changed, and the estimated value R _est (λ) of the spectral reflectance of the skin is calculated for each. In the third step, the difference between the measured value R _measure (λ) and the estimated value R _est (λ) of the spectral reflectance of the skin is calculated, and parameters P0 to P10 that are smaller or smaller than the specified value are calculated. The numerical values of the parameters P0 to P10 thus obtained are determined to be the numerical values of the parameters P0 to P10 in the skin of the subject, and the skin is evaluated based on the numerical values.

第１工程で取得する、被験者の皮膚の拡散反射光の分光反射率の実測値Ｒ_measure(λ)は、可視光波長（略400〜700nm）で計測されたものとする。かかる実測値は、積分球方式の分光測色計、非接触の分光放射輝度計によるものだけでなく、マルチバンドカメラなどのカメラ画像の画素値RGB、CIE L^*a^*b^*といった表色値から近似して計算された分光反射率でもよい。 It is assumed that the actual measured value R _measure (λ) of the diffuse reflectance of the subject's skin acquired in the first step is measured at a visible light wavelength (approximately 400 to 700 nm). These measured values are not only those obtained by integrating sphere type spectrophotometers and non-contact spectral radiance meters, but also color values such as pixel values RGB and CIE L ^* a ^* b ^* of camera images such as multiband cameras. Spectral reflectance calculated by approximation from

第２工程の、皮膚の分光反射率の推定値の算出工程においては、まず、演算手段３にパラメータP0〜P10の初期値を入力する。この初期値は、医学論文や生体分析等から得られる一般的な値を入力する。例えば、ヘモグロビンの濃度P0の初期値（質量濃度）として8.0 [g/dL]を入力する。 In the second step of calculating the estimated value of the spectral reflectance of the skin, first, initial values of the parameters P0 to P10 are input to the calculation means 3. As the initial value, a general value obtained from a medical paper or a biological analysis is input. For example, 8.0 [g / dL] is input as the initial value (mass concentration) of the hemoglobin concentration P0.

次に、入力したパラメータP0（酸化ヘモグロビン濃度ｗ_hemo)、P1（還元ヘモグロビン濃度ｗ_dhemo）、P2（ビリルビン濃度ｗ_bill）、P3（カロチン濃度ｗ_caro）の初期値、これらの内部色素のモル吸光係数の既定値、パラメータP5（真皮の厚みＤ_d）の初期値、真皮散乱係数Ｓ_d(λ)の既定値を用いて、上述の式(5)により真皮の分光反射率Ｒ_dermis(λ)を算出し、上述の式(6)により真皮の分光透過率Ｔ_dermis(λ)を算出する。
そしてこれらの算出値を用いて上述の式(4)により真皮と皮下組織の２層分の分光反射率Ｒ_dh(λ)を求める。 Next, initial values of input parameters P0 (oxygenated hemoglobin concentration w _hemo ), P1 (reduced hemoglobin concentration w _dhemo ), P2 (bilirubin concentration w _bill ), P3 (carotene concentration w _caro ), molar absorption of these internal dyes Using the default value of the coefficient, the initial value of the parameter P5 (dermis thickness D _d ), and the default value of the dermal scattering coefficient S _d (λ), the spectral reflectance R _dermis (λ) of the dermis according to the above equation (5). _Is calculated, and the spectral transmittance T _dermis (λ) of the dermis is calculated by the above equation (6).
Then, using these calculated values, the spectral reflectance R _dh (λ) for the two layers of the dermis and the subcutaneous tissue is obtained by the above equation (4).

一方、入力したパラメータP4（メラニン濃度ｗ_mela）の初期値、メラニンのモル吸光係数の既定値、パラメータP6（表皮の厚みＤ_e）の初期値、表皮の表皮散乱係数Ｓ_e(λ)の既定値を用いて、上述の式(2)により表皮の分光反射率Ｒ_epi(λ)を算出し、上述の式(3)により表皮の分光透過率Ｔ_epi(λ)を算出する。 On the other hand, the default parameters P4 input initial value (melanin concentration w _mela), the default value of the molar extinction coefficient of melanin, the initial value of the parameter P6 (epidermal thickness D _e), epidermal scattering coefficient of the skin S _e (lambda) Using the values, the spectral reflectance R _epi (λ) of the epidermis is calculated by the above equation (2), and the spectral transmittance T _epi (λ) of the epidermis is calculated by the above equation (3).

そして、これら表皮の分光反射率Ｒ_epi(λ)と表皮の分光透過率Ｔ_epi(λ)、及び先に算出した真皮と皮下組織の２層分の分光反射率Ｒ_dh(λ)を用いて上述の式(1)により、皮膚の表皮、真皮及び皮下組織の３層の分光反射率Ｒ’(λ)を求める。 Then, using the spectral reflectance R _epi (λ) of the epidermis, the spectral transmittance T _epi (λ) of the epidermis, and the spectral reflectance R _dh (λ) of the two layers of the dermis and subcutaneous tissue calculated previously. The spectral reflectance R ′ (λ) of the three layers of the epidermis, dermis and subcutaneous tissue of the skin is obtained by the above formula (1).

また、角層の初期散乱係数Ｓ_SC(λ)と角層中のケラチンの濃度ｗ_SCSとｗ_SCKから角層の変換散乱係数Ｓ_SC(λ)’を求め（式A5-1）、角層の初期吸収係数Ｋ_sc(λ)と角層に含まれるケラチンの濃度ｗ_SCSとｗ_SCKから角層の変換散乱係数Ｋ_SC(λ)’を求める（式A5-2）。そしてこれらと角層の厚みＤ_SCとから式(A4)により角層の分光透過率Ｔ_SC(λ)を得る。 Also, the stratum corneum converted scattering coefficient S _SC (λ) ′ is obtained from the stratum corneum initial scattering coefficient S _SC (λ) and the keratin concentrations w _SCS and w _{SCK in the} stratum corneum (Formula A5-1). The conversion scattering coefficient K _SC (λ) ′ of the stratum corneum is obtained from the initial absorption coefficient K _sc (λ) of the above and the keratin concentrations w _SCS and w _{SCK of the} keratin (formula A5-2). Then, the spectral transmittance T _SC (λ) of the stratum corneum is obtained from these and the stratum corneum thickness D _{SC by} the formula (A4).

