A method for determining optical constants of a transparent solid based on a layered sample transmission spectrum analysis method

Abstract

The application discloses a method for measuring optical constants of transparent solid based on a layered sample transmission spectrum analysis method, and belongs to the fields of spectroscopy and optical measurement. The principle of the application is that: layering flat sample materials with the same thickness, measuring the transmittance of two layered combination samples, deriving the transmittance t and reflectance r of light vertically through a single layer sample with a thickness of L through algebraic operation, then obtaining the attenuation factor y and the interface reflectance R through an analytical method, and further obtaining the extinction coefficient k and the refractive index n of the sample, so as to realize the measurement of the optical constants of the transparent solid. The application solves the problem of inconsistent conditions of measuring the reflection and transmission spectrum of the single layer sample in the prior art, and also solves the iteration error and the time-consuming calculation problem existing in the layered sample transmission spectrum inversion method, and greatly simplifies the experimental measurement and solving calculation process.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of spectroscopy and optical measurement, and particularly relates to a method for measuring optical constants of transparent solid based on a layered sample transmission spectrum analytical method. BACKGROUND

[0002] A method for determining optical constants based on spectral reflectance and transmittance of a single-layer sample is generally by setting the refractive index and extinction coefficient of infrared optical material as n and k respectively, and then the attenuation coefficient α = 4πk / λ, where λ is the wavelength of light in vacuum. The infrared optical material is made into a plane-parallel mirror, which is placed in air (refractive index is 1 and extinction coefficient is 0) for measurement. When the light is vertically incident on the mirror, according to the Fresnel law and Snell's law, the interface reflectivity on the interface between the mirror and air is represented as R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ]. Considering the multiple reflections of light on the two interfaces of the mirror, while ignoring the interference effect, when the infrared light with intensity I0 is vertically irradiated on the mirror with thickness L, the reflected light intensity I R and the transmitted light intensity I T are the non-coherent superposition of the multiple reflections and transmissions of light on the two interfaces of the mirror, and then the reflectivity r and the transmittance t of the light after passing through the mirror are represented as and

[0003] The problem of the above method is that the conditions for measuring reflectivity and transmittance are inconsistent, wherein the transmittance is measured by vertical incidence, and the reflectivity is measured by approximately vertical incidence.

[0004] Another researcher stacks the sample with the same thickness, measures the transmittance under different stacking combinations, and then uses the inversion method to determine the optical constants of the material, but the inversion method also has problems: mainly in the problems of time-consuming calculation and iteration error. SUMMARY

[0005] The present application aims to provide a method for measuring optical constants of transparent solid based on a layered sample transmission spectrum analytical method, which solves the problem of inconsistent conditions for measuring reflectivity and transmittance of single-layer sample double-spectrum method, and avoids the problems of iteration error and time-consuming calculation of layered sample inversion method.

[0006] The present application is achieved by the following technical solutions:

[0007] A method for measuring optical constants of transparent solid based on a layered sample transmission spectrum analytical method, comprising the following steps:

[0008] S1, multiple sample layers of the same material and consistent specifications and thickness L are stacked and placed in parallel to obtain a stacked sample;

[0009] S2, a spectrometer is used to measure the transmittance t1 of light vertically through a single layer sample and the transmittance t of light vertically through the stacked sample, respectively; n ;

[0010] S3, according to t1 and t obtained in step S2, the transmittance t and the reflectance r of the single layer sample are obtained; n

[0011] S4, according to the transmittance t and the reflectance r of the single layer sample obtained in step S3, the attenuation factor y is obtained by analytical solution; further, the attenuation coefficient a and the extinction coefficient k of the sample are obtained;

[0012] S5, according to the transmittance t and the reflectance r of the single layer sample obtained in step S3, the interface reflectance R is obtained by analytical solution, and the interface reflectance R is obtained by Fresnel law and Snell law; further, the refractive index n of the sample is obtained.

