TEXTILE SURFACE STRUCTURE IMPORTANCE AND KUBELKA-MUNK
THEORY USE IN COLOUR MATCH CALCULATIONS
Martinia Ira Joaneli1, Djurdjica Parac Osterman1, Darko Golob2
1 - Faculty of Textile Technology, University of Zagreb, Croatia
2 - Faculty of Mechanical engineering, Institute of textiles,University of Maribor, Slovenia
Abstract
One of the parameter of greatest interest in the production of coloured surfaces is their colour constancy and one of the most serious practical problems attend the change in colour appearance with change in conditions regarding the surface characteristics. The colour appearance of textile surfaces is usually modeledthrough Kubelka–Munk theory. The Kubelka–Munk colour model describes the reflectance of coloured sample as a function of absorption spectrum K(λ), a scattering spectrum S(λ)and the reflectance spectrum of the substrate. When there is a variation in measurement of samples dyed with different shaded dyestuff in corresponding concentrations, certain differences will occur in K/S values and the reliability of K-M operations will become a question.In this paper the aim was to point out the shortcomings of Kubelka – Munk theory and to analyze the influence and the importance of surface structure of sample and also the size of measured surface through the performance of K–M colour match calculation on yellow and blue dyed samples. Due to this aim certain calculation of predicted colour values were performed using numerical software tool MATLAB. Using MATLAB, simulation of coloured samples based on K/S values were made and than compared to the results of the real measured dyed samples, also the correction of concentration were performed. The results were also analyzed statistically.
Key Words: Kubelka-Munk, optical data of dyes, surface structure influence, colour calculation, Matlab
1.INTRODUCTION
In most industrial colour matching processes, the aim is to produce a sample having a spectral reflectance function as close as possible to that of the standard. For colour matching, it is desirable to produce colour constant samples which maintain the same colour appearance under wide range of parameters, considering that thetextile samples are highly heterogeneous in structure,andthat number of parameters highly affects the accuracy in colour matching operations.
It is the fact that one of the most important aspects of a textile material is its appearance which can be described as a summary of visually perceived attributes of colour and structure uniquely defined by the reflectance spectrum of the sample. Knowledge of the surface – spectral reflectance of surfaces is important in colour applications, including computer colour estimation and colour reproduction[1], [2], [3], [4].
In textile industry, the most common approach to the optical properties of the substrate and colorant is through Kubelka–Munk theory, expressed in 1931. Due to its simplicity and directly applicable form of its expression, the theory of Kubelka–Munk was immediately accepted for application to industrial problems and was also recommended and introduced by CIE. Introduction of Kubelka –Munk theory to predict the reflectance of admixture of colorants and also the CIE recommendations for the description of colour by three mathematical numbers, brought revolutionary changes in colour science. Reflection, absorption and scattering occur when opaque surfaces are exposed to light. Light interacting with a textile material involves absorption and scattering of light by dye molecules and fibers [1], [2].
These two phenomena, exactly, are incorporated in the Kubelka–Munk colour model which describes the reflectance of a colour sample as a function of an absorption spectrum K(and a scattering spectrum of substrate S(
(1)
Provided the K/S ratio is known for a textile and for a given wavelength of light, the reflectance ratio can be calculated in reverse mode by the following equation:
(2)
The original theory was developed for pigmented layers and assumed infinite substrate width, diffuse illumination and reflectance, and homogeneous colorant distribution[5], [6].
These conditions are rarely met in textiles. Textile surface is heterogeneous layers and in most modern spectrophotometers, the illumination is collimated and the reflectance is diffuse.
In textile cases, not only the color of the material itself is crucial, but also the colour characteristics of undyed substrate and the optical properties of their mixing can be difficult to predict.
The theory derived by Kubelka – Munkaims at predicting such optical properties and has been widely used by the color industry. If this theory has enough accuracy for most industrial applications, it is found to be inexact in many circumstances. The systematic discrepancy between the model and the reality is a serious indication that the theory is either too much simplified or built on wrong assumptions[7], [8], [9], [10].
In this work, the application of the Kubelka – Munk theory was examined and also certain predictions using KM theory were performed to expose the main differences between prediction and reality, and to illustrate the possibilities of eventual shortcomings of the theory that might appear in colour match prediction operations.
