A gas refractive index measuring device and method based on a michelson interferometer

Abstract

The application provides a gas refractive index measuring device and method based on a Michelson interferometer. Based on the Michelson interference principle, one interference arm of the Michelson interferometer is sealed as a gas chamber, and a plane mirror at the end is replaced by a grating. When the refractive index of the gas in the chamber changes, the diffraction exit angle of the grating and the propagation path of the light in the chamber will change, the interference pattern is changed, and the refractive index can be calculated through the inversion of the change of the number of interference fringes or the interference phase. The structure is simple and convenient.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field related to optical measurement, and particularly relates to a gas refractive index measuring device and method based on a Michelson interferometer. BACKGROUND

[0002] The gas refractive index is an important inherent property of the gas medium and is one of the important measurement objects in the field of optical precision measurement. The accurate measurement of the gas refractive index has important significance in the fields of quantum vacuum metrology, atmospheric monitoring and photogrammetry. The laser interference technology is an important technical means commonly used for refractive index measurement. The basic principle is that the change of the refractive index of the gas medium causes the change of the optical path, and the change of the optical path difference causes the change of the interference image or signal, from which the change of the optical path compared with the vacuum environment is calculated to obtain the refractive index of the gas medium. The Twyman-Green interferometer, the Fabry-Perot resonant cavity and the Michelson interferometer are often used for gas refractive index measurement.

[0003] The Michelson interferometer is the most common optical interferometer. The basic optical structure is composed of a beam splitter and two plane mirrors. The amplitude splitting method is used to generate double-beam interference. By adjusting, both equal-thickness interference and equal-inclination interference fringes can be generated. The Michelson interferometer has simple principle structure and high optical path difference measurement precision, and is widely used in the field of optical metrology. However, in order to realize the scanning of the optical path difference, the Michelson interferometer needs to move one of the mirrors with high-precision moving parts, which increases the structural complexity and puts forward higher requirements for the design and control of the structure. SUMMARY

[0004] To solve the above problems, the application provides a gas refractive index measuring device and method based on a Michelson interferometer, which has simple structure and the ability to measure the gas refractive index in real time and conveniently.

[0005] A gas refractive index measuring device based on a Michelson interferometer, comprising a laser light source, a pre-collimation mirror assembly, an interferometer main body, an imaging mirror assembly, a detector and a computer. The interferometer main body comprises a beam splitter, a plane mirror and a grating. The passage between the beam splitter and the grating is set as a sealed cavity for accommodating the gas to be measured.

[0006] The exit light of the laser light source enters the interferometer main body after collimation by the pre-collimation mirror assembly. The beam splitter divides the light into two interference arms. One interference arm returns along the original path after being reflected by the plane mirror. The other interference arm also returns after being diffracted by the grating. The included angle between the direction of the light returned after being diffracted by the grating and the incident direction of the interference arm incident to the grating is related to the refractive index of the gas to be measured.

[0007] The light returned by the two interference arms meets in space to form interference fringes, and the interference fringes are imaged to a detector by the imaging mirror assembly; the detector converts the received interference fringes into an electrical signal input to a computer, and the computer obtains the refractive index of the gas to be measured according to the number of interference fringes.

[0008] Further, the grating is fixedly inclined at a Littrow angle.

[0009] Further, the Littrow angle of the grating is 10.9434°.

[0010] Further, the ruling density of the grating is 100 lp / mm, and the wavelength of the outgoing light of the laser light source is 633.5 nm.

[0011] A gas refractive index measurement method based on a gas refractive index measurement device based on a Michelson interferometer, comprising the following steps:

[0012] Assuming that the direction in which the wavefront of the light reflected by the plane mirror is located is the X-axis, the direction in which the light reflected by the plane mirror is located is the Y-axis, and the foot point of the light reflected by the plane mirror on the corresponding wavefront is the origin, then the intersection point of the wavefronts corresponding to the two light returned by the two interference arms is X(x, 0), and x is the horizontal coordinate of the intersection point X;

[0013] The mapping relationship between the light intensity I(x) of the interference fringes at the intersection point X and the refractive index n of the gas to be measured is as follows:

[0014]

[0015] Where I0 is the light intensity of the outgoing light of the laser light source, σ is the wave number of the outgoing light of the laser light source, σ L is the Littrow wave number of the grating, θ L is the Littrow angle of the grating;

[0016] The Fourier transform of the light intensity I(x) is obtained to obtain the single side spectrum, and the inverse Fourier transform of the single side spectrum is obtained to obtain the complex interferogram;

[0017] The original phase of the outgoing light of the laser light source is obtained according to the real and imaginary parts of the complex interferogram, and the continuous phase distribution is obtained after the original phase is unfolded, wherein the phase interval corresponding to each interference fringe period is 2π, and the phase change in the whole sampling interval corresponding to the continuous phase distribution is divided by 2π to obtain the number of interference fringes N fringe ;

[0018] According to the mapping relationship between the spatial frequency f x of the interference fringes and the number of interference fringes N fringe , N fringe = f x• Δx inverts the spatial frequency f of the interference fringes x where Δx is a known system fixed parameter determined by the detector size, imaging magnification and grating effective area;

[0019] According to the spatial frequency f x The mapping relationship between the refractive index n Invert the refractive index n of the gas to be measured.

