An optimization method for the Clapper-Yule spectrum prediction model of digital printing

Abstract

The present invention discloses a method for optimizing a digital printing monochrome Clapper-Yule spectrum prediction model. S1: using a microelement method to theoretically model ink droplet oscillation, fully considering the stress conditions during the oscillation spreading process; S2: numerically solving and simulating the theoretical oscillation model, and comparing and verifying; S3: after the feasibility of the morphology is preliminarily verified by simulation, the accuracy of the model is finally determined by experimental fitting. S4: based on the spreading morphology of a single ink droplet, a monochrome Clapper-Yule spectrum prediction model is established, and the feathering effect and printing accuracy problems in field printing are taken into account in the prediction model; S5: experimental design and experimental comparison of the spectrum prediction model; the present invention establishes a monochrome Clapper-Yule optimization model based on the spreading morphology of a single ink droplet in field printing, combined with the feathering effect of printing, and performs a comprehensive optimization and correction on the monochrome spectrum prediction in physical morphology, so as to obtain a more accurate prediction result of the spectral reflectance of printed products.

Description

Technical Field

[0001] The invention relates to the field of integrated technology of fluidics and spectroscopy, and in particular to a method for optimizing a monochrome Clapper-Yule spectrum prediction model based on the spreading morphology of a single ink droplet in inkjet printing. Background Art

[0002] In modern digital inkjet printing, true color reproduction is the key to ensuring the quality of printed products. In order to further improve the true color reproduction, it is particularly important to develop and apply accurate halftone spectrum prediction models. Halftone print images are presented on the paper surface in the form of ink dots, and the spectral reflectance of the image ultimately depends on the morphological characteristics of the ink dot spread and the optical properties of light transmitted between the ink dot, paper, and air. Therefore, in-depth research on the microscopic spreading morphology of ink droplets on paper and the light propagation characteristics under this morphology not only helps to optimize the spectral reflectance prediction, but is also a key step to ensure that the quality and visual effects of printed products meet the expected standards.

[0003] Significant progress has been made in the study of ink droplet spreading. The main research contents focus on the following categories: theoretical modeling of droplet impacting the wall, exploration of the formation process of deposited ink droplets, and exploration of the contact angle of droplet impacting the wall. Existing methods explore the deposition behavior of droplets and ink droplets after they hit the solid wall, and discuss the influence of some ink properties and printing parameters on the printing quality. However, they are insufficient in exploring the oscillation spreading process of a single ink droplet in solid printing and simulating the spreading morphology.

[0004] Regarding the prediction of printed product colors, existing studies are based on the split-program Clapper-Yule spectral reflectance model, combined with specific experiments to correct the transmittance of the ink layer, the dot area ratio of the halftone print, etc., in order to continuously optimize the prediction accuracy of the spectral model. However, the actual ink droplet spreading morphology is not combined, and the ink droplets are always treated as standard cylinders in the spreading morphology, resulting in a certain difference between the spectral prediction results and the actual measured results.

[0005] The monochrome Clapper-Yule spectral prediction model based on the spreading morphology of a single ink droplet in solid printing proposed in this invention mainly focuses on the spreading of a single ink droplet, and explores its spreading process and spreading morphology on the printed paper. After determining the true morphology, combined with the program-based Clapper-Yule spectral reflectance model, the monochrome spectral reflectance prediction optimization of halftone digital prints is performed by fully considering the feathering effect and printing accuracy in the actual printing process. This new optimization model significantly improves the prediction accuracy of monochrome prints, and provides a more comprehensive and accurate perspective and method for printing color prediction. Summary of the invention

[0006] The present invention provides a method for optimizing a printed matter spectral reflectance prediction model according to the actual spreading morphology of a single ink droplet, and improves the accuracy of existing monochrome printed matter spectral reflectance prediction based on actual printing parameters.

[0007] The technical solution of the present invention is as follows:

[0008] A digital printing monochrome Clapper-Yule spectrum prediction model optimization method, the steps are as follows:

[0009] Step 1: Use the microelement method to model the ink droplet oscillation theory, fully consider the force conditions during the oscillation spreading process, and establish a theoretical model of the ink droplet spreading morphology;

[0010] Step 2: Solve the theoretical model numerically and by simulation, and compare and verify;

[0011] Step 3: After preliminary verification of the feasibility of the morphology, the accuracy of the model is finally determined through experimental fitting.

