Note: Descriptions are shown in the official language in which they were submitted.
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TITLE
Method for color matching
Field of Invention
The invention relates to a method for color matching a reference color
formulation to a defined color shade standard. The process has applications in
the field
of color-imparting and special-effect-imparting surface coatings. It can be
used in color
laboratories, in particular in matching color shades of unknown pigmentation,
as well as
in production of paints in matching paint batches to a defined color shade
standard.
Description of Related Art
The matching of shades of unknown pigmentation is a central problem in all
coloristic areas of a paint company. If color standards have to be matched and
tinting is
to be done, the number of always required tinting steps is a decisive measure
for the
economic efficiency of the process. If no measuring and analysis techniques
are
available, the number of tinting steps needed to develop a color shade is
inevitably
closely connected to the experience of the respective colorist. The absence of
well-
skilled personnel then always leads to a significant increase of expenses for
the tinting
process.
When matching color shades of unknown pigmentation, nowadays complete
possibilities of metrological support is exploited. With a view to support the
elaboration
process of matching colors of unknown pigmentation further instrumentally,
various
methods have been developed and are applicable from a theoretical point of
view. The
diversity of the procedures in practical use already indicates that all of
these
approaches are of approximate nature.
The first step of elaboration of a color shade within a given resin system is
the
recipe calculation on the basis of reflectance spectroscopy and an appropriate
radiative
transfer model to describe the diffusion of light through particulate media.
Only for
effect color shades generally an additional step of microscopic image analysis
to
identify the effect-mediating components is carried out in advance. The
sprayed-out
formula worked out by means of recipe calculation may noticeably deviate from
a
satisfactory match for several reasons: (i) Limitations of the theoretical
radiative transfer
model when handling the non-linearities between optical material parameters
and the
respective pigment volume concentration, (ii) interactions between the
pigments leading
to larger agglomerates depending on the pigment to volume ratio, (iii) scaling
up
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problems if laboratory elaborations have to be manufactured in production
under
completely different side conditions, (iv) deviations in the physical
structure of the
embedding medium compared to the calibration window, (v) process errors as
incorrect
weighed-in quantities, wrong temperatures, unacceptable production or
application
conditions.
Visual estimation of the correction is increasingly more difficult with larger
color
differences, or when complex adjustments of all colorants of a formulation are
required.
If the remaining color differences are unacceptable the determined recipe has
to be
modified in further steps until it hits the given acceptance target. In order
to support the
tinting process with the introduction of computer-aided color recipe
calculation in color
laboratory and production, methods have been developed to accelerate the
tinting
process metrologically and free from the experience of colorists as far as
possible. All
of these methods use special algorithms of recipe calculation based on the 2-
flux model
of Schuster-Kubelka-Munk (P. Kubelka and F. Munk, "Ein Beitrag zur Optik der
Farbanstriche", T. Tech. Phys. 12, p. 593, 1931) for isotropically reflecting
surface
coatings or multi-flux models for anisotropically reflecting special effect
colors (P. S.
Mudgett and L. W. Richards, "Multiple scattering calculations for technology",
Appl. Opt.
10, p. 1485, 1971). In the iiterature various approaches as the correction
factor method
and derived variants are discussed, which all are of approximate character,
since for an
exact physical/mathematical formulation insufficient information is available.
For the
realisation of exact theoretical approaches the expenditure is generally much
too high
and does not have relationship to the gain. In the correction factor approach
from the
comparison between the formulated and calculated concentrations of a sprayed-
out
recipe correction factors are generated which approximately allow for a
characterisation
of the color strength differences between the materials available for the
elaboration of
color shades and the raw materiais used for the generation of optical material
parameters. By means of this correction factor procedure subsequently all new
calculated recipes are modified. However, this method becomes numerically
unstable, if
during the correction the amount of one or more recipe components approaches
zero.
In addition beyond the actual recipe constituents no further tinting
components
can be defined.
The objective of the present invention was therefore to avoid the restrictions
of
conventional methods for recipe correction and to increase the efficiency of
shading
processes. Furthermore the objective of the present invention was to provide a
method
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for matching reference color formulations to a defined color shade standard,
which
method reduces the number of tinting steps particularly in color development
in color
laboratories and batch adjustment in the production of paints. The method
shall be
applicable to color shade standards of unknown or of known pigmentation.
