CN102749307A - Measuring method of optical constant of semi-transparent solid material - Google Patents

Abstract

A measuring method of optical constant of a semi-transparent solid material aims at resolving the problem that the existing double-thickness transmission method cannot achieve the effect that two samples with identical thickness are utilized to achieve measurement of the optical constant. The method includes step one measuring transmission spectrum and step two calculating optical constant, wherein the step two includes step 1 supposing refraction index of the optical constant of the semi-transparent solid material is n0, absorption index is k0, largest iteration number N is 10000, and iteration accuracy e is 10-7, step 2 selecting and calculating two transmission spectrum measuring value T single and T overlapping under wavelength lambada I, conducting substitution of the two values in a reflectivity calculating function, step 3 substituting calculated rho and single sample transmission spectrum measuring value T single i into an absorption index function, step 4 substituting calculated rhoi and calculated ki into a refraction index calculating function; step 5 evaluating calculation results, namely substituting calculated ni and ki into an evaluation function; and step 6 analyzing calculation results. The measuring method is used for optical constant of the semi-transparent material.

Description

The measuring method of translucent solid material optical constant

Technical field

The present invention relates to a kind of measuring method of trnaslucent materials optical constant.

Background technology

Transmission beam method is to obtain the common method of translucent solid material optical constant, and the difference of measuring samples thickness can be divided into two types as required: single thickness transmission beam method and two thickness transmission beam methods.Needing simultaneous Kramers-Kronig (K-K) dispersion relation formula in single thickness transmission beam method computation process, is the method comparatively widely of using at present, but adopts short-cut method structure K-K relational expression to realize that finding the solution of optical constant and its process are loaded down with trivial details.Use two thickness transmission beam method principles of two different-thickness samples simple; Need not adopt the K-K relational expression, and not need to simplify, but the key of its realization is to obtain spectral transmission data under the different-thickness; Utilize the photometry method to calculate again; Like people such as Li Quanbao (Li Quanbao, Song Ping Wen, Wei Tian thoroughfare .Hg _1-xCd _xThe Te optical constant is measured. infrared technique, and 1996,18 (5): 17-20), the magnitude people (Su Xing of Soviet Union; Li Zhengfen, Liu Chengzan, Chen Yan, Zhao Yunsheng. a kind of optical constant of infrared selenide glass and anti-reflection film thereof. infrared technique; 1991,13 (5): 15-18), all adopt the sample of two different-thickness; Measure its spectral transmission data respectively, carry out Inversion Calculation then, its computing method are only applicable to the calculating of the sample spectra transmission data of two different-thickness.Yet; Most of translucent solid materials are single thickness sample; Use two thickness transmission beam methods of two different-thickness samples in actual measurement, to have some inconvenience, cause at present two thickness transmission beam methods can not satisfy the measurement that utilizes two same thickness samples to realize its optical constant.

Summary of the invention

The measuring method that the purpose of this invention is to provide a kind of trnaslucent materials optical constant can not satisfy the problem of utilizing two same thickness samples to realize the measurement of its optical constant to solve at present two thickness transmission beam methods.

The present invention solves the problems of the technologies described above the technical scheme of taking to be: said method comprises the steps: step 1, measures transmitted spectrum: utilize Fourier spectrometer to measure the normal direction transmitted spectrum measured value T of monolithic sample _Single, and then utilize the normal direction transmitted spectrum measured value T after Fourier spectrometer is measured the sample stack of two same thickness L _Folded

Step 2, find the solution optical constant:

The refractive index n of step 2 one, the translucent solid material optical constant of supposition ₀, absorption index k ₀, maximum iteration time N=10000, iteration precision e=10 ^-7

Step 2 two, choose the measurement wavelength X _iFollowing two kinds of transmitted spectrum measured value T _SingleAnd T _FoldedBring reflectivity into and calculate function, j=j+1, and wavelength X is measured in supposition _iThe refractive index n of second transparent solid material optical constant _i=n ₀, absorption index k _i=k ₀, expression formula is:

Wherein, ρ _iFor solid material in wavelength X _iThe calculating reflectivity, L is the monolithic sample thickness, j is an iterations;

Step 2 three, the ρ that formula 1-1 is calculated _iWith monolithic sample transmitted spectrum measured value T _{Single i}Bring the absorption index computing function into, expression formula does

Wherein, k _iFor solid material in wavelength X _iAbsorption index;

Step 2 four, with the ρ that calculates among the formula 1-1 _iWith the k that calculates among the formula 1-2 _iBring refractive index into and calculate function, expression formula does

$n_i=\frac{(1+{\mathrm{\ρ}}_i)+{[{(1+{\mathrm{\ρ}}_i)}^2-{(1-{\mathrm{\ρ}}_i)}^2(1+{k_i}^2)]}^{\frac{1}{2}}}{1-{\mathrm{\ρ}}_i}$

Wherein, n _iFor solid material in wavelength X _iRefractive index;

Step 2 five, evaluation calculation result: with the n that calculates _iAnd k _iBring evaluation function into, expression formula does

$E=\mathrm{Max}\left(\right|\frac{n-n_i}{n_i}|,|\frac{k-k_i}{k_i}\left|\right)$

Wherein, Max () is for getting max function;

Step 2 six, analysis result: if E>=10 that evaluation function calculates ^-7, the n that then formula 1-2 and formula 1-3 is calculated _jAnd k _jSubstitute n ₀, k ₀, return step 2 two, the E that in step 2 five, calculates＜10 ^-7, perhaps j＞N meets the demands.

The present invention has following beneficial effect: compare with the existing transmission beam method that is used for opaque solid material, remarkable advantage of the present invention is: 1, only use the sample of two same thickness, just can realize the measuring method of translucent solid material optical constant; 2, computation process adopts alternative manner, avoids introducing the inconvenience that intelligent algorithm is brought; 3, can combine with the Fourier spectrometer Survey Software, directly read transmittance spectra data and calculate, widen the range of application of Fourier spectrometer, have potential commercial value.

Description of drawings

Fig. 1 measures monolithic sample transmitted spectrum synoptic diagram for Fourier spectrometer; Fig. 2 measures the transmitted spectrum synoptic diagram of two sample stacks for Fourier spectrometer; Fig. 3 is the process flow diagram of the inventive method; Fig. 4 is the transmittance spectra data figure of 2mm zinc selenide and two 2mm zinc selenide stacks; Fig. 5 measures the absorption index curve of zinc selenide for adopting the inventive method; Fig. 6 measures the refractive index curve of zinc selenide for adopting the inventive method.

Embodiment

Embodiment one: the method for this embodiment comprises the steps: that said method comprises the steps: step 1, measures transmitted spectrum: utilize Fourier spectrometer to measure the normal direction transmitted spectrum measured value T of monolithic sample _Single, and then utilize the normal direction transmitted spectrum measured value T after Fourier spectrometer is measured the sample stack of two same thickness L _Folded

Step 2, find the solution optical constant:

The refractive index n of step 2 one, the translucent solid material optical constant of supposition ₀, absorption index k ₀, maximum iteration time N=10000, iteration precision e=10 ^-7

Step 2 two, choose the measurement wavelength X _iFollowing two kinds of transmitted spectrum measured value T _SingleAnd T _FoldedBring reflectivity into and calculate function, j=j+1, and wavelength X is measured in supposition _iThe refractive index n of second transparent solid material optical constant _i=n ₀, absorption index k _i=k ₀, expression formula is:

Wherein, ρ _iFor solid material in wavelength X _iThe calculating reflectivity, L is the monolithic sample thickness, j is an iterations;

Step 2 three, the ρ that formula 1-1 is calculated _iWith monolithic sample transmitted spectrum measured value T _{Single i}Bring the absorption index computing function into, expression formula does