[0013] Further, the thickness of the air layer between adjacent samples in the stacked sample in step S1 satisfies the condition of not considering the interference effect.

[0014] Further, the thickness of the single layer sample satisfies that the transmittance curve of the double layer sample falls between t 2 and t / (2-t).

[0015] Further, the multiple sample layers placed in parallel are two sample layers placed in parallel, specifically comprising the following steps:

[0016] S1, two samples of the same material and consistent specifications and thickness L are stacked and placed in parallel to obtain a stacked sample;

[0017] S2, a spectrometer is used to measure the transmittance t1 of light vertically through a single layer sample and the transmittance t of light vertically through the stacked sample, respectively;

[0018] t1=t(1)

[0019]

[0020] S3, formula (1), (2) are solved by t1 and t2:

[0021] t=t1(3)

[0022]

[0023] S4, according to the transmittance t and the reflectance r of the single layer sample obtained in step S3, the attenuation factor y is further obtained as: ​

[0024]

[0025] Then the attenuation coefficient a and the extinction coefficient k of the sample are respectively:

[0026] a = -ln(y) / L (6)

[0027] k = -λln(y) / (4πL) (7)

[0028] wherein λ is the wavelength of the light in vacuum;

[0029] S5, further obtaining the interface reflectivity R according to the transmittance t and the reflectivity r of the single-layer sample obtained in step S3:

[0030]

[0031] Further, the interface reflectivity R is obtained from the Fresnel law and the Snell law, i.e. R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], and the refractive index n of the sample is obtained as:

[0032]

[0033] Further, the plurality of sample layers are placed in parallel as three sample layers, and specifically comprising the following steps:

[0034] S1, placing three samples of the same material and consistent specifications and having a thickness of L in parallel to obtain a layered sample;

[0035] S2, using a spectrometer to measure the transmittance t1 of light vertically passing through one sample and the transmittance t3 of light vertically passing through three samples respectively:

[0036] t1 = t (1)

[0037]

[0038] S3, obtaining t from t1 and t3 by simultaneously solving equations (1) and (10):

[0039] t = t1 (3)

[0040]

[0041] S4, further obtaining the attenuation factor y according to the transmittance t and the reflectivity r of the single-layer sample obtained in step S3:

[0042]

[0043] The attenuation coefficient a and the extinction coefficient k of the sample are respectively:

[0044] a = -ln(y) / L (6)

[0045] k = -ln(y) / (4pL) (7)

[0046] Wherein, the wavelength of light in vacuum is λ;

[0047] According to the transmittance t and the reflectance r of the single-layer sample obtained in step S3, the interface reflectance R is further obtained:

[0048]

[0049] According to the Fresnel law and the Snell law, the interface reflectance R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ] is obtained, and the refractive index n of the sample is obtained:

[0050]

[0051] Further, the transmittance t and the reflectance r formula in step S3 are respectively:

[0052] t = (1-R) 2 exp(-aL) / [1-R 2 exp(-2aL)] (12)

[0053] r = R[1+(1-R) 2 exp(-2aL) / [1-R 2 exp(-2aL)]] (13)

[0054] Wherein, the interface reflectance R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], n and k are the refractive index and the extinction coefficient of the sample respectively, the attenuation coefficient a = 4p k / λ, λ is the wavelength of light in vacuum, and L is the thickness of the single-layer sample.

[0055] Compared with the prior art, the present application has the following beneficial effects:

[0056] The present application stacks the same thickness of flat sample material, measures the transmittance of two kinds of stacked sample, and derives the reflectance of single layer sample through algebraic operation, so that the optical constants of transparent solid material can be determined by using the dual spectrum analysis method of single layer sample without measuring the reflectance. The method solves the problem of inconsistent conditions of measuring reflectance and transmittance spectrum in dual spectrum method, and avoids the iteration error and time-consuming calculation of inversion method. The present application has the characteristics of simple experimental measurement and small calculation amount.