Summary of the Invention
The present invention is directed to a method for matching a reference color
formulation to a defined color shade standard of unknown or of known
pigmentation
comprising the following steps:
1. Measuring a reflectance spectrum RST of the color shade standard,
2. Mixing a paint according to a recipe for the color shade standard and
applying the paint to a substrate,
3. Measuring the reflectance spectrum RPT of the applied paint,
4. Recalculating the theoretical reflectance spectrum RRPT for the recipe of
the
applied paint,
5. Calculating the difference spectrum AR between the measured reflectance
spectrum RPT of the applied paint obtained in step 4 and the recalculated
reflectance
spectrum RRPT obtained in step 5,
6. Adjusting the reflectance spectrum RsT of the color shade standard with
the difference spectrum AR obtained in step 6, creating a modified reflectance
spectrum RSTM of the color shade standard,
7. Calculating a recipe on basis of the modified reflectance spectrum RSTM,
8. Mixing a paint according to the recipe calculated in step 8 and applying
the
paint to a substrate,
9. Optionally measuring the reflectance spectrum RPT of the applied paint
and
repeating steps 4 to 8, if the color difference between the reflectance
spectrum
of the applied paint RPT and the modified reflectance spectrum RsTM of the
color shade
standard is not acceptable. This is done until a given match criterion is
fulfilled.
Alternatively the present invention is directed to a method for matching a
reference
color formulation to a defined color shade standard of unknown or of known
pigmentation comprising
1. Determining color coordinates CsT of the color shade standard,
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2. Mixing a paint according to a recipe for color shade standard and appiying
the paint
to a substrate,
3. Determining the color coordinates CPT of the applied paint,
4. Recalculating the theoretical color coordinates CRPT for the recipe of the
applied
paint,
5. Calculating the difference OC between the determined color coordinates CPT
of the
applied paint obtained in step 3 and the recalculated color coordinates CRPT
obtained
in step 4,
6. Adjusting the color coordinates CST of the color shade standard with the
difference of the color coordinates OC obtained in step 5, creating modified
color
coordinates CsTM of the color shade standard,
7. Calculating a recipe on basis of the modified.color coordinates CsTM ,
8. Mixing a paint according to the recipe calculated in step 7 and applying
the paint
to a substrate,
9. Optionally determining the color coordinates C PT of the applied paint and
repeating steps 4 to 8 if the color difference between the color coordinates
of the
applied paint CPT and the modified color coordinates CSTM of the color shade
standard
is not acceptable. This is done until a given match criterion is fulfilled.
The color coordinates as, e.g., the triplet of tristimulus values. or the L*,
a*, b*
values of the CIELab color space can be derived from the measured reflectance
spectra in a way well-known to person skilled in the art of colormetrics or
can be
measured directly with an appropriate measuring device.
It goes without saying that the method of the present invention is applicable
if the
first tinting step in a color matching process doesn't lead to an acceptable
result, i.e., if
the sprayed out paint formulated on the basis of the identified recipe for the
color shade
standard doesn't match the color shade standard and the difference is not
acceptable.
Brief Description of Drawings
Figure I is a schematic flow diagram of the procedure of the present
invention.
Figures 2 to 4 show the course of development of a green solid color shade
comprising five colorants: white, carbon black, yellow, blue, and green.
Figure 5 shows the change of the target spectrum for a single correction step.
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Figure 6 displays the difference spectrum OR between standard and the various
performed correction steps.
Figures 7 to 11 show the development of a violet gonioapparent color shade
comprising a flop control agent (fca) and five colorants: Al, Mica-blue, red,
violet, and
carbon black. The concentration variation for all recipe constituents is given
as a
function of tinting steps.
Figure 7 depicts the reflectance surface of the standard as a function of
wavelength and observation angle.
Figure 8 shows the color difference between standard and sprayed-out recipe as
a function of tinting steps.
Figure 9 displays the concentration variation for all recipe constituents as a
function of tinting steps.
Figure 10 shows the color difference between standard and sprayed-out recipe
as a function of tinting steps for the conventional correction factor method
Figure .11 displays the concentration variation for all recipe constituents as
a
function of tinting steps for the conventional correction factor method.
Detailed Description of the Embodiments
The method of the present invention is based on a comparison of spectral data
of measured reflection spectra (or alternatively on a comparison of the
corresponding
color coordinates) of color shades of known pigmentation and the corresponding
theoretical expectation values. The more samples are available, the more
information
can be collected about the coloristic deviations between the materials used
for the
pigment calibration and the actually employed raw materials for the color
matching.
