CN108872156B - Method and device for predicting ink component proportion based on reciprocal of spectral reflectance - Google Patents

Method and device for predicting ink component proportion based on reciprocal of spectral reflectance Download PDF

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CN108872156B
CN108872156B CN201810747072.0A CN201810747072A CN108872156B CN 108872156 B CN108872156 B CN 108872156B CN 201810747072 A CN201810747072 A CN 201810747072A CN 108872156 B CN108872156 B CN 108872156B
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李婵
王一格
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Anhui Antai New Style Packaging Materials Co ltd
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Shenzhen Jinjia Group Co Ltd
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Abstract

The invention discloses a method and equipment for predicting the proportion of ink components based on reciprocal spectral reflectance, wherein the method comprises the following steps: establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component proportion of each base ink and a nonlinear term according to the linear relation between the reciprocal of the spectral reflectance of the mixed ink and the component proportion of each base ink; and acquiring the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink, and predicting the component proportion of each base ink according to the established mathematical model. The invention predicts the component ratio of each base ink in the mixed ink by obtaining the reciprocal of the spectral reflectance of the mixed ink and the reciprocal of the spectral reflectance of each base ink. The method is simple and effective, and only has one undetermined parameter, thereby improving the efficiency and saving the time.

Description

Method and device for predicting ink component proportion based on reciprocal of spectral reflectance
Technical Field
The invention relates to the field of computer color matching, in particular to a method and equipment for predicting ink component proportion based on reciprocal spectral reflectance.
Background
Computer color matching is a method for product research and development, production, quality control and the like in the relevant coloring industries such as textile, printing and dyeing, paint manufacturing and the like, thoroughly changes the current situation of the industry which mainly relies on manual experience for color matching, and reduces the production cost.
In the field of packaging printing, most of the color matching models used at present are based on Kubelka-Munk (K-M for short) theory, and describe the optical characteristics (absorption coefficient and scattering coefficient) and the component proportion of the pigment through a linear addition mathematical relationship. The researchers have pointed out that in the K-M color matching model, the optical characteristics of the pigments and the component ratios are not always in a linear relationship; additionally, the use of additive relationships to describe the optical behavior of colorants when mixed is also inaccurate. For the "non-linearity" and "non-additivity" problems of K-M color models, it is believed by scholars that the cause of non-linearity is material surface reflection, and it is desirable to improve the linearity of the K-M color model by modifying the spectral reflectance values. Moreover, researchers have proposed optimization of color matching models using numerical processing methods such as recursion, fitting, regularization, nonlinear programming, and the like. The method improves the color matching prediction accuracy to a certain extent, but the method is based on the fact that the optical coefficient and the proportion are linearly related. Meanwhile, researchers also propose nonlinear color matching models based on complex frequency spectrum theory, neural networks, particle swarm optimization methods and the like, and obtain good color matching effects, but the methods are complex in calculation and have more undetermined parameters of the models.
Accordingly, the prior art is yet to be improved and developed.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide a method and an apparatus for predicting the ratio of ink components based on the reciprocal of the spectral reflectance, which aims to solve the problems of the prior art that the process for predicting the ratio of each base ink component in the mixed ink is complicated and the number of undetermined parameters of the model is large.
The technical scheme of the invention is as follows:
a method for predicting the proportion of ink components based on the reciprocal of spectral reflectance comprises the following steps:
establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component proportion of each base ink and a nonlinear term according to the linear relation between the reciprocal of the spectral reflectance of the mixed ink and the component proportion of each base ink;
and acquiring the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink, and predicting the component proportion of each base ink according to the established mathematical model.
Preferably, the mathematical model is as follows:
Figure BDA0001724630110000021
in the formula, Pt(λ) represents the reciprocal of the spectral reflectance of the mixed ink, Pc,i(λ) represents the reciprocal of the spectral reflectance of each base ink, CiDenotes the component ratio of each base ink, ε (λ) denotes a nonlinear term, and n denotes the number of base inks.
