Method for measuring transparent solid optical constant based on laminated sample transmission spectrum analytical method

Abstract

The invention discloses a method for measuring a transparent solid optical constant based on a laminated sample transmission spectrum analytical method, which belongs to the field of spectroscopy and optical measurement, and adopts the principle that flat sample materials with the same thickness are laminated, and the transmissivity of two laminated combined samples is measured; the transmissivity t and the reflectivity r when light vertically passes through a single-layer sample with the thickness L are derived through algebraic operation, then an attenuation factor y and the interface reflectivity R are obtained through an analytical method, then the extinction coefficient k and the refractive index n of the sample are obtained, and therefore the optical constant of the transparent solid is measured. According to the invention, the problem of inconsistent reflection and transmission spectrum measurement conditions of a single-layer sample double-spectrum method in the prior art is solved, the problems of iteration error and time consumption in calculation in a laminated sample transmission spectrum inversion method are also solved, and the experimental measurement and solving calculation process is greatly simplified.

Description

Technical Field

[0001] The invention belongs to the field of spectroscopy and optical measurement, and in particular relates to a method for measuring optical constants of transparent solids based on a stacked sample transmission spectrum analysis method. Background Art

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

[0003] The problem with the above method is that the conditions for measuring reflectivity and transmittance are inconsistent, wherein the transmittance is measured using a vertical incidence method, while the reflectivity is measured using a nearly vertical incidence method.

[0004] Other researchers stacked samples of the same thickness, measured the transmittance under different stacking combinations, and then used the inversion method to determine the optical constants of the material. However, the inversion method also has problems: mainly manifested in the time-consuming calculation and the existence of iterative errors. Summary of the invention

[0005] The purpose of the present invention is to provide a method for determining the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method, which not only solves the problem of inconsistent reflection and transmission spectrum conditions measured by the single-layer sample double spectrum method, but also avoids the iterative error and time-consuming calculation problems of the stacked sample inversion method.

[0006] The present invention is achieved through the following technical solutions:

[0007] A method for measuring the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method comprises the following steps:

[0008] S1, stacking and placing multiple samples of the same material, consistent specifications and thickness L in parallel to obtain a stacked sample;

[0009] S2, use a spectrometer to measure the transmittance t1 of light passing vertically through a single-layer sample and the transmittance t1 of light passing through a stacked sample. n ;

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

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

[0012] S5, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, the interface reflectance R is obtained by analytical solution, and then the interface reflectance R is obtained by Fresnel's law and Snell's law, and the refractive index n of the sample is further obtained.

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

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

[0015] Furthermore, the plurality of samples are stacked and placed in parallel as two samples are stacked and placed in parallel, which specifically includes the following steps:

[0016] S1, stack and place two samples of the same material, with the same specifications and thickness L in parallel to obtain a stacked sample;

[0017] S2, use a spectrometer to measure the transmittance t1 of light passing vertically through one sample and the transmittance t2 of light passing through two samples:

[0018] t1=t(1)

[0019]

[0020] S3, combining equations (1) and (2), from t1 and t2 we can get:

[0021] t=t1(3)

[0022]

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

[0024]

[0025] The attenuation coefficient α and extinction coefficient k of the sample are:

[0026] α=-ln(y) / L (6)

[0027] k=-λln(y) / (4πL) (7)

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

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

[0030]

[0031] Then, according to Fresnel's law and Snell's law, the interface reflectivity R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], and the refractive index n of the sample is obtained as:

[0032]

[0033] Furthermore, the plurality of samples are stacked and placed in parallel as three samples are stacked and placed in parallel, which specifically includes the following steps:

[0034] S1, stack and place three samples of the same material, with the same specifications and thickness L in parallel to obtain a stacked sample;

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

[0036] t1=t(1)

[0037]

[0038] S3, combining equations (1) and (10), from t1 and t3 we can get:

[0039] t=t1(3)

[0040]

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

[0042]

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

[0044] α=-ln(y) / L (6)

[0045] k=-λln(y) / (4πL)(7)

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

[0047] S5, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, the interface reflectance R is further obtained as:

[0048]

[0049] Then, according to Fresnel's law and Snell's law, the interface reflectivity R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], and the refractive index n of the sample is obtained as:

[0050]

[0051] Furthermore, the formulas for transmittance t and reflectance r in step S3 are respectively:

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

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

[0054] Among them, the interface reflectivity R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], n and k are the refractive index and extinction coefficient of the sample respectively, the attenuation coefficient α=4πk / 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 invention has the following beneficial effects:

[0056] The present invention stacks up flat sample materials of the same thickness, measures the transmittance of two stacked combination samples, and can derive the reflectance of a single-layer sample through algebraic operations. Thus, the optical constants of a transparent solid material can be determined by using a double-spectrum analysis method of a single-layer sample without measuring the reflectance. This method not only solves the problem of inconsistent conditions for measuring reflection and transmission spectra by the double-spectrum method, but also avoids the iterative error and time-consuming calculation problems of the inversion method. The present invention has the characteristics of simple experimental measurement and small calculation amount.

