Patent Grant
8108169
The present invention generally relates to the field of coatings, and more specifically relates to translucent coatings for absorbent substrates.
Two challenging problems in applications involving translucent coatings such as wood stains are: (1) the variation of the colorant-mixture rule with the absorbent substrate (e.g., type of wood) on which the translucent coatings is applied; and (2) the requirement that the texture (e.g., wood grain) of the absorbent substrate be visible through the translucent coating within a prescribed contrast. For instance, if the colorant-formulation algorithm is left unconstrained and asked for a match to the type of absorbent substrate, the result might be an opaque layer with the right “average” reflectance but with no texture left visible.
In one embodiment, the present invention is a method and apparatus for matching translucent coatings of absorbent substrates. In one embodiment, a method for matching a color of a sample includes generating a plurality of recipes, each of the recipes representing a mixture of one colorant and a clear vehicle and defining a concentration of the one colorant and a concentration of the clear vehicle, applying each of the recipes to one or more absorbent substrates, determining an absorption value and a scattering value for each of the recipes as applied to the absorbent substrates, storing the recipes in a database, where each of the recipes is stored with an associated absorption value and an associated scattering value, selecting a first recipe from among the recipes stored in the database, and evaluating a quality of the first recipe as a match to the color of the sample.
The teachings of the present invention can be readily understood by considering the following detailed description in conjunction with the accompanying drawings, in which:
In one embodiment, the invention provides a method and apparatus for matching translucent coatings for absorbent substrates, such as wood stains. In one embodiment, the coatings comprise one or more colorants suspended in a clear vehicle (e.g., a binder). One embodiment of the invention comprises a three-stage process including two calibration stages and one matching stage.
In a further embodiment, the set of colorant mixtures includes one or more white colorant-based mixtures, one or more black colorant-based mixtures, and one or more chromatic colorant-based mixtures. The white colorant-based mixtures include one or more mixtures of the white colorant plus the clear vehicle (in varying ratios for each mixture). The black colorant-based mixtures include one or more mixtures of the black colorant plus the clear vehicle (in varying ratios for each mixture) and one or more mixtures of the black colorant plus the white colorant plus the clear vehicle (in varying ratios for each mixture). The chromatic colorant-based mixtures include, for each chromatic colorant, one or more mixtures of the chromatic colorant plus the clear vehicle (in varying ratios for each mixture); one or more mixtures of the chromatic colorant plus the white colorant plus the clear vehicle (in varying ratios for each mixture); and one or more mixtures of the chromatic colorant plus the white colorant plus the black colorant plus the clear vehicle (in varying ratios for each mixture).
Having prepared or received the set of colorant mixtures, the method 100 proceeds to step 106, where each colorant mixture in the set of colorant mixtures is applied to a black substrate and to a white substrate (e.g., on a standard black/white chart). This produces a first set of substrates from which calibration data can be obtained.
In step 108, the method 100 measures (e.g., using a spectrophotometer) the reflectance of each colorant mixture as applied to the first set of substrates. This produces, for each colorant mixture, at least two reflectance measurements: a first reflectance measurement of the colorant mixture on the black substrate and a second reflectance measurement of the colorant mixture on the white substrate.
In step 110, the method 100 calculates, for each colorant mixture in the set of colorant mixtures, absorption (K) and scattering (S) values, in accordance with the two reflectance measurements obtained in step 108. In one embodiment, the K and S values are obtained from the two reflectance measurements using the two-constant Kubelka-Munk model with incomplete hiding (e.g., as described by H. S. Shah et al. in “Kubelka-Munk Analysis of Absorptance in the Presence of Scattering Including Surface-Reflection Correction to Transmittance,” Color Research and Application, Vol. 10 (1985), pp. 26-31), which is herein incorporated by reference in its entirety. In a further embodiment, the K and S values are also calculated for the colorant concentrations in each of the colorant mixtures in the set of colorant mixtures.
In step 112, the method 100 stores (e.g., in a database) the K and S values and the colorant concentrations associated with each of the colorant mixtures in the first set of colorant mixtures.
In step 114, the method 100 applies each colorant mixture in the set of colorant mixtures to one or more absorbent substrates of particular types (e.g., if the absorbent substrates are wood, these may include pine, cedar, birch, etc.). This produces a second set of substrates from which calibration data can be obtained. In addition, the second set of substrates comprises a bare absorbent substrate (i.e., an absorbent substrate to which no colorant mixture has been applied) for each type of absorbent substrate to which the colorant mixtures are applied. In other words, if the second set of substrates includes a colorant mixture that is applied to a pine wood substrate, a bare pine wood substrate is also included in the second set of substrates.