2. EXPERIMENTAL
The analyses in this paper were carried out in a few main steps. All measurements were carried out spectrophotometricaly on remission spectrophotometer DataColor type SF600+CT, with four instrument apertures of different sizes (apertures “L”=2,6 cm, “M”=2 cm, “S”=0,9cm and “US”=0,6 cm), using d/8 geometry. Chosen sampleof cotton knitted fabric was measured in warp directions, on front side and back side of the sample.
First step in experimental work in this paper was to provide a precise analyze of undyed samples, in aim of précising the importance of substrate structure and its appearance characteristics influence in colour match prediction operations.
For the analyze cotton knitted fabric of following characteristics (cotton knitted fabric, 25x1 tex, amount of twist 654 twist per meter, direction of twist in yarns Z. Surface density per cm: vertical density Dv=19, horizontal density Dh=9, surface mass240 g/m2), and was measured and analyzed on both side of the specimen due to the distinguished differences in surface structure characteristics between front and back side.
Also, the main parameter calculation procedure was set. Predicted calculation were made by simulation that can predict the colour parameter values for chosen dyestuff on given textile surfaces and this was performed by using the numerical software tool MATLAB.
The computation procedure was as follows;
The implementation of computer matching based on Kubelka – Munk theory requires the optical data file for each dye and for each type of substrate which are stored in the computer auxiliary memory service. So for the computation of the k/sdye value known as dye optical data, for chosen dyestuff and chosen concentration, the data of calibration samples stored in the database for given dyestuff mentioned prior and choused for dyeing performed further in this work, were used and were implemented in equation 3.
(3)
The computations were performed in order to achieve the constant value which represent the definition of every dyestuff and are changed with the concentration.
In the equation 3, also the data of blank specimen of calibration samples used from the database for the given dyestuff were implemented as the K/Sundyed sample value.
Table 1: Optical data of dyestuff (k/sdye), obtained for chosen dyestuff in given concentration
k/sdyeYellow 0,75% / Yellow 2% / Blue 0,75% / Blue 2%
13,21 / 9,76 / 14,04 / 10,26
The k/sdye value obtained was used in further work as the constant value of dye in simulation process which was performed in order to produce the predicted coloured samples on different substrate for the chosen dyestuff of given concentration.
Using k/sdye value, the predicted K/Sdyed samples values were computed, for textile samples chosen for analyses and dyeing in this work. The predicted K/Sdyed sample values were computed using expression (4), using the measured K/S values of chosen undyed samples. Calculations were performed for values obtained for all conditions of measurement mentioned prior.
(4)
In attempt to analyze the objectivity and accuracy of colour matching and reproduction procedure, the simulated coloured samples were provided and all colorimetric parameters values were calculated Predicted K/Sdyed sample values were necessary base for these calculations so remission R values could be calculated in the reverse mode, using expression (2). Remission values obtained for every 20 nm in the range of visible spectrum, were further used for tristimulus values calculations. Tristimulus values are the basis of colorimetry and their accurate calculation is highly desired. In order to compute the tristimulus values, the relative energy of the illuminant, and the colour matching functions must be multiplied together at each wavelength and then summed. All this procedures were performed using MATLAB numerical software tool which is suitable for the implementations of colour-science algorithms[11].
Chosen textile sample was dyed with yellow and blue shaded direct dyestuff used also in simulation procedure, suitable for cotton dyeing, in two corresponding concentrations, 0,75% and 2%. Samples were dyed in „Linitest“apparatus in liquor ratio 1:20. After the dyeing, driedsample was measured spectrophotometrically also on front side and back side of the sample. The results obtained were compared to the simulated values calculating the dE and dK/S values.
After the analyze of dyed samples, the recipe correction of concentration was performed based on the calibration data stored in database, in order to give a more precise analyze of the problem presented in this paper.
Results obtained for undyed, dyed and simulated samples were, further, analyzed statistically to provide the answer on which colour parameter would be established the most significant.
It is important to mention that for the analyze in this work, the sample are measured on both sides to point out the importance and the influence of the differences in structure and surface roughness of the sample on colour appearance.