Exploiting the complete information accumulated in all tinting steps so far a
procedure
for recipe correction of solid and effect color shades with convergence
behaviour
emerges, when using the method of the present invention. Generally, when using
the
new method a recipe stabilizes after three to five correction steps. Compared
to
conventional procedures a termination criterion can be defined, allowing for
an almost
automation and acceleration of the elaboration process of formulas.
Furthermore, the
procedure offers the possibility to define further tinting components in
addition to the
actual recipe constituents. The method can be applied to dry as well as wet
paint
materials.
The invention will be explained in greater detail below.
G
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The term "reflection spectrum" shall mean reflection spectrum in case of solid
color shades and reflection surface in case of special effect color shades.
In step 'f of the present invention the reflectance spectrum RST of a color
shade
standard to be matched is measured. Measuring is done with a spectrophotometer
at a
single measuring geometry (as, e. g., 45 /0 or d/8 ) for solid color shades
and at
multiple measuring geometries by means of a goniospectrophotometer suited for
special effect color shades. The color shade standard can be a cured or dried
paint
layer, a wet paint layer, or any other color standard of arbitrary character.
When
measuring the reflectance spectrum of wet paint films usual methods and
devices for
measuring wet paint films can be used.
In step 2 of the present invention a paint sample is mixed according to a
recipe
for the color shade standard. The paint is mixed according to the known recipe
in case
of a color shade standard of known pigmentation or according to the calculated
recipe
in case of a color shade standard of unknown pigmentation.
The color shade standard can be for example a color shade standard of
unknown pigmentation, so that first of all a recipe must be calculated for the
color
shade. The color shade standard can also be a color shade standard of known
pigmentation, e.g., a color standard for the production of paints of known
composition/pigmentation. In that case the actual paint production batch is to
be
matched to the given color shade standard.
Therefore in case of color shade standards of unknown pigmentation the color
shade standard has to be matched with an available colorant system by
calculating a
recipe on basis of the measured reflectance spectrum. This is done according
to a
procedure of recipe calculation well-known to a person skilled in the art.
Recipe
calculation is usually based on a given colorant system.
Colorant system should be understood to mean any system of absorption
pigments and/or special-effect pigments comprising ail pigments which shall be
used
for the production of paints. The number and choice of pigment components are
not
subject to restrictions here. They may be adapted in any manner to the
relevant
requirements, e.g. according to the requirements of the paint manufacturer or
its
customers.
Prerequisite of the recipe calculation is the knowledge of the optical
material
parameters of all colored constituents of the available colorant system. They
have to be
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determined experimentally in advance for any colorant of the system by means
of a
calibration echelon. The respective calibration echelon to be produced is of
course
closely connected to the radiative transfer model utilized. In the isotropic
case two
material parameters have to be determined, namely the scattering and
absorption
coefficients, respectively. For this purpose at least two different blends of
different
coloristic behaviour have to be measured. The model explicitly accounting for
the
anisotropy of scattering events contains further wavelength-dependent material
constants used for the parameterisation of the phase function. In case of a
neural
network model the optical properties of all pigments are hidden and captured
in the
weights of the network structure.
Then the paint is applied to a substrate. The subsequent measurement of the
reflectance spectrum RPT of the applied paint can be carried out with the wet
paint
layer or the cured or dried paint layer. Preparation and application of the
paint sample
can be done in a usual way. The paint can be sprayed out onto metal test
panels for
example. Optionally the applied paint layer can be cured or dried under
desired
conditions. Furthermore usual methods and devices for measuring reflectance
data of
wet paint films can be used. The choice, wet or dried paint layer, depends on
the
available standard.
Subsequently the reflectance spectrum RPT of the applied paint layer is
measured (step 3). This is carried out as explained in step I of the present
invention.
In step 4 of the present invention the theoretical reflectance spectrum RRPT
of the
recipe of the applied paint is recalculated. This can be done e.g. before or
after carrying
out step 2 or before or after carrying out step 3. The theoretical reflectance
spectrum
RPTR is recalculated on basis of the optical material parameters of the
colored pigments
of the recipe, which have been experimentally determined in advance and e.g.
stored in
a database.
In a next step (step 5) the difference spectrum AR between the measured
reflectance spectrum RP-r of the applied paint obtained in step 3 and the
recalculated
reflectance spectrum RRPT obtained in step 4 is calculated.