[0057] The present invention studies the influence of material optical constants and sample thickness on the transmittance curves of single-layer and double-layer samples through numerical simulation, analyzes the causes of transmittance measurement errors, and provides a specific method to reduce the measurement error: adjust the thickness of the single-layer sample so that the transmittance curve of the double-layer sample falls as close to t as possible. 2 The intermediate position between the two, which is less than t / (2-t), will help improve the experimental measurement accuracy of the transmittance of the stacked samples, and thus achieve accurate determination of the optical constants. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a schematic diagram of the experimental principle of the present invention.

[0059] Figure 2 The transmittance curves t1 and t2 of the zinc selenide (ZnSe) stacked sample.

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

[0061] Figure 4 This is a graph of the extinction coefficient of zinc selenide (ZnSe) sample material.

[0062] Figure 5 This is a graph of the refractive index of zinc selenide (ZnSe) sample material. DETAILED DESCRIPTION

[0063] The present invention is further described in detail below in conjunction with specific embodiments, which are intended to explain the present invention rather than to limit it.

[0064] A method for determining the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method. Assuming that the refractive index and extinction coefficient of the transparent flat material are n and k respectively, the attenuation coefficient α = 4πk / λ, where λ is the wavelength of light in a vacuum. The flat material is placed in air (refractive index is 1, extinction coefficient is 0), and it is assumed that the light is incident vertically. According to Fresnel's law and Snell's law, the interface reflectivity R at the interface between the flat material and the air is [(n-1) 2 +k 2 ] / [(n+1) 2 +k2 ]. Considering the multiple reflections of light on the two interfaces and ignoring the interference effect, the transmittance t and reflectance r of light passing vertically through a flat sample with a thickness of 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] The flat samples of the same material, the same specifications and the same 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 t1 of light passing vertically through a flat sample, the transmittance t2 of two flat stacked samples and the transmittance t3 of 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 passing vertically through a single flat sample with a thickness of L. Combining equations (3) and (4), we can obtain:

[0072] t=t1(6)

[0073]

[0074] If we combine equation (3) and equation (5), we can get:

[0075] t=t1(6)

[0076]

[0077] That is, the reflectivity r and transmittance t of light passing 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) as a whole into equation (2) to obtain:

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

[0079] Eliminating R from equations (1) and (9) yields:

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

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

[0082]

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

[0084] α=-ln(y) / L (12)

[0085] k=-λln(y) / (4πL)(13)

[0086] Substituting formula (11) into formula (9) we can get:

[0087]

[0088] Then from R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 The refractive index of the available material is

[0089]

[0090] Therefore, it is only necessary to measure the transmittance of the stacked sample, which can be a combination of t1 and t2, or a combination of t1 and t3, and then calculate the transmittance t and reflectance r of the light passing vertically through a single-layer flat sample with a thickness of L through equations (6) and (7), or (6) and (8), and substitute them into equations (11) and (14) to obtain y and R, and then use equations (12), (13) and (15) to obtain the attenuation coefficient, extinction coefficient and refractive index of the sample material.

[0091] Example 1

[0092] The two samples selected in the embodiment are laser-grade zinc selenide (ZnSe) discs with a diameter of 25.4 mm and a thickness of 6 mm. The measured thicknesses are 6.01 mm and 6.05 mm respectively. The transmission 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) are measured in the spectral range of 5-18 μm using a FOLI20 Fourier transform infrared spectrometer (transmittance accuracy ≤ 0.1% T). The resolution of the spectrometer is 4 cm -1 The measurements were carried out at room temperature (about 25.1°C) and 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. Figure 2 As shown. Further calculations show that the transmittance and reflectance curves of the zinc selenide (ZnSe) single layer sample are as follows: Figure 3 As shown. Further calculations show that the extinction coefficient and refractive index curves of the zinc selenide (ZnSe) sample material are as follows: Figure 4 , Figure 5 shown.

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

[0094] like Figure 5 As shown in the figure, the red line is the refractive index, and the black filled area surrounded by the green line is the uncertainty of the refractive index. Figure 5 The relative uncertainty of the refractive index is also given by the black line. It can be seen that in the range of (5-15) μm, the relative uncertainty of the refractive index of zinc selenide is less than 0.5%, and in the range of (7-12, 13-14) μm, the relative uncertainty of the refractive index is less than 0.25%. Compared with the relative uncertainty of the extinction coefficient, the measurement accuracy of the refractive index is higher. From formula (15), when the extinction coefficient is less than 1.0×10 －4 When the interface reflectivity R plays a dominant role, the extinction coefficient has almost no contribution to the refractive index. At this time, the refractive index can be The calculation is performed with sufficient precision.