得られた３層の分光反射率Ｒ’(λ)と、角層の分光透過率Ｔ_sc(λ)と、角層表面の境界面反射率（k₁）と角層の内部反射率（k₂）とから、式(A1)により被験者の分光反射率の推定値Ｒ_est(λ)を算出する。 The spectral reflectance R ′ (λ) of the three layers obtained, the spectral transmittance T _sc (λ) of the stratum corneum, the interface reflectance (k ₁ ) of the stratum corneum surface, and the internal reflectance (k of the stratum corneum) ₂ ) From the equation (A1), the estimated value R _est (λ) of the subject's spectral reflectance is calculated.

次に、こうして算出された分光反射率の推定値Ｒ_est(λ)と、被験者の分光反射率の実測値Ｒ_measure(λ)とを対比するために、推定値Ｒ_est(λ)と、被験者の分光反射率の実測値Ｒ_measure(λ)との差として、誤差（あるいは類似度）を算出する。 Next, in order to compare the estimated spectral reflectance R _est (λ) thus calculated with the measured spectral reflectance R _measure (λ) of the subject, the estimated value R _est (λ) and the subject An error (or similarity) is calculated as a difference from the measured value R _measure (λ) of the spectral reflectance.

算出された誤差が規定値より小さくなる、または、誤差がゼロで推定値と実測値が完全一致した場合には、その推定値の算出に用いたパラメータP0〜P10を被験者の皮膚の内部情報と決定する。一方、算出された誤差が規定値より大きい場合は、パラメータP0〜P10の値をさらに変化させて、再度分光反射率の推定値Ｒ_est(λ)を算出し、得られた算出値と分光反射率の実測値との誤差を算出する。この誤差が規定値よりも小さくなるか、誤差が最小となるまでパラメータP0〜P10の変更と誤差の算出を繰り返す。こうして規定値よりも小さくなる、または誤差がほぼゼロになる推定値Ｒ_est(λ)を与えるパラメータP0〜P10を決定し、この値を被験者の皮膚内部情報と決定する。ここで、規定値は、もし、算出された誤差が色差ΔEabであれば、色差ΔEabが好ましくは5.0以下、より好ましくは3.0以下程度になるように設定し、また誤差を二乗平均平方根誤差RMSEとして求めた場合は、色差が5.0以下程度に該当するRMSE値として定めることが好ましい。なお、誤差が最小となる場合に代えて誤差が規定値よりも小さくなる場合を求めることにより、計算時間を短縮することが可能となる。 If the calculated error is smaller than the specified value, or if the error is zero and the estimated value and the actual measurement value completely match, the parameters P0 to P10 used to calculate the estimated value are set as internal information of the subject's skin. decide. On the other hand, when the calculated error is larger than the specified value, the values of the parameters P0 to P10 are further changed to calculate the spectral reflectance estimation value R _est (λ) again, and the obtained calculated value and the spectral reflection are calculated. The error from the measured value of the rate is calculated. The parameters P0 to P10 are changed and the error calculation is repeated until the error becomes smaller than the specified value or the error is minimized. In this way, the parameters P0 to P10 that give the estimated value R _est (λ) that becomes smaller than the specified value or the error is almost zero are determined, and this value is determined as the skin internal information of the subject. Here, if the calculated error is the color difference ΔEab, the specified value is set so that the color difference ΔEab is preferably 5.0 or less, more preferably about 3.0 or less, and the error is defined as the root mean square error RMSE. When obtained, it is preferable to determine the RMSE value corresponding to a color difference of about 5.0 or less. It is possible to reduce the calculation time by obtaining a case where the error is smaller than the specified value instead of the case where the error is minimized.

パラメータP0〜P10の数値を変えて分光反射率の推定値の算出を繰り返し、被験者の皮膚の内部情報と決定してよいパラメータP0〜P10を見出す手法としては、最小二乗法などの最適化手法を用いることができる。 As a method of finding parameters P0 to P10 that may be determined as internal information of the subject's skin by repeatedly calculating the estimated value of spectral reflectance by changing the values of parameters P0 to P10, an optimization method such as least squares is used. Can be used.

なお、上述の実施例では、内部色素のモル吸光係数として文献値を使用するとしたが、これらをパラメータとして変化させて被験者の分光反射率の推定値を算出してもよい。 In the above-described embodiment, literature values are used as the molar extinction coefficient of the internal dye. However, the estimated values of the spectral reflectance of the subject may be calculated by changing these values as parameters.

式(A1)において変化させるパラメータとしては、角層表面の境界面反射率（ｋ₁）、角層の内部反射率（ｋ₂）、角層に含まれるケラチンの濃度（ｗ_SCSとｗ_SCK）、角層の厚みＤ_SC、皮膚内部色素濃度（ｗ_hemo、ｗ_dhemo、ｗ_bill、ｗ_caro、ｗ_mela等）、表皮の厚みＤ_e及び真皮の厚みＤ_dのいずれか一つ以上をパラメータとすればよく、いずれをパラメータとするかについては特に制限はない。ただし、美容上の皮膚の評価ファクターとして有用だが、従来科学的に妥当な計測値を得られていない角層の厚さ、角層に含まれるケラチンの濃度、皮膚内部色素濃度等をパラメータとし、それらの数値を決定すると本発明の意義が高まる。 The parameters to be changed in the formula (A1) include the boundary surface reflectance (k ₁ ) of the stratum corneum surface, the internal reflectance (k ₂ ) of the stratum corneum, and the concentration of keratin contained in the stratum corneum (w _SCS and w _SCK ). , the thickness D _SC of the stratum corneum, the skin inside the dye concentration _{_{(w hemo, w dhemo, w}} bill, w caro, etc. w _mela), any one or more of the thickness D _e and dermis of a thickness D _d of the epidermis parameters There is no particular limitation as to which parameter is used. However, it is useful as an evaluation factor for cosmetic skin, but the thickness of the stratum corneum, the concentration of keratin contained in the stratum corneum, the concentration of pigment in the skin, etc., which have not been obtained from scientifically valid measurement values, are parameters. When these numerical values are determined, the significance of the present invention increases.

