JP2010501854A - Color matching method - Google Patents

Abstract

The present invention relates to a method for color matching a reference color formulation to a specified color standard. The method is: 1. a step of measuring a reflection spectrum R _ST of a color standard; 2. mixing the paint according to the prescription for the color standard and applying the paint to the substrate; 3. measuring the reflection spectrum R _PT of the coating material; _4. recalculating the theoretical reflection spectrum R _RPT for the coating formulation; 5. calculating a difference spectrum ΔR between the measured reflection spectrum R _PT and the recalculated reflection spectrum R _RPT of the coating material; 6. adjusting the reflection spectrum R _ST of the color tone standard using the difference spectrum ΔR; _7. calculating a prescription based on the modified reflectance spectrum R _STM ; Mixing the paint according to the formulation and applying the paint to the substrate.
[Selection] Figure 1

Description

  The present invention relates to a method for color matching a reference color formulation to a specified color standard. The method has application in the field of color imparting and special effect imparting surface coatings. It can be used in color laboratories, especially when matching to the color shades of unknown pigmentation, and also in the manufacture of paints when matching paint batches to a specified color standard.

  Matching to an unknown pigmented color tone is a central problem in all color areas of paint companies. The number of tinting steps required at all times is a decisive measure for the economic efficiency of the process if it must be matched to a color standard and if tinting is to be performed. If measurement and analysis techniques are not available, the number of tinting steps required for tone development will necessarily be closely related to the experience of individual color engineers. In that case, unless there is a highly skilled person, the cost of the tinting process will always increase significantly.

  The possibility of metrological support is now fully utilized when matching to the color of an unknown pigment. Various methods have been developed for the purpose of further supporting the refinement process to match the color of unknown pigments with the equipment, and can be applied from a theoretical point of view. The various procedures already in use suggest that all these approaches are approximate.

  The first step in color refinement within a given resin system is a prescription calculation based on reflection spectroscopy and an appropriate radiative transfer model describing the diffusion of light through a particulate medium. Only for the effect color tone, in general, an additional step of microscopic image analysis for identifying the effect mediating component is performed in advance. The spray application equation derived using the recipe calculation can deviate significantly from satisfactory agreement for several reasons: (i) between the optical material parameters and the respective pigment volume concentration Limitations of the theoretical radiative transfer model when dealing with non-linearities of (ii) interactions between pigments resulting in larger agglomerates depending on the pigment to volume ratio, (iii) production under completely different incidental conditions Scale-up issues when laboratory refinement has to be developed, (iv) physical structure deviation of the embedded media compared to the calibration window, (v) inaccurate weighing, inadequate Process errors such as extreme temperature, unacceptable manufacturing conditions or coating conditions.

  Visual estimation of the correction becomes more difficult when the color difference is greater or when complex adjustments of all the colorants in the formulation are required. If the remaining color difference is unacceptable, the determined recipe must be modified in further steps until a given acceptable target is reached. In order to support the tinting process through the introduction of computer-aided color prescription calculations in color laboratories and manufacturing, methods have been developed to speed up the tinting process metrologically and to minimize the experience of color engineers. I came. All of these methods apply to the Schuster-Kubelka-Munk two-beam model (P. Kubelka and F. Munk, “Ein Beitragzur Optik der Farbrichiche”, T. Tech. Phys. 12 for isotropic reflective surface coatings. , P. 593, 1931) or multi-flux model (PS Mudgett and LW Richards, “Multiple scattering calculation for technology”, Appl. Opt. 10, p. 1485, 1971) using a special algorithm of prescription calculation. The literature discusses various techniques such as the correction factor method and its variations, but they are all approximate because they do not provide sufficient information on the exact physical / mathematical formulation. To achieve an accurate theoretical approach, the cost is generally too high and does not relate to gain. The correction factor method, by comparing the formulation concentration of the spray coating formulation with the calculated concentration, approximates the characterization of the color intensity difference between the material available for color refinement and the raw material used to generate the optical material parameters. A correction factor is generated that enables This correction factor procedure is then used to modify all new calculation recipes. However, this method becomes numerically unstable when the amount of one or more prescription components approaches zero during correction.