In step 116, the method 100 measures (e.g., using a spectrophotometer) the reflectance of each colorant mixture as applied to the second set of substrates. This produces, for each combination of colorant mixture and absorbent substrate type, one reflectance measurement. In addition, a reflectance measurement is taken for each bare absorbent substrate in the second set of substrates.
In step 118, the method 100 calculates, for each combination of colorant mixture and absorbent substrate, absorption (K) and scattering (S) values. In one embodiment, the method 100 uses an approximation discussed in greater detail below in connection with EQN. 1 to derive the values for K and S. Using this approximation, it is possible to derive K with a one-dimensional zero-solver, using the measurement and a approximated value of S, evaluated from the known recipes of the colorant mixtures.
In step 120, the method 100 stores (e.g., in a database) the K and S values and the colorant concentrations associated with each of combination of colorant mixture and absorbent substrate. The method 100 then terminates in step 122.
Thus, the method 100 generates a plurality of “points” that may be used to populate a database, where each point represents a “recipe,” i.e., the loadings or gram fractions of various colorant components arranged in the order ‘(clear, colorant1, colorant2, . . . , colorantn).’ The vector is a vector of loadings, designated by c. Thus, the point representing a given sample for ‘coloranti’ is on the axis ‘(clear, coloranti).’
In one embodiment of the method 100, the method 100 stores a user-provided mixture of clear vehicle plus multiple colorants as a point in the database. Such points represent what are referred to as “full recipes,” since they include multiple colorants and thus do not reside on an axis. These mixtures are calibrated in a manner similar to that described above for the clear vehicle plus one colorant mixtures.
The method 200 is initialized at step 202 and proceeds to step 204, where the method 200 identifies the substrate type of the sample (e.g., type of wood), so that the subsequent procedure uses only the portions of the calibration data (discussed above) that are based on the same type of substrate. The substrate type may be identified indirectly based on user input (e.g., the user says the substrate type is pine) or directly based on measurement of the sample (e.g., using a spectrophotometer). For example, the method 200 may identify the type of the substrate based on the ΔH between the sample and the calibration data. ΔH is a Commission Internationale de l'Eclairage (CIE)-defined quantity that compares two colors (i.e., colloquially, the hue difference between two colors). More specifically, ΔH is the total difference between the two colors (ΔE), minus the lightness difference (ΔL), minus the chroma difference (←C), being evaluated as:
ΔH is more fully described in ASTM International, D 2244-07, “Standard Practice for Calculation of Color Tolerances and Color Differences from Instrumentally Measured Color Coordinates,” ASTM International, 2007, which is herein incorporated by reference in its entirety.
Having identified the substrate type, the method 200 proceeds to step 206 and identifies a set of one or more colorants to be used in matching colorant mixtures from the database to the colorant mixture coating the sample. In other words, any colorant mixture or point from the database that is ultimately matched to the coating on the sample should include at least one of the colorants from the identified set. In one embodiment, the set of colorants is specified by the user, for example based on heuristics such as the chemical or physical properties of the desired colorant mixture. In one embodiment, the colorants available for inclusion in the set of colorants include the white colorant, the black colorant, and the chromatic colorants. In a further embodiment, the identified set of colorants also includes user-specified guidelines such as a minimum and/or maximum number of colorants from the set of colorants that must be used in each colorant mixture or point that is matched to coating on the sample. In a further embodiment still, the user-specified guidelines also include a required contrast ratio (i.e., ratio of luminance over black to luminance over white) for each colorant mixture or point that is matched to the coating on the sample.
In step 208, the method 200 measures the reflectance of the coating on the sample, as well as the reflectance of the substrate. In one embodiment, the reflectance measurements are averaged over several spatially separated readings to compensate for variations in two-dimensional texture or pattern (e.g., wood grain) of the substrate.
In step 210, the method 200 selects one or more colorant mixtures or points from the database, based on the reflectance measurements made in step 208 and on the set of colorants identified in step 206. In one embodiment, the one or more colorant mixtures includes the N (N>0) points that have the smallest ΔE (i.e., color difference) relative to the coating on the sample. In one embodiment, the reflectance measurements of the points in the database are used to adjust the K and S values from the standard calibration process (described with respect to
The method 200 then terminates in step 212.
As discussed above, the method 200 may be used to match the color of a coating on a sample to one or more points in a database of colorant mixtures. In one embodiment, some of the points in the database may represent colorant mixtures including multiple colorants. In addition, the method 200 may account for multiple colorants in making this match.
Consider, for example a formula {right arrow over (c)}=[c1, c2, . . . , cN] representing a colorant mixture with N colorants, where ci is the concentration of the ith colorant in the colorant mixture. Each point in the database has a formula {right arrow over (c)} and an associated reflectance measurement (R(λ)). In one embodiment, there is only one reflectance measurement for each point.
