Multi-angle spectral reflectance estimation device, multi-angle spectral reflectance estimation method, multi-angle spectral reflectance estimation program, computer color matching device, computer color matching method, and computer color matching program

Abstract

To provide a computer color matching device capable of reproducing a sample color on a metal substrate.SOLUTION: A first color coordinate conversion unit 105 converts the multi-angle spectral reflectance of a sample color for each wavelength in the visible light band, measured using a multi-angle spectrophotometer, into first color coordinates. A reflectance estimation unit 104 estimates the angular spectral reflectance for one or more inks and their mixing ratios selected by the ink / mixing ratio selection unit 102 on the basis of the calibration curve stored in the calibration curve storage unit 103. A second color coordinate conversion unit 106 converts the multi-angle spectral reflectance estimated for each wavelength by the reflectance estimation unit 104 into second color coordinates. A color matching unit 107 varies one or more inks or their mixing ratios until the difference between the first color coordinates and the second color coordinates is minimized, and determines the mixing ratio of one or more inks that minimizes the difference between the first color coordinates and the second color coordinates as the color match corresponding to the sample color.SELECTED DRAWING: Figure 32

Description

[Technical Field]

[0001] The present invention relates to a multi-angle spectral reflectance estimation device, a multi-angle spectral reflectance estimation method, a multi-angle spectral reflectance estimation program, a computer color matching device, a computer color matching method, and a computer color matching program. [Background technology]

[0002] Patent Documents 1 to 3 describe computer color matching devices or related technologies. Computer color matching is the process of using a computer to select one or more ink colors to be used and determine the mixing ratio of multiple ink colors in order to reproduce a sample color in a printed matter. Hereinafter, computer color matching will sometimes be abbreviated as CCM. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent Publication No. 2021-76550 [Patent Document 2] Japanese Patent Application Publication No. 2023-75718 [Patent Document 3] International Publication No. 2015 / 005152 Summary of the Invention [Problem to be solved by the invention]

[0004] Typically, the Kubelka-Munk equation is used in CCM. According to the Kubelka-Munk equation, the relationship between the K / S value, which is the ratio of the absorption coefficient K to the diffusion coefficient S of the developed colorant layer, and the spectral reflectance R is K / S=(1-R) 2 / 2R. However, the Kubelka-Munk equation is based on the premise that light is not affected by the substrate, such as when printing on white paper or dyeing white fabric, because the light is diffusely reflected without being absorbed by the substrate, or the colorant layer is thick enough to completely absorb the light that enters the colorant layer. Depending on the type of substrate, the Kubelka-Munk equation may not hold true when printing with a thin ink layer of approximately 0.3 μm to 6 μm thickness.

[0005] In particular, when printing on a metal substrate, such as an aluminum can, an ink layer with a thickness of approximately 0.3 μm to 6 μm cannot completely conceal the metal substrate. Light incident on the ink layer reaches the metal substrate and is reflected by the metal substrate, and the reflected light passes through the ink layer and emerges from the surface of the ink layer. Therefore, the Kubelka-Munk equation does not hold true, and CCM using the Kubelka-Munk equation cannot produce color matching results that are practical.

[0006] One or more embodiments aim to provide a multi-angle spectral reflectance estimation device, a multi-angle spectral reflectance estimation method, and a multi-angle spectral reflectance estimation program that can accurately estimate the multi-angle spectral reflectance when one or more inks and their mixing ratios are selected to reproduce a sample color on a metal substrate.One or more embodiments aim to provide a computer color matching device, a computer color matching method, and a computer color matching program that can obtain practically usable color matching results that can reproduce a sample color on a metal substrate even when printing an ink on the metal substrate with a film thickness that does not completely conceal the metal substrate. [Means for solving the problem]

[0007] A first aspect of one or more embodiments includes a multi-angle spectral reflectance acquisition unit that acquires the multi-angle spectral reflectance of each color ink for each wavelength obtained by dividing a visible light band at predetermined wavelength intervals, based on a calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance, for printed samples in which each ink of a plurality of primary color inks is applied to a metal substrate at different mixing ratios of each ink and a colorless ink, and for printed samples in which each ink of the primary color inks other than a white ink is applied to the white ink at different mixing ratios, using a multi-angle spectrophotometer; and The multi-angle spectral reflectance estimation device includes a concentration conversion unit that converts the acquired multi-angle spectral reflectance for each wavelength of the ink of each color based on the calibration curve into a concentration for each wavelength of a first ink that has a light absorption effect at least for all wavelengths in a wavelength band of 400 nm to 700 nm, or a second ink that has a light diffusion effect at least for all wavelengths in a wavelength band of 420 nm to 670 nm; a concentration integration unit that integrates the converted concentrations for each wavelength; and a reflectance estimation unit that estimates, based on the calibration curve, the multi-angle spectral reflectance corresponding to the integrated concentration for each wavelength to be the multi-angle spectral reflectance for each wavelength when the one or more inks in the selected mixing ratio are printed on the metal substrate.

[0008] In a second aspect of one or more embodiments, a multi-angle spectral reflectance curve for each wavelength obtained by dividing a visible light band into predetermined wavelength intervals is measured in advance using a multi-angle spectrophotometer, for printed samples in which each ink of a plurality of primary color inks is mixed with a colorless ink at different mixing ratios and the printed samples in which each ink of the primary color inks other than a white ink is mixed with the white ink at different mixing ratios and the printed samples in which the primary color inks are ... The present invention provides a multi-angle spectral reflectance estimation method, which acquires reflectance, converts the acquired multi-angle spectral reflectance for each wavelength of ink of each color based on the calibration curve to a concentration for each wavelength of a first ink that has a light absorption effect at least for all wavelengths in a wavelength band of 400 nm to 700 nm, or a second ink that has a light diffusion effect at least for all wavelengths in a wavelength band of 420 nm to 670 nm, integrates the converted concentrations for each wavelength, and estimates, based on the calibration curve, that the multi-angle spectral reflectance corresponding to the integrated concentration for each wavelength is the multi-angle spectral reflectance for each wavelength when the one or more inks in the selected mixing ratio are printed on the metal substrate.

[0009] A third aspect of one or more embodiments is a method for producing a multi-angle spectral reflectance measurement system comprising: a first step of acquiring, on a computer, a multi-angle spectral reflectance for each wavelength obtained by dividing a visible light band at predetermined wavelength intervals for a printed sample in which each ink of a plurality of primary color inks is applied to a colorless ink at different mixing ratios, and a printed sample in which each ink of the primary color inks other than a white ink is applied to the white ink at different mixing ratios, based on a calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance, the calibration curve being based on measurement results obtained by previously measuring, using a multi-angle spectrophotometer, multi-angle spectral reflectance for each wavelength obtained by dividing a visible light band at predetermined wavelength intervals for the printed sample; and a second step of acquiring, on a computer, a multi-angle spectral reflectance for each ink of a plurality of primary color inks applied to the metal substrate from the concentration of the ink other than the colorless ink at a selected mixing ratio, based on the calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance for the printed sample. The present invention provides a multi-angle spectral reflectance estimation program that executes the following steps: a second step of converting, based on the calibration curve, the acquired multi-angle spectral reflectance for each wavelength of the ink of each color into a concentration for each wavelength of a first ink that has a light absorption effect at least for all wavelengths in a wavelength band of 400 nm to 700 nm, or a second ink that has a light diffusion effect at least for all wavelengths in a wavelength band of 420 nm to 670 nm; a third step of integrating the converted concentrations for each wavelength; and a fourth step of estimating, based on the calibration curve, the multi-angle spectral reflectance corresponding to the integrated concentration for each wavelength to be the multi-angle spectral reflectance for each wavelength when the one or more inks in the selected mixing ratio are printed on the metal substrate.

[0010] A fourth aspect of one or more embodiments provides a computer color matching device including the above-described multi-angle spectral reflectance estimation device; a first color coordinate conversion unit that converts multi-angle spectral reflectances for each wavelength, obtained by dividing a visible light band of a selected sample color at predetermined wavelength intervals, measured using a multi-angle spectrophotometer, into first color coordinates in a predetermined color space; a second color coordinate conversion unit that selects one or more inks to be printed on a metal substrate to be printed and their mixing ratios, and converts the multi-angle spectral reflectances for each wavelength estimated using the multi-angle spectral reflectance estimation device into second color coordinates in the predetermined color space when the one or more inks in the selected mixing ratios are printed on the metal substrate; and a color matching unit that changes the one or more inks or their mixing ratios until a difference between the first color coordinates and the second color coordinates is minimized, and determines, as a color match corresponding to the sample color, the mixing ratio of one or more inks that minimizes the difference between the first color coordinates and the second color coordinates.

[0011] A fifth aspect of one or more embodiments provides a computer color matching method including: using a multi-angle spectrophotometer to measure multi-angle spectral reflectances for each wavelength obtained by dividing a visible light band of a selected sample color by a predetermined wavelength interval; converting the measured multi-angle spectral reflectances for each wavelength into first color coordinates in a predetermined color space; selecting one or more inks to be printed on a metal substrate as a printing target and a mixing ratio thereof; estimating the multi-angle spectral reflectances for each wavelength when the one or more inks in the selected mixing ratios are printed on the metal substrate using the multi-angle spectral reflectance estimation method; converting the estimated multi-angle spectral reflectances for each wavelength into second color coordinates in the predetermined color space; changing the one or more inks or their mixing ratios until a difference between the first color coordinates and the second color coordinates is minimized; and determining, as a color match corresponding to the sample color, the mixing ratio of the one or more inks that minimizes the difference between the first color coordinates and the second color coordinates.

