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Fundamental scattering quantities for the determination of reflectance and transmittance  
Fundamental scattering quantities for the determination of reflectance and transmittance
According to the CIE International Illumination Vocabulary (ILV), reflectance is defined as "the ratio between the reflected radiant flux (or luminous flux) and the incident flux under given conditions", while transmittance is defined as " the relationship between the radiant flux (or luminous flux) transmitted and the incident flux under the given conditions. " Both quantities describe the interaction of the radiant flux with objects, but only for certain conditions.
These conditions include the irradiated area of ​​the surface (& # 119860; i ), the area of ​​the object where the optical radiation is evaluated (& # 119860; r ), or the solid irradiation and detection angles (& # 120596; i and & # 120596; r ). Therefore, when reporting the value of reflectance or transmittance, these conditions must be explicitly specified these measurement conditions. Thus, quantities such as diffuse reflectance, specular reflectance, diffuse transmittance or, regular transmittance or others have been defined to implicitly include well-established geometric measurement conditions. Many other quantities could be defined, and each one would have a different value for a given sample, which would provide very different results, thus, the measurement of reflectance and transmittance under certain conditions is far from being a characterization. complete overview of the interaction of radiant flux with objects.

The bidirectional reflectance distribution function (BRDF) and the scattering distribution function bidirectional dispersion and bidirectional surface reflectance - surface reflectance (BSSRDF), which relate the radiance at the surface to the irradiance and the incident radiant flux, respectively, are consider the fundamental scattering magnitudes used to determine the reflectance of objects. However, in the case of translucent materials in which optical radiation is transmitted below the surface, this radiance depends not only on the irradiance and the incident radiant flux, but also on the size of the area radiated from the surface.

The BRDF Bidirectional Reflectance Distribution Function is only invariable for "large enough" irradiated areas, and cannot be used to predict radiance for smaller irradiated areas.
The BSSRDF Bidirectional Reflectance Distribution Function - Surface can include scattering contributions that occur both below and above the surface, both subsurface and insurface when the radiance is evaluated in an irradiated position, which makes it dependent on the irradiation area. Therefore, BRDF and BSSRDF cannot be considered fundamental scattering quantities for determining reflectance and transmittance under all irradiation conditions.

To obtain a more general description, it is necessary to define quantities that allow the derivation of reflectance and transmittance for any condition.

In the article, the definition of two different scattering magnitudes has been proposed, one that exclusively describes surface reflection and the other that exclusively describes subsurface scattering and subsurface scattering; these quantities are completely independent of the irradiation conditions and, therefore, can be considered more fundamental than the BRDF and the BSSRDF. Therefore, the proposed quantities should allow the reflectance and transmittance of an object to be calculated under any irradiation condition.
The conclusions drawn from the presented study have been supported by measurements.

Link to the article

The work is a collaboration between the Institute of Optics "Daza de Valdés" of the CSIC, the Department of Applied Mathematics and Computer Science at the Technical University of Denmark, and the University of Poitiers, Institut Pprime UPR 3346 CNRS., The Physikalisch-Technische Bundesanstalt, and the Université de Lyon
Investigación financiada por el Ministerio de Ciencia e Innovación y la Agencia Estatal de Investigación
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