Creating Custom 3D-Printing Material Colors Using Optical Modeling of Waste Plastic (SpecOptiBlend)

This open-source software aids in identifying the ideal ratio of each spectral data component for the reconstruction of a sample when only its spectral information is available. Here, it was used to reconstruct Western University's Purple color but, it can be applied to any other color.

A Background

1. Subtractive Color Mixing:
   • Light interacts with substances (dyes/pigments).
   • Certain wavelengths are absorbed, and others are reflected.
   • Results in perceived colors.

Subtractive Mixing:

Additive Mixing:

2. Kubelka-Munk Theory
   • It models how light interacts with an opaque substance.
   • It is used to predict how light is absorbed and scattered.
   • Absorption (K), and Scattering (s)
   • 

Objectives

To reconstruct the reflectance curve of the target sample by finding the optimized proportion of each color in the mix to reach the lowest color difference and RMS.

• Reflectance ~> XYZ values ~> L*, a*,b*
• Objective Function (Finds proportions to minimize ∆𝐸 𝑎𝑛𝑑 𝑅𝑀𝑆 𝑏𝑎𝑠𝑒𝑑 𝑜𝑛 𝑘𝑢𝑏𝑒𝑙𝑘𝑎−𝑀𝑢𝑛𝑘 𝑣𝑎𝑙𝑢𝑒𝑠 𝑎𝑠 𝑖𝑛𝑖𝑡𝑖𝑎𝑙 𝑔𝑢𝑒𝑠𝑠 simultaneously)
• Add weights to crucial parts of the spectrum. (400-450 nm) and (620-700nm).
• Optimizations to compare:
  • L-BFGS-B
  • Nelder-Mead
  • SLSQP
• Reconstruct using the optimized proportions.

Results

• Experiment Verification:
  • Reconstructed navy blue and western purple to confirm experiment results.
  • Reconstructed Lego Pink as an industrial Example.
• Impact of Color Variety:
  • Tested reconstruction accuracy using different color sets:
    • Reconstructing both target colors with only four colors: cyan, magenta, black, and green.
• Software Testing:
  • Utilized online color pickers to initiate reconstruction with RGB values.

1. Reconstruction of the Western Purple using three optimization algorithms.
   • the reconstructed color using the plastics and Nelder-Mead method. 
   • the original purple used to reproduce.

2. Reconstruction of the Navy Blue using three optimization algorithms (8 initial colors).
   • the reconstructed color using the plastics and Nelder-Mead method. 
   • the original purple used to reproduce.

3. Reconstruction of the Lego Pink using the optimized algorithm (8 initial colors). (Nelder-Mead)

##Conclusion

1. Nelder-Mead Optimization provides the closest results to actual colors compared to other algorithms.
2. Limitations of Online RGB Values:

• Online RGB lacks spectral data, limiting its use in precise color mixing returning a DeltaE of 17 for Western Purple.
• Essential for initial reconstructions; comparison samples may not be directly available.

3. A greater number of colors improves accuracy due to enhanced data availability at each wavelength.