[0012] A sixth aspect of one or more embodiments provides a computer color matching program that causes a computer to execute the following steps: a fifth step of converting multi-angle spectral reflectances for each wavelength, obtained by dividing a visible light band of a selected sample color by a predetermined wavelength interval, measured using a multi-angle spectrophotometer, into first color coordinates in a predetermined color space; a sixth step of selecting one or more inks to be printed on a metal substrate to be printed and their mixing ratios; a seventh step of estimating, using the multi-angle spectral reflectance estimation program, the multi-angle spectral reflectances for each wavelength when the one or more inks in the selected mixing ratios are printed on the metal substrate; an eighth step of converting the estimated multi-angle spectral reflectances for each wavelength into second color coordinates in the predetermined color space; and a ninth step of changing the one or more inks or their mixing ratios until a difference between the first color coordinates and the second color coordinates is minimized, and determining, as a color match corresponding to the sample color, the mixing ratio of one or more inks that minimizes the difference between the first color coordinates and the second color coordinates. [Effects of the Invention]

[0013] According to one or more embodiments of the multi-angle spectral reflectance estimation device, the multi-angle spectral reflectance estimation method, and the multi-angle spectral reflectance estimation program, it is possible to estimate with high accuracy the multi-angle spectral reflectance when one or more inks and their mixing ratios are selected to reproduce a sample color on a metal substrate. According to one or more embodiments of the computer color matching device, the computer color matching method, and the computer color matching program, it is possible to obtain a practical color matching result that can reproduce a sample color on a metal substrate, even when printing an ink on a metal substrate with a film thickness that does not completely conceal the metal substrate. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is a block diagram illustrating a computer color matching device according to one or more embodiments. [Figure 2A]FIG. 2A is a first example of printing on a metal substrate with ink, showing direct printing in which ink is applied directly to the metal substrate. [Figure 2B] FIG. 2B is a second example of printing on a metal substrate with ink, showing printing on white paint in which a base coat is applied to the metal substrate and ink is applied to the base coat. [Figure 3A] FIG. 3A is a third example of printing on a metal substrate with ink, showing printing on a film in which a film is attached to the metal substrate and ink is applied to the film. [Figure 3B] Figure 3B is a fourth example of printing with ink on a metal substrate, showing printing on a film and white paint, in which a film is attached to the metal substrate, a primer is applied to the film, and then ink is applied to the primer. [Figure 4A] FIG. 4A is a diagram showing specular reflection when light is incident on a metal substrate. [Figure 4B] FIG. 4B shows the diffuse reflection of light incident on white paint. [Figure 5A] Figure 5A is a conceptual diagram showing the reflection of light when light is incident on the ink in the direct printing sample shown in Figure 2A, when the ink containing a pigment with a high light absorption effect does not conceal the metal substrate. [Figure 5B] Figure 5B is a conceptual diagram showing the reflection of light when light is incident on the ink in the white paint print sample shown in Figure 2B, when the ink containing a pigment with a high light absorption effect does not conceal the base paint. [Figure 6A] Figure 6A is a conceptual diagram showing the diffusion state of light when light is incident on the ink in the direct printing sample shown in Figure 2A, when the ink containing a pigment with a high light diffusion effect does not conceal the metal substrate. [Figure 6B] Figure 6B is a conceptual diagram showing the state of light diffusion when light is incident on the ink in the white paint print sample shown in Figure 2B, when the ink containing a pigment with a high light diffusion effect does not conceal the base paint. [Figure 7A]FIG. 7A is a diagram showing the relationship between the light receiving unit arranged at an angle of 45 degrees in a multi-angle spectrophotometer and the angle of incidence of light. [Figure 7B] FIG. 7B is a diagram showing the relationship between the light receiving unit arranged at an angle of 15 degrees in the multi-angle spectrophotometer and the angle of incidence of light. [Figure 8] FIG. 8 is a characteristic diagram showing calibration curves indicating the reflectance at an angle of 45 as 15 and a wavelength of 450 nm for a direct print sample and a print sample on white paint, each of which is made by mixing black ink and colorless ink. [Figure 9] FIG. 9 is a characteristic diagram showing calibration curves indicating the reflectance at an angle of 45 as 15 and a wavelength of 450 nm for a direct print sample and a print sample on white paint, each of which is made by mixing white ink and colorless ink. [Figure 10] FIG. 10 is a characteristic diagram showing calibration curves indicating the reflectance at an angle of 45 as 15 and a wavelength of 450 nm for a direct print sample and a print sample on white paint, both of which are made by mixing black ink and white ink. [Figure 11] FIG. 11 is a characteristic diagram showing calibration curves indicating the reflectance at an angle of 45 as 45 and a wavelength of 450 nm for a direct print sample and a print sample on white paint, both of which are made by mixing black ink and white ink. [Figure 12] FIG. 12 is a characteristic diagram showing calibration curves at an angle of 45 as 15 and a wavelength of 450 nm for a direct print sample and a print sample on white paint, each of which is made by mixing yellow ink and colorless ink. [Figure 13] FIG. 13 is a characteristic diagram showing calibration curves at an angle of 45 as 15 and a wavelength of 600 nm for a direct print sample and a print sample on white paint, in which the ink is a mixture of yellow ink and colorless ink. [Figure 14] FIG. 14 is a characteristic diagram showing calibration curves at an angle of 45 as 15 and a wavelength of 450 nm for a direct print sample and a print sample on white paint, each of which is made by mixing yellow ink and white ink. [Figure 15]FIG. 15 is a characteristic diagram showing calibration curves at an angle of 45 as 15 and a wavelength of 600 nm for a direct print sample and a print sample on white paint, each of which is made by mixing yellow ink and white ink. [Figure 16] FIG. 16 is a characteristic diagram showing a calibration curve of a print sample on white paint, in which the ink, which is a mixture of the yellow ink and the colorless ink having a wavelength of 450 nm shown in FIG. 12, is applied, with the vertical axis enlarged. [Figure 17] FIG. 17 is a characteristic diagram showing the K / S value according to the Kubelka-Munk equation based on the calibration curve shown in FIG. [Figure 18] FIG. 18 is a characteristic diagram showing a calibration curve of the direct printing sample at a wavelength of 600 nm shown in FIG. [Figure 19] FIG. 19 is a characteristic diagram showing the K / S value according to the Kubelka-Munk equation based on the calibration curve shown in FIG. [Figure 20] Figure 20 is a characteristic diagram showing calibration curves at an angle of 45 as 15 at a wavelength of 450 nm for a direct printing sample made by mixing black ink and colorless ink, a direct printing sample made by mixing white ink and colorless ink, and a direct printing sample made by mixing black ink and white ink, with the horizontal axis representing reflectance and the vertical axis representing the concentration of black ink or white ink. [Figure 21] Figure 21 is a characteristic diagram showing calibration curves at an angle of 45 as 15 at a wavelength of 600 nm for a direct printing sample made by spreading an ink mixture of black ink and colorless ink, a direct printing sample made by spreading an ink mixture of white ink and colorless ink, and a direct printing sample made by spreading an ink mixture of black ink and white ink, with the horizontal axis representing reflectance and the vertical axis representing the concentration of black ink or white ink. [Figure 22A] FIG. 22A is the same as FIG. 12, and is a characteristic diagram showing the calibration curves at a wavelength of 450 nm for a direct print sample and a print sample on white paint, in which the ink is a mixture of yellow ink and colorless ink. [Figure 22B] FIG. 22B is the same characteristic diagram as FIG. 8, showing the calibration curves at a wavelength of 450 nm for a direct print sample and a print sample on white paint, in which ink obtained by mixing black ink and colorless ink is applied. [Figure 23A] FIG. 23A is the same characteristic diagram as FIG. 13, showing the calibration curves at a wavelength of 600 nm for a direct print sample and a print sample on white paint, in which the ink is a mixture of yellow ink and colorless ink. [Figure 23B] FIG. 23B is a characteristic diagram showing calibration curves at a wavelength of 600 nm for a direct print sample and a print sample on white paint, in which ink obtained by mixing black ink and colorless ink is applied. [Figure 24A] FIG. 24A is a characteristic diagram showing a calibration curve at a wavelength of 450 nm, in which the horizontal and vertical axes of FIG. 20 are reversed. [Figure 24B] FIG. 24B is a characteristic diagram showing a calibration curve at a wavelength of 600 nm, in which the horizontal and vertical axes of FIG. 21 are reversed. [Figure 25A] FIG. 25A is the same as FIG. 14, and is a characteristic diagram showing the calibration curves at a wavelength of 450 nm for a direct print sample and a print sample on white paint, in which the ink is a mixture of yellow ink and white ink. [Figure 25B] FIG. 25B is a characteristic diagram showing the calibration curves at a wavelength of 450 nm for a direct print sample and a print sample on white paint, both of which are made by mixing black ink and white ink and are similar to FIG. [Figure 26A] FIG. 26A is the same as FIG. 15, and is a characteristic diagram showing the calibration curves at a wavelength of 600 nm for a direct print sample and a print sample on white paint, in which the ink is a mixture of yellow ink and white ink. [Figure 26B] FIG. 26B is a characteristic diagram showing calibration curves at a wavelength of 600 nm for a direct print sample and a print sample on white paint, both of which are made by mixing black ink and white ink and then drawing down the ink. [Figure 27A] FIG. 27A is a characteristic diagram showing a calibration curve at a wavelength of 450 nm for a direct print sample made by mixing black ink and white ink. [Figure 27B] FIG. 27B is a characteristic diagram showing a calibration curve at a wavelength of 600 nm for a direct print sample made by mixing black ink and white ink. [Figure 28A]FIG. 28A is a characteristic diagram showing a calibration curve at a wavelength of 450 nm, in which the horizontal and vertical axes of FIG. 27A are reversed. [Figure 28B] FIG. 28B is a characteristic diagram showing a calibration curve at a wavelength of 600 nm, in which the horizontal and vertical axes of FIG. 27B are reversed. [Figure 29] FIG. 29 is a characteristic diagram showing calibration curves for a direct printing sample drawn with a mixture of black ink and white ink, and a direct printing sample drawn with a mixture of white ink and colorless ink. [Figure 30] FIG. 30 is a flowchart showing the preparatory processing required for the multi-angle spectral reflectance estimation device, multi-angle spectral reflectance estimation method, and multi-angle spectral reflectance estimation program according to one or more embodiments, and the computer color matching device, computer color matching method, and computer color matching program according to one or more embodiments. [Figure 31] FIG. 31 is a flowchart illustrating the operation of a computer color matching device according to one or more embodiments, a computer color matching method according to one or more embodiments, and processing performed by a computer color matching program according to one or more embodiments. [Figure 32] FIG. 32 is a block diagram illustrating an example of a functional configuration when a computer color matching device according to one or more embodiments performs color matching. [Figure 33] FIG. 33 is a block diagram illustrating the functional configuration of a multi-angle spectral reflectance estimation device according to one or more embodiments. [Figure 34] FIG. 34 is a graph showing the reflectance by wavelength of a sample color and a matching result displayed on a display unit of a computer color matching device according to one or more embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0015] Hereinafter, a multi-angle spectral reflectance estimation device, a multi-angle spectral reflectance estimation method, a multi-angle spectral reflectance estimation program, a computer color matching device, a computer color matching method, and a computer color matching program according to one or more embodiments will be described with reference to the accompanying drawings.