本発明の皮膚の評価方法は、以上のようにして求めたパラメータの数値に基づいて皮膚を美容目的で評価する方法である。例えば、パラメータとして、皮膚内部色素濃度を求めると、得られた内部色素濃度の数値は科学的に妥当な数値となるから、皮膚の表皮あるいは真皮における内部色素濃度により皮膚の美容上の色の評価をすることができる。角層の厚さを得るとターンオーバーの良否を評価することができ、ケラチンの濃度を得ると反射的に角層における水分や脂質の保持状態もわかるので、これらにより皮膚の代謝状態を評価することができる。さらには、ターンオーバーや皮膚の代謝状態等と、くすみなどの見た目との関係も評価することができる。 The skin evaluation method of the present invention is a method for evaluating skin for cosmetic purposes based on the numerical values of the parameters obtained as described above. For example, when the skin internal pigment concentration is obtained as a parameter, the obtained internal pigment concentration value is scientifically valid. Therefore, the cosmetic color of the skin is evaluated by the internal pigment concentration in the epidermis or dermis of the skin. Can do. When the thickness of the stratum corneum is obtained, the quality of turnover can be evaluated, and when the concentration of keratin is obtained, the state of moisture and lipid retention in the stratum corneum can be reflexively determined, and thus the metabolic state of the skin is evaluated. be able to. Furthermore, the relationship between the turnover and the metabolic state of the skin and the appearance such as dullness can be evaluated.

本発明の化粧料の評価方法は、化粧料の適用前後の角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか一つ以上を、本発明の皮膚の評価方法により推定し、化粧料の適用前後の推定値の変化に基づいて化粧料の作用を評価する方法である。上述のように、本発明の皮膚の評価方法によれば、角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚み等を精度高く求めることができ、角層の分光透過率も推定できるから、化粧料の適用前後のそれらの数値を比較することにより、化粧料の作用を正確に評価することができる。例えば、美白化粧料の適用前後でメラニン濃度の変化を調べることにより、その化粧料の美白作用の有無、あるいは美白作用の程度を評価することができ、保湿化粧料の適用の前後で角層の分光透過率の変化を調べることにより、その化粧料の保湿作用を評価することができる。 The cosmetic evaluation method according to the present invention includes the interface reflectance of the stratum corneum surface before and after application of the cosmetic, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, and the concentration of pigment in the skin. In this method, one or more of the thickness of the epidermis and the thickness of the dermis is estimated by the skin evaluation method of the present invention, and the action of the cosmetic is evaluated based on the change in the estimated value before and after the application of the cosmetic. . As described above, according to the skin evaluation method of the present invention, the boundary surface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the concentration of pigment in the skin The thickness of the epidermis and the thickness of the dermis can be determined with high accuracy, and the spectral transmittance of the stratum corneum can also be estimated. By comparing these values before and after the application of the cosmetic, the action of the cosmetic can be accurately determined. Can be evaluated. For example, by examining the change in melanin concentration before and after application of whitening cosmetics, the presence or absence of the whitening effect of the cosmetics or the degree of whitening can be evaluated. By examining the change in spectral transmittance, the moisturizing effect of the cosmetic can be evaluated.

本発明の化粧料の推奨方法は、被験者の角層表面の境界面反射率、角層の内部反射率、角層に含まれるケラチンの濃度、角層の厚み、皮膚内部色素濃度、表皮の厚み及び真皮の厚みのいずれか一つ以上を本発明の皮膚の評価方法により求め、得られた数値に基づいて化粧料を被験者に推奨する方法である。本発明の皮膚の評価方法を用いると、角層の厚み、角層に含まれるケラチンの濃度、皮膚内部色素濃度、角層表面の境界面反射率、表皮の厚み、真皮の厚み等を正確に求めることができるから、被験者の皮膚に適用することを推奨すべき化粧料も選択できるようになる。この場合、予め、多数の被験者について、種々の化粧料の適用前後の角層の厚み、角層に含まれるケラチンの濃度、皮膚内部色素濃度、角層表面の境界面反射率、表皮の厚み、真皮の厚み等を求め、これらの数値の特徴的なパターンから皮膚の状態を識別し、各パターンの皮膚に適した化粧料を調べておく。一方、当該被験者の皮膚のパターンと、予め調べておいた皮膚のパターンとそれに適した化粧料との関係から、当該被験者の皮膚に推奨すべき化粧料を選択できるようにしてもよい。 The recommended method of the cosmetic composition of the present invention is the interface reflectance of the stratum corneum surface of the subject, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the skin internal pigment concentration, and the thickness of the epidermis. In addition, one or more of the thickness of the dermis and the thickness of the dermis are obtained by the skin evaluation method of the present invention, and the cosmetic is recommended to the subject based on the obtained numerical values. Using the skin evaluation method of the present invention, the thickness of the stratum corneum, the concentration of keratin contained in the stratum corneum, the concentration of internal pigment in the skin, the interface reflectance of the stratum corneum surface, the thickness of the epidermis, the thickness of the dermis, etc. Therefore, it is possible to select a cosmetic that should be recommended to be applied to the skin of the subject. In this case, for a large number of subjects in advance, the thickness of the stratum corneum before and after the application of various cosmetics, the concentration of keratin contained in the stratum corneum, the concentration of internal pigment in the skin, the interface surface reflectance of the stratum corneum, the thickness of the epidermis, The thickness of the dermis is obtained, the skin condition is identified from the characteristic patterns of these numerical values, and cosmetics suitable for the skin of each pattern are examined. On the other hand, a cosmetic to be recommended for the skin of the subject may be selected from the relationship between the skin pattern of the subject, the skin pattern examined in advance, and a cosmetic suitable for the pattern.

以下、実施例に基づいて本発明を具体的に説明する。 Hereinafter, the present invention will be specifically described based on examples.

参考例１（角層の初期散乱係数Ｓ_SC(λ)と初期吸収係数Ｋ_SC(λ)の算出）
以下の(1)〜(4)の手順に従い、角層の初期散乱係数Ｓ_SC(λ)と初期吸収係数Ｋ_SC(λ)を算出した。 Reference example 1 (calculation of initial scattering coefficient S _SC (λ) and initial absorption coefficient K _SC (λ) of stratum corneum)
The initial scattering coefficient S _SC (λ) and initial absorption coefficient K _SC (λ) of the stratum corneum were calculated according to the following procedures (1) to (4).