In the comparison between the measured reflectance spectrum RPT of the
applied paint according to the recipe and the reflection spectrum RRPT
theoretically
recalculated for the same formula generally differences may be found, which
can be
traced back to the limits of the standardisation abilities of colorants, the
recipe
dependent interactions of the coloring components among each other, the finite
accuracy of the optical material parameters, limitations of the employed
theoretical
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model, variations in the application conditions, and measuring errors. The
difference
between measured and recalculated reflectance spectrum is a measure for the
mentioned deficiencies.
Therefore in step 6 the reflectance spectrum RST of the color shade standard
is
adjusted with the difference spectrum AR obtained in step 5 obtaining thereby
a
modified reflectance spectrum RSTM of the color shade standard.
The modified reflectance spectrum of the color shade standard RSTM is
subsequently matched by usual recipe calculation. This can be done by varying
the
components of the initial recipe and eventually adding additional defined
tinting
components, which are available in the given colorant system. A modified
recipe on
basis of the modified reflectance spectrum RSTM is calculated (step 7)_ The
calculated
modified recipe is again mixed and sprayed-out_ The sprayed-out paint is
spectrophotometrically measured.
If the color difference between the reflectance spectrum of the applied paint
RPT
and the modified reflectance spectrum RSTM of the color shade standard is not
acceptable, steps 4 to 8 have to be repeated until a given match criterion is
fulfilled.
The assessment of the quality of a match can be made strictly visually or
instrumentally, or a combination of both ' approaches may be utilised. In case
of an
instrumental assessment depending on the area of application (as, e. g.,
Refinish,
Industrial or OEM coating) and associated acceptance solid various metrics may
serve
as a termination criterion for the color development process. Typically the
residual color
difference in a uniform color space (as, e. g., CIELab-76 or DIN-99) or a
specific color
difference formula (as, e. g., CIE94 or CIEDE2000) is adopted for this
purpose, where a
threshold value is agreed on separating accepted and rejected color regions.
In case of
gonioapparent colors a generalisation of the formalism has to be made to
properly
account for the angular dependence of the color appearance.
A strict mathematical termination criterion may be formulated based on an
analysis of the convergence properties of the individual concentrations of all
recipe
components as a function of the number of correction steps. The functional
behaviour
of the individual concentrations of all components as a function of correction
steps has
to be approximated by an appropriate model function, which can be fitted to
the
experimental results by means of an efficient fitting routine to determine the
model
parameters. For a three-parameter function at least three data sets are needed
for the
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estimation of the fitting parameters: the first sprayed-out recipe, the first
sprayed-out
correction, and the calculated second correction.
Using the estimated parameter values, the asymptotic behaviour of the model
function can be calculated. If the concentration variation with the number of
correction
steps is correctly described by the model function the instrumental
elaboration process
can now be terminated by a unique mathematical criterion.
The quality of the asymptotic recipe derived from three parameter sets is
closely
related to the applicability of the model function and to the influence of
statistical and
systematic errors. Both error sources inevitably lead to deviations from the
"ideal"
asymptotic recipe and are discernible in special cases, if for instance the
asymptotic
concentration of a recipe constituent for a monotonically decreasing
(increasing)
function is higher (lower) than the value of the last experimental data set
(second
calculated concentration). It is obvious to disregard this asymptotic recipe
and to
proceed with a normal recipe correction step. The data accuracy can be
improved
further by estimating more than three correction steps. The subsequently
available
fourth data set for the asymptotic reduces the influence of all error sources
considerably
(over-determined set of equations!) and generally leads to an almost "ideal"
corrected
asymptotic recipe. At least now the recipe correction procedure can be
terminated,
since all instrumental potentialities for improvement of a recipe have been
exhausted.
Experiments have clearly revealed that the convergence behaviour of the
devised
method is significantly better than linear and can be approximated by an
appropriate
model function to a sufficient degree of accuracy. Hence the performance of
the
correction method is clearly superior to the conventional linearised approach
and
certainly leads to a reduction in the number of hits in the shading process.
The model
function can also be utilised to extrapolate to correction step infinite. In
this sense a
simple analysis tool can be added to the correction scheme to reduce the
number of
hits by extrapolation and to additionally improve the convergence performance
on the
one hand, and on the other to establish a tool clearly indicating the limits
of instrumental
recipe correction (termination criterion).
