The document describes two main methods to correct predicted dye concentrations in color matching: 1. Numerical increments - increasing each dye concentration by 1% successively and recalculating color coordinates. 2. Using differentiation of reflectance - leveraging the differentiation of target and standard reflectance to quickly reach the correct recipe with minimal iterations. It also outlines the general steps to predict dye concentrations which include measuring standard and substrate reflectance, calculating Kubelka-Munk functions, identifying dye properties, forming equations to solve for concentrations, calculating color differences, and applying corrections if needed.

1. COMPUTER COLOUR MATCHING STEPS TO
PREDICT CONCENTRATION
CHAPTER-8
Granch Berhe

2. Correction to predicted Recipe
• The correction can be applied in different ways. The important methods are:
• i. numerical increments in connection of each dye
• ii. correction by using the differential of K-M function of standard color
w.r.t. Reflectance
A. Numerical increments in connection of each dye
• In this method the concentration of dyes are increased by 1% of computed
concentration successively for each dye and tristimulus values are computed
each time using 16 equations
• sample Concentration Color coordinate’s
• Standard - Xt Yt Zt
• fiber program C1 C2 C3 X0 Y0
• predated c2 c3X1 Y1 Z1
• Predated C1 c2+0.01c2 c3 X2 Y2 Z2
• Predated C1 c2 c3+0.01c3 X3 Y3 Z3

3. B. Using of differentiation of Reflectance
The differentiation of reflectance of the target and standard provides a method
to reach to correct recipe with minimum iterations.
Color Matching Using Sixteen Points Reflectance Data
The Present computational mentods use 16 wavelengths data for determining
color recipe for a given shade. CHE color parameters of customer standard are
determined by its spectral rteckeetance values, which in turn depend on
concentration of each dye for three dyes combination we have:
• X = F2 (c1,c2,c3)
• Y = F2(c1,c2,C3)
• Z= F3 (c1,c2,c3)
• Where:
• F1,F2,F3 are non –linear functions of dyestuff concentrations
• The linearization of equations result inherent inaccuracies, and therefore
concentration computed ar first retail will have more of less errop. The first
solution can be improved by iteration method. Thus even for 16-point
computations the determnunations of color recipe are carried out in two ways
– Determination of initial recipe
– Improvement solution by iteration

4. Read XYZ of standard & data for
dyes & substrates
Select appropriate combinations of dyes
Negative concentration or out side tolerance?
Calculate reflectance curve and XYZ of sample
Compare XYZ of standard ,close enough
Calculate
Correction to
concentration
Calculate color difference for different illuminants, metamersim, cost of dyes.
Calculation is made for all possible combinations from selected dyes?
Print out results
Steps to Predict Concentration

5. A/ 1. Measure reflectance of target standard
2. Measure reflectance of subs trace
3. Calculate K .M Function of Standard
4. Calculate K.M function of subs tract
B/ Take optical data of three dyes for calculating recipe at 16 wavelengths
C/ 1. Identify Smax and (K/S/ Max, and f(Rframex path) mx surs.
2. Represent K.M function with variables for both standard and subs tract
3. Form a mate
4. Solve c1,C2$C3
D/ 1. Calculate K.M function of the sample ( dye mixture ) a 16 wake length data
2. calculate Refraction of the sample ( dye mixture) a 16 wow length data
E/ 1. Calculate Tristumalus malue of standard
2. calculate Tristimulus value of dye mixture ( sample)
F/ 1. Apply color Difference formula
2. Indicate the lightless, red greenness & Blue yellow CASs of the sample
3. Take correction
4. fist give over covert ion
Steps to Predict Concentration

6. A/ 1. Measure reflectance of target standard
2. Measure reflectance of subs trace
3. Calculate K .M Function of Standard
4. Calculate K.M function of subs tract
B/ Take optical data of three dyes for calculating recipe at 16 wavelengths
C/ 1. Identify Smax and (K/S/ Max, and f(Rframex path) mx surs.
2. Represent K.M function with variables for both standard and subs tract
3. Form a mate
4. Solve c1,C2$C3
D/ 1. Calculate K.M function of the sample ( dye mixture ) a 16 wake length data
2. calculate Refraction of the sample ( dye mixture) a 16 wow length data
E/ 1. Calculate Tristumalus malue of standard
2. calculate Tristimulus value of dye mixture ( sample)
F/ 1. Apply color Difference formula
2. Indicate the lightless, red greenness & Blue yellow CASs of the sample
3. Take correction
4. fist give over covert ion
Steps to Predict Concentration