(1)実測分光反射率の取得
まず、以下の実測分光反射率を計測した．
・白色アクリル板の実測分光反射率：Ｒ_w(λ)
・黒色アクリル板の実測分光反射率：Ｒ_B(λ)
・白色アクリル板に載せた角層サンプルの実測分光反射率：Ｒ_WC(λ)
・黒色アクリル板に載せた角層サンプルの実測分光反射率：Ｒ_BC(λ)
ここで、白色アクリル板と黒色アクリル板の屈折率は、それぞれ1.43とした。 (1) Acquisition of measured spectral reflectance
First, the following measured spectral reflectance was measured.
・ Measured spectral reflectance of white acrylic plate: R _w (λ)
・ Measured spectral reflectance of black acrylic plate: R _B (λ)
・ Actual spectral reflectance of a stratum corneum sample placed on a white acrylic plate: R _WC (λ)
・ Actual spectral reflectance of a stratum corneum sample placed on a black acrylic plate: R _BC (λ)
Here, the refractive indexes of the white acrylic plate and the black acrylic plate were 1.43, respectively.

(2)実測分光反射率から理想的な分光反射率への変換
(1)で得た実測分光反射率Ｒ(λ)（但し、Ｒ(λ)：Ｒ_w(λ)、Ｒ_B(λ)、Ｒ_WC(λ)又はＲ_BC(λ)）から、空気と物体表面の屈折率の差によって生じる鏡面反射と内部反射を除いた、クベルカムンク理論における理想的な分光反射率Ｒ'(λ)（但し、Ｒ'(λ)：Ｒ_w'(λ)、Ｒ_B'(λ)、Ｒ_WC'(λ)又はＲ_BC'(λ)）へ、Soundersonが提案した式（J. Saunderson， Journal of Optical Society of America, Vol. 32, No.12, pp. 727-729, 1942.）に基づいて、次式(10)により変換した。 (2) Conversion from measured spectral reflectance to ideal spectral reflectance
From the measured spectral reflectance R (λ) obtained in (1) (where R (λ): R _w (λ), R _B (λ), R _WC (λ) or R _BC (λ)) The ideal spectral reflectance R ′ (λ) in Kubelka-Munk theory excluding specular reflection and internal reflection caused by the difference in refractive index of the object surface (where R ′ (λ): R _w ′ (λ), R _B '(λ), R _WC ' (λ) or R _BC '(λ)), a formula proposed by Sounderson (J. Saunderson, Journal of Optical Society of America, Vol. 32, No. 12, pp. 727- 729, 1942.) and converted according to the following equation (10).

式中、
ｋ₁は空気と物体との境界面で空気側から入射した光が反射したときの境界面反射率であり、
ｋ₂は空気と物体との境界面で物体側から入射した光が物体内部へ反射したときの境界面反射率、即ち内部反射率である。これらの具体的な数値としては、Juddらが報告したデータ（D. Judd，Journal of research of the National Bureau of Standards. Vol. 29, pp. 329-332, 1942.）から、アクリル板の屈折率1.43に対応するｋ₁=0.031、ｋ₂=0.543を用いた。 Where
k ₁ is the interface reflectance when light incident from the air side is reflected at the interface between air and an object.
k ₂ is the interface reflectivity when light incident from the object side at the interface between the air and the object is reflected inside the object, that is, the internal reflectivity. These figures are based on the data reported by Judd et al. (D. Judd, Journal of research of the National Bureau of Standards. Vol. 29, pp. 329-332, 1942.). K ₁ = 0.031 and k ₂ = 0.543 corresponding to 1.43 were used.

(3)無限角層厚の分光反射率の算出
(2)で算出した分光反射率Ｒ_w'(λ)、Ｒ_B'(λ)、Ｒ_WC'(λ)又はＲ_BC'(λ)を用いて、無限角層厚の分光反射率Ｒ_∞(λ)を湊らの式（湊幸衛，千葉大学工学部研究報告, Vol.19, No. 36, pp. 203-208, 1968.）に基づいて次式(11)により算出した。 (3) Calculation of spectral reflectance of infinite angle layer thickness
Using the spectral reflectance R _w ′ (λ), R _B ′ (λ), R _WC ′ (λ) or R _BC ′ (λ) calculated in (2), the spectral reflectance R _∞ of the infinite angle layer thickness (λ) was calculated by the following equation (11) based on our equation (Yukie Tsuji, Chiba University Faculty of Engineering Research Report, Vol. 19, No. 36, pp. 203-208, 1968.).

(4)角層の初期散乱係数Ｓ_SC(λ)と初期吸収係数Ｋ_SC(λ)の算出
次式(12)により、角層の初期散乱係数Ｓ_SC(λ)と初期吸収係数Ｋ_SC(λ)を算出した。 (4) Calculation of the initial scattering coefficient S _SC (λ) and the initial absorption coefficient K _SC (λ) of the stratum corneum By the following equation (12), the initial scattering coefficient S _SC (λ) and the initial absorption coefficient K _SC ( λ) was calculated.

ここで、Ｘは角層の厚みで、レーザー変位計を用いて角層の断面曲線を計測することにより、0.40[μｍ]を採用した。

Here, X is the thickness of the stratum corneum, and 0.40 [μm] was adopted by measuring the cross-sectional curve of the stratum corneum using a laser displacement meter.

(5)実測分光反射率の検討
(1)で計測した実測分光反射率を図５Ａ、図５Ｂに示し、図６に(4)で算出した角層の初期散乱係数Ｓ_sc(λ)と初期吸収係数Ｋ_sc(λ)を示す。また、図７にNielsenらが計測したケラチンの吸収係数（K. Nielsen, L. Zhao, J. Stamnes, K. Stamnes and J. Moan, Proc. Solar Radiation and Human Health, p. 35-46, 2008.）を示す。これらの図から、角層は低波長側で吸収係数が高く、角層の分光吸収係数にはケラチン成分が反映していることがわかる。 (5) Examination of measured spectral reflectance
The measured spectral reflectance measured in (1) is shown in FIGS. 5A and 5B, and FIG. 6 shows the initial scattering coefficient S _sc (λ) and initial absorption coefficient K _sc (λ) of the stratum corneum calculated in (4). . Fig. 7 shows the absorption coefficient of keratin measured by Nielsen et al. (K. Nielsen, L. Zhao, J. Stamnes, K. Stamnes and J. Moan, Proc. Solar Radiation and Human Health, p. 35-46, 2008). .) From these figures, it can be seen that the stratum corneum has a high absorption coefficient on the low wavelength side, and the keratin component is reflected in the spectral absorption coefficient of the stratum corneum.