[0012] Step 4: Based on the spreading morphology of a single ink droplet, a monochrome Clapper-Yule spectrum prediction model is established, and the feathering effect and printing accuracy in solid printing are taken into account in the prediction model; the printing accuracy is mainly reflected in the dot area rate of the printed product and the number of ink dots per inch (dpi) of the printer;

[0013] Step 5: Experimental design and experimental comparison of spectral prediction model.

[0014] Furthermore, the specific method of Step 1 is:

[0015] Step 1.1: In order to make the ink droplets spread stably on the paper without splashing or rebounding, the dimensionless parameter K defined by Kappel and Mundo is used to constrain the physical parameters of the ink droplets;

[0016] Step 1.2: Determine a widely existing oscillating spreading form. The existing forms of droplet impacting the wall and spreading are mostly spherical or spherical;

[0017] Step 1.3: According to the shape determined in Step 1.2, perform force analysis. The forces during spreading oscillation are as follows: surface tension, internal pressure, viscosity and inertia;

[0018] Furthermore, the specific method of Step 2 is:

[0019] Step 2.1: There is no fixed analytical solution for the ink droplet oscillation differential equation. With the help of numerical simulation software, the theoretical numerical solution of the equation is solved;

[0020] Step 2.2: In the simulation solution, multiphase is described by the VOF method. According to the VOF method, the continuity equation and the flow momentum balance equation of the fluid are derived, and the simulation solution is obtained; wherein, multiphase refers to the fluid movement in which two or more different phases of matter exist at the same time;

[0021] Step 2.3: Compare the spreading radius and height of the theoretical numerical solution and the simulation solution; and compare the theoretical spreading morphology and the simulation spreading morphology; the theoretical spreading morphology is determined by the S1.2 model selection, and the simulation spreading morphology is directly obtained from the simulation process.

[0022] Furthermore, the specific method of Step 3 is:

[0023] Step 3.1: Based on the established spherical-segment model, the peak height and equilibrium radius of a single ink droplet in the spreading equilibrium state are measured, and the spreading contact angle is continuously changed to perform fitting verification of the spreading morphology;

[0024] Furthermore, the specific method of Step 4 is:

[0025] Step 4.1: According to the spreading morphology, derive the continuous change of the thickness of the halftone single ink droplet ink layer;

[0026] Step 4.2: Derive the relationship between the ink drop volume and the spreading area according to the spreading morphology, and measure the ink drop spreading area. Combine the two areas to derive the feathering effect of the print;

[0027] Step 4.3: Use the wavelength function Replace the definition of short-range light in the classic split-program Clapper-Yule model;

[0028] Furthermore, the specific method of Step 5 is:

[0029] Step 5.1: Since the experiment is a single ink droplet spreading form, in order to eliminate the influence of interaction between ink droplets, the monochrome spectral reflection prediction experimental conditions should ensure that there is no adhesion between ink droplets. According to the actual printing dpi and probability calculation, the maximum dot area rate used for testing is calculated;

[0030] Step 5.2: Calculate the spectral reflectance of the new model and the classic Clapper-Yule model by selecting parameters, and draw the spectral reflectance curve for comparison;

[0031] Step 5.3: Convert the spectral reflectance to the CIE1976Lab uniform color space and calculate the color difference between the predicted value of each model and the measured value using the color difference formula ;

[0032] The beneficial effects of the present invention are as follows:

[0033] The present invention establishes a monochrome Clapper-Yule optimization model based on the spreading morphology of a single ink droplet in solid printing and the feathering effect of printing. The model performs a comprehensive optimization and correction on the monochrome spectrum prediction in physical form to obtain a more accurate prediction result of the spectral reflectance of printed products, which greatly promotes the development of digital printing technology, especially in color management and quality control. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the force analysis diagram of the microelement method of the present invention;

[0035] Figure 2 This is a diagram of a spherical segment type oscillation model of the present invention;

[0036] Figure 3 Comparison between the simulated and theoretical morphologies of ink droplets at a contact angle of 30°;

[0037] Figure 4 Comparison between the simulated and theoretical morphologies of ink droplets at a contact angle of 40°. DETAILED DESCRIPTION

[0038] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solution of the present invention.