[0095] It can be seen from Example 1 that the present invention can determine the optical constants of transparent solid materials by measuring the transmittance of the stacked sample without measuring the reflectance and without using the inversion method for iterative calculation. The present invention not only solves the problem of inconsistent conditions for measuring reflection and transmission spectra by the dual-spectrum method, but also avoids the iterative error and time-consuming calculation of the inversion method, thereby providing a method for determining the optical constants of transparent solids with simple experimental measurement and simple calculation.

[0096] In addition, the present invention studies the relationship between the transmittance of single-layer and double-layer samples, and points out that the transmittance t of the single-layer sample limits the value range of the transmittance t2 of the double-layer sample, that is, t 2<t2 < t / (2 - t). When the transmittance accuracy of the spectrometer is 0.001, the conclusion is given that the transmittance t of the single-layer sample required by the model of the present invention should be greater than 0.004 and less than 0.953. Further, the thickness of the single-layer sample should be reasonably adjusted so that the transmittance curve of the double-layer sample尽可能落在大于t 2 and less than the intermediate position between the two of t / (2 - t), which will help 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 the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method, characterized in that: The following steps are involved: S1, stacking and placing multiple samples of the same material, consistent specifications and thickness L in parallel to obtain a stacked sample; S2, use a spectrometer to measure the transmittance t1 of light passing vertically through a single-layer sample and the transmittance t1 of light passing through a stacked sample. n ; S3, based on t1 and t obtained in step S2 n , the transmittance t and reflectance r of the single-layer sample are obtained; S4, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, the attenuation factor y is obtained by analytical solution; and the attenuation coefficient α and the extinction coefficient k of the sample are further obtained; S5, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, the interface reflectance R is obtained by analytical solution, and then the interface reflectance R is obtained by Fresnel's law and Snell's law, and the refractive index n of the sample is further obtained.

2. The method for determining the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method according to claim 1, characterized in that: The thickness of the air layer between adjacent samples of the stacked samples in step S1 satisfies the condition of not considering the interference effect.

3. The method for determining the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method according to claim 1, characterized in that: The thickness of the single-layer sample satisfies the transmittance curve of the double-layer sample at t 2 and t / (2-t).

4. The method for determining the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method according to claim 2, characterized in that: The multiple samples are stacked and placed in parallel, that is, two samples are stacked and placed in parallel, and specifically include the following steps: S1, stack and place two samples of the same material, with the same specifications and thickness L in parallel to obtain a stacked sample; S2, use a spectrometer to measure the transmittance t1 of light passing vertically through one sample and the transmittance t2 of light passing through two samples: t1=t (1) S3, combining equations (1) and (2), from t1 and t2 we can get: t=t1(3) S4, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, the attenuation factor y is further obtained as: The attenuation coefficient α and extinction coefficient k of the sample are: α=-ln(y) / L (6) k=-λln(y) / (4πL) (7) Where λ is the wavelength of light in vacuum; S5, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, the interface reflectance R is further obtained as: Then, according to Fresnel's law and Snell's law, the interface reflectivity R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], and the refractive index n of the sample is obtained as:

5. The method for determining the optical constants of transparent solids based on the stacked sample transmission spectrum analysis method according to claim 2, characterized in that: The plurality of samples are stacked and placed in parallel, that is, three samples are stacked and placed in parallel, and specifically comprises the following steps: S1, stack and place three samples of the same material, with the same specifications and thickness L in parallel to obtain a stacked sample; S2, use a spectrometer to measure the transmittance t1 of light passing vertically through one sample and the transmittance t3 of light passing through three samples: t1=t(1) S3, combining equations (1) and (10), from t1 and t3 we can get: t=t1 (3) S4, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, further obtain the attenuation factor y: The attenuation coefficient α and extinction coefficient k of the sample are: α=-ln(y) / L (6) k=-λln(y) / (4πL) (7) Where λ is the wavelength of light in vacuum; S5, according to the transmittance t and reflectance r of the single-layer sample obtained in step S3, the interface reflectance R is further obtained as: Then, according to Fresnel's law and Snell's law, the interface reflectivity R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], and the refractive index n of the sample is obtained as:

6. A method for measuring optical constants of transparent solids based on stacked sample transmission spectrum analysis according to claim 4 or 5, characterized in that: The formulas for transmittance t and reflectance r in step S3 are: t=(1-R) 2 exp(-αL) / [1-R 2 exp(-2αL)] (12) r=R[1+(1-R) 2 exp(-2αL) / [1-R 2 exp(-2αL)]] (13) Among them, the interface reflectivity R = [(n-1) 2 +k 2 ] / [(n+1) 2 +k 2 ], n and k are the refractive index and extinction coefficient of the sample respectively, the attenuation coefficient α=4πk / λ, λ is the wavelength of light in vacuum, and L is the thickness of the single-layer sample.

Images