[0020] Advantages:

[0021] 1. The application provides a gas refractive index measuring device based on a Michelson interferometer, based on the Michelson interference principle, one of the interference arms of the Michelson interferometer is closed as a gas chamber, and the end plane mirror is replaced with a grating; when the refractive index of the gas in the chamber changes, the diffraction exit angle of the grating and the propagation path of the light in the cavity will change, the interference pattern will change, and the refractive index can be calculated from the change of the interference fringe number or the interference phase, which is simple in structure and convenient and fast.

[0022] 2. The application provides a gas refractive index measuring method based on a Michelson interferometer, based on the change relationship between the refractive index and the fringe number and the spatial frequency, the light intensity of the interference fringes is Fourier transformed to obtain the fringe number, then the spatial frequency of the fringes is obtained according to the fringe number, and finally the refractive index is calculated from the spatial frequency, so that the refractive index of the gas in the cavity is measured in real time and conveniently. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 It is a basic device principle diagram for gas refractive index measurement of a Michelson interferometer based on a single grating and a single mirror structure;

[0024] Figure 2 It is a diffraction effect diagram when the Littrow wave number and the general wave number are incident on the grating surface respectively;

[0025] Figure 3 It is an optical path difference analysis diagram of the measurement interferometer image plane;

[0026] Figure 4 It is a comparison diagram of interference fringes when the gas refractive index is 1.0000 and 1.0003 respectively;

[0027] Figure 5 It is a schematic diagram of the change of the Littrow wavelength of the grating when the refractive index changes;

[0028] Figure 6 It is a schematic diagram of the change of the interference fringe number in the sampling interval when the refractive index changes;

[0029] Figure 7Schematic diagram of the phase change at different pixel positions when the refractive index changes;

[0030] Figure 8 Schematic diagram of the phase inversion process of interferometric data. DETAILED DESCRIPTION

[0031] In order to enable those skilled in the art to better understand the solution of the present application, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0032] like Figure 1 As shown, a gas refractive index measuring device based on a Michelson interferometer includes a laser light source, a pre-collimating lens assembly, an interferometer body, an imaging lens assembly, a detector, and a computer; wherein the interferometer body includes a beam splitter, a plane reflector, and a grating, and the passage between the beam splitter and the grating is configured as a sealed cavity for accommodating the gas to be measured;

[0033] When the gas to be measured is prepared, the outgoing light from the laser light source enters the interferometer body after being collimated by the pre-collimator assembly and is split into two interference arms by the beam splitter. One interference arm is reflected by the plane mirror and returns along the original path, while the other interference arm is diffracted by the grating and also returns. The angle between the direction of the light returning after diffraction by the grating and the incident direction of the interference arm on the grating is related to the refractive index of the gas to be measured.

[0034] The light rays returned by the two interferometer arms meet in space to form interference fringes, which are then imaged by the imaging mirror assembly to the detector. The detector converts the received interference fringes into electrical signals and inputs them into a computer. The computer obtains the refractive index of the gas to be measured based on the number of fringes in the interference fringes.

[0035] It should be noted that the interferometer body of the present invention is modified based on the structure of the Michelson interferometer. The plane mirror at the end of one arm of the interferometer is changed to a grating fixed at the Littrow angle, and the space between the beam splitter and the grating of this arm is enclosed to form a gas chamber, which can be pumped and de-gased, and the device measures the refractive index of the gas in the chamber.

[0036] That is, the measuring device core in the present application is an interferometer part, the interference principle of the interferometer is similar to that of a spatial heterodyne interferometer, spatial modulation of the interference optical path difference is realized through diffraction of a grating, and Fizeau interference fringes are formed. Incident light enters the interferometer through a collimator, is divided into two arms by a beam splitter. In one arm, the light is incident on a plane mirror along the optical axis and returns to the beam splitter along the same path; while in the other arm, according to the diffraction of the grating, only light of a specific wavelength can return along the optical axis when the incident light is incident along the optical axis, and this wavelength can be referred to as the Littrow wavelength. Light of other wavelengths returns at an angle to the optical axis, and the size of the angle is determined by the wavelength difference between the incident wavelength and the Littrow wavelength, as shown in Figure 2 .