Wherein, k _iFor solid material in wavelength X _iAbsorption index;

Step 2 four, with the ρ that calculates among the formula 1-1 _iWith the k that calculates among the formula 1-2 _iBring refractive index into and calculate function, expression formula does

$n_i=\frac{(1+{\mathrm{\ρ}}_i)+{[{(1+{\mathrm{\ρ}}_i)}^2-{(1-{\mathrm{\ρ}}_i)}^2(1+{k_i}^2)]}^{\frac{1}{2}}}{1-{\mathrm{\ρ}}_i}$

Wherein, n _iFor solid material in wavelength X _iRefractive index;

Step 2 five, evaluation calculation result: with the n that calculates _iAnd k _iBring evaluation function into, expression formula does

$E=\mathrm{Max}\left(\right|\frac{n-n_i}{n_i}|,|\frac{k-k_i}{k_i}\left|\right)$

Wherein, Max () is for getting max function;

Step 2 six, analysis result: if E>=10 that evaluation function calculates ^-7, the n that then formula 1-2 and formula 1-3 is calculated _jAnd k _jSubstitute n ₀, k ₀, return step 2 two, the E that in step 2 five, calculates＜10 ^-7, perhaps j＞N meets the demands.

Embodiment two: combine 1 embodiment of figure explanation, the derivation of formula described in the step 2 two of this embodiment

is following: the normal direction emission ratio of monolayer material

$R_i={\mathrm{\ρ}}_i+{\mathrm{\ρ}}_i{T}_i{e}^{-\frac{4\mathrm{\π}{\mathrm{kL}}_i}{\mathrm{\λ}}}---(2-1)$

The normal direction transmittance $T_i=\frac{{(1-{\mathrm{\ρ}}_i)}^2{e}^{-\frac{4\mathrm{\π\; KL}}{{\mathrm{\λ}}_i}}}{1-{{\mathrm{\ρ}}_i}^2{e}^{-\frac{8\mathrm{\π\; KL}}{{\mathrm{\λ}}_i}}}---(2-2)$

Wherein, boundary reflection rate ρ _iSatisfy

${\mathrm{\ρ}}_{\text{i}}=\frac{{(n_i-1)}^2+{k_i}^2}{{(n_i+1)}^2+{k_i}^2}---(2-3)$

When transmitted ray gets into two layers of thickness L ₁And L ₂Material the time, total normal direction transmittance T of materials at two layers ₁₊₂For

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00001944109500021.png"\; state="\{\{state\}\}">T</figure-callout>}}_{1+2}=\frac{T_2{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00001944109500021.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}{1-R_1{R}_2}---(2-4)$

If two sample thickness are identical, through two samples be superimposed the test its overall transmission ratio, following by formula (2-1) to formula (2-5) equationof structure process;

Because thickness of sample is identical, then satisfy

R ₁＝R ₂ T ₁＝T ₂ ?(2-5)

Bringing formula (2-5) into formula (2-4) can know

${\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00001944109500021.png"\; state="\{\{state\}\}">T</figure-callout>}}_{1+2}=\frac{{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00001944109500021.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}^2}{1-{R_1}^2}---(2-6)$

Bring monolayer material thickness L into formula (2-1), and bring formula (2-1) into formula (2-6), and distortion can be known

$1-\frac{{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00001944109500021.png"\; state="\{\{state\}\}">T</figure-callout>}}_1}^2}{{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00001944109500021.png"\; state="\{\{state\}\}">T</figure-callout>}}_{1+2}}={\mathrm{\&rho;}}_i+{\mathrm{\&rho;}}_i{T}_1{e}^{-\frac{4\mathrm{\&pi;kL}}{{\mathrm{\&lambda;}}_i}}---(2-7)$

Can know transmittance calculating reflectivity ρ by formula (2-7) through individual layer and double layer material _i

Formula in the step 2 three is found the solution and can be drawn by formula (2-2).