Preferably, before the mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component ratio of each base ink, and the nonlinear term is established based on a linear relationship between the reciprocal of the spectral reflectance of the mixed ink and the component ratio of each base ink, the mathematical model includes:
and determining the wave band with the optimal linear correlation degree between the reciprocal of the spectral reflectivity of the modeling sample and the component proportion of the modeling sample.
Preferably, the step of determining the two wavelength bands with the best linear correlation degree between the inverse spectral reflectance of the modeling sample and the component proportion of the modeling sample specifically comprises:
establishing a plurality of modeling samples, and recording the proportion of the base ink components of each modeling sample;
calculating the reciprocal of the spectral reflectivity of the modeling sample in the wavelength range of 400nm-700 nm;
and establishing a plane rectangular coordinate system by taking the wavelength as a horizontal coordinate and the reciprocal of the spectral reflectivity of the modeling sample as a vertical coordinate, and selecting the optimal waveband from the plane rectangular coordinate system.
Preferably, the relationship among the nonlinear term, the reciprocal of the spectral reflectance of each base ink, and the component ratio of each base ink is defined as follows:
Figure BDA0001724630110000031
in the formula,. epsilon. (lambda.) represents a nonlinear term, C1、C2、C3… and CnDenotes the component ratio, P, of each base inkC,1、PC,2、PC,3… and PC,nThe reciprocal of the spectral reflectance of each base ink is represented, n represents the number of base inks, and m represents a coefficient.
Preferably, the step of obtaining the reciprocal of the spectral reflectance of the mixed ink and the reciprocal of the spectral reflectance of each base ink and predicting the component ratio of each base ink according to the established mathematical model is followed by:
calculating the reciprocal of the spectral reflectivity of the mixed ink at each sampling wavelength according to the predicted component proportion, and solving the reciprocal of the spectral reflectivity to obtain the spectral reflectivity of the mixed ink;
comparing the obtained spectral reflectivity with the actual spectral reflectivity of the mixed ink, and obtaining the optimal m value according to the comparison result;
and calculating the component ratio of each base ink in the mixed ink according to the optimal m value and outputting the component ratio.
Preferably, a cubic spline interpolation method is used to obtain the optimal m value.
The present invention also provides an electronic device, comprising:
a processor adapted to implement the instructions, an
A storage device adapted to store a plurality of instructions, the instructions adapted to be loaded and executed by a processor to:
establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component proportion of each base ink and a nonlinear term according to the linear relation between the reciprocal of the spectral reflectance of the mixed ink and the component proportion of each base ink;
and acquiring the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink, and predicting the component proportion of each base ink according to the established mathematical model.
Preferably, the mathematical model is as follows:
Figure BDA0001724630110000041
in the formula, Pt(λ) represents the reciprocal of the spectral reflectance of the mixed ink, Pc,i(λ) represents the reciprocal of the spectral reflectance of each base ink, CiDenotes the component ratio of each base ink, ε (λ) denotes a nonlinear term, and n denotes the number of base inks.
Preferably, before establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component ratio of each base ink, and the nonlinear term, based on a linear relationship between the reciprocal of the spectral reflectance of the mixed ink and the component ratio of each base ink, the mathematical model includes:
and determining the wave band with the optimal linear correlation degree between the reciprocal of the spectral reflectivity of the modeling sample and the component proportion of the modeling sample.
Has the advantages that: according to the invention, a corresponding mathematical model is established according to the relation among the reciprocal of the spectral reflectivity of the mixed ink, the reciprocal of the spectral reflectivity of each base ink, the component proportion of each base ink and the nonlinear term, and the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink are further obtained, so that the component proportion of each base ink in the mixed ink is predicted. The method is simple and effective, and only has one undetermined parameter, thereby improving the efficiency and saving the time.
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FIG. 1 is a flow chart of a preferred embodiment of a method for predicting ink composition ratios based on reciprocal spectral reflectance according to the present invention.
Fig. 2 is a block diagram of an electronic device according to a preferred embodiment of the invention.