実施例１（角層の厚みと角層の分光透過率の推定）
実施例１：式(A1)のパラメータの取得
20代〜30代の女性5名の前腕部位の拡散反射光の分光反射率を計測した。この場合、分光反射率の計測は、全てコニカミノルタ社製分光測色計cm2600dを用い、測定径／照明径をφ8mm／φ11mmとし、波長400〜700nmを10nmおきに計測した。 Example 1 (Estimation of stratum corneum thickness and stratum corneum spectral transmittance)
Example 1: Acquisition of parameter of formula (A1)
Spectral reflectance of diffuse reflected light was measured at the forearm of five women in their 20s and 30s. In this case, all the spectral reflectances were measured using a spectral colorimeter cm2600d manufactured by Konica Minolta, measuring diameter / illumination diameter was φ8 mm / φ11 mm, and wavelengths of 400 to 700 nm were measured every 10 nm.

前述の式(A1)のパラメータとして、次のP0〜P10を考え、全探索方式により、これらのパラメータを求めた。
P0：真皮の酸化ヘモグロビンの濃度（ｗ_hemo）( 式(8) )
P1：真皮の還元ヘモグロビンの濃度（ｗ_dhemo）( 式(8) )
P2：真皮のビリルビンの濃度（ｗ_bill）( 式(8) )
P3：真皮のカロチンの濃度（ｗ_aro ）( 式(8) )
P4：表皮のメラニンの濃度（ｗ_mela ）( 式(7) )
P5：真皮の厚み（Ｄ_d ）( 式(5)、(6) )
P6：表皮の厚み（Ｄ_e ）( 式(3)、(2) )
P7：角層の厚み（Ｄ_sc）( 式(A4) )
P8：角層に含まれるケラチンの濃度ｗ_scsとｗ_sck（式(A5-1)、(A5-2））
P9：角層表面の境界面反射率（k₁）( 式(A1) )
P10：角層の内部反射率（k₂）( 式(A1) ) Considering the following P0 to P10 as the parameters of the above-described formula (A1), these parameters were obtained by the full search method.
P0: Concentration of oxyhemoglobin in the dermis (w _hemo ) (Equation (8))
P1: Concentration of reduced hemoglobin in the dermis (w _dhemo ) (equation (8))
P2: Concentration of bilirubin in the dermis (w _bill ) (equation (8))
P3: Concentration of carotenes in the dermis (w _aro ) (equation (8))
P4: Concentration of melanin in the epidermis (w _mela ) (Equation (7))
P5: Thickness of the dermis (D _d ) (Equations (5), (6))
P6: Skin thickness (D _e ) (Equations (3), (2))
P7: Thickness of stratum corneum (D _sc ) (formula (A4))
P8: Concentration of keratin contained in the stratum corneum w _scs and w _sck (formula (A5-1), (A5-2))
P9: Interfacial reflectance of stratum corneum surface (k ₁ ) (Formula (A1))
P10: Internal reflectance of stratum corneum (k ₂ ) (Formula (A1))

この場合、皮膚内部色素濃度（ｗ_hemo、ｗ_dhemo、ｗ_bill、ｗ_mela）、真皮の厚みＤ_d 、表皮の厚みＤ_e、角層表面の境界面反射率ｋ₁の探索範囲は、経験的にヒトの皮膚が有する範囲とした。また、角層の内部反射率ｋ₂は0.5〜0.6、角層の厚みＤ_SC、は1.25 [μｍ]、ケラチンの濃度度ｗ_SCSとｗ_SCKは0.1〜1.0 [mol/L]の範囲で変化させた。そして、指定した範囲で各パラメータを連続的に変化させて推定した分光反射率と計測した分光反射率との平均二乗誤差RMSEが最小となるパラメータを求めた。 In this case, the skin inside the dye concentration _{_{(w hemo, w dhemo, w}} bill, w mela), the thickness of the dermis D _d, the search range of the boundary surface reflectance k ₁ of thickness D _e, horny layer surface of the epidermis, empirical The range that human skin has. In addition, the internal reflectance k ₂ of the stratum corneum is 0.5 to 0.6, the stratum corneum thickness D _SC is 1.25 [μm], and the keratin concentration levels w _SCS and w _SCK are in the range of 0.1 to 1.0 [mol / L]. I let you. Then, a parameter having a minimum mean square error RMSE between the spectral reflectance estimated by continuously changing each parameter in the specified range and the measured spectral reflectance was obtained.

この５名の分光反射率曲線を図８に示す。
５名の角層の厚みＤ_SCを推定した。その結果、角層の厚みの平均は12.3 [μｍ]で、標準偏差は2.68 [μｍ]であった。 The spectral reflectance curves of these five persons are shown in FIG.
The thickness of the five of the stratum corneum was estimated D _SC. As a result, the average thickness of the stratum corneum was 12.3 [μm], and the standard deviation was 2.68 [μm].

一方、５名の女性の前腕部のRiver Diagnostics社製の共焦点ラマン分光装置Skin analyzer を用いてラマンスペクトルを計測し、「ラマンスペクトル解析による角層厚測定法」（カネボウ化粧品価値創成研究所）（清水教男，中川典昭，尾藤宏達，内藤智，酒井進吾，“ラマンスペクトル解析による角層厚計測”，日本香粧品学会誌, Vol.34, No.3, pp. 220-221,2010.）により角層の厚みを計測した。この場合、皮膚表面から一定深度までレーザーを照射し、各深度での2700〜3100 [cm^-1]のラマンスペクトルを取得し、正規化したラマンスペクトルの2880 [cm^-1]の強度が0.6となるときの深度を角層厚として求めた。 On the other hand, the Raman spectrum was measured using the confocal Raman spectrometer Skin Analyzer manufactured by River Diagnostics on the forearms of five women, and the "corneal layer thickness measurement method by Raman spectrum analysis" (Kanebo Cosmetics Value Creation Laboratory) (Noriaki Shimizu, Noriaki Nakagawa, Hirotoshi Oto, Satoshi Naito, Shingo Sakai, “Measurement of stratum corneum thickness by Raman spectrum analysis”, Journal of the Japan Cosmetic Society, Vol.34, No.3, pp. 220-221, 2010. ) To measure the thickness of the stratum corneum. In this case, the laser is irradiated from the skin surface to a certain depth, the Raman spectrum of 2700-3100 [cm ^-1 ] at each depth is obtained, and the intensity of 2880 [cm ^-1 ] of the normalized Raman spectrum is 0.6. The depth at which it was obtained was determined as the stratum corneum thickness.