[0037] According to the basic working principle of the interference device, as shown in the accompanying Figure 3 , for any point X(x, 0) on the interference image plane, wavefront 1 and wavefront 2 are two outgoing wavefronts from the two arms that pass through the point, and the propagation paths of the light rays in the two arms are A-C-O and A-B-D-E, respectively. The difference in length between the two propagation paths is the optical path difference at point X. When the inclination angle of the outgoing wavefront is γ, the optical path difference at point X can be expressed as:

[0038] OPD=x·sinγ (1)

[0039] where OPD is the abbreviation of optical path difference, which means optical path difference;

[0040] For the interferometer, the inclination angle of the outgoing wavefront can be obtained from the diffraction relationship of the grating surface. According to the grating equation, when the Littrow wavelength and other wavelengths of light are incident on the grating, there are:

[0041]

[0042] where d grating is the grating constant of the grating, θ L is the Littrow angle of the grating, m is the diffraction order, σ L is the Littrow wave number of the grating, and σ is the wave number of the incident light. By comparing the two equations in (2) and approximating, we get:

[0043] σsinγ=2(σ-σ L )tanθ L (3)

[0044] Then the optical path difference on the interference image plane can be expressed as:

[0045]

[0046] Then the theoretical expression of the intensity distribution of Fizeau interference fringes on the image plane can be expressed as:

[0047]

[0048] In the above analysis, the refractive index of the environment during the diffraction of the grating is considered to be 1. When the influence of the refractive index n of the grating environment is considered, the diffraction angle of the light is related to the refractive index, and the distribution of the optical path difference of the interference avoidance also changes accordingly. Considering the refractive index n, the diffraction relationship in equation (4) can be written as:

[0049]

[0050] Among them, σ n,L is the Littrow wave number corresponding to the refractive index n. Based on the diffraction relationship, the optical path difference can be re-analyzed to obtain the theoretical expression of the interference fringes including the refractive index effect:

[0051]

[0052] It can be seen from the expression that in the interferometer measurement device proposed in the present invention, the influence of the refractive index is mainly to cause the drift of the grating Littrow wave number, and the changed Littrow wave number is σ L / n.

[0053] In this way, use the attached Figure 1 In the device shown, when the refractive index of the gas in the cavity changes, the Littrow wavenumber of the grating changes. According to equation (7), the spatial frequency of the interference fringes also changes. Thus, if the wavelength of the incident light is known, the measured interferogram can be inverted. The refractive index of the gas in the cavity can be measured based on the number of fringes in the interferogram or the change in the interference phase. The number of fringes and phase of the interferogram can be obtained using an inversion method based on Fourier transform. This measurement method has the same advantages as the spatial heterodyne interferometer: it has a simple structure and the ability to measure multiple spectral lines simultaneously, allowing for convenient real-time calibration.

[0054] When the refractive index of the gas in the interferometer arm cavity is changed, according to the grating equation (6), the diffraction angle of the light changes, and the inclination angle of the wavefront on the image plane changes, which changes the optical path difference distribution, resulting in a change in the spatial frequency of the interference fringes. The present invention shows an example. The Littrow angle of the grating used in the interferometer is 10.9434°, the diffraction order used is -6, the grating line density is 100lp / mm, and the wavelength of the incident light is 633.5nm. When the refractive index of the gas in the cavity is 1.0000 and 1.0003 respectively, the interference fringes are compared. Figure 4 As shown, the spatial frequency of the interference fringes changes significantly.

[0055] Furthermore, by continuously changing the refractive index of the gas in the cavity from 1.0000 to 1.0003, the change of the interferometer Littrow wavelength can be observed as follows: Figure 5 As shown, it can be observed that the number of fringes within the sampling range changes as Figure 6 As shown, the phase changes of 5 pixel positions such as 1, 256, 512, 768, and 1024 are as follows Figure 7 As shown in the figure, it can be seen that the Littrow wavelength, number of interference fringes, and interference phase all show a linear trend with the refractive index. The refractive index of the gas under test can be inversely solved by using the change in the number of fringes or phase.

[0056] The number of fringes and phase of the interference pattern can be obtained by Fourier inversion method. The basic steps are as follows: Figure 8 As shown, the following steps are included:

[0057] Assuming that the direction of the wavefront of the light reflected by the plane mirror is the X-axis, the direction of the light reflected by the plane mirror is the Y-axis, and the foot point of the wavefront corresponding to the light reflected by the plane mirror is the origin, then the intersection of the wavefronts corresponding to the two light rays returned by the two interference arms is X(x,0), where x is the horizontal coordinate of the intersection point X;

[0058] The mapping relationship between the light intensity I(x) at the intersection point X of the interference fringes and the refractive index n of the gas to be measured is constructed as follows:

[0059]

[0060] Where I0 is the intensity of the emitted light from the laser light source, σ is the wave number of the emitted light from the laser light source, and σ L is the Littrow wave number of the grating, θ L is the Littrow angle of the grating;

[0061] Perform Fourier transform on the light intensity I(x) to obtain the spectrum, then extract the single-sided spectrum and perform inverse Fourier transform to obtain the complex interference pattern;

[0062] The original phase of the outgoing light of the laser light source is obtained according to the real and imaginary parts of the complex interference pattern. The continuous phase distribution is obtained after the original phase is expanded. The phase interval corresponding to each interference fringe period is 2π. The phase change in the entire sampling interval corresponding to the continuous phase distribution is divided by 2π to obtain the interference fringe number N. fringe ;

[0063] According to the spatial frequency f of the interference fringes x and the number of interference fringes N fringe The mapping relationship N fringe =f x ·Δx inverts the spatial frequency f of the interference fringes xwhere Δx is a known system fixed parameter determined by the detector size, imaging magnification and grating effective area;

[0064] According to the spatial frequency f x The mapping relationship between the refractive index n The refractive index n of the measured gas is inversed.

[0065] That is, the number of interference fringes N fringe Then, the spatial frequency f x of the fringes can be calculated. x The expression of f L is known system parameters, so the refractive index n can be directly calculated from the spatial frequency.

[0066] Of course, the present application can have other various embodiments, and those skilled in the art can make various corresponding changes and modifications according to the present application without departing from the spirit and essence of the present application. However, these corresponding changes and modifications shall belong to the protection scope of the claims attached to the present application.

Claims

1. A gas refractive index measuring device based on a Michelson interferometer, characterized in that: It includes a laser light source, a front collimating mirror assembly, an interferometer body, an imaging mirror assembly, a detector, and a computer; wherein the interferometer body includes a beam splitter, a plane reflector, and a grating, and the passage between the beam splitter and the grating is set as a sealed cavity for accommodating the gas to be measured; The outgoing light from the laser light source is collimated by the front collimator assembly and then enters the interferometer body. It is then split into two interference arms by the beam splitter. One interference arm is reflected by the plane mirror and then returns along the original path. The other interference arm is also returned after being diffracted by the grating. The angle between the direction of the light returning after diffraction by the grating and the incident direction of the interference arm on the grating is related to the refractive index of the gas to be measured. The light rays returned by the two interferometer arms meet in space to form interference fringes, which are then imaged by the imaging mirror assembly to the detector. The detector converts the received interference fringes into electrical signals and inputs them into a computer. The computer obtains the refractive index of the gas to be measured based on the number of fringes in the interference fringes.

2. The gas refractive index measuring device based on Michelson interferometer according to claim 1, characterized in that: The grating is tilted and fixed at the Littrow angle.

3. The gas refractive index measuring device based on Michelson interferometer according to claim 2, characterized in that: The Littrow angle of the grating is 10.9434°.

4. The gas refractive index measuring device based on Michelson interferometer according to claim 1, characterized in that: The line density of the grating is 100 lp / mm, and the wavelength of the output light of the laser light source is 633.5 nm.

5. A method for measuring gas refractive index based on the gas refractive index measuring device based on Michelson interferometer according to claim 1, characterized in that: The following steps are involved: Assuming that the direction of the wavefront of the light reflected by the plane mirror is the X-axis, the direction of the light reflected by the plane mirror is the Y-axis, and the foot point of the wavefront corresponding to the light reflected by the plane mirror is the origin, then the intersection of the wavefronts corresponding to the two light rays returned by the two interference arms is X(x,0), where x is the horizontal coordinate of the intersection point X; The mapping relationship between the light intensity I(x) at the intersection point X of the interference fringes and the refractive index n of the gas to be measured is constructed as follows: Where I0 is the intensity of the emitted light from the laser light source, σ is the wave number of the emitted light from the laser light source, and σ L is the Littrow wave number of the grating, θ L is the Littrow angle of the grating; Perform Fourier transform on the light intensity I(x) to obtain the spectrum, then extract the single-sided spectrum and perform inverse Fourier transform to obtain the complex interference pattern; The original phase of the outgoing light of the laser light source is obtained according to the real and imaginary parts of the complex interference pattern. The continuous phase distribution is obtained after the original phase is expanded. The phase interval corresponding to each interference fringe period is 2π. The phase change in the entire sampling interval corresponding to the continuous phase distribution is divided by 2π to obtain the interference fringe number N. fringe ; According to the spatial frequency f of the interference fringes x and the number of interference fringes N fringe The mapping relationship N fringe =f x ·Δx inverts the spatial frequency f of the interference fringes x , where Δx is a known fixed parameter of the system determined by the detector size, imaging magnification, and grating effective area; According to the spatial frequency f x The mapping relationship between the refractive index n The refractive index n of the gas to be measured is inverted.

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