Embodiment three: consult measuring method among Fig. 1, utilize Fourier spectrometer to record the normal direction transmittance spectra data T of individual layer sample _M1Consult measuring method among Fig. 2, utilize Fourier spectrometer to measure two normal direction transmitted spectrum T after the stack of same thickness sample again _M2

Through finding the solution the optical constant of sample on the computing machine that has loaded the inventive method, Fig. 3 has provided the process flow diagram of solution procedure, in conjunction with it embodiment of the present invention is described in further detail.

1) input initial parameter: wavelength X _i, individual layer and two tier approach are to sample transmitted spectrum wavelength X _iTwo kinds of transmitted spectrum value T _{Single i}And T _{Folded i}, thickness in monolayer L, initial solution n ₀, k ₀,, maximum iteration time N, j=0, iteration precision e.

2) find the solution optical constant:

1. wavelength X _iTwo kinds of transmitted spectrum value T _{Single i}And T _{Folded i}Bring reflectivity into and calculate function, expression formula is:

Wherein, ρ _iFor solid material in wavelength X _iThe calculating reflectivity, L is the monolithic sample thickness.

The ρ that 2. will 1. calculate _iWith the monolithic sample transmitted spectrum value T that measures _{Single i}Bring the absorption index computing function into, expression formula does

Wherein, k _iFor solid material in wavelength X _iAbsorption index.

3. will the 1. middle ρ that calculates _i2. the k that calculates in _iBring refractive index into and calculate function, expression formula does

$n_i=\frac{(1+{\mathrm{\&rho;}}_i)+{[{(1+{\mathrm{\&rho;}}_i)}^2-{(1-{\mathrm{\&rho;}}_i)}^2(1+{k_i}^2)]}^{\frac{1}{2}}}{1-{\mathrm{\&rho;}}_i}$

Wherein, n _iFor solid material in wavelength X _iRefractive index.

3) evaluation calculation result: with the n that calculates _iAnd k _iBring evaluation function into, expression formula does

$E=\mathrm{Max}\left(\right|\frac{n-n_i}{n_i}|,|\frac{k-k_i}{k_i}\left|\right)$

Wherein, Max () is for getting max function.

4) analysis result: if E>=10 that evaluation function calculates ^-7, the n that then formula 1-2 and formula 1-3 is calculated _jAnd k _jSubstitute n ₀, k ₀, return step 2 two, the E that in step 2 five, calculates＜10 ^-7, perhaps j＞N meets the demands.

Adopt the wavelength 1-20 μ m transmittance spectra data of the inventive method measurement 2mm zinc selenide and two 2mm zinc selenide stacks as shown in Figure 4.Fig. 5 measures the absorption index curve of zinc selenide for adopting the inventive method, and Fig. 6 measures the refractive index curve of zinc selenide for the employing method that the present invention introduced.

Claims (2)

1. the measuring method of a translucent solid material optical constant is characterized in that said method comprises the steps: step 1, measures transmitted spectrum: utilize Fourier spectrometer to measure the normal direction transmitted spectrum measured value T of monolithic sample _Single, and then utilize the normal direction transmitted spectrum measured value T after Fourier spectrometer is measured the sample stack of two same thickness L _Folded

Step 2, find the solution optical constant:

The refractive index n of step 2 one, the translucent solid material optical constant of supposition ₀, absorption index k ₀, maximum iteration time N=10000, iteration precision e=10 ^-7

Step 2 two, choose the measurement wavelength X _iFollowing two kinds of transmitted spectrum measured value T _SingleAnd T _FoldedBring reflectivity into and calculate function, j=j+1, and wavelength X is measured in supposition _iThe refractive index n of second transparent solid material optical constant _i=n ₀, absorption index k _i=k ₀, expression formula is:

Wherein, ρ _iFor solid material in wavelength X _iThe calculating reflectivity, L is the monolithic sample thickness, j is an iterations;

Step 2 three, the ρ that formula 1-1 is calculated _iWith monolithic sample transmitted spectrum measured value T _{Single i}Bring the absorption index computing function into, expression formula does

Wherein, k _iFor solid material in wavelength X _iAbsorption index;

Step 2 four, with the ρ that calculates among the formula 1-1 _iWith the k that calculates among the formula 1-2 _iBring refractive index into and calculate function, expression formula does

$n_i=\frac{(1+{\mathrm{\&rho;}}_i)+{[{(1+{\mathrm{\&rho;}}_i)}^2-{(1-{\mathrm{\&rho;}}_i)}^2(1+{k_i}^2)]}^{\frac{1}{2}}}{1-{\mathrm{\&rho;}}_i}$

Wherein, n _iFor solid material in wavelength X _iRefractive index;

Step 2 five, evaluation calculation result: with the n that calculates _iAnd k _iBring evaluation function into, expression formula does

$E=\mathrm{Max}\left(\right|\frac{n-n_i}{n_i}|,|\frac{k-k_i}{k_i}\left|\right)$

Wherein, Max () is for getting max function;

Step 2 six, analysis result: if E>=10 that evaluation function calculates ^-7, the n that then formula 1-2 and formula 1-3 is calculated _jAnd k _jSubstitute n ₀, k ₀, return step 2 two, the E that in step 2 five, calculates＜10 ^-7, perhaps j＞N meets the demands.

2. according to the measuring method of the said translucent solid material optical constant of claim 1, it is characterized in that the derivation of formula described in the step 2 two

is following: the normal direction emission ratio of monolayer material

$R_i={\mathrm{\&rho;}}_i+{\mathrm{\&rho;}}_i{T}_i{e}^{-\frac{4\mathrm{\&pi;}{\mathrm{kL}}_i}{\mathrm{\&lambda;}}}---(2-1)$

The normal direction transmittance $T_i=\frac{{(1-{\mathrm{\&rho;}}_i)}^2{e}^{-\frac{4\mathrm{\&pi;\; KL}}{{\mathrm{\&lambda;}}_i}}}{1-{{\mathrm{\&rho;}}_i}^2{e}^{-\frac{8\mathrm{\&pi;\; KL}}{{\mathrm{\&lambda;}}_i}}}---(2-2)$

Wherein, boundary reflection rate ρ _iSatisfy

${\mathrm{\&rho;}}_{\text{i}}=\frac{{(n_i-1)}^2+{k_i}^2}{{(n_i+1)}^2+{k_i}^2}---(2-3)$

When transmitted ray gets into two layers of thickness L ₁And L ₂Material the time, total normal direction transmittance T of materials at two layers ₁₊₂For

$T_{1+2}=\frac{T_2{T}_1}{1-R_1{R}_2}---(2-4)$

If two sample thickness are identical, through two samples be superimposed the test its overall transmission ratio, following by formula (2-1) to formula (2-5) equationof structure process;

Because thickness of sample is identical, then satisfy

R ₁＝R ₂ T ₁＝T ₂ ?(2-5)

Bringing formula (2-5) into formula (2-4) can know

$T_{1+2}=\frac{{T_1}^2}{1-{R_1}^2}---(2-6)$

Bring monolayer material thickness L into formula (2-1), and bring formula (2-1) into formula (2-6), and distortion can be known

$1-\frac{{T_1}^2}{T_{1+2}}={\mathrm{\&rho;}}_i+{\mathrm{\&rho;}}_i{T}_1{e}^{-\frac{4\mathrm{\&pi;kL}}{{\mathrm{\&lambda;}}_i}}---(2-7)$

Can know transmittance calculating reflectivity ρ by formula (2-7) through individual layer and double layer material _i

Formula in the step 2 three

is found the solution and can be drawn by formula (2-2).

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