このラマンスペクトル解析による実測角層厚は平均12.31 [μm]で、標準偏差は2.67 [μm]であった。したがって、ラマンスペクトル解析による実測角層厚と、分光反射率の測定から求めた角層厚との誤差率は平均1.44 [%]と低く、分光反射率から求めた角層の厚みの推定値は信頼できることがわかる。 The measured stratum corneum thickness by Raman spectrum analysis averaged 12.31 [μm], and the standard deviation was 2.67 [μm]. Therefore, the average error rate between the measured stratum corneum thickness by Raman spectrum analysis and the stratum corneum thickness obtained from the spectral reflectance measurement is as low as 1.44 [%] on average, and the estimated stratum corneum thickness obtained from the spectral reflectance is It turns out to be reliable.

実施例２（角層の分光透過率の推定）
実施例１と異なる別の被験者４名を対象として、実施例１と同様にして前腕部の分光反射率を計測した。図９に得られた分光反射率を示す。また、実施例１と同様にして、計測した分光反射率から全探索方式により、前述の式(A1)のパラメータを求め、角層分光透過率Ｔ_SC(λ)を推定した。この結果を図１０に実線で示す。 Example 2 (Estimation of spectral transmittance of stratum corneum)
The spectral reflectance of the forearm was measured in the same manner as in Example 1 for four different subjects different from those in Example 1. FIG. 9 shows the obtained spectral reflectance. Further, in the same manner as in Example 1, the parameter of the above-described formula (A1) was obtained from the measured spectral reflectance by a full search method, and the stratum corneum spectral transmittance T _SC (λ) was estimated. The result is shown by a solid line in FIG.

次に、４名の被験者から、分光反射率の計測と同一部位の角層サンプルを取得し、その角層サンプルから公知の手法により逆計算で分光透過率を求めた。この結果を図１０に破線で示す。 Next, a stratum corneum sample at the same site as the measurement of spectral reflectance was obtained from four subjects, and the spectral transmittance was obtained from the stratum corneum sample by inverse calculation using a known method. The result is shown by a broken line in FIG.

推定した角層の分光透過率は、低波長域の透過率が低く長波長域の透過率が高いという波長依存性を示した。実測から逆計算で得た角層の分光透過率も類似の波長依存性があることが分かる。推定した角層透過率と実測から逆計算して得た分光透過率との誤差RMSEを調べたところ、平均0.040であることから、角層透過率の推定値は信頼できるといえる。 The estimated spectral transmittance of the stratum corneum showed wavelength dependency that the transmittance in the low wavelength region was low and the transmittance in the long wavelength region was high. From the actual measurement, it can be seen that the spectral transmittance of the stratum corneum obtained by inverse calculation has a similar wavelength dependency. When an error RMSE between the estimated stratum corneum transmittance and the spectral transmittance obtained by inverse calculation from the actual measurement was examined, the average value was 0.040, and therefore it can be said that the estimated value of the stratum corneum transmittance is reliable.

比較例
図１１に示すように、角層内で多重反射が起こると仮定した光学モデルを定め、このモデルにより、角層の分光反射率を次のように推定した。 Comparative Example As shown in FIG. 11, an optical model assumed that multiple reflection occurs in the stratum corneum was determined, and the spectral reflectance of the stratum corneum was estimated as follows using this model.

まず、角層内での多重反射を想定すると、角層内の光の経路は図１１の矢印で表される。ここで、角層内で多重反射が生じた後に角層表面から出てくる光を分光反射率Ｒ_skin2(λ) と定義する。 First, assuming multiple reflections in the stratum corneum, the light path in the stratum corneum is represented by arrows in FIG. Here, light that emerges from the surface of the stratum corneum after multiple reflection occurs in the stratum _corneum is defined as spectral reflectance R _skin2 (λ).

分光反射率Ｒ_skin2(λ)を計算するための数式は、前述の式(4)の皮下組織と真皮の2層の分光反射率を推定する式を応用することで導くことができる。即ち、皮下組織の分光反射率をＲ_h(λ)、真皮の分光反射率Ｒ_dermis(λ)を、真皮の分光透過率をＴ_dermis(λ)とすれば、皮下組織と真皮の2層の分光反射率Ｒ_dh(λ)は次式(4)で表される。 The mathematical formula for calculating the spectral reflectance R _skin2 (λ) can be derived by applying the formula for estimating the spectral reflectance of the two layers of the subcutaneous tissue and the dermis in the formula (4). That is, _assuming that the spectral reflectance of the subcutaneous tissue is R _h (λ), the spectral reflectance of the dermis R _dermis (λ), and the spectral transmittance of the dermis is T _dermis (λ), the two layers of the subcutaneous tissue and the dermis are formed. The spectral reflectance R _dh (λ) is expressed by the following equation (4).

皮下組織に含まれている色素の影響は無視できるほど小さいので、皮下組織の分光反射率はＲ_h(λ)＝1.0 と一定値にすることもできる。この場合、式(4)は次式(4)’のように変換される。 Since the influence of the pigment contained in the subcutaneous tissue is negligibly small, the spectral reflectance of the subcutaneous tissue can be set to a constant value of R _h (λ) = 1.0. In this case, the equation (4) is converted into the following equation (4) ′.

式(4)においてＲ_h(λ)をＲ’(λ)、Ｔ_dermis(λ)をＴ_SC(λ)、Ｒ_dermis(λ)をＲ_SC(λ)に置き換えることで角層内で多重反射が生じた後に角層表面に出てくる光(分光反射率Ｒ_skin2(λ) )を計算する式(13)が導出できる。 In Formula (4), R _h (λ) is _replaced with R ′ (λ), T _dermis (λ) is _replaced with T _SC (λ), and R _dermis (λ) is replaced with R _SC (λ). Equation (13) for calculating the light (spectral reflectance R _skin2 (λ)) that appears on the stratum corneum surface after the occurrence of the above can be derived.

そして、分光反射率Ｒ_skin2(λ)を実際に計測される分光反射率Ｒ_est(λ)に変換する。即ち、ＳＣＥ条件で計測された場合には、次式(14)を採用する。 Then, the spectral reflectance R _skin2 (λ) is converted into the actually measured spectral reflectance R _est (λ). That is, when the measurement is performed under the SCE condition, the following equation (14) is adopted.

また、ＳＣＩ条件で計測された場合には、次式(15)を採用する。 Further, when measurement is performed under SCI conditions, the following equation (15) is adopted.