[0057] The present application studies the influence law of material optical constants and sample thickness on the transmittance curve of single layer and double layer sample through numerical simulation, analyzes the cause of transmittance measurement error, and gives the specific method to reduce the measurement error: adjusting the thickness of single layer sample to make the transmittance curve of double layer sample fall in the middle position between t 2 and t / (2-t) as far as possible, which will help to improve the experimental measurement accuracy of the transmittance of stacked sample, and then realize the accurate determination of optical constants. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 It is the experimental principle diagram of the present application.

[0059] Figure 2 It is the transmittance curve diagram t1 and t2 of zinc selenide (ZnSe) stacked sample.

[0060] Figure 3 It is the transmittance and reflectance curve diagram of zinc selenide (ZnSe) single layer sample.

[0061] Figure 4 It is the curve diagram of extinction coefficient of zinc selenide (ZnSe) sample material.

[0062] Figure 5 It is the curve diagram of refractive index of zinc selenide (ZnSe) sample material. DETAILED DESCRIPTION

[0063] The present application will be further described in detail below in combination with specific examples, which are the explanation but not the limitation of the present application.

[0064] A method for determining optical constants of transparent solid based on the transmittance spectrum analysis method of stacked sample, assuming that the refractive index and extinction coefficient of transparent flat material are n and k respectively, the attenuation coefficient α=4πk / λ, wherein λ is the wavelength of light in vacuum, the flat material is placed in air (refractive index is 1 and extinction coefficient is 0), and the light is assumed to be perpendicular to the incident, according to the Fresnel law and Snell law, the interface reflectance R=[(n-1) 2 +k 2 ] / [(n+1) 2 +k2 When the multiple reflections of light on two interfaces are considered and the interference effect is ignored, the transmittance t and reflectance r of light vertically through a flat sample with thickness L can be expressed as:

[0065] t = (1 - R) 2 exp(-αL) / [1 - R 2 exp(-2αL)] (1)

[0066] r = R[1 + (1 - R) 2 exp(-2αL) / [1 - R 2 exp(-2αL)] (2)

[0067]

[0068] When flat sample layers of the same material and specifications with thickness L are stacked and placed in parallel, the thickness of the air layer between adjacent samples should satisfy the condition that the interference effect does not need to be considered, then the transmittance tl of light vertically through a flat sample, the transmittance t2 of light vertically through two flat stacked samples, and the transmittance t3 of light vertically through three flat stacked samples can be expressed as:

[0069] t1 = t (3)

[0070]

[0071] where t and r are given by equations (1) and (2), i.e., the transmittance and reflectance of light vertically through a single flat sample with thickness L. By combining equations (3) and (4), we get:

[0072] t = t1 (6)

[0073]

[0074] If equations (3) and (5) are combined, we get:

[0075] t = t1 (6)

[0076]

[0077] That is, the reflectance r and transmittance t of light vertically through a single layer sample can be analytically obtained from the transmittance of the stacked sample. Let y = exp(-αL), and substitute equation (1) into equation (2) to get:

[0078] r = R (1 + ty) (9)

[0079] Then, by eliminating R from equations (1) and (9), we get:

[0080] ty 2 + [(r - 1) 2 - t2 ]y-t=0(10)

[0081] The solution of equation (10) is:

[0082]

[0083] The attenuation coefficient and extinction coefficient of the material are respectively

[0084] α=-ln(y) / L (12)

[0085] k=-λln(y) / (4πL) (13)

[0086] Substituting equation (11) into equation (9) and rearranging, we get:

[0087]

[0088] And the refractive index of the material is 2 +k 2 ] / [(n+1) 2 +k 2 ]

[0089]

[0090] Therefore, only the transmittance of the laminated sample needs to be measured, which can be a combination of t1 and t2, or a combination of t1 and t3, and then the transmittance t and reflectance r of light vertically through a single-layer flat sample with a thickness of L are calculated by equation (6) and equation (7), or equation (6) and equation (8), which are substituted into equation (11), equation (14) to obtain y and R, and then the attenuation coefficient, extinction coefficient and refractive index of the sample material are obtained by equation (12), equation (13) and equation (15).

