A full-color gamut structural color prediction and reproduction method based on multi-level micro-nano structures

Abstract

This application discloses a method for full-gamut structural color prediction and reproduction based on multi-level micro / nano structures. The method first establishes a multi-dimensional mapping relationship between the proportion of structural color primaries and the spectral reflectance of the predicted color. Then, it constructs a forward model for structural color prediction and a reverse model for structural color ratio prediction, achieving full-gamut color prediction and reproduction for any color and any tone. This is the first of its kind in the field of structural color research and has broad application prospects.

Description

Technical Field

[0001] This application relates to the technical field of spectral display, and in particular to a method for full-gamut structural color prediction and reproduction based on multi-level micro-nano structures. Background Technology

[0002] Structural colors hold the promise of enabling inkless printing and revolutionizing color production. They offer advantages in durability, high saturation, and high brightness, and can be widely applied in anti-counterfeiting, textiles, construction, high-density optical data storage, and virtual reality interaction. However, due to the highly complex color-forming mechanism of natural structural colors, although many researchers have generated monochromatic structural colors using surface microstructure processing techniques, generating full-color structural colors through micro / nanostructures remains an unsolved problem. Existing research methods for generating structural colors by adjusting micro / nanostructure parameters cannot reproduce all colors within the color gamut. The generation methods for structural color primary colors have not been systematically studied, a structural color prediction and reproduction model has not been established, and the goal of generating full-gamut structural colors through primary color mixing has not yet been achieved.

[0003] To address the above issues, it is necessary to propose a color modulation mechanism based on multi-level micro / nano structures, conduct systematic research on the establishment of a full-gamut structural color prediction and reproduction model and its solution algorithm, and realize full-gamut color prediction and reproduction of arbitrary colors and tones. Summary of the Invention

[0004] In view of this, this application provides a method for full-gamut structural color prediction and reproduction based on multi-level micro-nano structures, which can achieve accurate prediction and reproduction of structural colors of arbitrary tones.

[0005] This application provides a method for full-gamut structural color prediction and reproduction based on multi-level micro / nano structures, including:

[0006] A predictive model is established based on the KM model to establish the corresponding relationship between the proportion of primary colors in the mixed structural color and the spectral reflectance of the predicted color.

[0007] An optimization algorithm is used, and based on the prediction model, an inverse model of the spectral reflectance of the target color and the proportion of primary colors in the mixing mechanism is obtained;

[0008] Based on the inverse model, the spectral difference between the spectral reflectance of the target color and the spectral reflectance of the predicted color is obtained;

[0009] Based on the spectral difference, the optimal spectral reflectance for the predicted color is obtained.

[0010] Optionally, the specific process of building a prediction model based on the KM model is according to the formula,

[0011]

[0012] K is the absorption coefficient of the structural color unit, S is the scattering coefficient of the structural color unit, and r is the spectral reflectance of the predicted color.

[0013] Optionally, the specific process of obtaining the inverse model is according to the formula,

[0014] f (m) =f (t) +Φc;

[0015] in Φ is the identity matrix for the three primary colors, and c = [c1, c2, c3]. T This is a column vector representing the proportions of the structural color primary colors.

[0016] Alternatively, the spectral difference can be obtained using interior point algorithms, effective set algorithms, sequential quadratic programming algorithms, genetic algorithms, and simulated annealing algorithms.

[0017] Optionally, the optimal spectral reflectance is obtained according to the formula.

[0018] c = (DΦ) -1 D(f (s) -f (t) ).

[0019] The above-described method for full-gamut structural color prediction and reproduction based on multi-level micro-nano structures establishes a multi-dimensional mapping relationship between the structural color primary color ratio and the spectral reflectance of the predicted color, constructs a forward model for structural color prediction and a reverse model for structural color ratio prediction, and realizes full-gamut color prediction and reproduction of any color and any tone. Attached Figure Description

[0020] The technical solution and other beneficial effects of this application will become apparent from the following detailed description of specific embodiments in conjunction with the accompanying drawings.