[0039] A digital printing monochrome Clapper-Yule spectrum prediction model optimization method, the specific steps are as follows:

[0040] Step 1: Use the microelement method to analyze the force of the ink droplet oscillation spreading process, establish the theoretical model of the ink droplet spherical shape spreading morphology, and simulate the morphology of the ink droplet spreading on the hydrophobic coated paper, such as Figure 2 As shown;

[0041] At a certain moment of oscillation, the expansion radius of the ink drop in the horizontal direction is r, and the height is h. The force analysis of the ink drop is carried out using the microelement method, as shown in the following figure: Figure 1 As shown, the differential angle of the differential element is , the coordinates are ;

[0042] The force balance equation of the ink droplet in the r-axis direction is:

[0043] ;

[0044] in is the surface tension, is the static pressure, is the viscosity, is the inertial force.

[0045] Step 1.1: The force acting on the microelement in the circumferential direction, its projection force on the r-axis, and the contact force between the ink droplet and the paper surface together constitute the entire surface tension. The surface tension of the entire ink droplet is obtained by integral calculation:

[0046] ;

[0047] Step 1.2: The pressure projection of the surface tension on the inside and outside of the liquid film plus the static pressure projection along the circumferential direction:

[0048] ;

[0049] Step 1.3: Assume that the velocity gradient in the r-axis direction changes linearly, integrate the spherical ink droplet on (0, h), and obtain the projection of the resultant viscous force of the ink droplet on the r-axis:

[0050] ;

[0051] Step 1.4: Assume that during the oscillation, the change of r is linearly distributed from the center to the edge, and the change of velocity and acceleration is linearly distributed from the center to the edge. According to Newton's second law, the inertial force on the droplet is:

[0052] ;

[0053] The parameters in the above force analysis are shown in Table 1;

[0054] ;

[0055] Step 2: With the help of numerical simulation and emulation software, solve the ink droplet oscillation differential equation and simulate the actual printing process of the ink droplet to derive the equilibrium spreading radius and height; according to the radius and height, draw the spreading shape and compare it with the theoretical spherical segment model.

[0056] Step 2.1: Use the fourth-order Runge-Kutta method in MATLAB to solve the differential equation oscillation and calculate the initial parameters of the droplet. , select the parameters of maximum spread, minimum spread, and equilibrium position and substitute them into the calculation respectively, so as to select the most accurate spreading radius and spreading height.

[0057] Step 2.2: Use Geometry software to construct geometric bodies and meshes. The computational domain is a cuboid divided by hexahedral meshes. The size of each mesh is , multiphase is described by VOF method, continuity equation:

[0058] ;

[0059] Momentum balance for fluid flow:

[0060] ;

[0061] Represents the gradient of a vector.

[0062] The PISO algorithm is used to couple the droplet velocity and pressure in the momentum equation, and the slip boundary condition is adopted with a shear stress of 0 Pa.

[0063] According to the actual printing situation, the simulated ink drop parameter settings are shown in Table 2:

[0064] ;

[0065] Table 2 shows the setting and selection of parameters in the ink droplet oscillation differential equation in the embodiment. The calculation process is performed by simulation software, and only the parameters need to be substituted.

[0066] Step 2.3: Table 3 shows the comparison between the theoretical and simulation results of the oscillation spreading radius in the equilibrium state;

[0067] ;

[0068] Step 2.4: Figure 3 , Figure 4 The comparison between the simulated ink droplet morphology and the theoretical morphology is demonstrated when the deviation of the equilibrium spreading radius is small, such as at contact angles of 30° and 40°; the results show that at this contact angle, the ink droplet morphology is highly consistent with the theoretically predicted morphology curve.

[0069] Step 3: After verifying the feasibility of the spherical segment shape through simulation in Step 2, verify the accuracy of the spherical segment model through experiments.

[0070] Step 3.1: Use a microscopic ink droplet observer to observe the radius of a single ink droplet spread, and use a spiral micrometer to measure the peak height of the ink droplet in the balanced spreading state. Given the spreading radius and spreading peak height, and assuming that the ink droplet volume is known and the spherical-segment model is feasible, change different contact angles and fit the spherical-segment model. The experimental results show that the spherical-segment model is more accurate when the contact angle is 30°, which is basically consistent with the simulation results. It is determined that under this experimental condition, the spreading morphology of a single ink droplet is a spherical-segment type, and the contact angle is 30°; this step is simulated and fitted by numerical software, and the verification data is exported from the numerical software.

[0071] Step 4: According to the spreading morphology of spherical ink droplets, a monochrome Clapper-Yule spectrum prediction model is established, taking into account the feathering effect and printing accuracy during printing.