[0091] Example 1

[0092] The two samples selected for the example are uncoated laser-grade zinc selenide (ZnSe) discs with a diameter of 25.4 mm and a thickness of 6 mm, and the actual thicknesses are 6.01 mm and 6.05 mm, respectively. The transmittance spectra of the single-layer sample and the double-layer sample (separated by a silicone ring with a diameter of 25 mm and a thickness of 2 mm) were measured using a FOLI20 Fourier transform infrared spectrometer (transmittance accuracy ≤0.1%T) in the spectral range of 5-18 μm. The resolution of the spectrometer is 4 cm -1 -1 at room temperature (about 25.1°C) in an atmospheric environment. The transmittance of the single-layer and double-layer samples was measured 6 times, and the average values were calculated as t1 and t2, respectively, to determine the optical constants of zinc selenide. The transmittance curves are shown in Figure 2 The transmittance and reflectance curves of the zinc selenide (ZnSe) single-layer sample are calculated asFigure 3 As shown. Further calculations yielded the extinction coefficient and refractive index curves of the zinc selenide (ZnSe) sample material, as shown below. Figure 4 , Figure 5 As shown.

[0093] like Figure 4 As shown in the figure, the red line represents the extinction coefficient, and the black-filled area surrounded by the green line represents the uncertainty of the extinction coefficient. Figure 4 The relative uncertainty of the extinction coefficient is also shown by black lines. It can be seen that the extinction coefficient of zinc selenide in the 5-14 μm range is approximately 1.0 × 10⁻⁶. －6 From 14 to 18 μm, the extinction coefficient gradually increases to approximately 1.0 × 10⁻⁶. －4 In terms of relative uncertainty, the relative uncertainty of the extinction coefficient is less than 20% in the range of 5.0-11.5 μm; less than 10% in the range of (7.0-8.5, 14-18) μm; less than 5% in the range of (15.0-17.5) μm; and the best result is near 16 μm, with a relative uncertainty of less than 2%.

[0094] like Figure 5 As shown in the figure, the red line represents the refractive index, and the black-filled area surrounded by the green line represents the uncertainty of the refractive index. Figure 5 The relative uncertainty of the refractive index is also given by black lines. It can be seen that the relative uncertainty of the refractive index of zinc selenide is less than 0.5% in the (5-15) μm range, and less than 0.25% in the (7-12, 13-14) μm range. Compared with the relative uncertainty of the extinction coefficient, the measurement accuracy of the refractive index is higher. From equation (15), it is known that when the extinction coefficient is less than 1.0 × 10⁻⁶... －4 At this time, the interfacial reflectivity R plays a dominant role, and the value of the extinction coefficient contributes almost nothing to the refractive index. Therefore, the refractive index can be used as... The calculations are performed with sufficiently high precision.

[0095] As can be seen from Example 1, this invention, by measuring the transmittance of stacked samples, can analytically calculate and determine the optical constants of transparent solid materials without measuring reflectance or using inversion iterative calculations. This invention solves the problem of inconsistent conditions in measuring reflectance and transmission spectra in dual-spectrum methods, and avoids the iterative errors and computational time issues of inversion methods, thus providing a simple experimental and computationally convenient method for determining the optical constants of transparent solids.

[0096] Furthermore, this invention investigated the relationship between the transmittance of single-layer and double-layer samples, pointing out that the transmittance t of a single-layer sample limits the range of values ​​for the transmittance t2 of a double-layer sample, i.e., t 2t / (2-t). When the accuracy of the transmittance of the spectrometer is 0.001, the conclusion that the transmittance t of the single-layer sample should be greater than 0.004 and less than 0.953 is given for the model of the present application, further, the thickness of the single-layer sample should be reasonably adjusted so that the transmittance curve of the double-layer sample falls in the middle position between greater than t 2 t / (2-t) as far as possible, which will help to improve the experimental measurement accuracy of the transmittance of the laminated sample, and further improve the determination accuracy of the optical constants of the sample material.