  In addition, no further tint ingredients other than the actual prescription ingredients can be defined.

  The object of the present invention was therefore to avoid the limitations of conventional prescription correction methods and to increase the efficiency of the shading process. Furthermore, it was an object of the present invention to provide a method for matching a reference color formulation to a specified tone standard. However, according to the present method, the number of tinting steps is reduced, particularly in color development at the Color Research Laboratory and batch adjustment in the manufacture of paints. The method should be applicable to unknown or known pigmented color standards.

The present invention relates to a method of matching a reference color formulation to a specified color standard of unknown or known pigmentation, which comprises:
1. Measuring a reflection spectrum R _ST of a color standard;
2. Mixing the paint according to the formulation for the color standard and applying the paint to the substrate;
3. Measuring the reflection spectrum R _PT of the applied paint;
4). _{Recalculating the} theoretical reflectance spectrum R _RPT for the coating formulation;
5). Calculating a difference spectrum ΔR between the measured reflection spectrum R _PT of the coating paint obtained in step 4 and the recalculated reflection spectrum R _RPT obtained in step 5;
6). Generating a modified reflectance spectrum R _STM of the color standard by adjusting the reflectance spectrum R _ST of the color standard using the difference spectrum ΔR obtained in step 6;
7). Calculating a prescription based on the modified reflectance spectrum R _STM ;
8). Mixing the paint according to the formulation calculated in step 8 and applying the paint to the substrate;
9. In some cases, the reflection spectrum R _PT of the applied paint is measured,
If the color difference between the reflection spectrum R _PT of the coating material and the modified reflection spectrum R _STM of the color tone standard is not acceptable, the steps 4 to 8 are repeated. This is done until a given match criterion is met.

Alternatively, the present invention relates to a method for matching a reference color formulation to a specified color standard of unknown or known pigmentation, which comprises:
1. Determining a color coordinates C _ST of color shade standard,
2. Mixing the paint according to the formulation for the color standard and applying the paint to the substrate;
3. A step of determining the color coordinate C _PT of the coating material;
4). _{Recalculating the} theoretical color coordinates C _RPT for the coating formulation,
5). Calculating a difference ΔC between the determined color coordinate C _PT of the coating material obtained in step 3 and the recalculated color coordinate C _RPT obtained in step 4;
6). Generating a corrected color coordinate C _STM of the color standard by adjusting the color coordinate C _ST of the color standard using the color coordinate difference ΔC obtained in step 5;
7). Calculating a prescription based on the modified color coordinate C _STM ;
8). Mixing the paint according to the formula calculated in step 7 and applying the paint to the substrate;
9. Optionally, to determine the color coordinates C _PT of coating paint, if color difference between the corrected color coordinates C _STM color coordinates C _PT and color standard coating paint is unacceptable, and a step of repeating steps 4-8. This is done until a given match criterion is met.

Color coordinates, for example, tristimulus values or CIELab color space L ^* values, a ^* values, b ^* values, etc. are derived from the measured reflectance spectrum in a manner well known to those skilled in the colorimetric arts. Or can be measured directly using a suitable measuring device.

  Needless to say, the method according to the present invention is suitable if the first tinting step of the color matching process does not give acceptable results, i.e. a spray-coated paint formulated based on the identified recipe for the color standard. Is not applicable and the difference is unacceptable.

It is a schematic flowchart of the procedure which concerns on this invention. It shows the development process of a solid green color tone including five colorants: white agent, carbon black, yellow agent, blue agent, and green agent. It shows the development process of a solid green color tone including five colorants: white agent, carbon black, yellow agent, blue agent, and green agent. It shows the development process of a solid green color tone including five colorants: white agent, carbon black, yellow agent, blue agent, and green agent. The change of the target spectrum with respect to one correction | amendment process is shown. The difference spectrum ΔR between the standard and various implementation correction steps is displayed. It shows the development of an amber gonioparent color tone that includes a flop modifier (fca) and five colorants: Al, mica blue, red, amber, and carbon black. Concentration changes for all recipe components are given as a function of the number of tinting steps. A standard reflectance surface is shown as a function of wavelength and observation angle. The color difference between the standard and the spray application recipe is shown as a function of the number of tinting steps. The concentration change of all prescription components is displayed as a function of the number of tinting steps. The color difference between the standard and spray coating recipe for the conventional correction factor method is shown as a function of the number of tinting steps. The concentration change of all prescription components in the case of the conventional correction coefficient method is displayed as a function of the number of tinting steps.