3. RESULTS AND DISCUSSION
In application of the K–M theory in colour match prediction calculations, certain problems may occur while defining K/S values because of the significant influence of appearance of the substrate influenced by the size of the integrated sphere and the direction of measurement as well. When there is a variation in measurement of samples dyed with different shaded dyestuff in corresponding concentrations, certain differences will occur in K/S values and the reliability of colour match prediction operations will become a question.
The general approach considered for this study was to establish the precise analyze of parameters in a way to analyze the number and the nature of parameters that influence the results of colour match prediction while using the simple Kubelka-Munk expression that is widely used nowadays in textile practice. The precise definition of the importance and influence of size of measured surface and the surface characteristics of textile sample is a key answer for the accuracy in measurement and predictions in match prediction operations. In this paper the analyses were performed through the application of K–M theory on samples of two opposite hues, yellow and blue.
To provide the confirmation that the Kubelka Munk theory has certain shortcomings regarding the substrate influence, the simulation of coloured samples were performed using Kubelka Munk equations implemented in MATLAB software tools. By comparing the results of simulated samples, obtained exactly based on Kubelka-Munk theory, with results obtained on real samples after dyeing, the precise definition of importance and influence of size of measured surface and the substrate surface characteristics was pointed out.To confirm the prior analyze, the correction of concentration on given surfaces was performed in manner of real conditions.
Also the colouristic values of undyed, dyed and simulated samples were analyzed statistically to confirm the analyses performed in this paper.
3.1. Analyses of undyed samples
Considering the fact that summary of remission defines the amount of reflected and absorbed light which defines the surface structure, the first approach was considered concerns summary remission values. This represent the base of Kubelka-Munk calculationsgiven theK/S values as the definition of absorbed and scattered amount of light from given surface.
Table 2. shows the summary remission and summary K/S value for undyed samples for each size of the measured surface.
Table 2:Values of summary remission for undyed sample for each aperture size:
Aperture Size / front side / back side / front side / back sideL 2,7 cm / 2477,69 / 2451,81 / 0,4307 / 0,4789
M 2,0 cm / 2481,54 / 2452,59 / 0,4470 / 0,4817
S 0,9 cm / 2486,57 / 2452,55 / 0,4412 / 0,5012
US 0,6 cm / 2477,53 / 2421,07 / 0,4333 / 0,6356
Certain differences obtained for the given results shows the importance of surface structure characteristic influence as well as the size of measured surface influence. It was the aim to point out the importance of difference between surface structuresof both side of specimen which can highly affect the accuracy in analyses.
For back side of sample, summary R values on average are smaller, which was expected taking into account the roughness of the surface structure, so the certain amount of scatteredand diffused distribution of light is expected. These results are in correlation with summary K/S results which confirm the prior statement. Also the differences occurred are more accented for the smallest size of the measured surface (“US”).
This analyze showed influence of the surface structure on the behavior of light reflected from given surface as a function of wavelength and primarily proved the influence of textile surface structure which would caused certain colour difference in future eventual dyeing of the given specimen. Also measured surface size would influence to a measurement results within colour match prediction operation.
3.2. Simulation procedure
The purpose of these experiments was to test the ability of Kubelka Munk model to predict the results of transition from one fabric surface appearance to another.
The fact is that the Kubelka-Munk theory does not deal with surface phenomena. The theory actually describes what happens inside the substrate and if no surface correction is applied, the results might be very inaccurate. So based on K/S values provided from Kubelka Munk theory application, it was important to perform this simulation to point out discrepancies and differences that certainly will occur between colour match prediction values and real outcome of the dyeing cycle.The number of parameter influence the outcome result and one of the important is certainly the surface structure of dyed textile sample[7].
The reflection spectra for each dyestuff, taken from database and used later for real dyeing process, on chosen surface were calculated and then were integrated according the equations for tristimulus value calculations to obtain the CIELAB colour values. Simulated K/S value and also simulated CIELAB colour parameters values were calculated using k/sdye value for chosen dyestuff, used in further dyeing process performed in this work, on given surface using MATLAB software tool, as it was explained in experimental.
Results of simulated samples are presented in table 3.