Detailed Description
The invention provides a method and equipment for predicting the proportion of ink components based on the reciprocal of spectral reflectance, and the invention is further described in detail below in order to make the purpose, technical scheme and effect of the invention clearer and clearer. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, a method for predicting ink composition ratios based on reciprocal spectral reflectance includes the steps of:
s1, establishing mathematical models of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component proportion of each base ink and the nonlinear terms according to the linear relation between the reciprocal of the spectral reflectance of the mixed ink and the component proportion of each base ink;
and S2, acquiring the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink, and predicting the component proportion of each base ink according to the established mathematical model.
The invention establishes a mathematical model in advance, wherein the mathematical model comprises four parameters of the reciprocal of the spectral reflectivity of the mixed ink, the reciprocal of the spectral reflectivity of each base ink, the component proportion of each base ink and a nonlinear term, thus, the component proportion of each base ink can be predicted only by acquiring the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink. The base inks are mixed in accordance with the component ratios of the respective base inks thus obtained, so that the objective ink can be obtained. Compared with the traditional method, the method saves a plurality of complicated steps, saves time and improves efficiency.
Preferably, the mathematical model is as follows:
Figure BDA0001724630110000061
in the formula, Pt(λ) represents the reciprocal of the spectral reflectance of the mixed ink, CiDenotes the component ratio, P, of each base inkc,i(λ) represents the reciprocal of the spectral reflectance of each base ink, r (λ) represents the spectral reflectance of each base ink, ∈ (λ) represents a nonlinear term, and n represents the number of base inks. From the above formula, the prediction CiThe corresponding mathematical model is as follows:
Figure BDA0001724630110000062
as can be seen from the above mathematical model, it is only necessary to obtain the reciprocal of the spectral reflectance of the mixed ink and the reciprocal of the spectral reflectance of each base ink to predict the component ratio of each base ink. For example, the mixed ink is obtained by mixing two base inks, which are the base ink 1 and the base ink 2, respectively. Then CiHas the following relationship: min c1×Pc,1(λ)+c2×Pc,2(λ)+ε(λ)-Pt(λ) wherein Pc,1(lambda) and Pc,2(λ) is the reciprocal of the spectral reflectance, P, of the base ink 1 and the base ink 2t(lambda) is the reciprocal of the spectral reflectance of the mixed ink, c1And c2It is the ratio of the components of the base ink 1 and the base ink 2 that are sought. The method has simple steps and greatly improves the efficiency.
Preferably, the spectral reflectance of the mixed ink and the spectral reflectance of each base ink are measured by a spectrophotometer. The spectrophotometer can accurately measure the spectral reflectivity of the mixed ink and the spectral reflectivity of each base ink, and then the spectral reflectivity is inverted, so that the inverse of the spectral reflectivity of the mixed ink and the inverse of the spectral reflectivity of each base ink can be obtained, and the component proportion of each base ink is predicted according to the mathematical model.
Preferably, step S1 is preceded by:
and determining the wave band with the optimal linear correlation degree between the reciprocal of the spectral reflectivity of the modeling sample and the component proportion of the modeling sample. This makes it possible to determine the optimum wavelength band for each base ink.
Preferably, the step of determining the waveband with the best linear correlation degree between the inverse spectral reflectance of the modeling sample and the component proportion of the modeling sample specifically comprises:
establishing a plurality of modeling samples, and recording the proportion of the base ink components of each modeling sample;
calculating the reciprocal of the spectral reflectivity of the modeling sample in the wavelength range of 400nm-700 nm;
and establishing a plane rectangular coordinate system by taking the wavelength as a horizontal coordinate and the reciprocal of the spectral reflectivity of the modeling sample as a vertical coordinate, and selecting the optimal waveband from the plane rectangular coordinate system.
Two base inks of four colors red and blue (i.e., base inks in table 1 below) commonly used in UV offset inks were mixed two by two in the given component ratio and subjected to proofing. The respective base ink mixing component ratios are shown in table 1 below. During proofing, the mass of each base ink is accurately weighed according to the table 1, then the base inks are fully mixed, and the mixed ink is mixed at 230g/m by utilizing an IGT (ink-jet printing) adaptability instrument2The sample is drawn on the white cardboard, and after the sample strips are fully dried, the spectral reflectivity of all the sample strips in the wavelength range of 400nm-700nm is measured by using a spectrophotometer. Preferably, in order to reduce experimental error, the spectral reflectance of each numbered spline is obtained by three measurements and averaging. The specific ratios of the samples are shown in table 1 below:
TABLE 1 Primary color ink mix ratio settings
Figure BDA0001724630110000081
In table 1, numbers T01, T02, and T12 are modeled samples of a four-color blue and four-color red-based ink mixed formulation prediction experiment; numbers T10, T11, T12, T13, and T14 are target samples, and the above samples are collectively referred to as experimental samples. The following results are obtained through experiments and calculation: the linear correlation coefficient of the reciprocal spectral reflectance of the modeled sample to the component ratio of the modeled sample is shown in table 2 below:
TABLE 2 wavelength band for modeling samples with optimal linear correlation of reciprocal spectral reflectance and component ratio
Wavelength of light 500nm 0.9997
R2 610nm 0.9950
As can be seen from table 2 above and from the definition of the correlation coefficient, the closer the value of the linear correlation coefficient is to 1, the closer the linear relationship between the two is. Then the best bands for modeling the sample are 500nm and 610 nm.
The optimal band can be determined from table 2 above, however the key to the invention is to determine the value of the non-linear term or coefficient m. How to determine the optimum m value and output the component ratio of each base ink according to the optimum m value will be described in detail below.
Preferably, the relationship among the nonlinear term, the reciprocal of the spectral reflectance of each base ink, and the component ratio of each base ink is defined as follows:
Figure BDA0001724630110000091
Figure BDA0001724630110000092
in the formula,. epsilon. (lambda.) represents a nonlinear term, C1、C2、C3… and CnDenotes the component ratio, P, of each base inkC,1、PC,2、PC,3… and PC,nThe reciprocal of the spectral reflectance of each base ink is represented, n represents the number of base inks, and m represents a coefficient. For example, the mixed ink is obtained by mixing two base inks, and the base ink 1 has the component ratio c1The base ink 2 has a component ratio of c2Then, according to the above formula:
Figure BDA0001724630110000093
through a plurality of experiments, the value of m is most suitable within 0.2 to 2. The optimum m value is determined by specific experiments below.
Preferably, step S2 is followed by:
s3, calculating the reciprocal of the spectral reflectivity of the mixed ink at each sampling wavelength according to the predicted component proportion, and solving the reciprocal of the spectral reflectivity to obtain the spectral reflectivity of the mixed ink;
s4, comparing the obtained spectral reflectivity with the actual spectral reflectivity of the mixed ink, and obtaining the optimal m value according to the comparison result;
and S5, calculating the component ratio of each base ink in the mixed ink according to the optimal m value and outputting the component ratio.
In the step S3, the component ratio of each base ink in the mixed ink is calculated by defining different m values, and the m values and the component ratios corresponding to each base ink are recorded. And predicting the reciprocal of the spectral reflectivity of the mixed ink at each sampling wavelength according to the component proportion of each base ink, and solving the reciprocal of the predicted spectral reflectivity to obtain the spectral reflectivity of the mixed ink in the optimal waveband.
In step S4, the true spectral reflectance of the mixed ink is obtained by a spectrophotometer. The actual spectral reflectance has a certain error from the obtained spectral reflectance predicted in step S3. The two are compared, for example, the difference between the two is calculated, and the m value corresponding to the minimum difference is set as the optimal m value.
Preferably, the error between the obtained spectral reflectance and the true spectral reflectance calculated in step S3 is measured by the root mean square error RMSE, and the color difference index DE is increased because the spectral reflectance cannot be directly shown through the image. Thus, the most suitable m value can be selected by the color difference indexes DE and RMSE.
