Radiative Transfer Model for Complex Coating Color Matching
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Solution Overview
Problem
Traditional methods for formulating complex coating mixtures, such as those containing metallic and pearlescent pigments, are inadequate due to their inability to accurately model radiative transfer and predict color matching, often relying on brute-force strategies that are inefficient and prone to errors.
Innovation Solution
A computer-implemented method using radiative transfer equations and a goniospectrophotometric device to calculate reflectance data, allowing for the precise formulation of coatings that match the appearance of a target sample by modeling electromagnetic wave propagation and scattering effects within the coating mixture.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If traditional Kubelka-Munk Theory and two-flux approximation are used for formulating complex coating mixtures, then the formulation process is simplified, but the accuracy of color matching deteriorates because these methods cannot accurately model radiative transfer and angular-dependent reflectance of effect pigments
Solution Approach 1:
The patent changes the mathematical parameters and models used in formulation from simplified Kubelka-Munk Theory to comprehensive radiative transfer equations that account for angular-dependent reflectance. This involves using goniospectrophotometric data at multiple angles and wavelengths to accurately characterize effect pigments, thereby resolving the contradiction between formulation simplicity and color matching accuracy.
Solution Approach 2:
The patent replaces traditional brute-force formulation strategies with a physics-based radiative transfer model. This substitution uses fundamental optical principles to predict color behavior, eliminating the need for extensive trial-and-error combinations while achieving accurate color matching for complex coatings with effect pigments.
2Reliability
If brute-force strategies are used to work through every combination of tinters, then all possible formulations are evaluated, but the computation time and resources increase significantly
Solution Approach 1:
The patent replaces brute-force computational strategies with a physics-based radiative transfer model that directly predicts color outcomes. This substitution eliminates the need to evaluate every possible tinter combination by using fundamental optical principles to calculate reflectance behavior, thereby maintaining formulation reliability while dramatically reducing computation time.
Solution Approach 2:
The patent performs preliminary goniospectrophotometric measurements to characterize the optical properties of effect pigments before formulation. This preliminary action captures angular-dependent reflectance data that is then used in radiative transfer calculations, allowing for accurate color prediction without exhaustive combination testing.
3Device complexity
If angular-averaged properties are assumed in two-flux approximation, then the radiative transfer calculations are simplified, but the ability to predict angular-dependent color behavior deteriorates
Solution Approach 1:
The patent changes the fundamental assumption from angular-averaged properties to angular-resolved radiative transfer calculations. By using goniospectrophotometric measurements at multiple angles and incorporating these angle-dependent parameters into the radiative transfer model, the patent achieves accurate prediction of angular-dependent color behavior while maintaining manageable calculation complexity through systematic measurement approaches.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables efficient and reliable color matching of complex coatings by minimizing differences between predicted and measured reflectance, optimizing the use of pigments, and reducing metamerism, thus improving the accuracy and efficiency of coating formulation processes.
Implementation Method 1
calculating comprises performing a calculation using a radiative transfer equation
Implementation Method 2
modeling electromagnetic wave propagation and scattering effects within the coating mixture
Implementation Method 3
modeling electromagnetic wave propagation and scattering effects within the coating mixture
Implementation Method 4
obtaining, using a processor, reflectance data from a target coating
Data Source
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AI summary
The present invention relates to a computer-implemented method, a system, an apparatus and a non-transitory computer-readable medium including software that make use of calculations based on the radiative transfer equation or modifications thereof to numerically approximate obtained reflectance data for efficient color matching of an unknown target coating. The present invention is particularly useful for coatings that contain metallic, pearlescent, and other special effect pigments.