RU2102700C1 - Two-beam interferometer for measuring of refractive index of isotropic and anisotropic materials - Google Patents

Abstract

FIELD: measurement technology. SUBSTANCE: two-beam interferometer has laser light source 1 and semitransparent mirror 2. Plane of light incidence on mirror for exclusion of depolarization of radiation of laser 1 is parallel or perpendicular to laser radiation polarization plane. Interferometer is also provided with optical modulator 3 optical axis of which is at angle of 45 deg. to laser radiation polarization plane, polarizer 4 cross-positioned or parallel to laser radiation polarization plane. After passing through polarizer, beam gets on specimen 5 under test made as plane-parallel plate manufactured of material being tested. Interferometer has also two reflecting mirrors 7, 8 positioned at its output, photomultiplier 9 with slit at input, narrow-band amplifier 10, and recorder 11. EFFECT: higher accuracy of measurement. 2 dwg

Description

 The invention relates to measuring technique and can be used to measure the refractive indices of isotropic and anisotropic materials.

 Known multi-beam interferometer [1] containing a monochromatic radiation source, a polarizer, two mirrors forming a Fabry-Perot interferometer, a phase plate and a test sample on a goniometer mounted between the mirrors, a polarization compensator, an optical modulator, a photoelectronic multiplier, a narrow-band amplifier and a recording device, the principle the action of which is based on the measurement of such angles of incidence of the beam on the studied plate, at which the difference in the stroke of the Fabry-Perot interferometer changes by a total number of interference maxima. Since high requirements are imposed on the accuracy of manufacture and relative orientation of the plates of the interferometer [2], the disadvantage of this invention is the difficulty of manufacturing parts of the device and especially their alignment. In addition, a multi-beam interferometer is designed to measure the refractive indices of only isotropic materials.

The closest in technical essence to the proposed two-beam interferometer is the device described in [3] and consisting of a laser, a beam expander, a polarizer, two translucent and two reflecting mirrors forming the Mach-Zehnder interferometer, the test sample, located on a rotary table controlled by a computer , and registration systems. The principle of operation of this device is based on recording changes in the order of interference in the generated interference pattern associated with changes in the position of the studied plate of the sample. Further computer processing of the obtained experimental results by the approximate method of iterative linear interpolation is quite complicated, requires large labor costs and the use of expensive equipment. In addition, this reduces the accuracy of determining the refractive indices (the measurement error is not better than 10 ^-4 ).

 The aim of the invention is to improve the accuracy of determining refractive indices and simplify the measurement process.

 This goal is achieved by the fact that in a two-beam interferometer for measuring the refractive indices of isotropic and anisotropic materials (hereinafter referred to as a two-beam interferometer), it contains sequentially located sources of monochromatic radiation and a translucent mirror for dividing the radiation into two beams, in one of which a polarizer is installed in series, the test sample is a rotating goniometer device and a first reflecting mirror, in the second a second reflecting mirror, and at the output of the interferometer a photoum a scissor, reflecting mirrors are mounted perpendicular to the incident rays and form a Michelson interferometer, a direct registration of the interference order is introduced, consisting of an optical modulator installed between a translucent mirror and a polarizer, and a narrow-band amplifier connected to the output of the photomultiplier located at the output of the interferometer, and a recording device, input which is connected to the output of a narrowband amplifier.

 In FIG. 1 is a schematic diagram of a two-beam interferometer. In FIG. Figure 2 shows the experimentally measured dependence of the shift of the interference pattern on the rotation angles of the fused silica sample plate (the same dependence on the square of the rotation angle in the inset).

The proposed two-beam interferometer (Fig. 1) contains a source of monochromatic polarized radiation 1 (hereinafter referred to as a laser), a translucent mirror 2, the density of light incidence on which is parallel or perpendicular to the plane of polarization of laser radiation (PPIL) to exclude depolarization of laser radiation 1, an optical modulator 3, for example crystal electrooptical modulator, the optical axis of which makes an angle of 45 ^o with PPIL polarizer 4, a crossed or parallel PPIL, the sample 5 in the form of a plane-parallel plates of the test material mounted on a rotating goniometer device 6, two reflecting mirrors 7, 8 located at the output of the interferometer, a photomultiplier 9 with a slit at the input, a narrow-band amplifier 10 and a recording device 11, and a narrow-band amplifier 10 is connected to the output of the photomultiplier 9, and the input the recording device 11 is connected to the output of the narrowband amplifier 10.

The use of a Michelson interferometer instead of a Mach-Zehnder interferometer, firstly, allows to increase the sensitivity of the proposed device by 2 times due to the double passage of the beam through the sample and, secondly, eliminates the need to use an optical laser expanding laser beam and removes restrictions on the possible rotation angle of the sample (≲ 90 ^o ) due to the passage of the beam reflected from the mirror 7, along the same optical path. Thus, the mutual displacement of the centers of the interfering light beams during rotation of the sample is completely absent, which means that at large angles of rotation of the sample the contrast of the recorded interference pattern does not decrease and the resulting value of changes in the order of interference increases), which ultimately leads to a decrease in the error in determining the refractive indices of the studied samples.