[0072] Step 4.1: The ink droplet spreads into a spherical segment model, and the contact angle of the ink droplet is , and its spreading area on the paper is recorded as , and the volume of a single ink droplet is , under ideal conditions (without considering feathering), the spreading radius , consider a spherical ink droplet spreading on a plane, and its thickness decreases uniformly from the vertex of the spherical droplet to the surroundings. To simplify the description, assume that the thickness change in this space is a plane change observed from a cross section, then the continuously changing halftone dot ink layer thickness is:

[0073] ;

[0074] The relationship between the droplet volume, spreading radius and contact angle is as follows:

[0075] ;

[0076] In an ideal halftone print, the ink layer transmittance is It is a constant related to wavelength. The formula for calculating the transmittance of the ink layer in actual printing is:

[0077] ;

[0078] in It is the ink reflectivity when the measured dot area ratio a=1; represents the probability of light entering the measuring instrument; is the initial reflectivity of the printed surface; is the reflectivity of the print-air interface; is the reflectivity of the blank paper when the dot area ratio a=0. Substituting a=0 into the classic monochrome halftone Clapper-Yule model, the calculation formula is as follows:

[0079] ;

[0080] Represents the spectral reflectance of white paper;

[0081] According to Beer's law, the ink layer thickness directly affects the ink transmittance. In this embodiment, since the spreading shape of a single ink droplet on the paper is a spherical segment, the transmittance of the halftone dot is:

[0082] ;

[0083] Step 4.2: The penetration effect of ink droplets on hydrophobic coated paper is negligible, calculate the spreading radius , the actual observed (blurred edge) measured spreading radius is , then the non-stick feathering effect e of a single ink droplet is:

[0084] ;

[0085] The printing dot area ratio parameter is , then the non-sticky real dot area rate is:

[0086] ;

[0087] Based on the classic Clapper-Yule spectrum prediction model, a single ink droplet The multiple reflected lights on the surface are integrated to obtain the monochromatic Clapper-Yule spectrum prediction model under the influence of comprehensive factors:

[0088] ;

[0089] The first formula, represents the spectral reflectance, the first term of the second formula is the long-distance light, is the long-distance light coefficient, and the second term is the short-distance light coefficient. is the short-path light coefficient, which adds the short-path light to the long-path light.

[0090] Represents the transmittance of the ink layer that varies with the wavelength band; is the relationship between ink layer thickness, radius and contact angle; is the maximum ink layer thickness of a single ink drop; function By using cubic B-spline fitting, the wavelength-based range coefficient curve of the monochrome ink under this printing condition is obtained; in the fitting process, since the interval is 10nm, the step size of the fitting parameters is exactly 1nm.

[0091] Step 5: Select experimental parameters, compare the new model (monochromatic Clapper-Yule spectral prediction model) and the classic split-range Clapper-Yule spectral prediction model, and calculate the color difference from the spectral reflectance curve in the monochromatic case. Since Step 1- Step 3 are all verifying the spreading morphology of a single ink droplet, the monochromatic spectral model experimental verification should ensure that there is no adhesion between ink droplets.

[0092] Step 5.1: The test sample used is the standard sample IT8 / 7.3cmyk (eye one) with 946 color blocks, the printing paper is Fasson coated paper / AP104 / 60g, the printing ink is UV solar ink KGT-82, and the printer dpi is 1200. Specular reflection factor, according to the Fresnel equation , is the multiple internal reflection factor of light in the paper base, based on the paper selection . Measuring equipment: x-rite i1 pro2; using CIE standard In this embodiment, the new model is mainly used to verify the color prediction effect of monochrome halftones printed by CMY three-color inks separately, and the visible light is in the band of 380nm-730nm.

[0093] Step 5.2: Probabilistically calculate the theoretical ink dot adhesion under a fixed dot area ratio to guide the selection of the dot area ratio for the test monochrome color block. dpi is the number of dots per inch, the ink dot spreading radius is 0.018mm, the number of ink dots per unit area is n, 100 pixels are defined as the unit area, and the monochrome measurement color block is evenly distributed in the unit area. The dot area ratio can be defined as:

[0094] ;

[0095] In fact, we only need to calculate the maximum number of ink dots n that can be accommodated in the unit area of ​​100 pixels without adhesion, and we can theoretically calculate the maximum dot area ratio without adhesion between ink dots. Using the Euclidean plane grid placement problem to calculate, it is found that a maximum of 25 ink dots can be placed, so the theoretical maximum non-adhesive dot area ratio is 56.8%. Therefore, the experimental monochrome color block is selected below the dot area ratio of 56.8%, which can ensure the consistency of the single ink droplet spreading model (no adhesion between ink drops) and the monochrome spectrum model.

[0096] Step 5.4: Spectral prediction model calculation, first determine a to be 20% and 40%, , Substitute into Step 5.1 to calculate . Then by , , Calculate the transmittance of each ink layer , the contact angle of a single ink droplet is selected to be 30°, and the feathering effect e is 5%. Substitute the data after cubic B-spline fitting. Substitute the above parameters into the monochromatic spectrum prediction model according to the calculated wavelength band of 380nm-730nm to obtain the spectral reflectance of the example of the present invention.

[0097] Step 5.5: Convert the spectral reflectance to the CIE1976Lab uniform color space and calculate the difference between the predicted values ​​of each model and the measured values ​​using the color difference formula , as shown in Table 4;

[0098] ;

[0099] The method of the present invention is used to predict the spectral reflectance of digital prints, and it can be seen that the color difference of the new model is significantly reduced compared with the classic model. This shows that in a monochrome halftone image, when there is no adhesion between ink droplets, the actual spreading morphology of a single ink droplet will directly change the dot area ratio and ink layer transmittance in the spectral prediction, and then directly affect the spectral reflectance and color difference value, and the actual feathering effect has a greater impact on the spectral reflectance.

[0100] The above embodiments are only preferred embodiments of the present invention and are not limitations of the technical solutions of the present invention. Any technical solution that can be implemented on the basis of the above embodiments without creative work should be deemed to fall within the scope of protection of the patent of the present invention.