[0021] Figure 1 This is a three-dimensional schematic diagram of a multi-level micro / nano structure provided in an embodiment of this application;

[0022] Figure 2 This is a three-dimensional stereoscopic diagram of frequency modulation of a structural color rendering unit provided in an embodiment of this application;

[0023] Figure 3 This is a schematic diagram of the frequency modulation plane of a structural color rendering unit provided in an embodiment of this application;

[0024] Figure 4 This is a three-dimensional stereoscopic diagram of amplitude modulation of a structural color rendering unit provided in an embodiment of this application;

[0025] Figure 5 This is a schematic diagram of the amplitude modulation plane of a structural color rendering unit provided in an embodiment of this application;

[0026] Figure 6 This is a schematic diagram of a structural color prediction forward modeling provided in an embodiment of this application;

[0027] Figure 7 This is a schematic diagram of reverse modeling for structural color ratio prediction provided in an embodiment of this application. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0029] In the description of this application, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, features defined as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0030] In the description of this application, it should be noted that, unless otherwise expressly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection, an electrical connection, or a connection that allows communication between them; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0031] The following disclosure provides many different embodiments or examples for implementing different structures of this application. To simplify the disclosure, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the scope of this application. Furthermore, reference numerals and / or letters may be repeated in different examples; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or arrangements discussed. In addition, various specific examples of processes and materials are provided in this application, but those skilled in the art will recognize the application of other processes and / or the use of other materials.

[0032] This application is based on a full-gamut structural color prediction and reproduction method for multi-level micro-nano structures. The multi-level micro-nano structure referred to is the "all-dielectric nanopillar-structural color rendering unit-pixel" multi-level micro-nano structure.

[0033] Please refer to Figures 1-5 The "all-dielectric nanopillars-structural color rendering units-pixels" structure exists in three levels. The first level involves designing the size, height, and center-to-center distance of the all-dielectric nanopillars, all of which affect the color rendering effect. Photolithography is used to control the structural parameters of the all-dielectric nanopillars, establishing the first level of the multi-level micro / nanostructure. All-dielectric nanopillars with identical structural parameters are arranged regularly within a certain range to form structural color rendering units, constituting the second level of the multi-level micro / nanostructure. Several micro / nano-scale structural color rendering units aggregate to form the third level of the multi-level micro / nanostructure. Within the third level, color mixing is achieved using amplitude modulation and frequency modulation of the structural color rendering units, enabling control of brightness and saturation tonal levels. Frequency modulation expresses color information by the proportion of structural color rendering units of the same size within a single pixel; amplitude modulation arranges primary color units with the same scale spacing, expressing color information by the size of the structural color rendering units.

[0034] Please refer to Figure 6 , Figure 7 This application presents a method for full-gamut structural color prediction and reproduction based on multi-level micro / nano structures, comprising the following steps:

[0035] S1. Based on the KM model, establish a predictive model for the relationship between the proportion of primary colors in the mixed structural color and the spectral reflectance of the predicted color.

[0036] The structural color rendering unit is decomposed into many parallel sublayers, each possessing the same optical properties and a thickness dx. An incident luminous flux, i.e., a downward luminous flux i and an upward luminous flux j, occurs on the upper and lower surfaces of any sublayer. The differential forms of the downward luminous flux i and the upward luminous flux j are as follows:

[0037] di=(S+K)idx-Sjdx (1)

[0038] dj=-(S+K)jdx+Sidx (2)

[0039] Where K and S are the absorption coefficient and scattering coefficient of the structural color unit, respectively, and upward is defined as the positive direction.

[0040] To calculate the surface reflectance r of the structural color unit using the above differential form, we can let r = j / i, and using the differential rule of quotients, we have:

[0041]

[0042] Furthermore, we can obtain:

[0043]

[0044] Integrating the above equation based on the boundary conditions yields the predicted color reflectance value r, as shown in the following equation:

[0045]

[0046] Wherein, the reflectance r when x = 0 is the substrate reflectance value r. g a = 1 + K / S, b = (a 2 -1) 1 / 2 Therefore, the mixed color (K / S) can be obtained. mix,λ for:

[0047]

[0048] Represented as:

[0049]

[0050] Therefore, (K / S) can be calculated based on the proportions of the primary colors in the mixed structural color scheme [c1, c2, c3]. mix,λ This leads to the spectral reflectance r:

[0051]

[0052] S2. Using an optimization algorithm and based on the prediction model, obtain the inverse model of the spectral reflectance of the target color and the proportion of primary colors in the mixed structure.

[0053] A correlation model is constructed using a sample set of color patches with known proportions of mixed structural color primary colors and measured spectral values. Training samples are established; given the spectral reflectance of these samples and the corresponding proportions of the mixed structural color primary colors, a reconstruction matrix can be obtained. Then, by inputting arbitrary combinations of the proportions of the mixed structural color primary colors, the spectral reflectance of the sample surface is reconstructed, predicting the spectrum of the mixed colors. Methods such as pseudo-inverse, R-matrix, basis function reconstruction, and BP neural network are selected to fit the data. The optimal algorithm is chosen to construct a forward model for structural color prediction. The performance of the forward model is evaluated through spectral error assessment, and continuous improvement is implemented.

