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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:

subtractive

Additive Mixing:

subtractive

  1. 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)
    • kubelka-munk formula

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.

  1. 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.

  1. 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.
  1. A greater number of colors improves accuracy due to enhanced data availability at each wavelength.