[0016] In FIG. 1, a computer color matching device 100 (hereinafter, CCM device 100) according to one or more embodiments includes a central processing unit (hereinafter, CPU) 1, a non-transitory storage medium 2, an operation unit 3, and a display unit 4. The non-transitory storage medium 2 stores a computer-readable computer color matching program 20 (hereinafter, CCM program 20) according to one or more embodiments. The CPU 1 executes the CCM program 20. By the CPU 1 executing the CCM program 20, the CCM device 100 executes a computer color matching method (hereinafter, CCM method) according to one or more embodiments. The CCM program 20 includes a multi-angle spectral reflectance estimation program according to one or more embodiments.

[0017] The CCM device 100 selects one or more inks to be used to reproduce the sample color on a printed matter, performs color matching to determine the mixing ratio of the selected one or more inks, and displays the color matching results on the display unit 4.

[0018] In one or more embodiments, the metal substrate is, for example, an aluminum plate. When printing with ink on an aluminum plate, such as an aluminum can, as shown in FIG. 2A , ink 53 is applied to aluminum plate 51, and a colorless, transparent, thermosetting exterior coating 54 is applied to the surface of ink 53. Heat is applied to exterior coating 54, causing it to harden, thereby protecting the surface of ink 53. Ink 53 does not obscure aluminum plate 51. In FIG. 2A , the metal substrate to be printed is aluminum plate 51.

[0019] Instead of printing on aluminum plate 51 as shown in Figure 2A, as shown in Figure 2B, a white paint may be applied to aluminum plate 51 as a base paint 52, ink 53 may be applied to base paint 52, and an outer surface paint 54 may be applied to the surface of ink 53. Ink 53 does not conceal base paint 52. In Figure 2B, the metal substrate to be printed is aluminum plate 51 to which base paint 52 has been applied.

[0020] In one or more embodiments, the metal substrate is not limited to an aluminum plate. The metal substrate may be a steel plate. For example, when printing ink on a steel plate such as a steel can, a steel plate is used instead of the aluminum plate 51 in Figures 2A and 2B.

[0021] In one or more embodiments, as another example, as shown in Figure 3A, a film 55 is attached to an aluminum plate 51, ink 53 is applied to the film 55, and an exterior coating 54 is applied to the surface of the ink 53. The ink 53 does not conceal the film 55 or the aluminum plate 51. In Figure 3A, the metal substrate to be printed is the aluminum plate 51 with the film 55 attached.

[0022] As shown in Figure 3B, a film 55 is attached to an aluminum plate 51, a primer 52 is applied to the film 55, ink 53 is applied to the primer 52, and an outer surface paint 54 is applied to the surface of the ink 53. The ink 53 does not conceal the primer 52. In Figure 3B, the metal substrate to be printed is an aluminum plate 51 to which a film 55 is attached and to which a primer 52 is applied. A steel plate may be used instead of the aluminum plate 51 in Figures 3A and 3B.

[0023] In one or more embodiments described in detail below, printing on an aluminum plate 51 as shown in Fig. 2A or printing on an aluminum plate 51 coated with a primer 52 as shown in Fig. 2B will be exemplified. As shown in Fig. 2A, printing in which ink 53 is directly applied to aluminum plate 51 will be referred to as "direct printing," and directly printed ink 53 protected with an outer surface coating 54 will be referred to as "direct printing sample." As shown in Fig. 2B, printing in which primer coating 52 is applied to aluminum plate 51 and ink 53 is applied to primer coating 52 will be referred to as "printing on white paint," and ink 53 printed on white paint and protected with an outer surface coating 54 will be referred to as "printing on white paint sample."

[0024] As shown in Figure 3A, printing in which film 55 is attached to aluminum plate 51 and ink 53 is applied to film 55 will be referred to as printing on film, and the ink 53 printed on film and protected with outer surface paint 54 will be referred to as a print-on-film sample. As shown in Figure 3B, printing in which film 55 is attached to aluminum plate 51 and base paint 52 is applied to film 55 and ink 53 is applied to base paint 52 will be referred to as printing on film-white paint, and the ink 53 printed on film-white paint and protected with outer surface paint 54 will be referred to as a print-on-film-white paint sample.

[0025] Using Figures 4A to 6B, let us consider the behavior of light when it is incident on a direct print sample and a sample printed on white paint. Figure 4A shows the case where light is incident on an aluminum plate 51 from the direction indicated by the arrow when no ink 53 is applied. Since incident light is specularly reflected on a metal substrate, the light is reflected in the direction indicated by the arrow, which is the position of specular reflection. Figure 4B shows the case where light is incident on a base paint 52 from the direction indicated by the arrow when no ink 53 is applied. Since incident light is diffusely reflected on white paint, the light is diffusely reflected in multiple directions indicated by the arrows.

[0026] FIG. 5A conceptually illustrates the behavior of light incident on ink 53 in the direct printing sample shown in FIG. 2A, when the ink 53 contains a pigment with a high light absorption effect. An example of an ink containing a pigment with a high light absorption effect is black ink. When light is incident on ink 53 from the direction indicated by the solid arrow, a small portion of the incident light is reflected from the surface of ink 53 in the direction indicated by the solid arrow, which is the position of specular reflection. Most of the light incident on ink 53 is absorbed by ink 53, and because ink 53 does not obscure aluminum plate 51, some of the light reaches the surface of aluminum plate 51, as indicated by the dashed arrow.

[0027] The light that reaches the surface of aluminum plate 51 is specularly reflected as in Figure 4A, but most of the specularly reflected light is absorbed by ink 53, so a very small amount of light reflected by the surface of aluminum plate 51 emerges from the surface of ink 53, as shown by the dashed arrow line.

[0028] Figure 5B conceptually illustrates the behavior of light when it is incident on ink 53 in the white paint print sample shown in Figure 2B, where ink 53 is an ink containing a pigment with a high light absorption effect. As in Figure 5A, when light is incident on ink 53 from the direction indicated by the solid arrow, a small portion of the incident light is reflected from the surface of ink 53 in the direction indicated by the solid arrow. As shown by the dashed arrow, the small amount of light that reaches base paint 52 is diffusely reflected, as in Figure 4B, but most of the diffusely reflected light is absorbed by ink 53, so a small amount of diffusely reflected light exits the surface of ink 53, as shown by the dashed arrow.

[0029] FIG. 6A conceptually illustrates the behavior of light when it enters ink 53 in the direct printing sample shown in FIG. 2A, when the ink 53 contains a pigment with a high light diffusion effect. An example of an ink containing a pigment with a high light diffusion effect is white ink. When light enters ink 53 from the direction indicated by the solid arrow, a portion of the incident light is diffused and reflected on the surface of ink 53. A portion of the light that enters ink 53 is diffused inside ink 53, as indicated by the dashed arrow. A small amount of light reaches the surface of aluminum plate 51, as indicated by the dashed arrow.

[0030] Light that reaches the surface of aluminum plate 51 is specularly reflected as in Figure 4A, but the specularly reflected light is diffused inside ink 53. A small amount of the diffused light is emitted from the surface of ink 53 as indicated by the dashed arrow.

[0031] Figure 6B conceptually illustrates the behavior of light when it enters ink 53 in the white paint print sample shown in Figure 2B, when the ink 53 is an ink containing a pigment with a high light diffusion effect. When light enters ink 53 from the direction indicated by the solid arrow, a portion of the incident light is diffused and reflected from the surface of ink 53. Of the light that enters ink 53 and diffuses inside, as indicated by the dashed arrow, a small amount of light that reaches base paint 52 is diffusely reflected, as in Figure 4B. The diffusely reflected light is further diffused inside ink 53, and a small amount of the diffusely reflected light exits from the surface of ink 53.