Generally, the corresponding color coordinates as, e. g., the triplet of
tristimulus
values or the L*, a*, b* values of the more uniform CIELab color space can be
used in
the present invention instead of using the reflectance spectra, i.e. instead
of a spectral
match criterion a color space match criterion can also be applied.
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The color coordinates, e.g. the triplet of tristimulus values or the L*, a*,
b* values
of the CIELab color space can be derived from the measured reflectance spectra
in a
way well-known to a person skilled in the art or can be measured directly with
an
appropriate measuring device.
For carrying out the method of the present invention the order of steps 1 to 9
is
not rigidly fixed. All steps are used to carry out the method of the present
invention, but
if appropriate order of steps can be changed, e.g. step 4 can be done before
or after
step 2 or before or after step 3. A person skilled in the art is able to
evaluate any
appropriate logical order of steps.
A schematic flow diagram of the procedure of the present invention is given in
figure 1.
A standard panel of unknown pigmentation is used as color shade standard.
Generally the spectrum of the color shade standard is adjusted with the
spectral
difference between the measured spectrum RPT of the applied paint and the
corresponding recalculated spectrum RRPT for the same formula. For this
modified new
spectrum of the color shade standard again a new recipe is calculated based on
the
components used so far and eventually further tinting components. The
described
procedure is repeated until a defined termination criterion is fulfilled. This
means that
the procedure is repeated until the corrected color recipe has stabilized (i.
e., the
change of the concentrations of all components is sufficiently small or falls
short of a
given limiting value, respectively) and/or the remaining color difference hits
a pre-set
tolerance frame.
The spectral difference AR (AR = RPT - RPTR) between experimental sample
spectrum and the corresponding predicted reflectance spectrum is a measure of
the
total process error including failures of the radiative transfer model,
variations in the
physical structure of the characterisation data and mistakes in processing as,
e. g.,
incorrect colorant weighing or wrong application conditions. The latter two
systematic
error sources generally introduce an erratic component into the correction
process
having a negative impact on the convergence properties of any recipe
correction
method.
Compared to that, e.g., the known linear vector shading method does not make
use of all information generated in the course of the correction process. Only
the color
difference between the standard and e.g. the actual batch is considered, while
the
misfit between actual and predicted batch color positions or reflectance
functions is
totally ignored.
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If these systematic error contributions dominate the total process error, no
convergence within the limits defined by their behaviour can be expected,
since the
target is moving randomly. Only a tighter process control will help to re-
establish a well-
behaved recipe correction algorithm.
The correction method of the present invention offers the advantage of
excellent
convergence properties, whereby the number of correction steps can be
restricted in a
natural way. The convergence is sufficiently fast for all potential
operational areas; in
any case the procedure comes to a halt after three to five steps. A unique
termination
criterion indicating instrumental iirriitations of recipe correction could be
defined. Due to
these optimal properties of the correction procedure the elaboration of color
shades or
tinting of batches to a great extent can be automated. Furthermore, in the
course of
correction additional tinting components beyond the actual recipe constituents
can be
defined informally and used for the optimisation of the match results. The
existing
restriction of the correction factor method, namely that in the course of the
correction no
component can be thrown out of the recipe (numerical instability of the
correction factor
method), does as well no longer exist in the new procedure.
The direct approach to the difference in optical behaviour of the materials
used
for pigment calibration and the colorants available for the elaboration of a
color shade is
offered by a comparison between the measured reflectance spectrum of a color
shade
and the recalculated spectrum of the corresponding formula. Only in this way
specific
spectral differences can be made transparent and accounted for in the
correction.
Using this spectral information the reflectance spectrum of the standard is
modified and
subsequently matched again. Other procedures, as e.g., the method of
correction
factors, compare the concentrations of two recipes and as such fall back on
already
transformed quantities that no longer contain direct spectral information. The
risk of
metameric corrections is minimised by comparing spectral data, since within
the
algorithm for the actual correction step, which is based on a conventional
color recipe
calculation for the modified spectrum of the standard, the figure of merit of
the iteration
is the optimum curve fitting applying a suitable weighting function.
Finally the present invention provides a highly flexible and effective
procedure for
recipe correction to match a given color shade standard which can be used for
elaboration of color shades and color development in color laboratories as
well as for
batch adjustment in production of paints.
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The invention is explained more detailed in the following examples.
EXAMPLES
Example 1
Recipe correction of a cireen solid color shade
Figures 2 to 4 show the course of development of a green solid color shade
comprising the five colorants white, carbon black, yellow, blue, and green.