Particularly, through experiments and establishment of corresponding coordinates, when m is 0.4, the average color difference index and the root mean square error of all samples in the experimental samples are minimum values (table 3), so that the value of the number m of the nonlinear terms is more suitable for being 0.4; the specific results of the results of predicting the proportions of the components of each base ink in the experimental sample are shown in table 4 below:
TABLE 3 evaluation of the component ratio prediction accuracy of the experimental samples (color difference calculation conditions: D65 illuminant/2 degree field)
Figure BDA0001724630110000101
TABLE 4 prediction of the proportions of the components of the four primary colors red (T02) of the experimental samples
Figure BDA0001724630110000102
Figure BDA0001724630110000111
As can be seen from table 4, when m in the experimental samples is 0.4, the component ratio prediction result of the red-based ink of each sample is very close to the actual ratio, and the error is 1.57%; in addition, table 4 shows the calculation results of the component ratios using the all band prediction. As can be seen, the method has obviously lower precision than the method provided by the invention. Although the mathematical models of the two methods are similar, the parameter setting is also similar, and the least square method is adopted for calculation, the full-waveband prediction has no strict linear correlation relationship between most wavebands and the component proportion of each base ink, and the method only adopts the waveband with the optimal linear correlation degree for calculation, so that the error is greatly reduced.
In step S5, the optimum value m obtained by the analysis is substituted into the mathematical model to predict the current ratio of each base ink component, and the ratio is output. In this way, the optimum ratio of the components of each base ink can be obtained. Thereby obtaining the target ink according to the optimal proportion of each base ink component.
Preferably, the reciprocal of the spectral reflectance at each sampling wavelength is obtained using a cubic spline interpolation method. The Cubic Spline Interpolation (Spline Interpolation) is called as Spline Interpolation for short, and is a smooth curve passing through a series of shape value points.
According to the experiment, the method provided by the invention is simple and effective, and the efficiency is greatly improved.
Referring to fig. 2, the present invention also provides an electronic device 10, which includes:
a processor 110 adapted to implement instructions, an
A storage device 120 adapted to store a plurality of instructions adapted to be loaded and executed by the processor 110:
establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component proportion of each base ink and a nonlinear term according to the linear relation between the reciprocal of the spectral reflectance of the mixed ink and the component proportion of each base ink;
and acquiring the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink, and predicting the component proportion of each base ink according to the established mathematical model.
Preferably, the mathematical model is as follows:
Figure BDA0001724630110000121
in the formula, Pt(λ) represents the reciprocal of the spectral reflectance of the mixed ink, Pc,i(λ) represents the reciprocal of the spectral reflectance of each base ink, CiDenotes the component ratio of each base ink, ε (λ) denotes a nonlinear term, and n denotes the number of base inks.
Preferably, before the mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component ratio of each base ink, and the nonlinear term is established based on a linear relationship between the reciprocal of the spectral reflectance of the mixed ink and the component ratio of each base ink, the mathematical model includes:
and determining the wave band with the optimal linear correlation degree between the reciprocal of the spectral reflectivity of the modeling sample and the component proportion of the modeling sample.
The details of the electronic device 10 are described in detail in the above steps, and are not described herein.
It is to be understood that the invention is not limited to the examples described above, but that modifications and variations may be effected thereto by those of ordinary skill in the art in light of the foregoing description, and that all such modifications and variations are intended to be within the scope of the invention as defined by the appended claims.

Claims (8)

1. A method for predicting the proportion of ink components based on the reciprocal of spectral reflectance is characterized by comprising the following steps:
establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component proportion of each base ink and a nonlinear term according to the linear relation between the reciprocal of the spectral reflectance of the mixed ink and the component proportion of each base ink;
obtaining the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink, and predicting the component proportion of each base ink according to the established mathematical model;
the mathematical model is as follows:
Figure FDA0002765580380000011
in the formula, Pt(λ) represents the reciprocal of the spectral reflectance of the mixed ink, Pc,i(λ) represents the reciprocal of the spectral reflectance of each base ink, CiDenotes the composition ratio of each base ink, ∈ (λ) denotes a nonlinear term, and n denotes the number of base inks;
before establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component ratio of each base ink, and the nonlinear term according to the linear relationship of the reciprocal of the spectral reflectance of the mixed ink and the component ratio of each base ink, the mathematical model includes: and determining the wave band with the optimal linear correlation degree between the reciprocal of the spectral reflectivity of the modeling sample and the component proportion of the modeling sample.