  The method according to the invention is based on a comparison (or a comparison of the corresponding color coordinates) of the spectral data of the measured reflectance spectrum of a known pigmented hue and the corresponding theoretical expected value. The more samples available, the more information about the color shift between the material used for pigment calibration and the material actually used for color matching can be collected. When the method according to the present invention is used, a prescription correction procedure for solid colors and effect colors having convergence behavior can be obtained by using all the information accumulated in all the tint processing steps so far. When using the new method, the formulation generally stabilizes after 3-5 correction steps. In contrast to conventional procedures, it is possible to define termination criteria that allow for almost complete automation and acceleration of the formula refinement process. In addition, this procedure offers the possibility to define additional tint components in addition to the actual formulation components. The method is applicable not only to wet paint materials but also to dry paint materials.

  The present invention is described in more detail below.

  The term “reflection spectrum” shall mean the reflection spectrum in the case of solid tones and the reflecting surface in the case of special effect tones.

In step 1 according to the present invention, the reflection spectrum R _{ST of the} color standard to be matched is measured. Measurements are made using a spectrophotometer in the case of solid tones with a single measurement geometry (eg 45 ° / 0 ° or d / 8 °, etc.) and in the case of special effect tones This is done with multiple measurement geometries using a spectrophotometer. The color standard can be a cured or dry paint layer, a wet paint layer, or any other color standard with optional characteristics. When measuring the reflection spectrum of a wet paint film, it is possible to use conventional methods and equipment for measuring wet paint films.

  In step 2 according to the invention, the paint sample is mixed according to the recipe for the color standard. The paint is mixed according to a known formulation in the case of known pigmented color standards or according to a calculated recipe in the case of unknown pigmented color standards.

  The color standard may be, for example, an unknown pigmented color standard. In that case, you must first calculate the prescription for the color. The color standard may also be a known pigmented color standard, for example a color standard for producing a known composition / pigmented paint. In that case, the actual paint production batch will be matched to a given color standard.

  Thus, in the case of an unknown pigmented color standard, it must be matched to the color standard using available colorant systems by calculating a prescription based on the measured reflectance spectrum. This is done according to prescription calculation procedures well known to those skilled in the art. The recipe calculation is usually based on a given colorant system.

  Colorant system shall be taken to mean any system of absorbent pigments and / or special effect pigments, including all pigments used in the manufacture of paints. The number and selection of pigment components is not limited here. They can be adapted in any way according to the relevant requirements, for example according to the requirements of the paint manufacturer or its customers.

  A precondition for formula calculation is that the optical material parameters of all coloring components of the available colorant system are known. They must be experimentally determined beforehand for any colorant in the system by means of a calibration echelon. Each calibration echelon created is of course closely related to the radiative transfer model utilized. If isotropic, two material parameters must be measured, namely the scattering coefficient and the absorption coefficient, respectively. For this purpose, at least two different blends with different chromatic behavior must be measured. A model that specifically accounts for the anisotropy of the scattering event contains additional wavelength-dependent material constants that are used to parameterize the phase function. In the case of a neural network model, the optical properties of all pigments are hidden and incorporated into the network structure load.

  Next, a paint is applied to the substrate. Subsequent measurement of the reflection spectrum RPT of the applied paint can be carried out using a wet paint layer or a cured paint layer or a dry paint layer. Preparation and application of the paint sample can be carried out in the usual way. The paint can be sprayed onto, for example, a metal test panel. Optionally, the applied paint layer can be cured or dried under desired conditions. In addition, conventional methods and apparatus for measuring wet paint film reflectance data can be used. The choice of wet or dry paint layer depends on available standards.

Subsequently, the reflection spectrum R _PT of the applied paint layer is measured (step 3). This is done as described in step 1 of the present invention.

In step 4 according to the present invention, the theoretical reflection spectrum R _RPT of the coating paint recipe is recalculated. This can be performed, for example, before or after step 2 or before or after step 3. The theoretical reflection spectrum R _PTR is recalculated based on the optical material parameters of the color pigment of the formulation. The optical material parameters are experimentally determined in advance and stored, for example, in a database.

In the next step (step 5), a difference spectrum ΔR between the measured reflection spectrum R _PT of the coating paint obtained in step 3 and the recalculated reflection spectrum R _RPT obtained in step 4 is calculated.

In general, a difference may be found when comparing the measured reflection spectrum R _PT of the coating paint based on the prescription and the reflection spectrum R _RPT theoretically recalculated with the same formula. Differences can be traced to colorant standardization capabilities, mutual prescription-dependent interactions of color components, finite accuracy of optical material parameters, constraints on the theoretical model used, variations in coating conditions, and measurement error limits . The difference between the measured reflectance spectrum and the recalculated reflectance spectrum is a measure of the stated defect.

Accordingly, in step 6, the reflection spectrum R _ST of the color standard is adjusted using the difference spectrum ΔR obtained in step 5, thereby obtaining the modified reflection spectrum R _STM of the color standard.

Subsequently, the modified reflectance spectrum R _STM of the tone standard is matched by normal prescription calculations. This can be done by changing the ingredients of the initial formulation or eventually adding additional defined tint ingredients. However, these components are those that are available for a given colorant system. A modified recipe based on the modified reflectance spectrum R _STM is calculated (step 7). Again, the calculated correction recipe is mixed and sprayed. Spray coated paint is measured spectrophotometrically.

If the color difference between the reflection spectrum R _PT of the applied paint and the modified reflection spectrum R _STM of the color standard is unacceptable, steps 4-8 must be repeated until a given match criterion is met.

  Assessment of the quality of the match can be done visually or by instrumentation, or a combination of both approaches can be utilized. For instrument evaluation, depending on the application field (eg, refinish coating, industrial coating, or OEM coating, etc.) and the associated receptive solid, various metrics can serve as the termination criteria for the color development process. Typically, residual color differences in uniform color space (such as CIELab-76 or DIN-99) or specific color difference formulas (such as CIE94 or CIEDE2000) are employed for this purpose. In that case, the threshold value corresponds to the separation between the acceptable color area and the unacceptable color area. In the case of gonioapparent colors, generalization of the mathematical form must be done to properly take into account the angular dependence of the color appearance.

  The exact mathematical termination criteria can be formulated based on an analysis of the convergence of the individual concentrations of all prescription components as a function of the number of correction steps. The functional behavior of the individual concentrations of all components as a function of the number of correction steps must be approximated by an appropriate model function that can be fitted to the experimental results by an efficient fitting routine for determining model parameters. In the case of a three parameter function, at least three data sets are required to estimate the fit parameters: a first spray application recipe, a first spray application correction, and a calculated second correction.

  Using the estimated parameter values, it is possible to calculate the asymptotic behavior of the model function. If the concentration change with the number of correction steps is accurately described by the model function, at this point, the instrument refinement process can be terminated with its own mathematical criteria.

  The quality of asymptotic prescriptions derived from the three parameter sets is closely related to the applicability of model functions and the effects of statistical and systematic errors. Both sources of error inevitably cause deviations from the “ideal” asymptotic prescription, but in special cases, for example, the asymptotic concentration of the prescription component in the monotonically decreasing (increasing) function is the last experimental data set (second If it is higher (lower) than the value of (calculated density), it can be identified. It is natural to proceed with a normal prescription correction process ignoring this asymptotic prescription. By estimating with more than three correction steps, the data accuracy can be further improved. A fourth data set that is subsequently available asymptotically significantly reduces the influence of all error sources (overdetermined expression set!), And generally yields an almost “ideal” corrected asymptotic prescription. At least at this point, it is possible to finish the prescription correction procedure because all the potential for prescription improvement by the device has been exhausted.

