Radiative transfer theory solid color-matching calculations

Pierce, Percy E.; Marcus, Robert T.

doi:10.1002/(sici)1520-6378(199704)22:2<72::aid-col3>3.0.co;2-0

Cited by 11 publications

(4 citation statements)

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“…Pierce-Marcus, Hirata-Walker, Mudgett-Richards Mudgett and Richards (1971), Walker (1994), Pierce and Marcus (1997), Hirata (2004 Ben-David, Gordon, QSSA Gordon and Brown (1974), Gordon et al (1975), Gordon (1989); Ben-David (1995, 1997 Figure 1 is a schematic diagram of light distribution in the plane-parallel layer. We assume a semi-infinite or infinite layer with a non-reflecting bottom surface.…”

Section: Extendedmentioning

confidence: 99%

Analytical Approaches to Model Light Transmission through Turbid Media

Sokoletsky¹,

Budak²

2018

Preprint

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The transmission of light is one of the key optical processes in the terrestrial environment (the atmosphere and underlying surfaces). The dependence of light transmittance on the illumination/observation conditions and optical properties of the atmosphere–underlying system can be studied using the integro-differential radiative transfer equation. However, for numerous applications a set of analytical equations is needed to describe the transmitted light intensity and flux. In this paper, we describe various analytical techniques to study light transmittance through light scattering and absorbing media. A physical significance and improved mathematical accuracy of approximations are provided using the analytical models for the diffusion exponent, average cosine of the light field, spherical and plane albedos. The accuracy of various approximations is studied using exact radiative transfer calculations with various scattering phase functions, single-scattering albedos, observational conditions, and optical depths.

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Section: Extendedmentioning

confidence: 99%

Analytical Approaches to Model Light Transmission through Turbid Media

Sokoletsky¹,

Budak²

2018

Preprint

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“…The mathematical function describing the interaction of light with pre-dyed fibers has led to the development of many predictive models for determining reflectance, tristimulus values or parameters of a given color (Pierce, 1997). the mixing laws, which are additive, subtractive or a combination of the two (Burlone, 1990).…”

Section: Color Mixing Modelsmentioning

confidence: 99%

Prediction of Color Attributes Through Geometrical Modeling

Mathur

Seyam

Hinks

et al. 2008

Research Journal of Textile and Apparel

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Today, Jacquard woven fabric producers are able to digitally control each warp yarn individually, pre-program the variable pick density and speed for each filling yarn, and automatically change a pattern without stopping the weaving process. Jacquard CAD systems dramatically reduce the time to produce fabric from the artwork or target design The process of weave/color selection for each area of the pattern is, however, still highly dependent on the CAD system operator who works from a particular color gamut. Multiple weaving trials are required to get a sample that matches the original artwork since the process requires the designer‘s subjective evaluation. The lack of automatic selection of weaves/color matching prompts this research. This paper addresses the development of a geometric model for predicting the color contribution of each warp and filling yarn on the fabric surface in terms of construction parameters. The combination of geometric modeling and existing color mixing equations enables the prediction of the final color of different areas of a Jacquard pattern. The model was verified experimentally and a close agreement was found between a color mixing equation and the experimental measurements.

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“…A number of techniques have been developed to calculate the reflectance in such cases, in particular radiative transfer theory (RT) . RT does not admit an analytic solution, except under certain simplifying assumptions, but a stable numerical solution has been developed—the discrete ordinate method—which is widely used .…”

Section: Introductionmentioning

confidence: 99%

Random walk analysis for reflection and transmission of turbid media

Rogers

2016

Color Research & Application

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The reflection and transmission of light from a turbid slab is determined by considering a photon random walk within the medium. The reflection and transmission is obtained using the Beer-Lambert law on each path through the slab. Path length probability densities are derived, then all paths are summed weighted by their probabilities. The results are simple expressions for the reflection and the transmission in terms of the physical properties of the medium.

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Radiative transfer theory solid color-matching calculations

Cited by 11 publications

References 0 publications

Analytical Approaches to Model Light Transmission through Turbid Media

Analytical Approaches to Model Light Transmission through Turbid Media

Prediction of Color Attributes Through Geometrical Modeling

Random walk analysis for reflection and transmission of turbid media

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