こうして導出した式(14)の適合性を調べるにあたり、パラメータの組み合わせで誤差を相殺することを避けるために、全てのパラメータを変化させるのではなく、一部のパラメータは被験者の血液検査による実測値と医学データからの平均的な値を用いた。パラメータの設定は以下のとおりである。 In examining the suitability of Eq. (14) derived in this way, not all parameters are changed in order to avoid canceling the error by the combination of parameters. And average values from medical data were used. The parameter settings are as follows.

酸化ヘモグロビンの濃度（ｗ_hemo）：被験者の血液検査による実測値を代入
還元ヘモグロビンの濃度（ｗ_dhemo）：被験者の血液検査による実測値を代入
ビリルビンの濃度（ｗ_bill）：被験者の血液検査による実測値を代入
カロチンの濃度（ｗ_caro ）：医学データから33.7 [mol/L]を代入
真皮の厚み（Ｄ_d）：医学データから0.2 [cm]を代入
表皮の厚み（Ｄ_e）：医学データから0.02 [cm]を代入
角層表面の境界面反射率（k₁）：0.027
角層の内部反射率（k₂）：0.52 _Oxygenated hemoglobin concentration (w _hemo ): Substitute the measured value of the subject's blood test Substituted hemoglobin concentration (w _dhemo ): Substitute the measured value of the subject's blood test Bilirubin concentration (w _bill ): Measured by the subject's blood test Substitute value Carotene concentration (w _caro ): 33.7 [mol / L] from medical data Substitute dermis thickness (D _d ): 0.2 [cm] from medical data Substitute skin thickness (D _e ): From medical data Substituting 0.02 [cm] for the interface reflectance of the stratum corneum surface (k ₁ ): 0.027
Internal reflectance of the stratum corneum (k ₂ ): 0.52

メラニンの濃度（ｗ_mela ）、角層の厚み（Ｄ_sc）、角層に含まれるケラチンの濃度ｗ_scsとｗ_sckは連続的に変化させた。そして、推定した分光反射率と実測分光反射率の誤差が最小となるときの分光反射率を、ＳＣＥ条件で計測した被験者1名の顔の分光反射率について、式(A2)と式(14)で推定した。結果を図１２に示す。図１２において、実線は実測値である。
本発明の従う式(A2)による分光反射率は、実測値に良く適合している。一方、式(14)は適合が悪く、特に、角層およびメラニンの吸収係数のピークがある波長域で適合が劣る。以上より、式(A2)が有効である事がわかる。 The melanin concentration (w _mela ), the stratum corneum thickness (D _sc ), and the keratin concentrations w _scs and w _sck contained in the stratum corneum were continuously changed. Then, the spectral reflectance when the error between the estimated spectral reflectance and the measured spectral reflectance is minimum is measured with respect to the spectral reflectance of the face of one subject measured under the SCE condition. Equations (A2) and (14) Estimated by The results are shown in FIG. In FIG. 12, a solid line is an actual measurement value.
The spectral reflectance according to the formula (A2) according to the present invention is well suited to the actually measured value. On the other hand, the equation (14) is poorly matched, and particularly poorly matched in the wavelength region where the stratum corneum and the melanin absorption coefficient peaks are present. From the above, it can be seen that the formula (A2) is effective.

１評価システム
２入力部
３演算手段
３Ａ記憶部
３Ｂ計算部 DESCRIPTION OF SYMBOLS 1 Evaluation system 2 Input part 3 Calculation means 3A Storage part 3B Calculation part

Claims

As an estimation formula for the spectral reflectance of the skin, the following formula (A1) that estimates the spectral reflectance of diffuse reflected light is used,
(Where
λ is the visible light wavelength,
k ₁ is the interface reflectivity when light incident from the air layer side is reflected at the interface between the stratum corneum and the air layer (hereinafter referred to as the interface reflectivity of the stratum corneum surface),
k ₂ is the internal interface reflectance when the light incident from the stratum corneum side at the interface between the stratum corneum and the air layer is reflected again into the stratum corneum (hereinafter referred to as the internal reflectivity of the stratum corneum),
T _sc (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )
In formula (A1), the interface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the concentration of pigment in the skin, the thickness of the epidermis and the thickness of the dermis one or more parameters as to calculate the spectral reflectance of the skin estimate R _est (λ), estimated value R _est and (lambda), the measured value of the spectral reflectance of the skin corresponding to R _measure (λ) An estimated value R _est (λ) that makes the difference between the two values smaller than the specified value or the smallest difference is obtained, and one or more of the parameters are determined according to the parameters used to calculate the estimated value R _est (λ) at that time Skin evaluation method.

The evaluation according to claim 1, wherein the formula (A1) 'for estimating the spectral reflectance including specular reflection light and diffuse reflection light is used as an estimation formula of the spectral reflectance of the skin, instead of the formula (A1). Method.

The evaluation method according to claim 1 or 2, wherein the spectral transmittance T _SC (λ) of the stratum corneum is obtained by the following formula (A4).
S _SC (λ) ′ is the scattering coefficient of the stratum corneum in consideration of light scattering by keratin in the stratum corneum (hereinafter referred to as the conversion scattering coefficient of the stratum corneum),
K _SC (λ) ′ is the scattering coefficient of the stratum corneum considering light absorption by keratin in the stratum corneum (hereinafter referred to as the conversion absorption coefficient of the stratum corneum),
_DSC is the thickness of the stratum corneum. )

The evaluation method according to claim 3, wherein the converted scattering coefficient S _SC (λ) 'of the stratum corneum and the converted absorption coefficient K _SC (λ)' of the stratum corneum are obtained by the following equations (A5-1) and (A5-2).
(Where
S _SC (λ) is an initial scattering coefficient which is a light scattering amount normalized by a unit concentration,
K _sc (λ) is the initial absorption coefficient, which is the light absorption normalized by the unit concentration,
W _SCS and W _SCK are keratin concentrations in the stratum corneum. )

The skin evaluation method according to any one of claims 1 to 4, wherein the following formula (1) is used as R '(λ).
[In Formula (1),
R _epi (λ) is the spectral reflectance of the epidermis expressed by the following equation (2):
T _epi (λ) is the spectral transmittance of the epidermis, expressed by the following equation (3),
R _dh (λ) is the spectral reflectance of the two layers of the dermis and subcutaneous tissue and is expressed by the following equation (4):
R _dermis (lambda) is represented by the spectral reflectance of the dermis by the following formula (5),
T _dermis (lambda) is represented by the spectral transmittance of the dermis by the following equation (6),
(However,
a _d (λ) = (S _d (λ) + K _d (λ)) / S _d (λ),
a _e (λ) = (S _e (λ) + K _e (λ)) / S _e (λ),
b _d (λ) = (a _d (λ) ² −1) ^1/2 ,
b _e (λ) = (a _e (λ) ² −1) ^1/2 ,
D _d is the dermis thickness,
_De is the skin thickness,
K _d (λ) is the dermal absorption coefficient,
K _e (λ) is the skin absorption coefficient,
S _d (λ) is the dermal scattering coefficient,
S _e (λ) is the skin scattering coefficient. )
R _h (λ) is the spectral reflectance of the subcutaneous tissue. ]