  Experiments clearly demonstrate that the converging behavior of the devised method is significantly better than the linear method and can be approximated with adequate model functions with sufficient accuracy. Thus, the performance of the correction method is clearly superior to the conventional linearization method, which reliably reduces the number of hits in the shading process. It is also possible to extrapolate to the infinite correction process using a model function. In this sense, a simple analysis tool can be added to the correction scheme to reduce the number of hits by extrapolation, while further improving convergence performance on the one hand, and on the other hand the limits of prescription correction by the instrument (termination criteria). It is possible to establish a tool that clearly shows

In general, instead of using a reflection spectrum, the corresponding color coordinates, for example, tristimulus values, tri-values of tristimulus values or more equivalent CIELab color space L ^* values, a ^* values, b ^* values, are represented by the present invention. Can be used. That is, a color space matching criterion can be applied instead of the spectral matching criterion.

Color coordinates, for example, tristimulus values or CIELab color space L ^* values, a ^* values, b ^* values, can be derived from the measured reflectance spectrum in a manner well known to those skilled in the art, or It can be measured directly using an appropriate measuring device.

  When carrying out the method according to the invention, the order of steps 1 to 9 is not strictly fixed. All steps are used to carry out the method according to the invention, but the order of the steps can be changed if necessary. For example, step 4 can be performed before or after step 2 or before or after step 3. One skilled in the art can evaluate any suitable logical sequence of steps.

  A schematic flow diagram of the procedure according to the present invention is shown in FIG.

  A standard panel of unknown pigmentation is used as a color standard.

In general, the spectrum of the color standard is adjusted using the spectral difference between the measured spectrum R _PT of the coated paint and the corresponding spectrum R _RPT recalculated with the same formula. Again, for this modified new spectrum of color standards, a new recipe is calculated based on the components used so far and finally further tint components. The described procedure is repeated until the specified termination criteria are met. This means that until the corrected color recipe stabilizes (ie until all the concentration changes of all components are sufficiently small or below a given limit) and / or the residual color difference is a preset tolerance. Means that the procedure is repeated until

The spectral difference ΔR (ΔR = R _PT −R _PTR ) between the spectrum of the experimental sample and the corresponding predicted reflectance spectrum is due to inadequate radiative transfer models, variations in the physical structure of the characterization data, processing errors such as A measure of total process error including accurate colorant weighing or improper application conditions. The latter two systematic error sources generally introduce an unstable factor in the correction process and adversely affect the convergence of any prescription correction method.

  In contrast, for example, known linear vector shading methods do not utilize all the information that occurs during the correction process. Only the color difference between the standard and for example the actual batch is only taken into account, and any mismatch or reflectance function between the actual color position and the predicted batch color position is completely ignored.

  If these systematic error contributions dominate over the total process error, the targets move randomly, so convergence within the limits defined by their behavior cannot be expected. Only stricter process control will only help to rebuild a recipe correction algorithm that works well.

  The correction method according to the present invention has the advantage of excellent convergence, thereby limiting the number of correction steps in a natural way. Convergence is fast enough over all possible operating areas, and in either case, the procedure ends after 3-5 steps. You can define your own termination criteria that indicate the prescription correction limits by the device. Based on this optimal nature of the correction procedure, tone refinement or batch tinting can be automated to a significant degree. Furthermore, in the process of correction, it is possible to irregularly define additional tint components other than the actual prescription components and use them for optimizing the matching results. Moreover, the existing limitation of the correction factor method, ie the constraint that the component cannot be removed from the recipe in the course of correction (the numerical instability of the correction factor method) no longer exists in the new procedure.