[0032] Thus, when light is incident on the direct print sample and the direct print sample is viewed from the outside, the light observed is determined by a combination of specular or diffuse reflection of light on the surface of ink 53, absorption of light within ink 53, diffuse reflection of light within ink 53, and specular reflection of light on the surface of aluminum plate 51. When light is incident on the white paint print sample and the white paint print sample is viewed from the outside, the light observed is determined by a combination of specular or diffuse reflection of light on the surface of ink 53, absorption of light within ink 53, diffuse reflection of light within ink 53, and diffuse reflection of light on the surface of base paint 52. The degree of specular reflection, diffuse reflection, and absorption in ink 53 is determined by the degree of light absorption or diffusion effect in ink 53.

[0033] The inks used for printing are assumed to be, for example, white, yellow (Y1), yellow (Y2), yellow (Y3), yellow (Y4), orange, red (R1), red (R2), red (R3), red (R4), red (R5), magenta, blue (B1), blue (B2), green, purple, black, and colorless. Inks other than colorless are primary color inks. The yellows Y1 to Y4 are yellow inks with different shades, the reds R1 to R5 are red inks with different shades, and the blues B1 and B2 are blue inks with different shades. Colorless refers to colorless inks that do not contain color pigments, such as inks called Victoria or Medium. Here, the inks used for printing are assumed to be a total of 18 inks, including 17 primary color inks and colorless ink, but the number of colors is not limited to 17.

[0034] The following preparations were made before CCM was performed: The 17 primary inks and a colorless ink were mixed in the following ratios: 100:0, 60:40, 30:70, 10:90, 3:97, and 1:99. These were then drawn out as shown in Figures 2A and 2B to obtain direct print samples and white-on-white print samples. The 16 primary inks (excluding white) were mixed in the following ratios: 100:0, 90:10, 60:40, 30:70, 10:90, 3:97, 1:99, and 0:100. These were then printed as shown in Figures 2A and 2B to obtain direct print samples and white-on-white print samples.

[0035] The measurer uses a multi-angle spectrophotometer to measure the multi-angle spectral reflectance of direct-printed samples and samples printed on white paint, each with a (17 x 6) pattern with different amounts of colorless ink and a (16 x 8) pattern with different amounts of white ink. Hereinafter, each direct-printed sample and each sample printed on white paint will be referred to as "each sample." The multi-angle spectral reflectance measured with the multi-angle spectrophotometer is a value corresponding to the degree of light reflection (specular reflection or diffuse reflection) and absorption, as described in Figures 5A to 6B, which differ depending on the type or concentration of pigments contained in the primary color ink. For example, an X-Rite MA-T12 multi-angle spectrophotometer can be used to measure the multi-angle spectral reflectance.

[0036] The above-mentioned mixing ratios of the 17 primary color inks and colorless ink, and the above-mentioned mixing ratios of the 16 primary color inks other than white and white ink are examples, and are not limited to the above-mentioned mixing ratios, and the number of patterns is also not limited.

[0037] As shown in FIGS. 7A and 7B, the multi-angle spectrophotometer includes a light-receiving unit positioned at a 45-degree angle and a light-receiving unit positioned at a 15-degree angle. The light-receiving unit positioned at a 45-degree angle receives reflected light of light incident from six angles: 45as-15, 45as15, 45as25, 45as45, 45as75, and 45as110. The light-receiving unit positioned at a 15-degree angle receives reflected light of light incident from six angles: 15as-45, 15as-30, 15as-15, 15as15, 15as45, and 15as80. The multi-angle spectrophotometer obtains spectral reflectances of 12 angles x 31 wavelengths measured at 10-nm intervals in the wavelength range of 400 nm to 700 nm, which is roughly the visible light band, based on the light-receiving signals received by each light-receiving unit for the reflected light of light incident from each angle.

[0038] Measuring the visible light band at 10 nm intervals is just one example, and the multi-angle spectrophotometer may acquire multi-angle spectral reflectance for each wavelength obtained by dividing the visible light band at predetermined wavelength intervals.

[0039] Figure 8 shows calibration curves showing the reflectance at an angle of 45 as 15 at a wavelength of 450 nm for each sample drawn down from inks mixed with black ink and colorless ink at each of the six mixing ratios mentioned above. The direct print sample and the print-on-white paint sample drawn down from inks mixed with black ink and colorless ink are abbreviated as the first direct print sample and the first print-on-white paint sample, respectively.

[0040] The calibration curves showing reflectance in Figure 8 and the following figures are Bezier curves based on the reflectance at six or eight points of each sample printed with inks mixed at six or eight mixing ratios. By plotting the calibration curve as a Bezier curve, it is possible to obtain the reflectance at any mixing ratio. A reflectance of 1 indicates perfect diffusion (100%). The method of generating a curve showing reflectance using the reflectance at multiple discrete points is not limited to Bezier curves.

[0041] As can be seen from Figure 8, the reflectance of each sample varies depending on the amount of colorless ink mixed with the black ink, i.e., the black ink concentration and the colorless ink concentration. Because angles 45a and 45b are close to specular reflection, strong reflection is measured. In the first direct printing sample, when the black ink concentration is between 1% and 10%, the aluminum plate 51 reflects light, resulting in a high reflectance exceeding 1. For each sample, as the black ink concentration increases, light is absorbed, resulting in a decrease in reflectance. Figure 8 shows reflectance at a wavelength of 450 nm, but because black ink does not have the characteristic of absorbing specific wavelengths, the calibration curve is similar for all wavelengths from 400 nm to 700 nm.

[0042] Figure 9 shows calibration curves showing the reflectance at an angle of 45 as 15 at a wavelength of 450 nm for each sample drawn down with ink obtained by mixing white ink and colorless ink at each of the six mixing ratios mentioned above. The direct print sample and the sample printed on white paint drawn down with ink obtained by mixing white ink and colorless ink are abbreviated as the second direct print sample and the second sample printed on white paint, respectively.

[0043] For the second sample printed on white paint, the reflectance remains constant at approximately 0.7, regardless of the mixing ratio of white ink to colorless ink. For the second sample printed directly, the reflectance exceeds that of the sample printed on white paint when the white ink is present in a concentration of approximately 1% to 50%, and when the white ink is present in a concentration of 60% or more, the reflectance is lower than that of the sample printed on white paint. Figure 9 shows the reflectance at a wavelength of 450 nm, but because white ink does not have the characteristic of absorbing specific wavelengths, the calibration curve is similar for all wavelengths from 400 nm to 700 nm.

[0044] Figure 10 shows calibration curves showing the reflectance at an angle of 45 as 15 at a wavelength of 450 nm for each sample drawn down with inks mixed at the eight mixing ratios mentioned above. The direct print sample and the print-on-white paint sample drawn down with inks mixed down with black ink and white ink are abbreviated as the third direct print sample and the third print-on-white paint sample, respectively.

[0045] For the third sample printed on white paint, the maximum reflectance is 0.71 when the white ink is 100%, and as the concentration of the black ink increases, the reflectance decreases as more light is absorbed. For the third sample printed directly, the maximum reflectance is 0.57 when the white ink is 100%, which is smaller than the 0.71 for the sample printed on white paint, and as the concentration of the black ink increases, the reflectance decreases as more light is absorbed. Because black ink and white ink do not have the characteristic of absorbing specific wavelengths, the calibration curve is similar for all wavelengths from 400 nm to 700 nm.

[0046] Figure 11 shows calibration curves for the reflectance at an angle of 45° as 45° at a wavelength of 450 nm for each sample of inks mixed at the eight mixing ratios mentioned above. For the third sample printed on white paint, the maximum reflectance is 0.7 when the white ink is 100%, while for the third sample printed directly, the maximum reflectance is 0.55 when the white ink is 100%, with the reflectance decreasing as the concentration of the black ink increases. Because black and white inks do not have the characteristic of absorbing specific wavelengths, the calibration curves are similar for all wavelengths between 400 nm and 700 nm.

[0047] Here, using yellow ink as an example, we will examine the calibration curves for each sample of mixed yellow ink and colorless ink, and for each sample of mixed yellow ink and white ink. Figures 12 and 13 show the calibration curves for the samples of mixed yellow ink and colorless ink at wavelengths of 450 nm and 600 nm at angles of 45 as 15, respectively.

[0048] As shown in Figure 12, yellow ink absorbs light at a short wavelength of 450 nm, so the calibration curve for a wavelength of 450 nm when yellow ink is mixed with a colorless ink is similar to the calibration curves for the first direct print sample and the first sample printed on white paint shown in Figure 8. As shown in Figure 13, the calibration curve for a wavelength of 600 nm when yellow ink is mixed with a colorless ink is similar for the sample printed on white paint to the calibration curve for the second sample printed on white paint shown in Figure 9. However, the calibration curve for the direct print sample is significantly different from the calibration curve for the second direct print sample shown in Figure 9.

[0049] Figures 14 and 15 show the calibration curves for wavelengths of 450 nm and 600 nm at angles of 45 as 15 for each sample of ink mixed with yellow ink and white ink. Because yellow ink absorbs light at the short wavelength of 450 nm, the calibration curve for the 450 nm wavelength when yellow ink and white ink are mixed is similar to the calibration curves for the third direct print sample and the third print-on-white paint sample shown in Figure 10. The calibration curve for the 600 nm wavelength when yellow ink and white ink are mixed shows that the reflectance of the direct print sample tends to increase as the concentration of the yellow ink increases. This is thought to be because the pigment in the yellow ink transmits light more easily than the pigment in the white ink.

[0050] Figure 16 shows, with the vertical axis enlarged, the calibration curve for a print sample on white paint drawn using an ink made by mixing the 450 nm yellow ink and colorless ink shown in Figure 12. Figure 17 shows the K / S value according to the Kubelka-Munk equation, based on the calibration curve shown in Figure 16. As shown in Figure 17, the K / S value for the print sample on white paint is almost linear, making it possible to perform CCM, which uses the K / S value to match colors.