Claims

1. A digital printing monochrome Clapper-Yule spectrum prediction model optimization method, characterized in that: The steps include: S1: Use the microelement method to analyze the force of the ink droplet oscillation and spreading process, and establish a theoretical model of the ink droplet spreading morphology; The specific process of S1 is as follows: S1.1: The dimensionless parameter K defined by Kappel and Mundo is used to constrain the physical properties of the ink droplets; S1.2: Determine the oscillation and spreading morphology of the ink droplets; S1.3: Based on the shape determined in S1.2, use the differential element method to perform force analysis, including: surface tension, internal pressure, viscous force and inertial force, and derive the differential equation of ink drop oscillation; At a certain moment of oscillation, the expansion radius of the ink droplet in the horizontal direction is r, and the height is h. The force analysis of the ink droplet is carried out using the differential element method. The differential angle of the differential element is dα, and the coordinates are (r d ,h d ); The force balance equation of the ink droplet in the r-axis direction is: F o,σ1，r +F p，r +F τ，r +F t，r =0 Among them, F σ,σ1,r is the surface tension, F p,r is the static pressure, F τ,r is the viscosity force, F t,r is the inertial force; The force acting on the microelement in the circumferential direction, its projection force on the r-axis, and the contact force between the ink droplet and the paper surface together constitute the entire surface tension. The surface tension of the entire ink droplet is calculated by integration: The pressure projection of surface tension on the inside and outside of the liquid film plus the static pressure projection along the circumferential direction: Assuming that the velocity gradient in the r-axis direction changes linearly, the spherical ink droplet is integrated on (0, h), and the projection of the resultant viscous force of the ink droplet on the r-axis is obtained as follows: Assuming that during the oscillation process, the change of r is linearly distributed from the center to the edge, and the change of velocity and acceleration is linearly distributed from the center to the edge, according to Newton's second law, the inertial force on the droplet is: Among them, σ represents the surface tension coefficient, l represents the maximum arc length of the rh plane, θ represents the contact angle of the ink droplet, R represents the Rh plane radius of the great circle, r represents the diffusion radius, h represents the spreading height, ρ represents the droplet density, and μ represents the droplet viscosity; S2: Numerical solution and simulation solution of the theoretical model of ink droplet spreading morphology, and comparative verification; S3: After preliminary verification of the feasibility of the morphology, the accuracy of the model is finally determined through experimental fitting; S3.1: Based on the established theoretical model of ink droplet spreading morphology, the peak height and spreading radius of a single ink droplet in the spreading equilibrium state are measured, and the spreading contact angle is continuously changed to perform fitting verification of the spreading morphology; S4: Establish a monochrome Clapper-Yule spectrum prediction model based on the single ink droplet spreading morphology, feathering effect, and printing accuracy; The specific process of S4 is as follows: S4.1: derive the continuous change of the thickness of the halftone single ink droplet according to the spreading morphology; The ink droplet spreads as a spherical segment model, the contact angle of the ink droplet is θ, and its spreading area on the paper is recorded as S dot , and the volume of a single ink droplet is V0. Under ideal conditions, the spreading radius Consider a spherical ink droplet spreading on a plane, and its thickness decreases evenly from the vertex of the spherical droplet to the surrounding areas; to simplify the description, the change in thickness in space is assumed to be a plane change observed from a cross section, then the thickness of the continuously changing halftone dot ink layer is: S4.2: According to the spreading morphology, the relationship between the ink drop volume and the spreading area is derived, and the ink drop spreading area is measured, and the feathering effect of the print is derived by combining the two areas; The relationship between the droplet volume, spreading radius and contact angle is as follows: In an ideal halftone print, the ink layer transmittance t(λ) is a constant related to the wavelength. The formula for calculating the ink layer transmittance in actual printing is: Where R i is the ink reflectivity when the measured dot area ratio a=1; K represents the probability of light entering the measuring instrument; r s is the initial reflectivity of the printed surface; r i is the reflectivity of the printed matter-air interface; r g is the reflectivity of the blank paper base when the dot area ratio a=0. Substituting a=0 into the classic monochrome halftone Clapper-Yule model, the calculation formula is as follows: R w Represents the spectral reflectance of white paper; According to Beer's Law, the thickness of the ink layer directly affects the ink transmittance. Since the spread of a single ink drop on paper is a spherical shape, the transmittance of the halftone dot is: The penetration effect of ink droplets on hydrophobic coated paper can be ignored. The spreading radius r0 is calculated. The actual observed and measured spreading radius is r c , then the non-stick feathering effect e of a single ink droplet is: The printing dot area ratio parameter is a p , then the non-sticky real dot area rate is: a=a p (1+e) S4.3: Use the wavelength function b(λ) to replace the definition of short-range light in the classical split-program Clapper-Yule model; S4.4: Substitute all the results in S4.1-S4.3 into the classic Clapper-Yule model to establish the monochromatic Clapper-Yule spectrum prediction model; According to the classic Clapper-Yule spectrum prediction model, the multiple reflected lights on a single ink droplet 0-r0 are integrated to obtain the monochromatic Clapper-Yule spectrum prediction model under the influence of comprehensive factors: In the first formula, R(λ) represents the spectral reflectance, the first term of the second formula is the long-distance light, (1-b(λ)) is the long-distance light coefficient, and the second term is the short-distance light, b(λ) is the short-distance light coefficient, and the short-distance light is added to the long-distance light; t(λ) represents the ink layer transmittance that varies with the wavelength; D(x,θ) is the relationship between the ink layer thickness and the radius and contact angle; D max is the maximum ink layer thickness of a single ink drop; S5: Experimental design and experimental comparison of the monochromatic Clapper-Yule spectrum prediction model.

2. The digital printing monochrome Clapper-Yule spectrum prediction model optimization method according to claim 1, characterized in that: The specific process of S2 is as follows: S2.1: Using numerical simulation software, obtain the theoretical numerical solution of the ink droplet oscillation differential equation; S2.2: Use simulation software to simulate the actual printing process of ink droplets, derive the continuity equation and the flow momentum balance equation of the fluid according to the VOF method, and obtain the simulation solution, and then simulate the oscillation and spreading of ink droplets; S2.3: Compare the spreading radius, height, and spreading shape of the theoretical numerical solution and the simulation solution.

3. The digital printing monochrome Clapper-Yule spectrum prediction model optimization method according to claim 1, characterized in that: The specific process of S5 is as follows: S5.1: According to the actual printed dpi and probability calculation, the maximum dot area rate used for testing is obtained; S5.2: Calculate the spectral reflectance of the monochromatic Clapper-Yule spectral prediction model and the classic split-program Clapper-Yule model by selecting parameters, and draw spectral reflectance curves for comparison; S5.3: Convert the spectral reflectance to the CIE1976Lab uniform color space and calculate the color difference ΔE between the predicted value of each model and the measured value using the color difference formula * ab.

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