R 0 = 1 a + b ctgh b S X = sinh b S X a sinh b S X + b cosh b S X R = 1 - R g ( a - b ctgh b S X ) a + b ctgh b S X - R g Inverse hyperbolic functions (area functions) The index 0 signifies the term referring to a perfectly black backing specimen or to a specimen without backing ( R g=0) Transmittance of the specimen or fraction of incident light transmitted by the specimen Reflectance in the ideal case of perfectly white backing Light reflectance of a specimen or fraction of incident light reflected from the specimen (the specimen generally being in contact with a backing) Intensity of light reflected from the backing, entering the specimen again Intensity of light transmitted by the specimen Intensity of light reflected by the specimen K ≡ ( d i * d x ) j = 0 - S = 2 ∊ = - ( d T d X ) X → 0 - SĬoefficient of absorption defined by the corresponding thickness of layerĪn asterisk above the letter signifies the term referring to perfectly diffused light (used only when necessary to distinguish)Ī ≡ S + K S = 1 2 ( 1 R ∞ + R ∞ ) b ≡ ( a 2 - 1 ) 1 2 = 1 2 ( 1 R ∞ - R ∞ ) } S ≡ ( d j * / d x ) j * → 0 = 2 σ = ( d R 0 d X ) X → 0Ĭoefficient of scatter defined by the corresponding thickness of layerĬoefficient of absorption defined by the average real path of light Intensity of light traveling inside the specimen towards its illuminated surfaceĬoefficient of scatter defined by the average real path of light Intensity of light traveling inside the specimen towards its unilluminated surfaceĪverage path of this light when passing through a layer of thickness dx Reflectance R, for instance, is then represented by the formulaĭistance from the unilluminated surface of the specimen (used to localize inside the specimen a plane parallel to its surfaces)ĭirection of light in reference to the surfaces of the specimen, expressed by the angle from normal The integrated equations may be adapted for practical use by introducing hyperbolic functions and the secondary constantsī = 1 2 ( 1 / R ∞ - R ∞ ), ( R ∞≡reflectivity). Consequently, they are exact under the same conditions. The Gurevic and Judd formulas, although derived in another way by their authors, may be got from the Kubelka-Munk differential equations too. Consequently, the different formulas Kubelka-Munk got by integration of their differential equations are exact when these conditions are fulfilled. Both systems become identical when u= v=2, that is, for instance, when the material is perfectly dull and when the light, is perfectly diffused or if it is parallel and hits the specimen under an angle of 60° from normal. d i = - 1 2 ( S + K ) u i d x + 1 2 S v j d x, d j = - 1 2 ( S + K ) v j d x + 1 2 S u i d x , Note: Author names will be searched in the keywords field, also, but that may find papers where the person is mentioned, rather than papers they authored.Use a comma to separate multiple people: J Smith, RL Jones, Macarthur. ![]() Use these formats for best results: Smith or J Smith.For best results, use the separate Authors field to search for author names.Use quotation marks " " around specific phrases where you want the entire phrase only.Question mark (?) - Example: "gr?y" retrieves documents containing "grey" or "gray". ![]()
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