Printer Colour Gamut Modeling with Kubelka-Munk Translucency
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Solution Overview
Problem
Current methods for determining the colour gamut of 3D printers are time-consuming or limit the realism of printed objects by ignoring translucency, especially when printing translucent objects.
Innovation Solution
A method using the Kubelka-Munk theory to model ink reflectance, involving printing samples with varying thickness and ink ratios, measuring reflectance, and fitting the data to derive coefficients for efficient gamut determination, which is stored in the print controller.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If current methods are used to determine colour gamut, then the gamut can be determined, but the process is time-consuming
Solution Approach 1:
The method performs preliminary measurements of reflectance for samples with varying thickness and ink ratios, then uses Kubelka-Munk theory to derive optical coefficients (absorption and scattering) in advance. These pre-derived coefficients are stored and used for rapid gamut determination without requiring repeated measurements, thus reducing measurement time while maintaining accuracy
Solution Approach 2:
The invention changes the approach from direct measurement of all possible colour combinations to measuring physical parameters (reflectance) of samples with controlled variations in thickness and ink ratios. By deriving optical coefficients from these parameter variations using Kubelka-Munk theory, the system achieves accurate gamut determination with fewer measurements
2Ease of manufacture
If traditional gamut determination methods are used, then the process is simplified, but translucency is ignored reducing realism
Solution Approach 1:
The invention extends the measurement parameters to include samples with varying thickness values, which directly affect translucency. By incorporating thickness as a variable parameter in the Kubelka-Munk model, the system captures translucency effects that traditional methods ignore, thereby improving realism while maintaining practical simplicity
Solution Approach 2:
The Kubelka-Munk theory acts as an intermediary model that connects measurable quantities (reflectance of samples with known thickness and ink ratios) to the desired output (colour gamut including translucency effects). This theoretical framework enables accurate translucency prediction without requiring complex direct measurements of all translucency scenarios
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 reduces the number of required measurements and samples, providing a more efficient and accurate determination of the colour gamut for translucent 3D objects, enhancing the realism of printed objects.
Implementation Method 1
for each printed sample measuring a reflectance by means of a spectrophotometer
Implementation Method 2
fitting the measured reflectances with a formula derived from the Kubelka-Munk theory comprising derivations of an absorption coefficient and a scattering coefficient of the ejected inks
Implementation Method 3
fitting the measured reflectances with a formula derived from the Kubelka-Munk theory comprising derivations of an absorption coefficient and a scattering coefficient of the ejected inks
Data Source
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AI summary
Method for determining a colour gamut of a printing system. The method comprises the steps of printing samples of an object on a substrate. The samples vary with respect to a thickness of the samples and ink ratios of the ejected inks. For each printed sample a reflectance is measured by means of a spectrophotometer. The measured reflectances are fit with a formula derived from the Kubelka-Munk theory comprising derivations of an absorption coefficient and a scattering coefficient of the ejected inks and transmission and/or reflection coefficients at interfaces between ink and air and vice versa, and between ink and substrate. A full colour gamut of the printer is determined by using the Kubelka-Munk theory by means of the derived coefficients and the derived coefficients are stored in a print controller of the printing system.