  By comparing the measured reflectance spectrum of the hue with the spectrum recalculated with the corresponding formula, the difference in the optical behavior between the material used for the pigment calibration and the colorant available for the refinement of the hue Direct methods are provided for. Only when this method is used, it is possible to clarify specific spectral differences and take them into account for correction. This spectral information can be used to modify the standard reflection spectrum and then rematch. Other procedures, such as the correction factor method, rely on an already transformed quantity that no longer contains direct spectral information because the concentrations of the two formulations are compared. Within the scope of the actual correction process algorithm based on the conventional color recipe calculation for the standard correction spectrum, the iterative effect measure is an optimal curve fit applying a suitable weight function, so the risk of conditional color matching correction Is minimized by comparing the spectral data.

  Finally, the present invention provides a very flexible and effective recipe correction procedure for matching to a given color standard that can be used for color refinement and color development in the color laboratory, as well as batch adjustment in paint production. To do.

  The invention is explained in more detail in the following examples.

Example 1
Prescription Correction of Green Solid Color Tone FIGS. 2 to 4 show the development process of a green solid color tone including five colorants: white agent, carbon black, yellow agent, blue agent, and green agent. The standard includes a green pigment and a second green component composed of complementary colors, ie yellow and blue. Such complementary colors are known to be very sensitive to changes in the amount of ingredients.

  FIG. 2 shows a standard reflection spectrum measured using a spectrophotometer as a function of wavelength.

  FIG. 3 shows the color difference between the standard and the spray application recipe as a function of the number of tinting steps.

  FIG. 4 displays the concentration change of all prescription components as a function of the number of tinting steps.

  As can be seen from the average decrease in residual color difference, by taking into account all the information collected in each correction step, the new procedure results in a significant improvement of the recipe from a chromatic point of view. Moreover, the dependency of the amount of all the prescription components with the increase in the number of correction steps shows a clear tendency toward a stable value. As expected, the convergence behavior of the devised spectral correction method in color space is clearly better than the linear method and clearly better than the linear vector shading method.

  Figures 5 and 6 are a collection of further details regarding the process of prescription correction in the reflectance space. FIG. 5 shows the change of the target spectrum for one correction process.

  FIG. 6 displays the difference spectrum ΔR between the standard and various implementation correction steps, justifying the theoretical expectation that ΔR rapidly decreases to the statistical measurement error level as the number of correction steps increases. Impressively prove sex.

  The curve labeled “V0” represents the standard measured reflectance spectrum (RST). The predicted match corresponding to this standard produces a theoretically predicted “R0” curve (RRPT). When mixed, sprayed and measured with this formulation, the panel produces an “A0” curve (RPT). The difference between the theoretically synthesized spectrum “R0” and the actually measured spectrum “A0” (RPT) is the result of all inherent preparation errors, application errors, measurement errors, and model errors of the entire process, eg Due to incompatibility of the characterization data set. When this difference spectrum ΔR = R0−A0 is subtracted from the standard spectrum “V0”, a new virtual target spectrum (V1 = RSTM) that takes into account all process errors is generated. Therefore, this virtual target matching is expected to provide results that are much closer to the final stationary solution of the matching problem than the previous process.

  When using the method according to the invention, the formulation was stabilized after two tinting steps. Satisfactory matching results were achieved.

Example 2
Prescription Correction of Special Effect Color Tones FIGS. 7 to 11 show the process of fully automatic prescription correction of special effect color tones using the procedure according to the present invention in comparison with the conventional correction coefficient method. However, it was implemented as a single process procedure.

  FIGS. 7-11 illustrate the development of an amber gonioparent color tone that includes a flop modifier (fca) and five colorants: Al, mica blue, red agent, amber, and carbon black. Concentration changes for all prescription components are given as a function of the number of tinting steps and as extrapolated asymptotic values derived from 3, 4, and 5 data sets.

  FIG. 7 shows a standard reflectance surface as a function of wavelength and observation angle.

  FIG. 8 shows the color difference between the standard and the spray application recipe as a function of the number of tinting steps.

  FIG. 9 displays the concentration change of all prescription components as a function of the number of tinting steps.

  FIG. 10 shows the color difference between the standard and spray coating recipe as a function of the number of tinting steps in the conventional correction factor method.