At each wavelength λ, one can synthesize the K and S values of the point from {right arrow over (c)} as Ksyn({right arrow over (c)}, λ) and Ssyn({right arrow over (c)}, λ), where the subscript “syn” refers to the fact that the K and S values are synthesized. From the measurement R(λ), one can calculate a K/S value, Kbat/Sbat({right arrow over (c)},λ), where the subscript “bat” refers to the fact that the K and S values relate to a batch of colorant mixture. With a single reflectance measurement, one is not able to calculate Kbat({right arrow over (c)},λ) and Sbat({right arrow over (c)}, λ) respectively.
The additive correction factors for K and S can thus be calculated as:
In the above, an approximation is made that Sbat({right arrow over (c)},λ)≈Ssyn({right arrow over (c)},λ). Using this approximation, it is possible to derive Kbat with a one-dimensional zero-solver, using the measurement R(λ) and the value of Sbat.
Assuming that a point having a formula {right arrow over (c)}0 has been obtained by matching a given target reflectance RT(λ) (obtained from measurement of the sample) using the calibration data, and that M points are available in the selected colorant mixtures, the following calculations would be performed by the method 200 in step 210:
First, for each of the M points, ΔK({right arrow over (c)}j, λ)=1, 2, . . . , M is calculated, for example using EQN. 1.
Second, a weighted additive correction factor is calculated from all of the M points. In one embodiment, the weighted additive correction factor is calculated as:
where ∥{right arrow over (c)}j−{right arrow over (c)}0∥ is the distance between the formulas {right arrow over (c)}j and {right arrow over (c)}0 in the concentration space. In other embodiments, however, other multi-dimensional approximation models (such as single interpolation or radial basis functions) may be used to calculate the weighted additive correction factor.
Finally, the coating on the sample is matched again by correcting the K value. In one embodiment, the following correction on the K value is used (although other multi-dimensional approximation models may be used to correct K):
K′syn({right arrow over (c)},λ)=Ksyn({right arrow over (c)},λ)+G({right arrow over (c)}0,λ) (EQN. 3)
To simplify the description, only database points are used in the following example. The same procedures can be applied for any number of points. Moreover, EQNs. 2 and 3 can be modified to correct for S as well as for K (by replacing K with S in the equations).
The method 300 is initialized at step 302 and proceeds to step 304, where the method 300 identifies a first point in the database, where the point represents a first colorant mixture in the database. The method 300 is invoked to evaluate the first point as a potential match to a coating on a sample. In
In step 306, the method 300 selects a set of one or more surrounding points in the database within a predefined threshold color difference (ΔE) of the first point. For example, if the coating on the sample were a wood stain, a suitable threshold ΔE might be approximately twenty-five. As an example,
In step 308, the method selects the first point as a selected point for evaluation. The method 300 then proceeds to step 310 and calculates the color difference (ΔE0) between a first synthesized spectral curve and the measured spectral curve for the selected point. In one embodiment, both the first synthesized spectral curve and the measured spectral curve are given by the calibration data associated with the selected point (e.g., as discussed with respect to the method 100). In one embodiment, this calculation involves no measurements related to any other points in the database.
In step 312, the method 300 calculates the weighted correction factor for the group of candidate points. Referring again to the example illustrated in
where {right arrow over (c)}0 is the formula of the first point (e.g., point 4000 in
In step 314, the method 300 synthesizes a second (new) synthesized spectral curve for the selected point, in accordance with the weighted correction factor. In one embodiment, the second synthesized spectral curve is synthesized based on a corrected absorption (K) value for the selected point, which is derived using the weighted correction factor. In one embodiment, the corrected K value is derived from the weighted correction factor in accordance with EQN. 3 as:
K°syn({right arrow over (c)}0,λ)=Ksyn({right arrow over (c)}0,λ)+G({right arrow over (c)}0,λ)
In this example, the selected point is assumed to be the first point (as indicated by the subscript 0); however, similar math holds for evaluation of the remainder of the candidate points.
In step 316, the method 300 calculates a second color difference (ΔE0′) between the second synthesized spectral curve of the selected point and the measured spectral curve of the selected point.
In step 318, the method 300 determines whether the second color difference ΔE0′ calculated in step 316 is greater than the first color difference ΔE0 calculated in step 310 by some threshold amount (e.g., at least one to two times greater). If the method 300 concludes in step 318 that the second color difference ΔE0′ is smaller than the first color difference ΔE0 by the threshold amount, then the method 300 proceeds to step 320 and classifies the selected point as a good match to the coating on the sample substrate.
