CN112818540B - Method for predicting performance of Berleman matrix on multilayer optical film - Google Patents

Abstract

The invention discloses a method for predicting the performance of a multilayer optical film by a Berleman matrix. The method comprises the steps of obtaining experimental spectral data and known data of materials of all layers; fitting the optical calculated values with the experimental values by using a Berleman 4 x 4 matrix; and obtaining the calculation result after optimization, and outputting data of the related parameters and the image. The method can accurately perform analog calculation on the thickness, the dispersion coefficient and the refractive index of the material to obtain a simulated value approximate to an analytic solution, and can calculate the refractive index change condition of the material under the conditions of wavelength change and wavelength invariance through the calculated dispersion coefficient.

Description

A Prediction Method of Berreman Matrix for the Properties of Multilayer Optical Films

technical field

The invention belongs to the field of optical simulation and optical device application, in particular to a method for predicting the performance of a multilayer optical film by a Berreman matrix.

Background technique

As a widely used industrial product, multilayer optical film has a wide range of applications in many fields because of its excellent optical properties and volume controllability, such as ITO glass, liquid crystal displays, optical alignment materials, photovoltaic coating materials , Photovoltaic packaging process, etc.

When the traditional method uses the Fresnel law method to calculate the ellipsometry parameters, it can only calculate the ellipsometry parameters of the sample under a specific incident light direction when facing anisotropic materials, which is undoubtedly difficult to adapt to the complex situation for multilayer film materials. The calculation of optical properties; and the Berreman 4×4 matrix method can be applied to composite materials with a combination of multi-layer isotropy and anisotropy, and the electric and magnetic fields in each layer can be directly solved according to Maxwell’s electromagnetic equations, and A 4×4 matrix is obtained through a series of derivations, which is the Berreman 4×4 matrix method.

Due to the existence of various materials in the multilayer optical film material, the dispersion coefficient, extinction coefficient, thickness, and pitch length are also different. It takes a long time to manually calculate the relevant parameters of each layer. The Berreman 4×4 matrix is used. The calculation method can quickly obtain the parameters of each layer of film.

Monte Carlo (Monte Carlo) algorithm is a mathematical statistical method, which is often used to solve problems of random processes. For optical simulation, using random number addressing and gradually reducing the gap between the calculated value and the experimental value is more efficient than manually setting parameters to calculate by the dichotomy method, and at the same time, approximate simulation results close to the analytical value can be obtained. Combining the Monte Carlo algorithm with the Berreman 4×4 matrix, the Monte Carlo method can be used to quickly obtain the Berreman 4×4 matrix close to the experimental value and the corresponding Jones matrix, and then Jones can be The matrix is converted to transmittance and absorbance.

In the process of querying the performance of multilayer optical films, the existing technology is generally to measure the thickness of the film by a thickness gauge, but it is difficult to accurately measure parameters such as dispersion coefficient that cannot be directly measured by the instrument. In "An Automatic Design Method of Monte Carlo Focal Plane Imaging Optical" invented by Hao et al., it introduces how to use the Monte Carlo method to optimize the application of imaging images in focal plane imaging, but does not cover how to optimize the application of multi-layer optical films. The performance parameters such as thickness are calculated by the Monte Carlo method. In order to fill this gap, the present invention uses the Berreman 4×4 matrix combined with the Monte Carlo method to simulate and calculate the thickness of each layer of the multilayer optical film. By comparing with the actual experimental results, we can intuitively predict parameters such as thickness, refractive index, and dispersion coefficient by comparing the simulation and actual results.

SUMMARY OF THE INVENTION

At present, in laboratory conditions and industrial production, optical materials such as glass, PMMA, quartz and other optical materials are often coated with a certain number of layers of optical coatings made of different materials to obtain the desired performance. The technical problem to be solved by the present invention is to provide a method that can obtain the approximate analytical value by the Monte Carlo method when the important parameters such as the thickness of each layer, refractive index, dispersion coefficient and extinction coefficient cannot be determined. Simulation value.

The object of the present invention is achieved by at least one of the following technical solutions.

A method for predicting properties of multilayer optical films by Berreman matrix, comprising the following steps:

S1. The experimental value measured by the experiment is the spectral data of the sample when the multilayer optical film is placed, and the background data when the sample is not placed, and then obtained by subtracting the sample data and the background data. Transmission or absorption data of multilayer optical films;

S2. For the parameters to be calculated, select the initial value and substitute it into the Berreman 4×4 matrix to obtain the simulation curve based on the initial value, and obtain the least square difference between the initial simulation value and the experimental value.

S3. For an initial simulation value in the simulation curve, select a random value around it and substitute it into the Berreman 4×4 matrix to obtain a simulation curve based on random values and obtain the least-squares difference χ between the random simulation value and the experimental value ² ;

的大小，若

则返回步骤S3中重新选取随机值，若

则跳至步骤S5；S4, compare χ ² with

size, if

Then return to step S3 to re-select the random value, if

Then skip to step S5;

的2.5％，若是，则跳至步骤S6，否则返回步骤S3 中，采用选取的随机值代替初始仿真值，采用χ²替换

并重新选取随机值进行计算，在选取新的随机值的时候缩减取值范围至原来的95.5％即高斯分布的2σ大小；S5, determine whether χ ² is less than

2.5% of , if yes, skip to step S6, otherwise return to step S3, use the selected random value to replace the initial simulation value, and use χ ² to replace

And re-select random values for calculation, when selecting new random values, reduce the value range to 95.5% of the original, that is, the 2σ size of the Gaussian distribution;

S6, output the final initial simulation value as a known parameter, and repeat steps S3 to S5 until all the initial simulation values in the simulation value curve are calculated, and output the optimal solution and the comparison chart;

S7. Repeat steps S3 to S6, and average the optimal solutions obtained for multiple times to ensure accuracy.

Further, in step S2, the parameters that need to be calculated and obtained include: thickness, refractive index, dispersion coefficient, extinction coefficient, and incident angle of light; for the parameters to be calculated, if the theoretical value or value range is known, then Set a value range and theoretical value according to the known parameters for calculation; when there is no theoretical value that can be referenced, select a material parameter theoretical value with similar material composition and the theoretical value of the above parameter can be consulted as the initial value;

Substitute the initial value into the Berreman 4×4 matrix for calculation, and use the calculated Jones matrix to obtain a simulation value curve based on the initial value, that is, the transmittance or absorptivity curve, and then obtain the initial simulation value according to the simulation value curve;

具体如下：Calculate the difference between the initial simulated and experimental values using the least squares method

details as follows:

In the formula, n represents the number of measured experimental values, that is, the measured experimental values and the initial simulation values are calculated under the condition that the wavelengths of each point correspond one-to-one.

Further, in step S3, a random value is selected around a parameter in the simulation value curve in a normal distribution manner: a random number is obtained at the origin with the initial simulation value, and the probability of the generated random number is relative to the initial simulation value. The position of , obeys the normal distribution; the generated random values are substituted into the Berreman 4×4 matrix for calculation, and the calculated Jones matrix is used to obtain the simulated value curve based on the random value, that is, the simulated transmittance or absorption rate curve, and then obtain For the random simulation value of the Monte Carlo method, calculate the least squares difference χ ² between the random simulation value and the experimental value, as follows:

In the formula, n represents the number of measured experimental values, that is, χ ² is calculated under the condition that the measured experimental values and random simulation values correspond to the wavelengths of each point one-to-one.

Further, the main form of the Berreman 4×4 matrix is:

where k _xx is a defined form of Snell's law:

k _xx =n _i sinθ _i ;

Among them, _ni is the refractive index of the incident plane. For example, _ni is 1 in vacuum, and _ni of glass plane is generally 1.5-1.9. The specific value depends on the composition material. The _ni used in the test is generally When the incident plane is a transparent material such as glass or quartz, the value of the refractive index can be easily found, and θ _i is the incident angle on the incident plane; all calculations using Snell's law can be classified into this category;

The Berreman 4x4 matrix includes, but is not limited to, various expanded derivations, conjugates, and transformed forms of the principal forms of the Berreman 4x4 matrix described above.

Further, the algorithm for calculating transmittance or absorptivity according to the Berreman 4×4 matrix is expressed as follows:

First, use the refractive index to find the ellipsometric dielectric tensor of the multilayer optical film material:

When the material is an isotropic material, n _x = _ny =n _z ;

Convert the angle of incidence to a new matrix in the form of Euler angles by coordinate transformation:

Then the matrix B is used to convert the dielectric tensor into the elliptical dielectric tensor in the elliptically polarized state. The conversion formula is as follows:

Thus, 9 elliptic dielectric constants such as ε _xx can be substituted back into the corresponding coefficients of the Berreman 4×4 matrix, and the four eigenvalues corresponding to the Berreman 4×4 matrix can be obtained and expressed as: q ₁ , q ₂ , q ₃ , q ₄ ;

The corresponding Jones matrix and the corresponding Jones vector can be obtained by transforming the eigenvalues. After multiplying the corresponding Jones vector by its conjugate, the transmittance or absorptivity of the corresponding wavelength can be obtained. After calculating the corresponding points of all the bands, the partial transfer matrix Tp(-d) corresponding to the transmittance or absorptivity of each layer can be obtained, and the Tp(-d) of each layer is multiplied continuously, that is The transition matrix T corresponding to the corresponding transmittance or absorptivity of the entire multilayer optical film in the Berreman 4×4 matrix can be obtained.

Further, the conversion formula between the partial transition matrix and the obtained eigenvalues is expressed as follows:

Tp(-d)=β ₀ I+β ₁ Δ _B +β ₂ Δ _B ² +β ₃ Δ _B ³ ;

Among them, I is the identity matrix, and q is the corresponding eigenvalues q ₁ , q ₂ , q ₃ , q ₄ , as follows:

Among them, when j=1, (k,l,m)=(2,3,4); when j=2, (k,l,m)=(1,3,4); when j=3, ( k,l,m)=(1,2,4); when j=4, (k,l,m)=(1,2,3);

The relationship between the transition matrix T and the Jones vector can be expressed as:

The Jones matrix can be expressed as:

The simulation value curve, ie, the transmittance or absorptivity curve of the multilayer optical film, can be obtained from the Jones matrix and the Jones vector.

Further, in step S6, the optimal solution includes all known parameters and χ ² corresponding to all known parameters; the comparison diagram is the comparison diagram between the final output simulation value and the initial value and the final output simulation Comparison chart of values and experimental values;

In step S7, under the same initial conditions, several sets of initial simulation value results that meet the requirements are obtained in the same way, and all the obtained initial simulation value points are averaged to obtain the average initial simulation value parameter and simulation value simulation value. The fitting curve of the simulation value corresponding to the average initial simulation value parameter and the comparison chart of the average initial simulation value and the experimental value are output.

The multilayer optical film may be a multilayer light-transmitting optical film, or a plurality of multilayer light-transmitting optical films may be stacked; the multilayer optical film includes one or more light-transmitting optical films; the light-transmitting optical film Optical film is to apply optical coating on optical material;

Optical materials include glass, PMMA, quartz and fluorite; optical coatings include liquid crystal, OLED optical materials, AMOLED optical materials;

If there is still space in the multilayer transparent optical film or it is symmetrical and hollow, substances with optical properties can also be added, including liquid crystal, OLED optical materials, AMOLED optical materials and motor globulin motor materials.

Further, the Monte Carlo method is used for optimization in steps S3 to S5, that is, a large number of random values within a certain range are selected for calculation, but the selection of random values in the present invention also conforms to the probability of taking values near the existing parameter values. The characteristics of the Gaussian distribution, that is, the probability of taking values close to the existing parameter values will be increased, and the probability distribution obeys the Gaussian distribution. This approach is not only in line with common sense, but also reduces the waste of computing power caused by completely random value calculations to save time.

Compared with the prior art, the present invention has the following advantages and beneficial effects:

The present invention proposes a method for predicting properties of multilayer optical films by Berreman matrix, wherein Berreman 4×4 matrix and Monte Carlo method are used. First, the calculation method based on the Berreman 4×4 matrix can accurately obtain the relevant spectral data of the multilayer optical film by using a small number of important parameters without considering other interference factors, which greatly improves the practicability and accuracy of the detection method. ; It is worth emphasizing that the Berreman 4 × 4 matrix equation is an exact solution of Maxwell's equations, which can be directly derived from Maxwell's equations without any restrictive assumptions, so its solution is also accurate. The advantage of the Berreman 4×4 matrix method is that only a few important parameters such as thickness, refractive index, pitch length, incident angle, etc., which are easy to measure, can accurately calculate the transmittance of the material and the Jones matrix of the material, and according to Jones ( Jones) matrix can also deduce more optical properties of the material to be discovered, with practicality and accuracy.

Secondly, using the Monte Carlo method to select a large number of random values for automatic calculation can reduce the workload of manual parameter adjustment, and at the same time can obtain relatively accurate simulation values. Trying low-efficiency problems can better automate and speed up detection methods. At the same time, since χ ² is set as a contrast, the effect of the simulation can be quantified effectively and intuitively.

The invention can simulate and calculate the thickness, dispersion coefficient and refractive index of the material more accurately and obtain the simulation value approximate to the analytical solution, and can calculate the refractive index of the material under the condition of wavelength change and wavelength constant through the calculated dispersion coefficient Changes.

Description of drawings

Fig. 1 is a kind of Berreman matrix of the present invention to the method for predicting the performance of multilayer optical film.

2 is a structural diagram of a multilayer optical film in an embodiment of the present invention;

Fig. 3 is the spectrogram of the experimental result obtained by experimental measurement in the embodiment of the present invention;

FIG. 4 is a comparison diagram of an initial simulation value set before simulation using a Monte Carlo method and an experimental result in an embodiment of the present invention;

5 is a comparison diagram of the final simulation result and the experimental result after the simulation in the embodiment of the present invention;

FIG. 6 is a schematic diagram of a comparison table between thickness addressing data of a simulation result obtained after the simulation ends and a set initial value in an embodiment of the present invention.

specific implementation

The present invention will be described in further detail below with reference to the examples, but it is not intended to limit the scope of the present invention.

For multi-layer optical films, the most common type of multi-layer optical films are various types of mobile phone stickers, and various types of liquid crystal cells and films made for solar photovoltaics are also common in laboratories. The materials are all multilayer film structures. However, if you want to know the relevant information of the multilayer film structure, such as the thickness, the general thickness gauge can only measure the thickness of the entire film, and whether the thickness of each layer of the film is uniform, if the non-uniformity is which layer has a problem, there is nothing you can do. . Therefore, in application, when using the present invention to scan multiple points on the optical film, comparing the thickness of each scanning point can effectively compare whether the thickness of each layer is uniform and the thickness distribution of each layer; comparing the refractive index of each point can be Whether the overall optical properties of the multilayer optical film are consistent and meet the requirements. At the same time, the method can also be used to predict the refractive index and dispersion coefficient of an unknown material or a series of mixtures under the condition of known thickness, and its optical performance index can be obtained quickly. It can also be used in conjunction with other measuring equipment according to the actual situation to obtain more parameters that you want to predict.

Example:

A method for predicting the properties of multilayer optical films by Berreman matrix, as shown in Figure 1, includes the following steps:

S1. The experimental value, that is, the transmittance or absorptivity data of the multilayer optical film, is measured experimentally. The equipment used in this embodiment is a USB 4000 spectrometer produced by Ocean Optics;

In this embodiment, the multilayer optical film is a double-layer soda-lime glass substrate. As shown in FIG. 2 , each layer of the glass substrate is coated with a silver coating and a poly(vinyl alcohol) coating respectively, with air in the middle. According to the theoretical value, the thickness range of each layer is: silver coating 10-20nm, PVA coating 15-30nm, air layer 2-5μm, the thickness of glass substrate has little influence on calculation and can be ignored; Parameters such as refractive index, dispersion coefficient and extinction coefficient can be obtained by consulting the data, so the main purpose of fitting is to know the thickness of each coating. The wavelength range of the measurement is in the range of 400 nm to 900 nm, and the purpose is to obtain the value of the thickness of each layer. The experimentally measured data are shown in Figure 3, the horizontal axis is the wavelength change, the vertical axis is the refractive index change, the horizontal axis is the wavelength range, and the vertical axis is the transmittance range.

S2. For the parameters to be calculated, select the initial value and substitute it into the Berreman 4×4 matrix to obtain the simulation curve based on the initial value, and obtain the least square difference between the initial simulation value and the experimental value.

The parameters that need to be calculated include: thickness, refractive index, dispersion coefficient, extinction coefficient, incident angle of light; for the parameters to be calculated, if the theoretical value or value range is known, set a parameter according to the known parameters. The value range and theoretical value are calculated; when there is no theoretical value for reference, select a material parameter theoretical value with a similar material composition and the theoretical value of the above parameter can be consulted as the initial value. When calculating the pitch, because the materials used are all It does not have a spiral, so set a maximum value to facilitate calculation;

Substitute the initial value into the Berreman 4×4 matrix for calculation, and use the calculated Jones matrix to obtain a simulation value curve based on the initial value, that is, the transmittance or absorptivity curve, and then obtain the initial simulation value according to the simulation value curve;

In the present embodiment, the comparison diagram of the simulation curve and the experimental curve before fitting by the Monte Carlo method is shown in FIG. 4 , the black solid line is the experimentally measured curve, and the black dotted line is the simulation curve of random values before fitting; The horizontal axis is the measurement wavelength range, and the vertical axis is the transmittance; the deviation between the transmittance curves is large, indicating that the initial data is far from the true value.

具体如下：Calculate the difference between the initial simulated and experimental values using the least squares method

details as follows:

In the formula, n represents the number of measured experimental values, that is, the measured experimental values and the initial simulation values are calculated under the condition that the wavelengths of each point correspond one-to-one.

S3. For an initial simulation value in the simulation curve, select a random value around it and substitute it into the Berreman 4×4 matrix to obtain a simulation curve based on random values and obtain the least-squares difference χ between the random simulation value and the experimental value ² ;

Select a random value around a parameter in the simulation value curve in the way of normal distribution: take the initial simulation value to obtain a random number at the origin, and the probability of the generated random number follows the normal distribution relative to the position of the initial simulation value; Substitute the generated random values into the Berreman 4×4 matrix for calculation, and use the calculated Jones matrix to obtain the simulated value curve based on random values, that is, the simulated transmittance or absorptivity curve, and then obtain the Monte Carlo method. The random simulation value of , calculates the least squares difference χ ² between the random simulation value and the experimental value, as follows:

In the formula, n represents the number of measured experimental values, that is, χ ² is calculated under the condition that the measured experimental values and random simulation values correspond to the wavelengths of each point one-to-one.

的大小，若

则返回步骤S3中重新选取随机值，若

则跳至步骤S5；S4, compare χ ² with

size, if

Then return to step S3 to re-select the random value, if

Then skip to step S5;

的2.5％，若是，则跳至步骤S6，否则返回步骤S3 中，采用选取的随机值代替初始仿真值，采用χ²替换

并重新选取随机值进行计算；S5, determine whether χ ² is less than

2.5% of , if yes, skip to step S6, otherwise return to step S3, use the selected random value to replace the initial simulation value, and use χ ² to replace

And re-select random values for calculation;

S6, output the final initial simulation value as a known parameter, and repeat steps S3 to S5 until all the initial simulation values in the simulation value curve are calculated, and output the optimal solution and the comparison chart;

The optimal solution includes all known parameters calculated by simulation and χ ² corresponding to all known parameters;

S7. Repeat steps S3 to S6, and average the optimal solutions obtained for multiple times to ensure accuracy.

Under the same initial conditions, several sets of initial simulation value results that meet the requirements are obtained, and all initial simulation values are averaged to obtain the average initial simulation value parameters and the simulation value fitting curve, and output the average initial simulation value parameters. The corresponding simulation value fitting curve and the comparison chart of the average initial simulation value and the experimental value.

In this embodiment, after the Monte Carlo method is used for simulation, the comparison diagram between the simulation curve and the experimental curve is shown in Figure 5, the black solid line is the experimentally measured curve, and the black dotted line is the simulation curve with random values before fitting ; The horizontal axis is the measurement wavelength range, and the vertical axis is the transmittance; it can be seen that the two curves are relatively close after fitting, and the corresponding data of the simulation curve can be obtained from Figure 6 at the same time. It can be seen that the difference χ ² between the calculated value calculated by the least squares method and the experimental value between the fitted value and the experimental value is reduced from the initial 173.4546 to 7.6818 at the end, the simulation result and the measurement result curve are very close, and the fitting is over The resulting least squares difference is less than 0.5% of the original.

At the same time, the simulated calculation values of each layer can also be obtained from it, as shown in Figure 6: the thickness of the silver coating is 17.4 nm, the thickness of the PVA coating is 27.1 nm, and the thickness of the air layer is 2.13 μm. From the comparison chart, it can be seen that the curve after optimization and fitting is very similar to the experimental curve. Generally, the calculated data can be regarded as the actual thickness of the material.

The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above embodiments. For those skilled in the art to which the present invention pertains, some simple deductions or substitutions can be made without departing from the concept of the present invention, which should all belong to the protection scope of the present invention.

Claims (8)

1. a Berreman matrix to the prediction method of multilayer optical film performance, is characterized in that, comprises the following steps: S1. Measure the experimental value through experiments, select the spectral data of the sample when the multilayer optical film is placed, and the background data when the sample is not placed, and then obtain the experimental value by subtracting the sample data and the background data. is the transmittance or absorptivity data of the multilayer optical film; S2. For the parameters to be calculated, select the initial value and substitute it into the Berreman 4×4 matrix to obtain the simulation curve based on the initial value, and obtain the least square difference between the initial simulation value and the corresponding experimental value.

S3. For an initial simulation value in the simulation curve, select a random value around it and substitute it into the Berreman 4×4 matrix, obtain a simulation curve based on the random value, and obtain the least-squares difference χ between the random simulation value and the experimental value ² ; Select a random value around a parameter in the simulation value curve in the way of normal distribution: take the initial simulation value to obtain a random number at the origin, and the probability of the generated random number follows the normal distribution relative to the position of the initial simulation value; Substitute the generated random values into the Berreman 4×4 matrix for calculation, and use the calculated Jones matrix to obtain a simulation value curve based on random values. The simulation value curve is the simulation transmittance or absorption rate curve, and then obtain For the random simulation value of the Monte Carlo method, calculate the least squares difference χ ² between the random simulation value and the experimental value, as follows:

In the formula, n represents the number of measured experimental values, and χ ² is calculated under the condition that the measured experimental values and random simulation values correspond to each point wavelength one-to-one; S4, compare χ ² with

size, if

Then return to step S3 to re-select the random value, if

Then skip to step S5; S5, determine whether χ ² is less than

2.5%, if yes, then jump to step S6, otherwise return to step S3, use the selected random value to replace the initial simulation value, and use χ ² to replace

And re-select random values for calculation, when selecting new random values, reduce the value range to 95.5% of the original, and 95.5% is the 2σ size of the Gaussian distribution; S6, output the final initial simulation value as a known parameter, and repeat steps S3 to S5 until all the initial simulation values in the simulation value curve are calculated, and output the optimal solution and the comparison chart; S7, repeating steps S3 to S6, and averaging the optimal solutions obtained multiple times to ensure accuracy; The Monte Carlo method is used for optimization in steps S3 to S5. 2. a kind of Berreman matrix according to claim 1 to the prediction method of multilayer optical film performance, it is characterized in that, in step S2, the parameter that needs to calculate and obtain comprises: thickness, refractive index, dispersion coefficient, extinction coefficient , the incident angle of light; for the parameters that need to be calculated, if the theoretical value is known, set a value range and theoretical value according to the known parameters for calculation; when there is no theoretical value that can be referenced, select a The theoretical value of the material parameter with similar material composition and the theoretical value of the above-mentioned parameters to be calculated can be consulted as the initial value; Substitute the initial value into the Berreman 4×4 matrix for calculation, and use the calculated Jones matrix to obtain the simulation value curve based on the initial value, the simulation value curve is the transmittance or absorption rate curve, and then obtain the initial simulation value according to the simulation value curve. value; Calculate the difference between the initial simulated and experimental values using the least squares method

details as follows:

In the formula, n represents the number of measured experimental values, and the measured experimental values and initial simulation values are calculated under the condition that the wavelengths of each point correspond one-to-one.

3. a kind of Berreman matrix according to claim 2 to the prediction method of multilayer optical film performance, it is characterized in that, the main form of Berreman 4 * 4 matrix is:

In the formula, K _xx is the defined form of Snell's law: K _xx =n _i sinθ _i ; where _ni is the refractive index of the incident plane, θ _i is the incident angle on the incident plane; ε _xx , ε _xy , ε _xz , ε _yx , ε _yy , ε _yz , ε _zx , ε _zy and ε _zz are the three the ellipsometry dielectric tensor in all directions in the coordinate system; Berreman 4x4 matrices include various expanded derivations, conjugates, and transformed forms of the principal forms of the Berreman 4x4 matrix described above. 4. a kind of Berreman matrix according to claim 3 to the prediction method of multilayer optical film performance, it is characterized in that, according to Berreman 4 * 4 matrix, the algorithm that seeks transmittance or absorptivity is expressed as follows: First, use the refractive index to find the ellipsometric dielectric tensor ε of the multilayer optical film material: When the material is an isotropic material, n _x = _ny =n _z ;

where ε _x , ε _y , ε _z are the components of the ellipsometry dielectric tensor in the x, y, z directions, respectively, and n _x , _ny , n _z are the components of the refractive index in the x, y, z directions, respectively ; For samples placed at any angle, through coordinate transformation, the incident angle can be converted into a new matrix in the form of Euler angles:

Among them, φ _E , θ _E , and ψ _E are the angles corresponding to the deflection of the original coordinates in the x, y, and z directions after the incident angle is converted into Euler angles; The matrix B is used to convert the dielectric tensor into the elliptical dielectric tensor in the elliptically polarized state. The conversion formula is as follows:

ε _xx , ε _xy , ε _xz , ε _yx , ε _yy , ε _yz , ε _zx , ε _zy and ε _zz are ellipsometry dielectric tensors in various directions in the three-dimensional coordinate system, so that the obtained ellipsometry Substitute the dielectric constant back into the Berreman 4×4 matrix, and solve the four eigenvalues corresponding to the Berreman 4×4 matrix, which are expressed as: q ₁ , q ₂ , q ₃ , q ₄ ; The corresponding Jones matrix and the corresponding Jones vector can be obtained by transforming the eigenvalues. After multiplying the corresponding Jones vector by its conjugate, the numerical value of the simulation value of the corresponding wavelength can be obtained; After the calculation of the corresponding point of the band, the partial transition matrix Tp(-d) corresponding to the simulation value of each layer is obtained, and the Tp(-d) of each layer is multiplied together to obtain the corresponding simulation value of the multilayer optical film as a whole in Berreman 4× 4 The corresponding transition matrix T in the matrix. 5. a kind of Berreman matrix according to claim 4 is to the prediction method of multilayer optical film performance, it is characterized in that, the conversion formula between partial transfer matrix and sought eigenvalue is expressed as follows: Tp(-d)=β ₀ I+β ₁ Δ _B +β ₂ Δ _B ² +β ₃ Δ _B ³ ; Among them, I is the identity matrix, and q is the corresponding eigenvalues q ₁ , q ₂ , q ₃ , q ₄ , as follows:

Among them, when j=1, (k,l,m)=(2,3,4); when j=2, (k,l,m)=(1,3,4); when j=3, ( k,l,m)=(1,2,4); when j=4, (k,l,m)=(1,2,3); Among them, d is the thickness of a single-layer optical film, and the optical film includes isotropic or anisotropic films; C represents the speed of light; ω is the angular velocity of elliptically polarized light at a certain wavelength; The relationship between the transition matrix T and the Jones vector is expressed as:

T ₁₁ , T ₁₂ , T ₁₃ , T ₁₄ , T ₂₁ , T ₂₂ , T ₂₃ , T ₂₄ , T ₃₁ , T ₃₂ , T ₃₃ , T ₃₄ , T ₄₁ , T ₄₂ , T ₄₃ , T ₄₄ are transition matrices elements in T; r _pp , rs _sp , rs _ss , _rp s together are the Jones vectors that make up the Jones matrix; The Jones matrix is expressed as:

The simulation value curve can be obtained from the Jones matrix and the Jones vector. 6. The method for predicting the performance of multilayer optical films by a Berreman matrix according to claim ¹ , wherein in step S6, the optimal solution includes all known parameters and the corresponding χ of all known parameters. ; Described comparison diagram is the comparison diagram between the simulation value of final output and initial value and the comparison diagram of simulation value of final output and experimental value; In step S7, under the same initial conditions, several sets of initial simulation value results that meet the requirements are obtained in the same way, and all the obtained initial simulation value points are averaged to obtain the average initial simulation value parameter and simulation value simulation value. The fitting curve of the simulation value corresponding to the average initial simulation value parameter and the comparison chart of the average initial simulation value and the experimental value are output. 7. The method for predicting the performance of a multi-layer optical film by a Berreman matrix according to claim 1, wherein the multi-layer optical film is a multi-layer transparent optical film or a multi-layer transparent optical film. The optical film is formed by stacking; the multilayer optical film includes one or more light-transmitting optical films; the light-transmitting optical film is an optical coating applied on an optical material; Optical materials include glass, PMMA, quartz and fluorite; optical coatings include liquid crystal, OLED optical materials, and AMOLED optical materials. 8. a kind of Berreman matrix according to claim 7 to the method for predicting the performance of multilayer optical film, it is characterized in that, if there is still space in the multilayer light-transmitting optical film or is up-down symmetry and hollow, can also add Substances with optical properties include liquid crystals, OLED optical materials, AMOLED optical materials, and motor globulin motor materials.

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