The standard
contains a green pigment and a second green component made of the
complementary
colors yellow and blue. Such complementary colors are known to react quite
sensitive
to changes of the amounts of ingredients.
Figure 2 depicts the reflectance spectrum of the standard as a function of
wavelength measured with a spectrophotometer.
Figure 3 shows the color difference between standard and sprayed-out recipe as
a function of tinting steps.
Figure 4 displays the concentration variation for all recipe constituents as a
function of tinting steps.
Through the consideration of all information collected at each correction step
the
new procedure leads to a significant improvement of the recipe from a
coloristic point of
view, as can be seen from the on the average decreasing residual color
difference. Also
the dependence of the amounts of all recipe components with increasing number
of
correction steps exhibits an unambigious tendency towards stable values. As
expected,
the convergence behaviour of the devised spectral correction method in color
space is
clearly better than linear and is obviously superior to the linear vector
shading
approach.
Figures 5 and 6 collect more details on the course of recipe correction in
reflectance space. Figure 5 shows the change of the target spectrum for a
single
correction step.
Figure 6 displays the difference spectrum AR between standard and the various
performed correction steps, impressively'vindicates the theoretical
expectation that AR
rapidly diminishes with increasing number of correction steps to a level the
statistical
measurement error.
The curve labelled "VO" represents the measured reflectance spectrum of the
standard (RST). The corresponding predicted match for this standard gives rise
to the
theoretically expected "RO" curve (RRPT). When mixing and spraying out this
recipe
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and measuring the panel leads to the "AO" curve (RPT). The difference of the
theoretically synthesized spectrum "RO" and the actually measured spectrum
"AO"
(RPT) is due to all inherent preparatory, application, measurement, and model
errors of
the entire process including the misfit of the characterisation data set.
Subtracting this
difference spectrum AR = RO - AO from the spectrum "VO" of the standard
creates a
new virtual target spectrum (V1 = RSTM) that accounts for the total process
error.
Therefore, matching of this virtual target is expected to provide results
considerably
closer to the final stationary solution of the matching problem than the
previous step.
After two tinting steps the recipe has been stabilized when using the method
according to the invention. A satisfactory matching result has been achieved.
Example 2
Recipe correction of a special effect color shade
Figures 7 to 11 show the course of a completely automated recipe correction of
a
special effect color shade using the procedure of the present invention in
comparison to
the conventional correction factor method, which has been implemented as
single-step
procedure.
Figures 7 to 11 show the development of a violet gonioapparent color shade
comprising a flop control agent (fca) and five colorants: Al, Mica-blue, red,
violet, and
carbon black. The concentration variation for all recipe constituents is given
as a
function of tinting steps as well as the extrapolated asymptotic values
derived from
three, four, and five data sets.
Figure 7 depicts the reflectance surface of the standard as a function of
wavelength and observation angle.
Figure 8 shows the color difference between standard and sprayed-out recipe as
a function of tinting steps.
Figure 9 displays the concentration variation for all recipe constituents as a
function of tinting steps.
Figure 10 shows the color difference between standard and sprayed-out recipe
as a function of tinting steps for the conventional correction factor method
Figure 11 displays the concentration variation for all recipe constituents as
a
function of tinting steps for the conventional correction factor method.
The special effect color shade contains as coloring constituents two
interference
pigments and three solid pigments. As can be seen from the reflection
indicatrix
depicted in Figure 7 the effect character of this color shade becomes obvious
in the
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angular variation. Furthermore, in Figure 8 and Figure 9 the remaining color
differences
according to CIELab-76 and the recipe composition as a function of correction
steps
have been integrated. While according to the known single-step method of
correction
factors no improvement could be achieved with the correction calculation, the
new
procedure due to the consideration of all information collected at every step
leads to a
significant improvement of the recipe from a coloristic point of view, as can
be seen
from the decreasing mean residual color difference. In the latter case also
the
dependence of the amounts of all recipe constituents shows a clear tendency
towards
stable values with increasing number of correction steps, while the correction
factor
method does not show any saturation tendency at all. In the discussed example
the
efficiency of the new correction method becomes obvious in the fact, that due
to the
relatively small residual color difference of the sprayed-out first recipe the
conventional
correction procedure from the tendency leads to a deterioration of the recipe
(pathological case), while the new method handles also this limiting case in a
completely unproblematic way.
After three tinting steps the recipe has been stabilized when using the method
of
the present invention. A satisfactory matching result has been achieved:
