CN100456079C - Film layer design method for clearing double layer film structure coated film glass reflection color - Google Patents

Abstract

This invention relates to a method for designing the coating of double membrane coated glass which can eliminate the reflective color, the steps show as follow: based on one kind of optical parameters of the coating, it creates the mathematics relationship between the optical parameters of double membrane coating and the reflective color's saturation of the coated glass to achieve the mathematics model, then it works out the optimization problem combining the annealing method with the Newton-Raphson method, the results gives the ideal optical parameters matching the coating.

Description

A kind of rete method for designing of eliminating double membrane structure coated glass reflected colour

Technical field

The present invention relates to a kind of rete method for designing of coated glass, relate in particular to the rete method for designing of eliminating double membrane structure coated glass reflected colour.

Background technology

Coated glass is in one or more layers metal of glass surface coating, metal oxide or other inorganic material, to change the optical property of glass, satisfies some particular requirement.Coated glass as glass pane is used because functional requirement often has two-layer or two-layer above membrane structure, also will satisfy requirement attractive in appearance simultaneously.Generally speaking, this reflected colour that needs coated glass certain color that is colourless or stable and controllable.And light is during through duplicature or multi-layer film structure, because the interference effect of film can present color.For the coated glass of double membrane structure, traditional handicraft is determined the optical parametric of certain thin film earlier for eliminating color, again another tunic is attempted the different thickness couplings or the refractive index of fine setting rete, progressively feels out suitable coupling rete.The exploration process is loaded down with trivial details, and the cycle is very long, cost height, inefficiency.

Summary of the invention

The purpose of this invention is to provide a kind of method for designing of eliminating the rete of double membrane structure coated glass reflected colour, serves as to eliminate the exploratory experiment that reflected colour carries out to simplify in the production of double membrane structure coated glass.

The method for designing of the rete of elimination double membrane structure coated glass reflected colour of the present invention, concrete steps are as follows:

If the refractive index n of double membrane structure coated glass one rete ₁, extinction coefficient k ₁, thickness h ₁Determined that another rete is the target rete of coated glass reflected colour to be eliminated, its refractive index, extinction coefficient and thickness are designated as n respectively ₂, k ₂And h ₂, and with n ₂, k ₂Expand into the function of lambda1-wavelength λ, utilize the parameters relationship of matrix method acquisition duplicature reflectivity and Film Optics parameter, R| _{H1, n1, k1}(h ₂, n ₂, k ₂, λ), R is the duplicature reflectivity, utilizes CIE matrix and L ^*a ^*b ^*The regulation of uniform colour space and R| _{H1, n1, k1}(h ₂, n ₂, k ₂, λ), obtain the parameter type S| of duplicature reflected colour color saturation _{H1, n1, k1}(h ₂, n ₂, k ₂, λ), and set up the mathematical model of eliminating the reflected colour problem, as the formula (1),

$\begin{array}{c}\min \left({S|}_{(h_1,n_1,k_1)}(h_2,n_2,k_2)\right)\\ h_2,n_2,k_2\∈D\end{array}---\left(1\right)$

Wherein D represents the parameter-definition territory, finds the solution formula (1), and obtaining to make S is one group of parameter h of minimum value ₂, n ₂, k ₂, can eliminate the optical parametric of the target rete of duplicature reflected colour exactly.

Find the solution formula (1), can adopt traditional alternative manner.Relate to a large amount of non-linear units because Film Optics calculates, in order to find the solution formula (1) fast and accurately, be solved to the two-step approach that adopts simulated annealing and Newton iteration method to combine, concrete steps are as follows:

1) uses simulated annealing solution formula (1), obtain one group of parameter h ₂, n ₂And k ₂Value;

2) h that obtains with step 1) ₂, n ₂And k ₂As the calculating initial value of Newton iteration method, find the solution formula (1) once more;

3) repeating step 1), 2) M time, M=1,2 ... positive integer in M the result who obtains, is obtained and is made the one group parameter h of S value for minimum ₂, n ₂And k ₂

The present invention uses computing method to seek theoretical optimal target rete parameter, produces in order to instruct practice, and result of calculation is reliable, can shorten relying on concrete experiment to seek the construction period of the target film layer parameter of eliminating the coated glass reflected colour.The result who utilizes this method to obtain instructs production practices to have tangible economic worth.

Description of drawings

Fig. 1 is a duplicature coated glass structural representation;

Fig. 2 is fixed thin-film refractive index n ₁, extinction coefficient k ₁Curve;

Fig. 3 is the refractive index n that can eliminate the target rete of duplicature reflected colour ₂, extinction coefficient k ₂Curve.

Embodiment

Below in conjunction with accompanying drawing and example the present invention is described in further details.

With the double membrane structure coated glass is example, and film 1 and film 2 are plated on the common white glass substrate 3 in order, and as shown in Figure 1, wherein I, R represent incident light and reflected light respectively.Two membranes material difference.Wherein the optical parametric of film 1 is determined, refractive index n ₁With extinction coefficient k ₁Curve as shown in Figure 2, thickness h ₁Be 274.6nm.Film 2 is for needing the target rete that can eliminate this double membrane structure coated glass reflected colour of design, and its refractive index, extinction coefficient and thickness are designated as n respectively ₂, k ₂And h ₂, and adopt the polynomial function that has than strong adaptability to launch n ₂, k ₂With the dispersion relation of lambda1-wavelength λ, as the formula (2),

n ₂＝x ₁λ ³+x ₂λ ²+x ₃λ+x ₄。(2)

k ₂＝x ₅λ ³+x ₆λ ²+x ₇λ+x ₈

X wherein ₁～x ₈It is undetermined constant.

Incide the light of duplicature film surface, its reflectivity can calculate with following formula:

$\left(\begin{array}{c}{E}_0\\ H_0\end{array}\right)=\left[\begin{array}{cc}\cos {\mathrm{\δ}}_1& \frac{i}{n}\sin {\mathrm{\δ}}_1\\ {\mathrm{in}}_1\sin {\mathrm{\δ}}_1& \cos {\mathrm{\δ}}_1\end{array}\right]\left[\begin{array}{cc}\cos {\mathrm{\δ}}_2& \frac{i}{n_2}\sin {\mathrm{\δ}}_2\\ {\mathrm{in}}_2\sin {\mathrm{\δ}}_2& \cos {\mathrm{\δ}}_2\end{array}\right]\left(\begin{array}{c}1\\ n_s\end{array}\right)E_s$

$=\left[\begin{array}{cc}A& \mathrm{iB}\\ \mathrm{iC}& D\end{array}\right]\left(\begin{array}{c}1\\ n_s\end{array}\right)E_s$

$R\left(\mathrm{\λ}\right)=\frac{{|E_0-H_0|}^2}{{|E_0+H_0|}^2}=\frac{{(n_{0}A-n_{s}D)}^2+{(n_0{n}_{s}B-C)}^2}{{(n_{0}A+n_{s}D)}^2+{(n_0{n}_{s}B+C)}^2}---\left(3\right)$

The film reflected colour is at light vertical incidence condition, then again

${\mathrm{\δ}}_1=\frac{2\mathrm{\π}}{\mathrm{\λ}}{n_1}^{\′}{h}_1,{\mathrm{\δ}}_2=\frac{2\mathrm{\π}}{\mathrm{\λ}}{n_2}^{\′}{h}_2---\left(4\right)$

E wherein _sBe electric field intensity in the glass, air refraction n ₀=1.0 and glass refraction n _s=1.52, n ' is film plural form refractive index, i.e. n '=n-ik.According to the international standard illumination council, i.e. CIE regulation, the tristimulus values of reflectance spectrum R (λ) be,

X＝∑R(λ)M _CIE|x

Y＝∑R(λ)M _CIE|y (5)

Z＝∑R(λ)M _CIE|z

M wherein _CIEBe the cie color matrix.L ^*a ^*b ^*The coordinate a of uniform colour space regulation ^*And b ^*For working as (X/X ₀＞0.008856, Y/Y ₀＞0.008856, X＞0.008856) time

a ^*＝500[(X/X ₀) ^1/3-(Y/Y ₀) ^1/3](6)

b ^*＝200[(Y/Y ₀) ^1/3-(Z/Z ₀) ^1/3]

Otherwise

a ^*＝3893.5(X/X ₀-Y/Y ₀)。(7)

b ^*＝1557.4(Y/Y ₀-Z/Z ₀)

X0, Y0 and Z0 are the tristimulus values of white spectrum in the formula.Color saturation then $S=\sqrt{(a^{*2}+b^{*2})}.$ Set up the mathematical model of eliminating the reflected colour problem, as the formula (1),

$\begin{array}{c}\min \left({S|}_{(h_1,n_1,k_1)}(h_2,n_2,k_2)\right)\\ h_2,n_2,k_2\∈D\end{array}---\left(1\right)$

Formula (2-7) substitution formula (1) is just obtained the mathematical form of complete optimization problem, and wherein undetermined constant is x ₁～x ₈And the thickness h of film 2 ₂

In the simulated annealing, the initial value of undetermined parameter is chosen arbitrarily, as gets x ₁=10, x ₂=10, x ₃=10, x ₄=10, x ₅=10, x ₆=20, x ₇=20, x ₈=20, h ₂=100.With the disturbance that random sampling produces the undetermined parameter value, under than the weak convergence condition, carry out global optimization computation, do not obtain more preferential treatment as continuous 100 random samplings and decide parameter value and then finish calculating.The undetermined parameter value that simulated annealing is obtained is used Newton iteration method to carry out local optimum at the curve fit problem of formula (1) and is calculated as initial value, obtains more excellent undetermined parameter value.Repeat aforementioned calculation process 24 times, therefrom select to make one group of minimum parameter of S value, x is arranged as final fitted results ₁=14.6, x ₂=-31.7, x ₃=21.0, x ₄=-2.7, x ₅=0.4, x ₆=-0.9, x ₇=0.7, x ₈=-0.1, h ₂=79.7nm, this moment, coated glass reflected colour color saturation was 0.With x ₁～x ₈Substitution formula (2) obtains target rete refractive index n ₂With extinction coefficient k ₂Curve as shown in Figure 3.

The condition of convergence of dispersion relation and simulated annealing, independent calculation times can be according to the Feature Selection of aimed thin film, to reach optimum calculating effect.The order of film 1 and film 2 does not influence the use of method in the example, and what promptly determine optical parametric in advance is that film 1 or film 2 can both be used the method for the invention.

Claims (2)

1, a kind of method for designing of eliminating the rete of double membrane structure coated glass reflected colour is characterized in that step is as follows:

If the refractive index n of double membrane structure coated glass one rete ₁, extinction coefficient k ₁, thickness h ₁Determined that another rete is the target rete of coated glass reflected colour to be eliminated, its refractive index, extinction coefficient and thickness are designated as n respectively ₂, k ₂And h ₂, and with n ₂, k ₂Expand into the function of lambda1-wavelength λ, utilize the parameters relationship of matrix method acquisition duplicature reflectivity and Film Optics parameter, R| _{H1, n1, k1}(h ₂, n ₂, k ₂, λ), R is the duplicature reflectivity, utilizes CIE matrix and L ^*a ^*b ^*The regulation of uniform colour space and R| _{H1, n1, k1}(h ₂, n ₂, k ₂, λ), obtain the parameter type S| of duplicature reflected colour color saturation _{H1, n1, k1}(h ₂, n ₂, k ₂, λ), and set up the mathematical model of eliminating the reflected colour problem, as the formula (1),

$\min \left(S{|}_{(h_1,n_1,k_1)}(h_2,n_2,k_2)\right)---\left(1\right)$

h ₂，n ₂，k ₂∈D

Wherein D represents the parameter-definition territory, finds the solution formula (1), and obtaining to make S is one group of parameter h of minimum value ₂, n ₂, k ₂, can eliminate the optical parametric of the target rete of duplicature reflected colour exactly.

2, according to the method for designing of the rete of right 1 described elimination double membrane structure coated glass reflected colour, it is characterized in that the two-step approach that the formula of finding the solution (1) adopts simulated annealing and Newton iteration method to combine finds the solution, concrete steps are as follows:

1) uses simulated annealing solution formula (1), obtain one group of parameter h ₂, n ₂And k ₂Value;

2) h that obtains with step 1) ₂, n ₂And k ₂As the calculating initial value of Newton iteration method, find the solution formula (1) once more;

3) repeating step 1), 2) M time, M=1,2 ... positive integer in M the result who obtains, is obtained and is made the one group parameter h of S value for minimum ₂, n ₂And k ₂

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