[0051] However, even if the ink is a mixture of the same yellow ink and colorless ink, it is not possible to use the K / S value to adjust the color of the directly printed sample. Figure 18 shows the calibration curve for the directly printed sample at a wavelength of 600 nm shown in Figure 13. Figure 19 shows the K / S value according to the Kubelka-Munk equation based on the calibration curve shown in Figure 18. In Figure 19, when the K / S value is, for example, 0.5, there are multiple densities of yellow ink with a K / S value of 0.5. Therefore, the density cannot be correctly converted to spectral reflectance.

[0052] Therefore, in one or more embodiments, the density of each primary color ink is converted to the density of a first ink that has a light absorbing effect over most wavelengths in the visible light range, and a second ink that has a light diffusing effect over most wavelengths. Typically, the first ink that has a light absorbing effect over most wavelengths in the visible light range is black ink, and the second ink that has a light diffusing effect over most wavelengths in the visible light range is white ink. Hereinafter, the case where the first ink is black ink and the second ink is white ink will be taken as an example. That is, in one or more embodiments, the density of each primary color ink other than black ink and white ink is converted to the density of black ink or white ink.

[0053] For example, when the black ink 53 is printed with a film thickness of 2.5 μm±0.5 μm on an aluminum plate 51 or a base coating 52, the reflectance at angles 45 as-15 and 45 as 45 measured by a multi-angle spectrophotometer is 0.3 (30%) or less at all wavelengths in the wavelength range of 400 nm to 700 nm. * a * b * L in color space * The white ink has a reflectance of 0.45 (45%) or more and 1 (100%) or less at angles 45 as-15 and 45 as 45 measured by a multi-angle spectrophotometer at all wavelengths in the wavelength band of at least 420 nm to 670 nm when ink 53 with a film thickness of 2.5 μm±0.5 μm is printed on aluminum plate 51 or undercoat 52. Alternatively, the white ink has a reflectance of 0.45 (45%) or more and 1 (100%) or less at angles 45 as-15 and 45 as 45 measured by a multi-angle spectrophotometer at all wavelengths in the wavelength band of at least 420 nm to 670 nm. * a* b * L in color space * The value is greater than or equal to 70 and less than or equal to 100

[0054] Here, the reflectance is shown when an X-Rite model MA-T12 multi-angle spectrophotometer is used, but the reflectance may also be measured using an equivalent multi-angle spectrophotometer.

[0055] In this way, the ink that has a light absorbing effect at least in the wavelength range of 400 nm to 700 nm is referred to as the first ink, and the ink that has a light diffusing effect at least in the wavelength range of 420 nm to 670 nm is referred to as the second ink. In one or more embodiments, the densities of the primary color inks other than the first and second inks are converted to the densities of the first ink or the second ink. This makes it possible to estimate the multi-angle spectral reflectance without using the K / S value from the Kubelka-Munk equation.

[0056] Taking the wavelength of 450 nm in a direct print sample made by mixing yellow ink and colorless ink shown in FIG. 12 as an example, if the concentration of the yellow ink is 40%, the reflectance is 0.15.

[0057] Figure 20 shows calibration curves at a wavelength of 450 nm at an angle of 45 as 15 for the first direct-printed sample, which is a mixed ink of black ink and colorless ink, the second direct-printed sample, which is a mixed ink of white ink and colorless ink, and the third direct-printed sample, which is a mixed ink of black ink and white ink. The horizontal axis represents reflectance, and the vertical axis represents the density of black ink or white ink. In Figure 20, the vertical axis represents the density of black ink for the first and third direct-printed samples, and the vertical axis represents the density of white ink for the second direct-printed sample. The reflectance on the horizontal axis is the same as the vertical axis in Figure 12, and is the reflectance at a wavelength of 450 nm at an angle of 45 as 15.

[0058] In Figure 20, the density of black or white ink corresponding to a reflectance of 0.15 is 35% for the first direct-printed sample and 13% for the third direct-printed sample. Because the density of the yellow ink is 40%, it is appropriate to convert it to the 35% density of the first direct-printed sample, which is close to the density at a wavelength of 450 nm. In other words, at a wavelength of 450 nm, the direct-printed sample with a 40% yellow ink density exhibits behavior equivalent to that of black ink, which is primarily absorbent.

[0059] In the direct printing sample shown in Figure 13, which is a mixture of yellow ink and colorless ink, the reflectance at a wavelength of 600 nm is 2.3 when the concentration of the yellow ink is 40%. Figure 21 shows calibration curves at a wavelength of 600 nm for the first to third direct printing samples at angles of 45 as 15, with the horizontal axis representing reflectance and the vertical axis representing the concentration of black ink or white ink. In Figure 21, the concentration of black ink or white ink corresponding to a reflectance of 2.3 is 10% for the second direct printing sample.

[0060] In the first and third direct-printed samples, there is no black ink density corresponding to a reflectance of 2.3. Therefore, at a wavelength of 600 nm in the direct-printed sample with a 40% yellow ink density, it is appropriate to convert it to a 10% white ink density in the second direct-printed sample. In other words, at a wavelength of 600 nm in the direct-printed sample with a 40% yellow ink density, the behavior is equivalent to that of white ink, which primarily diffuses and reflects.

[0061] Here, a direct print sample made by mixing yellow ink and colorless ink is used as an example, but direct print samples made by mixing other primary color inks and colorless ink can also be converted to the density of black ink or white ink in the same way. For direct print samples made by mixing each primary color ink and colorless ink, the density of each primary color ink can be converted for each wavelength to the density of black ink when black ink and colorless ink are mixed, or the density of white ink when white ink and colorless ink are mixed.

[0062] When converting the reflectance of each primary color ink at a predetermined density into the density of black ink when black ink and colorless ink are mixed, or the density of white ink when white ink and colorless ink are mixed, there may be only one option. In this case, the CCM device 100 automatically converts the density of each primary color ink into the density of the ink of that one option. When there are two options, the CCM device 100 converts the density of each primary color ink into the density of the black ink or white ink that is closest in density. For a direct print sample in which each primary color ink (excluding white) is mixed with white ink and drawn down, the CCM device 100 converts the density of each primary color ink into the density of black ink when black ink and white ink are mixed, or the density of white ink when white ink and colorless ink are mixed.

[0063] Here, we will explain how multi-angle spectral reflectance is estimated based on the calibration curve, using as an example a case where the inks selected to reproduce a color equivalent to a specified sample color by direct printing and their mixing ratios are 40% yellow ink, 2% black ink, and 58% colorless ink.

[0064] Figure 22A, the same as Figure 12, shows the calibration curves at an angle of 45 as 15 and a wavelength of 450 nm for a direct-printed sample and a sample printed on white paint, both made with a mixture of yellow ink and colorless ink. Because the concentration of the yellow ink is 40%, the reflectance of the direct-printed sample is 0.15. The reflectance of the sample printed on white paint is 0.02. Figure 22B, the same as Figure 8, shows the calibration curves at an angle of 45 as 15 and a wavelength of 450 nm for a first direct-printed sample and a first sample printed on white paint. Because the concentration of the black ink is 2%, the reflectance of the first direct-printed sample is 2.2. The reflectance of the first sample printed on white paint is 0.4.

[0065] Figure 23A shows the calibration curves at an angle of 45 as 15 and a wavelength of 600 nm for a direct-printed sample and a sample printed on white paint, both of which are made with a mixture of yellow ink and colorless ink, as in Figure 13. Because the concentration of the yellow ink is 40%, the reflectance of the direct-printed sample is 2.3. The reflectance of the sample printed on white paint is 0.7. Figure 23B shows the calibration curves at an angle of 45 as 15 and a wavelength of 600 nm for the first direct-printed sample and the first sample printed on white paint. Because the concentration of the black ink is 2%, the reflectance of the first direct-printed sample is 1.6. The reflectance of the first sample printed on white paint is 0.4.

[0066] As explained using Figure 20, the reflectance of 0.15 at a wavelength of 450 nm in the direct-printed sample when the yellow ink concentration is 40% is converted to a concentration of 35% in the first direct-printed sample. As shown in Figure 20, the reflectance of 2.2 in the direct-printed sample when the black ink concentration is 2% is 2% in the first direct-printed sample. Because the yellow ink concentration has been converted to the black ink concentration, the yellow ink concentration converted to the black ink concentration and the black ink concentration can be multiplied, and the multiplied concentration is 37%.

[0067] As explained using Figure 21, the reflectance of 2.3 at a wavelength of 600 nm in the direct-printed sample when the yellow ink concentration is 40% is converted to a concentration of 10% in the second direct-printed sample. As shown in Figure 21, the reflectance of 1.6 in the direct-printed sample when the black ink concentration is 2% is converted to a concentration of 1% in the first direct-printed sample. Because the yellow ink concentration is converted to the white ink concentration, the yellow ink concentration converted to the white ink concentration and the black ink concentration can be multiplied, resulting in a multiplied concentration of 11%.

[0068] Figure 24A shows the calibration curve for a wavelength of 450 nm, with the horizontal and vertical axes of Figure 20 reversed. The reflectance at 37% density for the first direct-printed sample is 0.2. In other words, if direct printing is performed using an ink mixture of 40% yellow ink, 2% black ink, and 58% colorless ink, the reflectance at a wavelength of 450 nm at an angle of 45 as 15 is estimated to be 0.2. Figure 24B shows the calibration curve for a wavelength of 600 nm, with the horizontal and vertical axes of Figure 21 reversed. The reflectance at 11% density for the second direct-printed sample is 2.2. In other words, if direct printing is performed using an ink mixture of 40% yellow ink, 2% black ink, and 58% colorless ink, the reflectance at a wavelength of 600 nm at an angle of 45 as 15 is estimated to be 2.2.