2. The method for predicting the proportion of the components of the ink based on the reciprocal of the spectral reflectance according to claim 1, wherein the step of determining the two wavelength bands in which the degree of the linear correlation between the reciprocal of the spectral reflectance of the modeled sample and the proportion of the components of the modeled sample is the best comprises:
establishing a plurality of modeling samples, and recording the proportion of the base ink components of each modeling sample;
calculating the reciprocal of the spectral reflectivity of the modeling sample in the wavelength range of 400nm-700 nm;
and establishing a plane rectangular coordinate system by taking the wavelength as a horizontal coordinate and the reciprocal of the spectral reflectivity of the modeling sample as a vertical coordinate, and selecting the optimal waveband from the plane rectangular coordinate system.
3. The method of predicting the ink component ratio based on the reciprocal of the spectral reflectance according to claim 1, wherein the relationship among the nonlinear term, the reciprocal of the spectral reflectance of each base ink, and the component ratio of each base ink is defined as follows:
Figure FDA0002765580380000021
in the formula,. epsilon. (lambda.) represents a nonlinear term, C1、C2、C3… and CnDenotes the component ratio, P, of each base inkC,1、PC,2、PC,3… and PC,nThe reciprocal of the spectral reflectance of each base ink is represented, n represents the number of base inks, and m represents a coefficient.
4. The method of predicting the proportions of the components of the ink based on the reciprocal of the spectral reflectance according to claim 3, wherein the step of obtaining the reciprocal of the spectral reflectance of the mixed ink and the reciprocal of the spectral reflectance of each of the base inks and predicting the proportions of the components of each of the base inks based on the established mathematical model is followed by:
calculating the reciprocal of the spectral reflectivity of the mixed ink at each sampling wavelength according to the predicted component proportion, and solving the reciprocal of the spectral reflectivity to obtain the spectral reflectivity of the mixed ink;
comparing the obtained spectral reflectivity with the actual spectral reflectivity of the mixed ink, and obtaining the optimal m value according to the comparison result;
and calculating the component ratio of each base ink in the mixed ink according to the optimal m value and outputting the component ratio.
5. The method for predicting the proportions of the components of the ink based on the reciprocal of the spectral reflectance according to claim 4, wherein the reciprocal of the spectral reflectance at each sampling wavelength is obtained by a cubic spline interpolation method.
6. An electronic device, comprising:
a processor adapted to implement the instructions, an
A storage device adapted to store a plurality of instructions, the instructions adapted to be loaded and executed by a processor to:
establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the component proportion of each base ink and a nonlinear term according to the linear relation between the reciprocal of the spectral reflectance of the mixed ink and the component proportion of each base ink;
and acquiring the reciprocal of the spectral reflectivity of the mixed ink and the reciprocal of the spectral reflectivity of each base ink, and predicting the component proportion of each base ink according to the established mathematical model.
7. The electronic device of claim 6, wherein the mathematical model is as follows:
Figure FDA0002765580380000031
in the formula, Pt(λ) represents the reciprocal of the spectral reflectance of the mixed ink, Pc,i(λ) represents the reciprocal of the spectral reflectance of each base ink, CiDenotes the component ratio of each base ink, ε (λ) denotes a nonlinear term, and n denotes the number of base inks.
8. The electronic device according to claim 6, wherein before establishing a mathematical model of the reciprocal of the spectral reflectance of the mixed ink, the reciprocal of the spectral reflectance of each base ink, the proportion of the components of each base ink, and the nonlinear term according to a linear relationship between the reciprocal of the spectral reflectance of the mixed ink and the proportion of the components of each base ink, the mathematical model comprises:
and determining the wave band with the optimal linear correlation degree between the reciprocal of the spectral reflectivity of the modeling sample and the component proportion of the modeling sample.
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