Claims

1. A method for determining optical constants of a transparent solid based on a transmission spectrum analysis method of a layered sample, characterized by, The method comprises the following steps: S1, The same material with consistent specifications and thickness. L Multiple samples are stacked in parallel to obtain stacked samples; S2, measure the transmittance of light perpendicularly through the single layer sample using the spectrometer t 1 and the transmittance through the laminated sample t n ; S3, the transmittance of the single-layer sample obtained from step S2 t 1 and t n , the transmittance t and reflectance r of the single-layer sample S4. Transmittance of the single layer sample obtained in step S3 t and reflectance r The attenuation factor y is obtained by analytical solution; further, the attenuation coefficient α and the extinction coefficient k of the sample are obtained S5, transmittance of the single layer sample obtained in step S3 t and reflectance r , the interface reflectance R is obtained by analytical solution, and the interface reflectance R is obtained by Fresnel law and Snell law, and the refractive index of the sample is further obtained n ; The thickness of the air layer between the adjacent samples in the sample layering in the step S1 satisfies the condition without considering the interference effect; The multiple sample layering parallel placement is 2 sample layering parallel placement, and specifically comprises the following steps: S1, The same material with consistent specifications and thickness. L Two samples are stacked in parallel to obtain a stacked sample; S2, measure the transmittance of light through a sample perpendicular to the sample using a spectrometer t 1, by the transmittance of two samples t 2: （1） （2） S3, from (1), (2) by t 1 and t 2 （3） （4） S4, transmittance of the single layer sample obtained according to step S3 t and reflectance r , further obtaining the attenuation factor y as: （5） The attenuation coefficient of the sample is then α and the extinction coefficient k are respectively （6） （7） wherein λ is the wavelength of light in vacuum; S5, the transmittance of the single layer sample obtained according to step S3 t and the reflectance r further obtaining the interface reflectance R as: （8） From the Fresnel law and Snell law, the interface reflectivity is obtained The refractive index of the sample is obtained as: n n = 1.45 （9）。 2. The method for determining optical constants of a transparent solid from a stack of sample transmission spectra according to claim 1, characterized in that, The multiple sample layering parallel placement is 3 sample layering parallel placement, and specifically comprises the following steps: S1, The same material with consistent specifications and thickness. L Three samples were stacked in parallel to obtain a stacked sample. S2, measure the transmittance of light through a sample perpendicular to the sample using a spectrometer t 1, by the transmittance of three samples t 3: （1） （10） S3, from (1), (10) by t 1 and t 3 （3） （11） S4, the transmittance of the single layer sample obtained according to step S3 t and the reflectance r , further obtaining the attenuation factor y as; （5） The attenuation coefficient of the sample is then α and the extinction coefficient k respectively （6） （7） wherein λ is the wavelength of light in vacuum; S5, the transmittance of the single layer sample obtained according to step S3 t and the reflectance r further obtaining the interface reflectance R as: （8） From the Fresnel law and Snell law, the interface reflectivity is obtained The refractive index of the sample is obtained n is: （9）。 3. A method for determining optical constants of a transparent solid from a stack of sample transmission spectra according to claim 1 or 2, characterized in that, The transmittance in the step S3 t and the reflectance r The formulas are respectively: t =(1- R ) 2 exp(- αL ) / [1- R 2 exp(-2 αL )](12) r = R [1+(1- R ) 2 exp(-2 αL ) / [1- R 2 exp(-2 αL )]] (13) wherein the interface reflectivity R = [( n − 1) 2 + k 2 ] / [( n + 1) 2 + k 2 ], n and k are the refractive index, the extinction coefficient, the attenuation coefficient of the sample, respectively α = 4π k / λ , λ λ is the wavelength of the light in vacuum, L is the thickness of the single-layer sample.

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