  FIG. 11 displays the concentration change of all prescription components in the case of the conventional correction coefficient method as a function of the number of tinting steps.

  The special effect color tone includes two interference pigments and three solid pigments as coloring components. As can be seen from the reflection indicatrix shown in FIG. 7, the effect characteristic of this color tone becomes clear with an angular change. Further, FIGS. 8 and 9 summarize the residual color difference and prescription composition based on CIELab-76 as a function of the number of correction steps. With the known single-step correction factor method, improvement could not be achieved by correction calculation, but a new procedure that considers all the information collected for each step can be seen from the fact that the average residual color difference is reduced. As such, it provides a significant improvement in formulation from a color perspective. In the latter case also, the dependency of the amount of all the prescription ingredients shows a clear tendency towards a stable value with increasing number of correction steps, but the correction factor method does not show any saturation tendency. In the example studied, the conventional correction procedure caused the prescription to deteriorate due to this tendency, due to the relatively small residual color difference of the sprayed first prescription (if abnormal), but the new The efficiency of the new correction method becomes clear from the fact that the method treats this extreme case in a completely trouble-free manner.

  When using the method according to the invention, the formulation was stabilized after three tinting steps. Satisfactory matching results were achieved.

Claims (9)

A method for matching a reference color scheme to a specified color standard,
1. Measuring a reflection spectrum R _ST of the color standard;
2. Mixing the paint according to the formulation for the color standard and applying the paint to a substrate;
3. Measuring the reflection spectrum R _PT of the coating material;
4). _{Recalculating the} theoretical reflection spectrum R _RPT for the coating formulation;
5). Calculating a difference spectrum ΔR between the measured reflection spectrum R _{PT of the} coating paint obtained in step 3 and the recalculated reflection spectrum R _RPT obtained in step 4;
6). Generating a modified reflectance spectrum R _STM of the color standard by adjusting the reflection spectrum R _ST of the color standard using the difference spectrum ΔR obtained in step 5;
7). Calculating a prescription based on the modified reflectance spectrum R _STM ;
8). Mixing the paint according to the formula calculated in step 7 and applying the paint to a substrate. If the reflectance spectrum R _{PT of the} paint applied in step 8 is measured and the residual color difference between the reflectance spectrum R _{PT of the} applied paint and the modified reflectance spectrum R _STM of the color standard is still unacceptable The method of claim 1, wherein 4-8 are repeated. A method for matching a reference color scheme to a specified color standard,
1. Determining a color coordinates C _ST of the color shade standard,
2. Mixing the paint according to the formulation for the color standard and applying the paint to a substrate;
3. Determining a color coordinate C _PT of the coating material;
4). _{Recalculating the} theoretical color coordinate C _RPT for the formulation of the applied paint;
5). Calculating a difference ΔC between the determined color coordinate C _{PT of the} coating paint obtained in step 3 and the recalculated color coordinate C _RPT obtained in step 4;
6). Generating the modified color coordinates C _STM of the color standard by adjusting the color coordinates C _ST of the color standard using the difference ΔC of the color coordinates obtained in step 5;
7). Calculating a prescription based on the modified color coordinates C _STM ;
8). Mixing the paint according to the formula calculated in step 7 and applying the paint to a substrate. The color coordinate C _{PT of the} paint applied in step 8 is determined experimentally and the residual color difference between the color coordinate C _{PT of the} applied paint and the modified color coordinate C _STM of the color standard is still unacceptable. 4. The method of claim 3, wherein steps 4-8 are repeated as the case may be.   The method of claim 2, wherein steps 4-8 are repeated until a given termination criterion is met.   The method of claim 4, wherein steps 4-8 are repeated until a given termination criterion is met.   The method according to claim 5 or 6, wherein the termination criterion is a mathematical termination criterion based on an analysis of the convergence of the individual concentrations of all prescription components as a function of the number of correction steps.   Use of the method according to any one of claims 1 to 7 for color refinement.   Use of the method according to any one of claims 1 to 7 for batch preparation in the manufacture of paints.

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