[0069] Next, we will explain how the multi-angle spectral reflectance is estimated based on the calibration curve, using as an example a case where one or more inks selected to directly reproduce a color equivalent to a given sample color and their mixing ratios are 40% yellow ink, 2% black ink, and 58% white ink.

[0070] Figure 25A, the same as Figure 14, shows the calibration curves at an angle of 45 as 15 for a wavelength of 450 nm for a direct-printed sample and a sample printed on white paint, both made with a mixture of yellow and white inks. Because the concentration of the yellow ink is 40%, the reflectance of the direct-printed sample is 0.1. The reflectance of the sample printed on white paint is 0.05. Figure 25B, the same as Figure 10, shows the calibration curves at an angle of 45 as 15 for a third direct-printed sample and a third sample printed on white paint, both made with a mixture of yellow and white inks. Because the concentration of the black ink is 2%, the reflectance of the third direct-printed sample is 0.35. The reflectance of the third sample printed on white paint is 0.38.

[0071] Figure 26A shows the calibration curves at an angle of 45 as 15 and a wavelength of 600 nm for a direct-printed sample and a sample printed on white paint, both of which are made with a mixture of yellow and white inks, as in Figure 15. Because the concentration of the yellow ink is 40%, the reflectance of the direct-printed sample is 0.7. The reflectance of the sample printed on white paint is 0.65. Figure 26B shows the calibration curves at an angle of 45 as 15 and a wavelength of 600 nm for a third direct-printed sample and a third sample printed on white paint. Because the concentration of the black ink is 2%, the reflectance of the third direct-printed sample is 0.35. The reflectance of the third sample printed on white paint is 0.38.

[0072] As shown in Figure 27A, the reflectance of 0.1 at a wavelength of 450 nm for the direct-printed sample when the yellow ink concentration is 40% and the reflectance of 0.35 at a wavelength of 450 nm for the direct-printed sample when the black ink concentration is 2% are converted to densities of 18% and 2%, respectively, for the third direct-printed sample. Multiplying these values ​​results in a density of 20%. As shown in Figure 27B, the reflectance of 0.7 at a wavelength of 600 nm for the direct-printed sample when the yellow ink concentration is 40% and the reflectance of 0.35 at a wavelength of 450 nm for the direct-printed sample when the black ink concentration is 2% are converted to densities of 0% and 2%, respectively, for the third direct-printed sample. Multiplying these values ​​results in a density of 2%.

[0073] Figure 28A shows the calibration curve for a wavelength of 450 nm, with the horizontal and vertical axes reversed from those of Figure 27A. The reflectance at 20% density for the third direct-printed sample is 0.09. In other words, if direct printing is performed using an ink mixture of 40% yellow ink, 2% black ink, and 58% white ink, the reflectance at a wavelength of 450 nm at an angle of 45 as 15 is estimated to be 0.09. Figure 28B shows the calibration curve for a wavelength of 600 nm, with the horizontal and vertical axes reversed from those of Figure 27B. The reflectance at 2% density for the third direct-printed sample is 3.5. In other words, if direct printing is performed using an ink mixture of 40% yellow ink, 2% black ink, and 58% white ink, the reflectance at a wavelength of 600 nm at an angle of 45 as 15 is estimated to be 0.35.

[0074] Figures 27A and 27B show only the calibration curve for the third direct print sample. In a direct print sample in which inks of each color except white are mixed with white ink, the ink density may need to be converted to the density of the white ink when mixed with a colorless ink. Figure 29 shows the calibration curves for the second and third direct print samples. As shown in Figure 29, when the reflectance exceeds 0.6, the calibration curve for the second direct print sample is used. The density of the white ink in the second direct print sample is a negative value.

[0075] As described above, the CCM device 100 can accurately estimate the multi-angle spectral reflectance when directly printed with one or more selected inks, based on a pre-generated calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance. The CCM device 100 can determine one or more inks and their mixing ratios that can reproduce a color similar to the sample color, based on the multi-angle spectral reflectance of the sample color measured using a multi-angle spectrophotometer and the estimated multi-angle spectral reflectance. Using a similar principle, the CCM device 100 can also accurately estimate the multi-angle spectral reflectance when printing on white paint with one or more selected inks, and can determine one or more inks and their mixing ratios that can reproduce a color similar to the sample color.

[0076] When only the direct printing shown in FIG. 2A is performed, the CCM device 100 can estimate the multi-angle spectral reflectance when directly printed with one or more inks based solely on the calibration curve of the directly printed sample. Therefore, if the printing on white paint shown in FIG. 2B is not performed, the CCM device 100 may retain only the calibration curve of the directly printed sample. When only the printing on white paint shown in FIG. 2B is performed, the CCM device 100 can estimate the multi-angle spectral reflectance when directly printed with one or more inks based solely on the calibration curve of the printing on white paint sample. Therefore, if the direct printing shown in FIG. 2A is not performed, the CCM device 100 may retain only the calibration curve of the printing on white paint sample.

[0077] Even when only direct printing is performed, or when both direct printing and printing on white paint are performed, the CCM device 100 preferably retains a calibration curve for the direct-printed sample and a calibration curve for the sample printed on white paint and references both. The CCM device 100 preferably references both the calibration curve for the direct-printed sample (first calibration curve) and the calibration curve for the sample printed on white paint (second calibration curve) to estimate the multi-angle spectral reflectance when directly printed with one or more inks. Using both the calibration curve for the direct-printed sample and the calibration curve for the sample printed on white paint together enables more accurate estimation of the multi-angle spectral reflectance in direct printing.

[0078] By using the calibration curve of the print sample on white paint, it is possible to estimate the multi-angle spectral reflectance when one or more inks are printed as ink 53 on base paint 52. The light absorptance of one or more inks can be determined based on the estimated multi-angle spectral reflectance. This light absorptance is the absorptance of the one or more inks themselves, without being affected by light reflected from aluminum plate 51, which is a metal substrate. Therefore, when CCM device 100 directly estimates the multi-angle spectral reflectance using the calibration curve of the print sample, accuracy can be improved by determining the angular spectral reflectance with reference to the absorptance of one or more inks.

[0079] 30 and 31, the operation of the CCM device 100, the CCM method executed by the CCM device 100, and the processing executed by the CCM program 20 will be described. Fig. 30 shows the processing for estimating multi-angle spectral reflectance and for the advance preparations required for CCM.

[0080] In Figure 30, in step S1, the user prepares ink samples by mixing each primary color ink with a colorless ink at different amounts of the colorless ink, and ink samples by mixing each primary color ink with a white ink at different amounts of the white ink. In step S2, the user prepares a direct print sample and a print-on-white paint sample for each ink sample. In step S3, the user uses a multi-angle spectrophotometer to measure the multi-angle spectral reflectance of each direct print sample and each print-on-white paint sample.

[0081] In step S4, the computer constituting the CCM device 100 or any other computer creates a calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance based on the results of the multi-angle spectral reflectance measurement, and then ends the preparation process. The calibration curve data is stored in the storage unit and written into the CCM program 20 so that it can be referenced when the CCM program 20 executes CCM.

[0082] In FIG. 31, in step S11, the user selects a sample color to be reproduced by direct printing or printing on white paint. In step S12, the user measures the multi-angle spectral reflectance of the sample color using a multi-angle spectrocolorimeter. In step S13, the CCM device 100 converts the measured multi-angle spectral reflectance into first color coordinates in a predetermined color space (fifth step). As the predetermined color space, L * a * b * The Munsell color system or the Munsell color system can be used. The Munsell color system is preferable because it is closer to the human visual perception of hue. When the Munsell color system is used as the predetermined color space, the hue, lightness, and saturation of the Munsell color chart are obtained as the first color coordinates.

[0083] In step S14, the user selects the substrate type, which can be a metal substrate for direct printing or a metal substrate coated with a primer for printing over white paint.

[0084] In step S15, the CCM device 100 selects one or more inks and their mixing ratios (sixth step). The user may select one or more inks and their mixing ratios in step S15. The inks to be selected include any one primary color ink other than colorless ink, a combination of any one primary color ink other than colorless ink with colorless ink, and a combination of a primary color ink of a color other than black with black ink. The inks to be selected also include a combination of a primary color ink of a color other than black and white with white ink, and a combination of a primary color ink of a color other than black and white with black ink and white ink. Two or more primary color inks of a color other than black and white may be combined.

[0085] In step S16, the CCM device 100 estimates the multi-angle spectral reflectance based on a calibration curve prepared in advance as shown in FIG. 30 (seventh step).

[0086] Specifically, the CCM device 100 acquires the multi-angle spectral reflectance for each wavelength of ink of each color from the densities of the inks other than the colorless ink among one or more inks in a selected mixing ratio that are printed on a metal substrate based on a calibration curve (first step). The CCM device 100 converts the acquired multi-angle spectral reflectance for each wavelength of ink of each color into the densities of the first or second ink based on the calibration curve (second step). The CCM device 100 integrates the converted densities for each wavelength (third step). The CCM device 100 estimates the multi-angle spectral reflectance corresponding to the integrated densities for each wavelength as the multi-angle spectral reflectance for each wavelength when one or more inks in the selected mixing ratio are printed on a metal substrate (fourth step).

[0087] In step S17, the CCM device 100 converts the estimated multi-angle spectral reflectance into second color coordinates in a predetermined color space (eighth step). If the predetermined color space in step S13 is the Munsell color system, the Munsell color system is also used in step S17. The CCM device 100 acquires the hue, lightness, and saturation of the Munsell color chart as the second color coordinates.