The evaluation method according to claim 5, wherein the absorption coefficient K _e (λ) of the epidermis is calculated by the following formula (7), and the absorption coefficient K _d (λ) of the dermis is calculated by the following formula (8).
( _Where ε _s1 (λ) is the molar extinction coefficient of the first skin internal pigment present in the epidermis, w _s1 is the molar concentration of the skin internal pigment, and ε _s2 (λ) is The molar extinction coefficient of the second skin internal pigment, w _s2 is the molar concentration of the internal skin pigment, and when there is a different pigment in the epidermis, the molar extinction coefficient and the molar concentration are similarly _expressed in Equation (7). The products are added.
In equation (8), ε _p1 (λ) is the molar extinction coefficient of the first skin internal pigment present in the dermis, w _p1 is the molar concentration of the skin internal pigment, and ε _p2 (λ) is the first 2 is the molar extinction coefficient of the pigment in the skin, and w _p2 is the molar concentration of the pigment in the skin, and when there is a different pigment in the dermis, the product of the molar extinction coefficient and the molar concentration is similarly expressed in Equation (8). Is added. )

The evaluation method according to any one of claims 1 to 6, wherein at least one of a melanin concentration in the epidermis, an oxidized hemoglobin concentration, a reduced hemoglobin concentration, a bilirubin concentration, and a carotene concentration in the epidermis is obtained as the skin internal pigment concentration.

The skin before and after the application of the cosmetic is evaluated by the evaluation method according to any one of claims 1 to 7, the boundary surface reflectance of the stratum corneum, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, and the stratum corneum Evaluation method for estimating the action of cosmetics based on changes in estimated values before and after application of cosmetics, estimating one or more of skin thickness, skin internal pigment concentration, epidermal thickness and dermis thickness .

Regarding the skin of the subject, the interface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, and the corners determined by the skin evaluation method according to any one of claims 1 to 6. A cosmetic recommendation method for recommending a cosmetic to a subject based on any one or more of layer thickness, skin internal pigment concentration, epidermal thickness, and dermis thickness.

Based on the spectral reflectance of the skin, the interface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the concentration of pigment inside the skin, the thickness of the epidermis and the thickness of the dermis A skin evaluation system that estimates any one or more of the thicknesses,
An input unit for the measured value R _measure (λ) of the spectral reflectance of the skin, and a calculation means;
The calculation means uses the following equation (A1) that estimates the spectral reflectance of diffuse reflected light as the estimation formula of the spectral reflectance of the skin,
(Where
λ is the visible light wavelength,
k ₁ is the interface reflectance of the stratum corneum surface,
k ₂ is the internal reflectivity of the stratum corneum,
T _SC (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )
In formula (A1), the interface reflectance of the stratum corneum surface, the internal reflectance of the stratum corneum, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the concentration of pigment in the skin, the thickness of the epidermis and the thickness of the dermis one or more parameters as to calculate the spectral reflectance of the skin estimate R _est (λ), estimated value R _est and (lambda), the measured value of the spectral reflectance of the skin corresponding to R _measure (λ) An estimated value R _est (λ) that makes the difference between the two values smaller than the specified value or the smallest difference is obtained, and one or more of the parameters are determined according to the parameters used to calculate the estimated value R _est (λ) at that time Output skin evaluation system.

The calculation means uses the following equation (A1) ′ for estimating the spectral reflectance including regular reflection light and diffuse reflection light, instead of the equation (A1), as an estimation equation of the spectral reflectance of the skin. 10. The evaluation system according to 10.

A computer program provided in the arithmetic device in the skin evaluation system according to claim 10,
As an estimated value of the spectral reflectance of the skin, an estimated value R _est (λ) of the diffuse reflected light of the skin is obtained by using the following equation (A1) as a boundary surface reflectance of the stratum corneum surface and an internal reflection of the stratum corneum. Calculating the ratio, the keratin concentration contained in the stratum corneum, the stratum corneum thickness, the skin internal pigment concentration, the thickness of the epidermis and the thickness of the dermis as parameters,
(Where
λ is the visible light wavelength,
k ₁ is the interface reflectance,
k ₂ is the internal reflectivity of the stratum corneum,
T _SC (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )
Calculating a difference between the estimated value R _est (λ) of the spectral reflectance of the skin and a measured value R _measure (λ) of the spectral reflectance of the skin that is input in advance;
Obtaining an estimated value R _est (λ) in which the difference is smaller than a specified value or the difference is minimized;
A computer program including a step of outputting a parameter used to calculate the estimated value R _est (λ).

A computer program included in the arithmetic device in the skin evaluation system according to claim 11,
As an estimated value of the spectral reflectance of the skin, an estimated value R _est (λ) including specular reflection light and diffuse reflection light is expressed by the following equation (A1) ′, and the boundary surface reflectance of the stratum corneum surface, the inside of the stratum corneum A step of calculating one or more of reflectance, the concentration of keratin contained in the stratum corneum, the thickness of the stratum corneum, the skin internal pigment concentration, the thickness of the epidermis and the thickness of the dermis, as parameters,
(Where
λ is the visible light wavelength,
k ₁ is the interface reflectance,
k ₂ is the internal reflectivity of the stratum corneum,
T _SC (λ) is the spectral transmittance of the stratum corneum, and has the keratin concentration and the stratum corneum thickness as parameters.
R ′ (λ) is an estimation formula for the spectral reflectance of the skin tissue below the epidermis based on the Kubelka-Munk theory, and has skin internal pigment concentration, epidermis thickness and dermis thickness as parameters. )
Calculating a difference between the estimated value R _est (λ) of the spectral reflectance of the skin and a measured value R _measure (λ) of the spectral reflectance of the skin that is input in advance;
Obtaining an estimated value R _est (λ) in which the difference is smaller than a specified value or the difference is minimized;
A computer program including a step of outputting a parameter used to calculate the estimated value R _est (λ).