CN103936296A - Film designing method capable of eliminating reflection color of double-film-structured coated glass with non-steep interfaces - Google Patents

Abstract

The invention relates to a film designing method capable of eliminating the reflection color of double-film-structured coated glass with non-steep interfaces, which belongs to the field of production and designing of coated glass. The method comprises the following concrete steps: directed at the double-film-structured coated glass with non-steep film interfaces, establishing an optical model of a five-film structure by using a Bruggeman effective medium approximate model to process the non-steep interfaces; constructing a mathematical relationship between the optical parameters of films of the five-film structure and color saturation of the reflection color of the coated glass so as to obtain a mathematical model; and on the premise that optical parameters of one film are determined, solving an optimization problem by using a two-step method composed of the simulated annealing method and the Newton iterative method so as to eventually give film parameters matching with ideal color saturation. Compared with other models which do not take diffusion into consideration and have a steep double-film structure, the method provided by the invention better accords with practical situations and has important guiding significance to designing and production of coated glass.

Description

A kind of elimination has the rete method of design of non-abrupt interface double membrane structure coated glass reflected colour

Technical field

The present invention relates to a kind of rete method of design of coated glass, relate in particular to and eliminate the rete method of design with non-abrupt interface double membrane structure coated glass reflected colour.

Background technology

Coated glass is by one or more layers metal of glass surface coating, metal oxide or other inorganic materials, to change the optical property of glass, meets some particular requirement.As the coated glass of window glass application, due to functional requirement, often there is two-layer or two-layer above membrane structure, also to meet requirement attractive in appearance simultaneously.Generally, this reflected colour that needs coated glass is colourless or stablizes certain controlled color.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 technology, for eliminating color, is first determined the optical parametric of certain thin film, then another tunic is attempted to the specific refractory power of different thickness matchings or fine setting rete, progressively feels out suitable coupling rete.Exploration process is loaded down with trivial details, and the cycle is very long, and cost is high, inefficiency.ZL200610053954.4 proposes to eliminate for double membrane structure coated glass the method for design of reflected colour, but this patent is not considered the non-abrupt interface forming due to diffusion between rete interface, rete and substrate in coating process, only can meet the design requirements of the coated glass with clear interface of some low temperature process acquisition, and coated glass and the practical situation with non-precipitous rete interface structure are differed to larger.

Summary of the invention

The object of this invention is to provide the rete method of design that a kind of elimination has non-abrupt interface double membrane structure coated glass reflected colour, to simplify the exploratory experiment carrying out as eliminating reflected colour in the production of double membrane structure coated glass.

Elimination of the present invention has the rete method of design of non-abrupt interface double membrane structure coated glass reflected colour, and its step is as follows:

Set up five Layer structure models for non-abrupt interface double membrane structure coated glass, upwards be designated as successively the first non-abrupt interface rete 1, the first filming layer 2, the second non-abrupt interface rete 3, the second coatings 4 and the 3rd non-abrupt interface rete 5 by substrate 6, establish the refractive index n of the first filming layer 2 ₂with optical extinction coefficient k ₂determine, thickness is designated as h ₂, the target rete that the second coatings 4 is coated glass reflected colour to be eliminated, its specific refractory power, optical extinction coefficient and thickness are designated as respectively n ₄, k ₄and h ₄, the refractive index n of substrate 6 ₆determine, the thickness of first, second, and third non-abrupt interface rete is known, is designated as successively h ₁, h ₃and h ₅, the refractive index n of the first non-abrupt interface rete ₁with optical extinction coefficient k ₁determine, utilize Bruggeman(Bruggeman) specific refractory power of the second non-abrupt interface rete is expressed as n by effective medium approximation model ₃=f(n ₂, k ₂, n ₄, k ₄), optical extinction coefficient is expressed as k ₃=f(n ₂, k ₂, n ₄, k ₄), the specific refractory power of the 3rd non-abrupt interface rete is expressed as to n ₅=f(n ₄, k ₄, n _air, k _air), optical extinction coefficient is expressed as k ₅=f(n ₄, k ₄, n _air, k _air), n _air, k _airrepresent respectively specific refractory power and the optical extinction coefficient of air, and by n ₂, k ₂, n ₄, k ₄, n ₆expand into the function of lambda1-wavelength λ.Utilize matrix method to set up the parameters relationship of five tunic reflectivity and Film Optics parameter, R| _{h1, h2, h3, h5, n1, k1, n2, k2}(h ₂, h ₄, n ₄, k ₄, λ), wherein R is the reflectivity of coated glass, utilizes CIE matrix and L ^*a ^*b ^*the regulation of uniform colour space and R| _{h1, h2, h3, h5, n1, k1, n2, k2}(h ₂, h ₄, n ₄, k ₄, λ), the parameter type S| of acquisition coated glass reflected colour fullness of shade _{h1, h2, h3, h5, n1, k1, n2, k2}(h ₂, h ₄, n ₄, k ₄, λ), set up thus the mathematical model of eliminating reflected colour, shown in (1),

min(S| _{h1,h2,h3,h5,n1,k1,n2,k2}(h ₂,h ₄,n ₄,k ₄)) （1）

h ₂,h ₄,n ₄,k ₄∈D

Wherein D represents parameter-definition territory, solves formula (1), and obtaining and making S is one group of parameter h of minimum value ₂, h ₄, n ₄, k ₄, elimination has the parameter of the target rete of non-abrupt interface double membrane structure coated glass reflected colour exactly.

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

1) use simulated annealing solution formula (1), obtain one group of parameter h ₂, h ₄, n ₄and k ₄value;

2) h obtaining with step 1) ₂, h ₄, n ₄and k ₄as the calculating initial value of Newton iteration method, again solve formula (1);

3) repeating step 1), 2) M time, M=1,2 ... positive integer, in M the result obtaining, obtains and makes S value for one group of minimum parameter h ₂, h ₄, n ₄and k ₄.

The present invention uses the target film layer parameter of method of calculation Search Theory optimum, produces in order to Guiding Practice, and calculation result is reliable, can shorten the construction period that relies on specific experiment to find the target film layer parameter of eliminating coated glass reflected colour.The result of utilizing the method to obtain instructs production practice to have obvious economic worth.

Brief description of the drawings

Fig. 1 has non-abrupt interface duplicature coated glass structural representation;

Fig. 2 is the curve of fixed thin-film refractive index;

Fig. 3 is the curve of fixed rete optical extinction coefficient;

Embodiment

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

With reference to Fig. 1, double membrane structure coated glass has the first filming layer 2 and the second coatings 4, consider the spread condition between interface, set up five Layer structure models, it between the first filming layer 2 and Bai Bo substrate 6, is the first non-abrupt interface rete 1, it between the first filming layer 2 and the second coatings 4, is the second non-abrupt interface rete 3, it between the second coatings 4 and air, is the 3rd non-abrupt interface rete 5, upwards be designated as successively the first non-abrupt interface rete 1 by substrate 6, the first filming layer 2, the second non-abrupt interface rete 3, the second coatings 4 and the 3rd non-abrupt interface rete 5, I in figure, R represents respectively incident light and reflected light.

If the refractive index n of the first filming layer 2 ₂with optical extinction coefficient k ₂determine, thickness is designated as h ₂, the target rete that the second coatings 4 is coated glass reflected colour to be eliminated, its specific refractory power, optical extinction coefficient and thickness are designated as respectively n ₄, k ₄and h ₄, the refractive index n of substrate 6 ₆determine, the thickness of first, second, and third non-abrupt interface rete is known, is designated as successively h ₁, h ₃and h ₅, the refractive index n of the first non-abrupt interface rete ₁with optical extinction coefficient k ₁determine, calculate for simplifying, establish in this example the refractive index n of the second coatings 4 ₄with optical extinction coefficient k ₄definite, to distinguish as shown in Figure 3 according to specific refractory power and the extinction coefficient curve of the definite rete of actual process operating mode, thickness is as shown in table 1.The thickness of the first filming layer 2 and the second coatings 4 is the film matching parameter that can eliminate this and have non-abrupt interface double membrane structure coated glass reflected colour that needs design, is designated as respectively h ₂and h ₄.

Table 1 thicknesses of layers data

The specific refractory power of the second non-abrupt interface rete and the 3rd non-abrupt interface rete and optical extinction coefficient adopt Bruggeman effective medium approximation model to calculate, and computation model is as follows:

$0=f\frac{{\mathrm{\&epsiv;}}_1-<\mathrm{\&epsiv;}>}{{\mathrm{\&epsiv;}}_1+2<\mathrm{\&epsiv;}>}+(1-f)\frac{{\mathrm{\&epsiv;}}_2-<\mathrm{\&epsiv;}>}{{\mathrm{\&epsiv;}}_2+2<\mathrm{\&epsiv;}>}---\left(2\right)$

In the time calculating the specific refractory power of the second non-abrupt interface rete and optical extinction coefficient, in formula (2), f represents the volume percent of the first filming layer in the second non-abrupt interface rete, ε ₁, ε ₂represent respectively the specific inductivity of the first filming layer 2 and the second coatings 4, < ε > represents the specific inductivity of the second non-abrupt interface rete.In the time calculating the specific refractory power of the 3rd non-abrupt interface rete and optical extinction coefficient, in formula (2), f represents the volume percent of the second coatings in the 3rd non-abrupt interface rete, ε ₁, ε ₂represent respectively the specific inductivity of the second coatings 4 and air, < ε > represents the specific inductivity of the 3rd non-abrupt interface rete.

In this example, specific refractory power and the optical extinction coefficient of the second non-abrupt interface rete between the 3rd non-abrupt interface rete and the first filming layer 2 and the second coatings 4 between the second coatings 4 and air, utilize the transformational relation of specific inductivity and specific refractory power and optical extinction coefficient all can express, wherein f all gets 0.5.

Incide the light on multilayer film surface, its reflectivity can calculate with following formula:

$\left[\begin{array}{c}C\\ B\end{array}\right]=M_1{M}_2{M}_3...M_p\left[\begin{array}{c}1\\ {\mathrm{\&eta;}}_s\end{array}\right]---\left(3\right)$

Wherein, p rete eigenmatrix is as follows:

$M_p=\left[\begin{array}{cc}\cos {\mathrm{\&delta;}}_p& i\sin {\mathrm{\&delta;}}_p/{\mathrm{\&eta;}}_p\\ i{\mathrm{\&eta;}}_p\sin {\mathrm{\&delta;}}_p& \cos {\mathrm{\&delta;}}_p\end{array}\right]---\left(4\right)$

Reflectivity: R=|r| ²(5)

Wherein reflection coefficient: $r=\frac{{\mathrm{\&eta;}}_0-Y}{{\mathrm{\&eta;}}_0+Y}=\frac{{\mathrm{\&eta;}}_{0}B-C}{{\mathrm{\&eta;}}_{0}B+C}---\left(6\right)$

In formula, film is admittance formula Y=C/B, η ₀the admittance of incident medium, η _sit is the specific refractory power of substrate.By film reflected colour for light vertical incidence condition,

δ _p＝(2π/λ)η _pd _p （7）

In formula, η _pfor the specific refractory power of medium, d _pfor the physical thickness of p media coating, λ is wavelength.

According to the international standard illumination council, i.e. CIE regulation, the tristimulus values of reflection spectrum R (λ) is,

X＝ΣR(λ)M _CIE|x

Y＝ΣR(λ)M _CIE|y （8）

Z＝ΣR(λ)M _CIE|z

Wherein M _cIEfor cie color matrix.L ^*a ^*b ^*the coordinate a that uniform colour space specifies ^*and b ^*for:

$\left\{\begin{array}{c}{a}^{*}=500\left[f\left(\frac{X}{X_0}\right)-f\left(\frac{Y}{Y_0}\right)\right];\\ b^{*}=200[f\left(\frac{Y}{Y_0}\right)-f\left(\frac{Z}{Z_0}\right)].\end{array}\right.---\left(9\right)$

Wherein,

X in formula ₀, Y ₀and Z ₀it is the tristimulus values of white spectrum.Fullness of shade by formula (2-12) substitution formula (1),

min(S| _{h1,h2,h3,h5,n1,k1,n2,k2}(h ₂,h ₄,n ₄,k ₄)) （1）

h ₂,h ₄,n ₄,k ₄∈D

Just obtain the mathematical form of complete optimization problem, wherein undetermined constant is the thickness h of the first filming layer 2 and the second coatings 4 ₂and h ₄.

In simulated annealing, the initial value of undetermined parameter is chosen arbitrarily, as gets h ₂=100, h ₄=50.Produce the disturbance of undetermined parameter value with stochastic sampling, under compared with weak convergence condition, carry out global optimization computation, determine parameter value and finish calculating as continuous 100 stochastic samplings do not obtain more preferential treatment.The undetermined parameter value that simulated annealing is obtained, as initial value, is used Newton iteration method to carry out local optimization calculating for the curve fit problem of formula (1), obtains more excellent undetermined parameter value.Repeating above-mentioned computation process can be as drawn a conclusion: when the second coatings 4 thickness are 105～150nm, the first filming layer 2 thickness are that 25～40nm or the second coatings 4 thickness are 265～310nm, when the first filming layer 2 thickness are 10～40nm, coated glass surface all can present comparatively desirable fullness of shade, realizes the colour killing of glass surface.

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.In example, the order of the first filming layer 2 and the second coatings 4 does not affect the use of method, and the first filming layer 2 of definite optical parametric and the second coatings 4 can both be applied the method for the invention and find the optimum matching thickness of eliminating multilayer film surface colour in advance.

Claims (2)

1. elimination has a rete method of design for non-abrupt interface double membrane structure coated glass reflected colour, and its step is as follows:

Set up five Layer structure models for non-abrupt interface double membrane structure coated glass, upwards be designated as successively the first non-abrupt interface rete 1, the first filming layer 2, the second non-abrupt interface rete 3, the second coatings 4 and the 3rd non-abrupt interface rete 5 by substrate 6, establish the refractive index n of the first filming layer 2 ₂with optical extinction coefficient k ₂determine, thickness is designated as h ₂, the target rete that the second coatings 4 is coated glass reflected colour to be eliminated, its specific refractory power, optical extinction coefficient and thickness are designated as respectively n ₄, k ₄and h ₄, the refractive index n of substrate 6 ₆determine, the thickness of first, second, and third non-abrupt interface rete is known, is designated as successively h ₁, h ₃and h ₅, the refractive index n of the first non-abrupt interface rete ₁with optical extinction coefficient k ₁determine, utilize Bruggeman effective medium approximation model that the specific refractory power of the second non-abrupt interface rete is expressed as to n ₃=f(n ₂, k ₂, n ₄, k ₄), optical extinction coefficient is expressed as k ₃=f(n ₂, k ₂, n ₄, k ₄), the specific refractory power of the 3rd non-abrupt interface rete is expressed as to n ₅=f(n ₄, k ₄, n _air, k _air), optical extinction coefficient is expressed as k ₅=f(n ₄, k ₄, n _air, k _air), n _air, k _airrepresent respectively specific refractory power and the optical extinction coefficient of air, and by n ₂, k ₂, n ₄, k ₄, n ₆expand into the function of lambda1-wavelength λ.Utilize matrix method to set up the parameters relationship of five tunic reflectivity and Film Optics parameter, R| _{h1, h2, h3, h5, n1, k1, n2, k2}(h ₂, h ₄, n ₄, k ₄, λ), wherein R is the reflectivity of coated glass, utilizes CIE matrix and L ^*a ^*b ^*the regulation of uniform colour space and R| _{h1, h2, h3, h5, n1, k1, n2, k2}(h ₂, h ₄, n ₄, k ₄, λ), the parameter type S| of acquisition coated glass reflected colour fullness of shade _{h1, h2, h3, h5, n1, k1, n2, k2}(h ₂, h ₄, n ₄, k ₄, λ), set up thus the mathematical model of eliminating reflected colour, shown in (1),

min(S| _{h1,h2,h3,h5,n1,k1,n2,k2}(h ₂,h ₄,n ₄,k ₄)) （1）

h ₂,h ₄,n ₄,k ₄∈D

Wherein D represents parameter-definition territory, solves formula (1), and obtaining and making S is one group of parameter h of minimum value ₂, h ₄, n ₄, k ₄, elimination has the parameter of the target rete of non-abrupt interface double membrane structure coated glass reflected colour exactly.

2. have the rete method of design of non-abrupt interface double membrane structure coated glass reflected colour according to the elimination described in right 1, it is characterized in that the two-step approach that the formula that solves (1) adopts simulated annealing and Newton iteration method to combine solves, concrete steps are as follows:

1) use simulated annealing solution formula (1), obtain one group of parameter h ₂, h ₄, n ₄and k ₄value;

2) h obtaining with step 1) ₂, h ₄, n ₄and k ₄as the calculating initial value of Newton iteration method, again solve formula (1);

3) repeating step 1), 2) M time, M=1,2 ... positive integer, in M the result obtaining, obtains and makes S value for one group of minimum parameter h ₂, h ₄, n ₄and k ₄.