 We describe the operation of the proposed device.

где φ′ угол, под которым свет распространяется внутри кристалла, отсчитываемый от направления нормали к поверхности образца,
n и d показатели преломления и толщины образца соответственно,
λ длина волны излучения лазера.When the plane-parallel plate of sample 6 rotates in one of the arms of the interferometer with the axis of rotation perpendicular to the direction of incident light, the interference pattern shifts at the output of the interferometer due to a change in the optical path of the beam passing through the sample 5. Registration of a change in the order of interference is carried out by interference modulation, which is significantly improves measurement accuracy [2]
We derive the working relation, which allows one to calculate the refractive index of the test sample 5 from the measured values of the changes in the order of interference when the sample 5 is rotated by a certain angle. Theoretically, the shift of the interference pattern k depending on the angle of rotation φ of the plate of sample 5 for the Michelson interferometer (similar to the Mach-Zehnder interferometer [3]) is described by the following relation:

where φ ′ is the angle at which light propagates inside the crystal, measured from the direction of the normal to the surface of the sample,
n and d are the refractive indices and thicknesses of the sample, respectively,
λ wavelength of laser radiation.

и cos(φ-φ′) = cosφ•cosφ′+sinφ•sinφ′ выражение (1) упрощается к виду

При малых углах вращения

и sin²φ = φ²≪ n² тогда

уравнение (3) преобразуется к виду

Из формулы (3) находим искомое соотношение для расчета n:

В формуле (4) угол φ также отсчитывается от нормали к поверхности образца и значение v 0 практически устанавливается по минимуму зависимости k v регистрирующее по изменению знака направления движения интерференционных максимумов в интерференционной картине, при прохождении через v 0.Given that

and cos (φ-φ ′) = cosφ • cosφ ′ + sinφ • sinφ ′, expression (1) simplifies to

At small angles of rotation

and sin ² φ = φ ² ≪ n ² then

equation (3) is converted to the form

From formula (3) we find the desired ratio for calculating n:

In formula (4), the angle φ is also counted from the normal to the surface of the sample and the value of v 0 is practically set to the minimum of the kv dependence, which registers by changing the sign of the direction of motion of the interference maxima in the interference pattern when passing through v 0.

The last equation is completely true for an isotropic sample, for which there is no need to take into account the mutual orientation of the sample and the transmission plane of the polarizer (SPP). For uniaxial crystals, the sample plate is cut out and set so that the optical axis is parallel to the vertical axis of rotation. Then, with a vertical IFR, an extraordinary refractive index n _{l is} measured, and with a horizontal ordinary refractive index n ₀ .

Предлагаемое устройство разработано для прецизионного измерения показателей преломления изотропных или кристаллических материалов. Приведем пример конкретного исполнения. В качестве источника монохроматического излучения 1 использован стабилизированный по длине волны излучения He-Ne лазер типа ЛГН-302.In the case of biaxial crystals, measurements of three refractive indices n ₁ , n ₂ and n ₃ can be carried out as follows:
1) in the presence of two different plates cut perpendicular to any two axes of the optical indicatrix, three measurements are taken when the three axes of the optical indicatrix are alternately set parallel to the vertically polarized light, and hence the rotation axis,
2) if there is one plate cut perpendicularly to one of the axes of the optical indicatrix (let, for example, axis 3), the measurement of refractive indices n ₁ and n ₂ are carried out according to paragraph 1. To determine n ₃ , measurements are made with light polarized perpendicular to the axis of rotation in one of the two geometries used to determine n ₁ and n ₂ (let, for example, n ₂ ). In this case, in equations (1) and (2) for the angle v 0, nn ₁ , and for v ≠ 0 0, the refractive index must be replaced by the angle-dependent effective refractive index / 3 /
n _eff = [n $\genfrac{}{}{0ex}{}{\text{-2}}{\text{1}}$ cos ² φ ¹ + n $\genfrac{}{}{0ex}{}{\text{-2}}{\text{3}}$ • sin ² φ ′] ^-1/2
Solving equations (1), (2) and (5) together, we find the desired value of the refractive index n ₃ , which depends on the measured values of the rotation angle φ of the plate and the corresponding change in the order of interference k for a known n ₁ :

The proposed device is designed for precision measurement of the refractive indices of isotropic or crystalline materials. We give an example of a specific implementation. As a source of monochromatic radiation 1, an LGN-302 type laser stabilized by the He-Ne radiation wavelength was used.