[0054] The ultimate goal of this invention is to achieve the prediction and reproduction of structural colors across the entire color gamut. Establishing a reverse model for predicting structural color ratios is crucial to achieving this goal. This invention utilizes optimization methods to achieve high-precision reversal of the established forward prediction model, establishes a reverse model for predicting structural color ratios, obtains the structural color primary color ratios based on the spectral reflectance of the target color, and then prepares an all-dielectric nanopillar composite structure to reproduce the target color.

[0055] The target color is reproduced using spectral matching, with the spectral reflectance of the target color being r. (s) The predicted color has a spectral reflectance of r. (m) ,

[0056]

[0057] In equation (9), This represents the spectral reflectance at the target color wavelength of 400 nm. This represents the spectral reflectance at the target color wavelength of 700nm.

[0058] Since the spectral reflectance of the target color is equal to the spectral reflectance of the predicted color, we can obtain:

[0059] (r (s) -r (m) )=0 (10)

[0060] Since the reflectivity R is related to the ratio of the material's absorption and scattering coefficients K / S, according to differential theory, at various wavelengths... It can be represented as:

[0061]

[0062] In equation (11), Indicates the spectral reflectance of the target color. This represents the spectral reflectance of the predicted color.

[0063] Rewrite the above equation in matrix form:

[0064] r (s) -r (m) =D(f (s) -f (m) (12)

[0065] in,

[0066] Substituting equation (12) into equation (10), we get:

[0067] D(f (s) -f (m) )=0 (13)

[0068] According to the KM theory, the ratio of the absorption coefficient to the scattering coefficient of a mixed medium (K / S) mix Represented as:

[0069] (K / S) mix =c1(K / S)1+c2(K / S)2+c3(K / S)3 (14)

[0070] Equation (14) can be further rewritten as:

[0071]

[0072] f (m) =f (t) +Φc (16)

[0073] in Φ is the identity matrix for the three primary colors, and c = [c1, c2, c3]. T This is a column vector representing the proportions of the structural color primary colors.

[0074] Substituting equation (16) into equation (13) yields:

[0075] DΦc=D(f (s) -f (t) (17)

[0076] S3. Based on the inverse model, obtain the spectral difference between the spectral reflectance of the target color and the spectral reflectance of the predicted color.

[0077] Then, using the proportion of the primary colors of the structural color rendering unit [a%, b%, c%] as the initial value for algorithm iteration, the spectral difference between the predicted color and the target color can be calculated by using interior point algorithm, effective set algorithm, sequential quadratic programming algorithm, genetic algorithm and simulated annealing algorithm.

[0078] S4. Based on the spectral difference, obtain the optimal spectral reflectance for the predicted color.

[0079] When the difference does not exceed a pre-set reasonable threshold, the optimal predicted value can be obtained, that is...

[0080] c = (DΦ) -1 D(f (s) -f (t) (18)

[0081] The above description is merely a preferred embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A method for full-gamut structural color prediction and reproduction based on multi-level micro / nano structures, characterized in that, include: A predictive model is established based on the KM model to establish the corresponding relationship between the proportion of primary colors in the mixed structural color and the spectral reflectance of the predicted color. The specific process of building a prediction model based on the KM model is according to the formula. ； The absorption coefficient of the structural color rendering unit. The scattering coefficient of the structural color rendering unit. To predict the spectral reflectance of colors; An optimization algorithm is used, and based on the prediction model, an inverse model of the spectral reflectance of the target color and the proportion of primary colors in the mixing mechanism is obtained; The specific process of obtaining the inverse model is according to the formula, ； in An identity matrix consisting of three primary colors. This is a column vector representing the proportions of the structural color primary colors; Based on the inverse model, the spectral difference between the spectral reflectance of the target color and the spectral reflectance of the predicted color is obtained; Based on the spectral difference, the optimal spectral reflectance for the predicted color is obtained; The optimal spectral reflectance is obtained according to the formula. ； Specifically, let the spectral reflectance of the target color be... The predicted color spectral reflectance is , ， In the formula, This represents the spectral reflectance at the target color wavelength of 400 nm. This represents the spectral reflectance at the target color wavelength of 700 nm. Since the spectral reflectance of the target color is equal to the spectral reflectance of the predicted color, we can obtain: ， Due to reflectivity The ratio of the material's absorption and scattering coefficients According to differential theory, at each wavelength... It can be represented as: In the formula, Indicates the spectral reflectance of the target color. Indicates the spectral reflectance of the predicted color. Rewrite the above equation in matrix form: ， in, , , .

2. The method for full-gamut structural color prediction and reproduction based on multi-level micro / nano structures according to claim 1, characterized in that, The methods for obtaining spectral differences include interior point algorithm, effective set algorithm, sequential quadratic programming algorithm, genetic algorithm, and simulated annealing algorithm.

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