Alternatively, if the method 300 concludes in step 318 that the second color difference ΔE0′ is not smaller than the first color difference ΔE0 by the threshold amount (e.g., at least three to four times greater than ΔE0), then the method 300 proceeds to step 322 classifies the selected point as a bad match to the coating on the sample substrate.
In step 324, the method 300 determines whether there are any points remaining to be evaluated in the group of candidate points. If the method 300 concludes in step 324 that there is at least one remaining candidate point, the method 300 proceeds to step 326 and selects a next point as the selected point for evaluation before returning to step 310 and proceeding as described above.
Alternatively, if the method 300 concludes in step 324 that there are no remaining candidate points, the method 300 terminates in step 328.
The method 300 therefore associates each candidate point with two color difference values, ΔEi and ΔEi′ (i=0, 1, . . . , N). As discussed above, from these values, one can assess the “goodness” of each candidate point as a match to the sample.
Alternatively, embodiments of the present invention (e.g., matching module 505) can be represented by one or more software applications (or even a combination of software and hardware, e.g., using Application Specific Integrated Circuits (ASIC)), where the software is loaded from a storage medium (e.g., I/O devices 506) and operated by the processor 502 in the memory 504 of the general purpose computing device 500. Thus, in one embodiment, the matching module for matching colorant mixtures to sample substrates described herein with reference to the preceding Figures can be stored on a computer readable medium (e.g., RAM, magnetic or optical drive or diskette, and the like).
It should be noted that although not explicitly specified, one or more steps of the methods described herein may include a storing, displaying and/or outputting step as required for a particular application. In other words, any data, records, fields, and/or intermediate results discussed in the methods can be stored, displayed, and/or outputted to another device as required for a particular application. Furthermore, steps or blocks in the accompanying Figures that recite a determining operation or involve a decision, do not necessarily require that both branches of the determining operation be practiced. In other words, one of the branches of the determining operation can be deemed as an optional step.
Embodiments of the present invention create a bridge between standard recipe matching techniques that use normally calibrated components, and extended recipe matching techniques that use added multidimensional known recipes. After the calibration procedure (e.g., as discussed with respect to
Although various embodiments which incorporate the teachings of the present invention have been shown and described in detail herein, those skilled in the art can readily devise many other varied embodiments that still incorporate these teachings.
This application claims the benefit of expired U.S. Provisional Patent Application Ser. No. 61/040,590, filed Mar. 28, 2008, which is herein incorporated by reference in its entirety.
| Number | Name | Date | Kind |
|---|---|---|---|
| 2774276 | Glasser et al. | Dec 1956 | A |
| 2882786 | Kaye | Apr 1959 | A |
| 3003388 | Hunter et al. | Oct 1961 | A |
| 3065350 | Graner | Nov 1962 | A |
| 3159742 | Davidson | Dec 1964 | A |
| 3314327 | Killpatrick et al. | Apr 1967 | A |
| 3389265 | Schreckendgust | Jun 1968 | A |
| 3406293 | Mowry | Oct 1968 | A |
| 3531208 | Ward | Sep 1970 | A |
| 6502049 | Takada et al. | Dec 2002 | B1 |
| 6934026 | McDonald et al. | Aug 2005 | B2 |
| 7042556 | Sun | May 2006 | B1 |
| 7116420 | Skierski | Oct 2006 | B2 |
| 7158672 | Johansson et al. | Jan 2007 | B2 |
| 7466415 | Gibson et al. | Dec 2008 | B2 |
| 7623241 | Brini et al. | Nov 2009 | B2 |
| 7756328 | Komiya et al. | Jul 2010 | B2 |
| 7995838 | Komiya et al. | Aug 2011 | B2 |
| 20030151611 | Turpin et al. | Aug 2003 | A1 |
| 20030156752 | Turpin et al. | Aug 2003 | A1 |
| 20030158617 | Turpin et al. | Aug 2003 | A1 |
| 20030158788 | Turpin et al. | Aug 2003 | A1 |
| 20030174882 | Turpin et al. | Sep 2003 | A1 |
| 20040131756 | Skierski et al. | Jul 2004 | A1 |
| 20040252883 | Johansson et al. | Dec 2004 | A1 |
| 20060181707 | Gibson et al. | Aug 2006 | A1 |
| 20060250668 | Komiya et al. | Nov 2006 | A1 |
| 20080015791 | Brini et al. | Jan 2008 | A1 |
| 20100232688 | Komiya et al. | Sep 2010 | A1 |
| Number | Date | Country | |
|---|---|---|---|
| 20090248338 A1 | Oct 2009 | US |
| Number | Date | Country | |
|---|---|---|---|
| 61040590 | Mar 2008 | US |