[0088] In step S18, the CCM device 100 determines whether the difference between the first color coordinates and the second color coordinates is minimum. If the difference between the first color coordinates and the second color coordinates is not minimum (NO), the CCM device 100 returns the process to step S15 and selects one or more other inks and their mixing ratios. The CCM device 100 may select one or more inks different from those previously selected, or may select a mixing ratio different from that previously selected for the same one or more inks. The CCM device 100 may select a different mixing ratio for one or more different inks.

[0089] The CCM device 100 repeats the processes of steps S15 to S18 until the difference between the first color coordinates and the second color coordinates becomes minimum in step S18 (ninth step). If the difference between the first color coordinates and the second color coordinates is minimum (YES), the CCM device 100 displays the color matching result corresponding to the sample color on the display unit 4 and ends the process.

[0090] In this way, the CCM device 100 changes one or more inks or their mixing ratios until the difference between the first color coordinates and the second color coordinates is minimized, and determines the mixing ratio of one or more inks that minimizes the difference between the first color coordinates and the second color coordinates as the color tone corresponding to the sample color.

[0091] 32 shows an example of the functional configuration of the CCM device 100 when the CCM device 100 executes CCM processing. When the CPU 1 shown in FIG. 1 executes the CCM program 20, the CCM device 100 becomes functionally equipped with an ink information storage unit 101, an ink mixing ratio selection unit 102, a calibration curve storage unit 103, a reflectance estimation unit 104, a first color coordinate conversion unit 105, a second color coordinate conversion unit 106, and a color matching unit 107.

[0092] The ink information storage unit 101 stores ink information for a total of 18 inks, including the above-mentioned 17 primary color inks and colorless ink. The ink information may be a number or the like that identifies each ink. The ink / mixing ratio selection unit 102 selects one or more inks from the 18 inks and selects the mixing ratio of the selected ink. The calibration curve storage unit 103 stores the calibration curves required for the reflectance estimation unit 104 to estimate the multi-angle spectral reflectance.

[0093] Specifically, the calibration curve storage unit 103 stores a calibration curve indicating the relationship between ink concentration and multi-angle spectral reflectance, based on the results of measuring in advance, using a multi-angle spectrophotometer, the multi-angle spectral reflectance for each wavelength obtained by dividing the visible light band at predetermined wavelength intervals for each print sample. The print samples include print samples in which each of a plurality of primary color inks is mixed at different ratios with a colorless ink and applied to a metal substrate, and print samples in which each of the primary color inks other than white ink is mixed at different ratios with the white ink and applied to a metal substrate.

[0094] As described above, when only direct printing is performed, the calibration curve storage unit 103 may store only the calibration curve for the direct printing sample. When only printing on white paint is performed, the calibration curve storage unit 103 may store only the calibration curve for the print-on-white paint sample. It is preferable that the calibration curve storage unit 103 stores both the calibration curve for the direct printing sample and the calibration curve for the print-on-white paint sample.

[0095] The reflectance estimation unit 104 receives an input of the substrate type selected by the operation unit 3. Based on the calibration curve stored in the calibration curve storage unit 103, the reflectance estimation unit 104 estimates the angular spectral reflectance for one or more inks and their mixing ratios selected by the ink / mixing ratio selection unit 102.

[0096] The reflectance estimation unit 104 constitutes a multi-angle spectral reflectance estimation device according to one or more embodiments. The reflectance estimation unit 104 executes a multi-angle spectral reflectance estimation method according to one or more embodiments. The reflectance estimation unit 104 is functionally configured by the CPU 1 executing a multi-angle spectral reflectance estimation program included in the CCM program 20.

[0097] As shown in FIG. 33 , the reflectance estimation unit 104 includes a multi-angle spectral reflectance acquisition unit 1041, a density conversion unit 1042, a density integration unit 1043, and a multi-angle spectral reflectance estimation unit 1044. The multi-angle spectral reflectance acquisition unit 1041, the density conversion unit 1042, and the multi-angle spectral reflectance estimation unit 1044 refer to the calibration curve stored in the calibration curve storage unit 103. Based on the calibration curve, the multi-angle spectral reflectance acquisition unit 1041 acquires the multi-angle spectral reflectance for each wavelength of ink of each color from the density of the ink, other than the colorless ink, among one or more inks having a selected mixing ratio to be printed on the metal substrate. The density conversion unit 1042 converts the acquired multi-angle spectral reflectance for each wavelength of ink of each color into the density for each wavelength of the first ink or the second ink, based on the calibration curve.

[0098] The density integration unit 1043 integrates the converted densities for each wavelength. The multi-angle spectral reflectance estimation unit 1044 estimates, based on the calibration curve, the multi-angle spectral reflectance corresponding to the integrated density for each wavelength as the multi-angle spectral reflectance for each wavelength when one or more inks in the selected mixing ratio are printed on a metal substrate. The multi-angle spectral reflectance estimated by the reflectance estimation unit 104 in this manner is supplied to the second color coordinate conversion unit 106 in FIG. 32.

[0099] In FIG. 32, a first color coordinate conversion unit 105 converts the multi-angle spectral reflectance of a selected sample color measured using a multi-angle spectrophotometer into first color coordinates in a predetermined color space. The multi-angle spectral reflectance is calculated by dividing the visible light band of the selected sample color at predetermined wavelength intervals. The second color coordinate conversion unit 106 converts the multi-angle spectral reflectance estimated for each wavelength provided by the reflectance estimation unit 104 into second color coordinates in the same color space as the first color coordinate conversion unit 105. The color matching unit 107 selects one or more inks from a plurality of primary color inks and colorless inks using the ink / mixing ratio selection unit 102 so as to minimize the difference between the first and second color coordinates, determines the mixing ratio of the selected ink or inks, and obtains a color matching result corresponding to the sample color. The display unit 4 displays the color matching result obtained by the color matching unit 107.

[0100] When the color matching unit 107 determines whether the difference between the first color coordinates and the second color coordinates is minimum, it is not necessary to compare the spectral reflectances at all 12 angles shown in Figures 7A and 7B. To reduce the amount of calculation, the color matching unit 107 may compare the spectral reflectances at a selected portion of the 12 angles to determine whether the difference between the first color coordinates and the second color coordinates is minimum.

[0101] The color adjusting unit 107 may display the reflectance for each wavelength of the sample color and the toning result on the display unit 4 in the form of a graph as shown in Fig. 34. Fig. 34 shows the spectral reflectance at one angle selected from the 12 angles. The color adjusting unit 107 may display the sample color and the color obtained as a result of toning side by side on the display unit 4.

[0102] While the above description focuses on direct printing, the CCM device 100 can also perform color matching to reproduce a color most similar to the sample color when printing on white paint, thereby achieving a color matching result suitable for practical use. The CCM device 100 can also perform color matching to reproduce a color most similar to the sample color when printing on film (as shown in FIG. 3A) and when printing on film and white paint (as shown in FIG. 3B), thereby achieving a color matching result suitable for practical use. In this case, the CCM device 100 uses a calibration curve generated based on the results of pre-measurement of the multi-angle spectral reflectance of the print sample on film and the print sample on film and white paint using a multi-angle spectrophotometer. By using the appropriate calibration curve for each metal substrate to be printed, the CCM device 100 can perform color matching to reproduce a color most similar to the sample color, thereby achieving a color matching result suitable for practical use.

[0103] The present invention is not limited to one or more of the above-described embodiments, and various modifications are possible without departing from the spirit of the present invention. The CCM device 100 can be configured by any combination of software and hardware. [Explanation of symbols]

[0104] 1. Central Processing Unit 2 Non-transitory storage medium 3 Control section 4 Display 20 Computer Color Matching Programs 100 Computer color matching device 101 Ink information storage unit 102 Ink mixture ratio selection section 103 Calibration curve storage unit 104 Reflectance estimation section 105 First color coordinate conversion unit 106 Second color coordinate conversion unit 107 Toning section 1041 Multi-angle spectral reflectance acquisition section 1042 Concentration conversion section 1043 Concentration integrator 1044 Multi-angle spectral reflectance estimation section

Claims

1. a multi-angle spectral reflectance acquisition unit that acquires the multi-angle spectral reflectance for each wavelength of ink of each color from the concentration of one or more inks of a selected mixing ratio printed on the metal substrate, other than the colorless ink, based on a calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance, the calibration curve being based on measurement results obtained in advance using a multi-angle spectrophotometer to measure the multi-angle spectral reflectance for each wavelength obtained by dividing a visible light band at predetermined wavelength intervals for printed samples in which each ink of a plurality of primary color inks is applied to a colorless ink at different mixing ratios, and for printed samples in which each ink of the primary color inks other than a white ink is applied to the white ink at different mixing ratios; a concentration conversion unit that converts the acquired multi-angle spectral reflectance for each wavelength of the ink of each color based on the calibration curve into a concentration for each wavelength of a first ink that has a light absorbing effect at least for all wavelengths in a wavelength range of 400 nm to 700 nm, or a concentration for each wavelength of a second ink that has a light diffusing effect at least for all wavelengths in a wavelength range of 420 nm to 670 nm; a concentration integrating unit that integrates the converted concentrations for each wavelength; a reflectance estimation unit that estimates, based on the calibration curve, the multi-angle spectral reflectance corresponding to the integrated concentration for each wavelength as the multi-angle spectral reflectance for each wavelength when the one or more inks having the selected mixing ratio are printed on the metal substrate; and A multi-angle spectral reflectance estimation device comprising:

2. the metal substrate is an aluminum plate or a steel plate, The print sample is a direct print sample in which ink is directly applied to the metal substrate, The calibration curve is generated based on the results of measuring the multi-angle spectral reflectance of the directly printed sample. The multi-angle spectral reflectance estimation device according to claim 1 .