Table 3: In table the results obtained in simulation process are presented
Yellow 0,75% / Yellow 2% / Blue 0,75% / Blue 2%Front side / L* / K/S / L* / K/S / L* / K/S / L* / K/S
L / 79,06 / 10,10 / 73,18 / 19,94 / 34,86 / 10,67 / 23,66 / 20,5
M / 79,00 / 10,10 / 73,14 / 19,94 / 34,86 / 10,67 / 23,66 / 20,5
S / 79,01 / 10,10 / 73,14 / 19,94 / 34,86 / 10,67 / 23,66 / 20,5
US / 79,03 / 10,10 / 73,15 / 19,94 / 34,86 / 10,67 / 23,66 / 20,5
Back side
L / 78,93 / 10,10 / 73,09 / 19,94 / 34,85 / 10,67 / 23,65 / 2,05
M / 78,94 / 10,10 / 73,10 / 19,94 / 34,85 / 10,67 / 23,65 / 20,5
S / 78,84 / 10,10 / 73,01 / 19,94 / 34,85 / 10,67 / 23,65 / 20,5
US / 78,15 / 10,10 / 72,44 / 19,94 / 34,81 / 10,67 / 23,64 / 20,5
From the results obtained it can be observed that in the procedure of colour match prediction computation, the influence of substrate surface structure or the size of measured surface are not implemented and they have no significant influence. The results shows no differences or discrepancies caused by the transition from one fabric surface appearance to another.This simulation procedure refers only to a colour characteristic and the differences due to a specimen surface or size of measured surface have not been achieved.
The problem is that this is not the case in practice. It was confirmed prior that in textile cases, not only the color of the dyestuff itself is mattered.The colour characteristics, surface characteristics and the physical properties of undyed substrate and the measurement conditions, and their interaction, also, influencing the results of final production and the possibility of their prediction is crucial.
3.3. Analyses of dyed samples
Samples chosen for the analyze in this work, were dyed in real dyeing process in yellow and blue shaded dyestuff used from the database for prior analyze, in two concentrations (0,75% and 2%).
The position of the simulated and real dyed samples in a*/b* space are showed on figure 1.
Figure 1: Position for dyed and simulated samples for front and back side of the sample, for blue and yellow dyestuff
This first analyze showed certain dependence of the behavior on the shade of the sample. It can be observed that the differences regarding the concentration of dyestuff are more accented for the yellow dyestuff which is correlated with the nature of yellow, and also the differences regarding the size of measured surface occurred, which was not indicated in the simulation process which proves to refers only to a colour characteristic.
The results of lightness and K/S values of real dyed samples were analyzed and are showed in table 4.
Table 4: Lightness L* and K/S values for dyed samples, for four size of measured surface and two concentrations:
Front side / Blue 0,75% / Blue 2% / Yellow 0,75% / Yellow 2%L* / K/S / L* / K/S / L* / K/S / L* / K/S
L / 36,35 / 9,38 / 27,96 / 15,96 / 78,16 / 9,31 / 72,28 / 17,54
M / 36,12 / 9,35 / 29,1 / 14,50 / 78,03 / 8,65 / 72,75 / 17,58
S / 37,79 / 8,33 / 29,08 / 14,35 / 78,22 / 9,33 / 73,23 / 16,02
US / 37,27 / 8,63 / 29,17 / 14,52 / 77,87 / 9,55 / 72,13 / 19,50
Back side / Blue 0,75% / Blue 2% / Yellow 0,75% / Yellow 2%
L* / K/S / L* / K/S / L* / K/S / L* / K/S
L / 33,16 / 11,98 / 25,98 / 19,24 / 76,52 / 12,84 / 70,66 / 23,76
M / 33,4 / 11,61 / 26,98 / 17,39 / 76,76 / 12,61 / 70,74 / 23,67
S / 32,69 / 12,34 / 26,45 / 18,60 / 77,48 / 11,98 / 70,91 / 23,12
US / 32,6 / 12,31 / 27,06 / 17,68 / 77,29 / 11,34 / 72,86 / 20,53
It is first observed that the surface of front side (smoother surface) produce higher lightness value (L*) of the same amount of dyestuff, as the result of the higher reflectance from the smoother surface occurred due to a surface structure. It is in correlation with the K/S value obtained higher for the back side (rougher surface) of the sample which confirm the influence of surface structure on appearance of colour and showed that the rougher surface, even equally coloured, will perform deeper colour.It was expects based on the preliminary analyze performed on undyed surfaces where the higher K/S sum occurred for the rougher surface with higher scattered and absorbed light.