 To modulate optical radiation, the ML-5 electro-optical modulator according to 2.081.038 TO was used from a lithium methaniobate crystal operating in the frequency doubling mode. We note here that other known means of interference modulation can be used as the optical modulator 3. To register optical modulated radiation, an FEU-51 photoelectric multiplier was used, the signal of which was recorded through a narrow-band amplifier 9, constructed according to well-known circuit diagrams, with a C1-83 oscilloscope. The measurements were carried out, for example, on a plane-parallel fused silica wafer. To provide a better interference pattern in the slit plane of the photomultiplier 9, a short focus lens can be used.

The experimental dependence of the shift in the interference pattern k on the rotation angle of fused silica sample 5 is shown in FIG. 2. As can be seen, at small angles φ, the dependence k (φ ² ) is linear, which corresponds to (4), which means that it confirms the truth of formula (3).

В последней формуле δn₁= δn абсолютная погрешность измерения показателя преломления n, рассчитанная по формуле (8).Let us estimate the error in determining n based on the measurement errors of the rotation angle dv of the interference order dk of the plate thickness δd and the laser light wavelength δλ for both measurements according to p. 1 and to p. 2. For this, we proceed from the formula

In the last formula, δn ₁ = δn is the absolute error in measuring the refractive index n, calculated by the formula (8).

где

и

Численная оценка погрешности произведена для n 1, 6, d 10 мм, λ 0,6328 мкм. Для максимального реально возможного угла вращения v 87^o расчет по формуле (3) приводит к значению индуцированного изменения порядка интерференции k 18,9 • 10³. Абсолютная погрешность измерения толщины пластинки образца 5 (фиг. 1) dd при d 10 мм может быть принята ровной 0,01 мкм, а погрешность определения порядка интерференции δk 0,007. Нестабильность серийно выпускаемых стабилизированных лазеров типа ЛГИ-302 составляет 3•10^-8 мкм. Измерение угла вращения с абсолютной погрешностью 1•10^-6 /1/ приводит к результирующему значению абсолютной погрешности δn, равной 4,4•10^-6, что более чем на порядок превышает точность измерения показателей преломления в /3/ и в 2 раза точнее измерений n стеклянных пластин.After appropriate calculations, from formulas (5) and (7) we obtain:

Where

and

A numerical estimate of the error was made for n 1, 6, d 10 mm, λ 0.6328 μm. For the maximum possible rotation angle v 87 ^{o, the} calculation by the formula (3) leads to the value of the induced change in the order of interference k 18.9 • 10 ³ . The absolute error in measuring the thickness of the plate of sample 5 (Fig. 1) dd at d 10 mm can be assumed to be equal to 0.01 μm, and the error in determining the order of interference δk is 0.007. The instability of commercially available stabilized lasers like LGI-302 is 3 • 10 ^-8 microns. The measurement of the rotation angle with an absolute error of 1 • 10 ^-6 / 1 / leads to the resulting value of the absolute error δn of 4.4 • 10 ^-6 , which is more than an order of magnitude greater than the accuracy of measuring the refractive indices in / 3 / and 2 times more accurate measuring n glass plates.

The absolute error of measurements of the refractive index n ₃ calculated by formula (11) for the same values of the outgoing parameters of the biaxial crystal for cesium bifthalate (n ₁ 1.6702 and n ₃ 1.5263) turns out to be 1.9 • 10 ^-6 , which is more than 2 times less error δn Thus, the measurement of refractive indices, according to paragraph 2, increases the accuracy of determining the refractive index, which makes it possible to recommend it for more accurate measurement of two refractive indices of biaxial crystals with the known third and one of the indices refractions n ₀ or n _e uniaxial crystals with a known other. In the latter case, the plane of polarization of light and the optical axis of the crystal under study are set perpendicular to the axis of rotation of the sample.

 The main advantage of the proposed two-beam interferometer is to increase the accuracy of determining refractive indices and simplify the measurement process by using the Michelson interferometer circuit and directly calculating the refractive index by formula (5) or (7). A quick measurement of n with low labor costs allows us to recommend the proposed device for express analysis by the refractive index of plane-parallel plates of isotropic and crystalline materials under industrial conditions.

Claims (1)

 A two-beam interferometer for measuring the refractive index of isotropic and anisotropic materials, containing a sequentially located source of monochromatic radiation and a translucent mirror for dividing the radiation into two beams, a sequentially placed polarizer, a goniometer mounted for rotation and designed to accommodate the sample, and the first reflecting mirror installed in the first divided beam, the second reflecting mirror located in the second beam, and the inter a photometer multiplier, characterized in that, in order to improve the accuracy of determining refractive indices and simplify the measurement process, it is equipped with a direct registration of interference orders, consisting of an optical modulator installed between a translucent mirror and a polarizer, and located at the output of the interferometer narrow-band amplifier associated with the output of the photomultiplier, and a recording device, the input of which is connected to the output of a narrow-band amplifier, and reflecting mirrors and half ozrachnoe mirror form a Michelson interferometer.

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