3. the metal substrate is an aluminum plate or a steel plate, The print samples include a direct print sample in which ink is directly applied to the metal substrate, and a white paint-on-print sample in which white paint is applied to the metal substrate as a base paint and ink is applied to the base paint, the calibration curves include a first calibration curve generated based on measurement results of multi-angle spectral reflectance of the direct print sample, and a second calibration curve generated based on measurement results of multi-angle spectral reflectance of the print-on-white paint sample, When estimating the multi-angle spectral reflectance when the one or more inks having the selected mixing ratio are directly applied to the metal substrate, the multi-angle spectral reflectance acquisition unit, the concentration conversion unit, and the reflectance estimation unit refer to both the first calibration curve and the second calibration curve. The multi-angle spectral reflectance estimation device according to claim 1 .

4. A multi-angle spectral reflectance estimation device according to any one of claims 1 to 3; a first color coordinate conversion unit that converts multi-angle spectral reflectances for each wavelength obtained by dividing a visible light band of a selected sample color by a predetermined wavelength interval, measured using a multi-angle spectrophotometer, into first color coordinates in a predetermined color space; a second color coordinate conversion unit that converts the multi-angle spectral reflectance for each wavelength estimated by the multi-angle spectral reflectance estimation device when one or more inks and their mixing ratios to be printed on a metal substrate to be printed and the selected inks are printed on the metal substrate at the selected mixing ratios into second color coordinates in the predetermined color space; a color matching unit that changes the one or more inks or their mixing ratios until a difference between the first color coordinates and the second color coordinates is minimized, and determines the mixing ratio of the one or more inks that minimizes the difference between the first color coordinates and the second color coordinates as a color match corresponding to the sample color; A computer color matching device comprising:

5. the first color coordinate conversion unit converts the measured multi-angle spectral reflectance for each wavelength into hue, lightness, and saturation of the Munsell color system; The second color coordinate conversion unit converts the multi-angle spectral reflectance for each estimated wavelength into hue, lightness, and saturation of the Munsell color system.

5. The computer color matching device of claim 4.

6. a calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance for each wavelength obtained by dividing a visible light band at predetermined wavelength intervals, the calibration curve being based on measurement results obtained in advance using a multi-angle spectrophotometer, for printed samples in which each ink of a plurality of primary color inks is applied to a colorless ink at different mixing ratios, and for printed samples in which each ink of the primary color inks other than a white ink is applied to the white ink at different mixing ratios, and the multi-angle spectral reflectance for each wavelength of each color ink is obtained from the concentration of the ink other than the colorless ink among one or more inks in a selected mixing ratio that are printed on the metal substrate; converting the acquired multi-angle spectral reflectance for each wavelength of the ink of each color based on the calibration curve into a concentration for each wavelength of a first ink having a light absorbing effect at least at all wavelengths in a wavelength range of 400 nm to 700 nm, or a concentration for each wavelength of a second ink having a light diffusing effect at least at all wavelengths in a wavelength range of 420 nm to 670 nm; The converted concentrations are integrated for each wavelength. Based on the calibration curve, the multi-angle spectral reflectance corresponding to the integrated concentration for each wavelength is estimated to be the multi-angle spectral reflectance for each wavelength when the one or more inks having the selected mixing ratio are printed on the metal substrate. Multi-angle spectral reflectance estimation method.

7. the metal substrate is an aluminum plate or a steel plate, The print sample is a direct print sample in which ink is directly applied to the metal substrate, The calibration curve is generated based on the results of measuring the multi-angle spectral reflectance of the directly printed sample. The method for estimating multi-angle spectral reflectance according to claim 6 .

8. the metal substrate is an aluminum plate or a steel plate, The print samples include a direct print sample in which ink is directly applied to the metal substrate, and a white paint-on-print sample in which white paint is applied to the metal substrate as a base paint and ink is applied to the base paint, the calibration curves include a first calibration curve generated based on measurement results of multi-angle spectral reflectance of the direct print sample, and a second calibration curve generated based on measurement results of multi-angle spectral reflectance of the print-on-white paint sample, When estimating the multi-angle spectral reflectance when the one or more inks having the selected mixing ratios are directly applied to the metal substrate, the multi-angle spectral reflectance for each wavelength of the ink of each color is obtained based on the first and second calibration curves, the obtained multi-angle spectral reflectance for each wavelength of the ink of each color is converted into a density for each wavelength of the first or second ink, and the multi-angle spectral reflectance corresponding to the integrated density for each wavelength is estimated to be the multi-angle spectral reflectance for each wavelength. The method for estimating multi-angle spectral reflectance according to claim 6 .

9. Using a multi-angle spectrophotometer, the band of visible light of the selected sample color is divided into predetermined wavelength intervals, and multi-angle spectral reflectance is measured for each wavelength; converting the measured multi-angle spectral reflectance for each wavelength into first color coordinates in a predetermined color space; selecting one or more inks and their mixing ratios to be printed on the metal substrate to be printed; estimating a multi-angle spectral reflectance for each wavelength when the one or more inks in the selected mixing ratio are printed on the metal substrate using the multi-angle spectral reflectance estimation method according to any one of claims 6 to 8; converting the estimated multi-angle spectral reflectance for each wavelength into second color coordinates in the predetermined color space; The one or more inks or their mixing ratios are changed until the difference between the first color coordinates and the second color coordinates is minimized, and the mixing ratio of the one or more inks that minimizes the difference between the first color coordinates and the second color coordinates is determined to be the color tone corresponding to the sample color. Computer color matching method.

10. converting the measured multi-angle spectral reflectance for each wavelength into hue, lightness, and saturation in the Munsell color system; The estimated multi-angle spectral reflectance for each wavelength is converted into the hue, lightness, and saturation of the Munsell color system.

10. The computer color matching method of claim 9.

11. On the computer, a first step of acquiring the multi-angle spectral reflectance for each wavelength obtained by dividing a visible light band at predetermined wavelength intervals for a printed sample in which each ink of a plurality of primary color inks is applied to a metal substrate at different mixing ratios of each ink to a colorless ink, and for a printed sample in which each ink of the primary color inks other than a white ink is applied to the white ink at different mixing ratios, based on a calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance, the calibration curve being based on measurement results obtained in advance using a multi-angle spectrophotometer, and based on the calibration curve showing the relationship between ink concentration and multi-angle spectral reflectance for each ink of a plurality of primary color inks applied to the metal substrate at predetermined wavelength intervals, based on the concentration of the ink other than the colorless ink among one or more inks in a selected mixing ratio that are printed on the metal substrate; a second step of converting the acquired multi-angle spectral reflectance for each wavelength of the ink of each color based on the calibration curve into a concentration for each wavelength of a first ink having a light absorbing effect at least at all wavelengths in a wavelength range of 400 nm to 700 nm, or a concentration for each wavelength of a second ink having a light diffusing effect at least at all wavelengths in a wavelength range of 420 nm to 670 nm; a third step of integrating the converted concentrations for each wavelength; a fourth step of estimating, based on the calibration curve, the multi-angle spectral reflectance corresponding to the integrated concentration for each wavelength as the multi-angle spectral reflectance for each wavelength when the one or more inks having the selected mixing ratio are printed on the metal substrate; A multi-angle spectral reflectance estimation program that executes the above.

12. the metal substrate is an aluminum plate or a steel plate, The print sample is a direct print sample in which ink is directly applied to the metal substrate, The calibration curve is generated based on the results of measuring the multi-angle spectral reflectance of the directly printed sample. The multi-angle spectral reflectance estimation program according to claim 11.

13. the metal substrate is an aluminum plate or a steel plate, The print samples include a direct print sample in which ink is directly applied to the metal substrate, and a white paint-on-print sample in which white paint is applied to the metal substrate as a base paint and ink is applied to the base paint, the calibration curves include a first calibration curve generated based on measurement results of multi-angle spectral reflectance of the direct print sample, and a second calibration curve generated based on measurement results of multi-angle spectral reflectance of the print-on-white paint sample, When estimating the multi-angle spectral reflectance when the one or more inks having the selected mixing ratio are directly applied to the metal substrate, the computer Executing the first, second, and fourth steps based on the first and second calibration curves. The multi-angle spectral reflectance estimation program according to claim 11.

14. On the computer, a fifth step of converting the multi-angle spectral reflectance for each wavelength obtained by dividing the visible light band of the selected sample color by predetermined wavelength intervals, measured using the multi-angle spectrophotometer, into first color coordinates in a predetermined color space; A sixth step of selecting one or more inks and their mixing ratios to be printed on the metal substrate to be printed; a seventh step of estimating a multi-angle spectral reflectance for each wavelength when the one or more inks in the selected mixing ratio are printed on the metal substrate using the multi-angle spectral reflectance estimation program according to any one of claims 11 to 13; and an eighth step of converting the estimated multi-angle spectral reflectance for each wavelength into second color coordinates in the predetermined color space; a ninth step of changing the one or more inks or their mixing ratios until a difference between the first color coordinates and the second color coordinates is minimized, and determining the mixing ratio of the one or more inks that minimizes the difference between the first color coordinates and the second color coordinates as a color mixture corresponding to the sample color; A computer color matching program that executes

15. The computer, as the fifth step, converting the measured multi-angle spectral reflectance for each wavelength into hue, lightness, and saturation of the Munsell color system; as the eighth step, converting the estimated multi-angle spectral reflectance for each wavelength into hue, lightness, and saturation of the Munsell color system; 15. The computer color matching program according to claim 14, which executes the following:

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