Displacement measurement method and system based on orbital angular momentum beam conjugate interference

Abstract

The invention discloses a displacement measurement method and system based on orbital angular momentum light beam conjugate interference, and the method comprises the steps: enabling linearly polarized light emitted by a laser to pass through an optical attenuator, a light beam expander, a quarter-wave plate and a vortex wave plate to form a light beam with orbital angular momentum, and enabling the light beam to pass through a beam splitter to be divided into a reference light beam and a measurement light beam. A measurement light beam is vertically incident on a reflection grating, and the mth-order diffraction light is incident on a first cube-corner prism and is reflected back to a diffraction grating to be subjected to secondary diffraction. And after the reference beam passes through the second cube-corner prism, the topological charge symbol of the reference beam is changed by the Dove prism. The reference light beam and the measurement light beam generate conjugate interference at the beam splitter prism, a petal-shaped interference pattern collected by the CCD is demodulated, and in-plane and out-of-plane two-dimensional displacement of the grating is calculated. The system has the characteristics of simple and compact structure, strong anti-interference capability, high precision and the like, and can be widely applied to the fields of high-end equipment manufacturing, semiconductor industry, precision metering and the like.

Description

Technical Field

[0001] The present invention relates to laser precision measurement technology, and in particular to a displacement measurement method and system based on orbital angular momentum light beam conjugate interference. Background Art

[0002] With the rapid development of ultra-precision manufacturing technology, especially in nanotechnology, optical measurement, and precision engineering, the accuracy and stability of displacement measurement have become particularly important. Traditional laser interferometers typically rely on the laser wavelength as a measurement reference, making the measurement susceptible to environmental factors (such as temperature changes and vibration), resulting in unstable measurement results. Grating interferometers use the grating pitch as a measurement reference rather than relying on the laser wavelength. This feature makes grating interferometers highly resistant to interference from environmental factors such as temperature, pressure, and vibration during the measurement process, thereby improving the stability and reliability of the system.

[0003] In recent years, vortex beams have shown great potential in optical measurement due to their ability to carry orbital angular momentum (OAM beams) and their unique phase properties. Conjugate interferometry based on OAM beams enables higher-precision and wider-range displacement measurements, extending the capabilities of existing measurement methods and possessing significant theoretical research value and practical application significance. Despite the great potential of OAM beams in displacement measurement, existing technologies primarily focus on out-of-plane (light propagation direction) displacement measurements and the combination of rotation and displacement measurements using the rotational Doppler effect. Summary of the Invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a displacement measurement method based on orbital angular momentum beam conjugate interferometry that does not change the optical configuration and can effectively realize out-of-plane and in-plane displacement measurement; another purpose of the present invention is to provide a displacement measurement system based on orbital angular momentum beam conjugate interferometry.

[0005] Technical solution: The displacement measurement method based on orbital angular momentum beam conjugate interferometry of the present invention comprises the following steps:

[0006] (1) The linearly polarized laser output by the laser passes through the light field control module to obtain a beam with orbital angular momentum;

[0007] (2) The light beam with orbital angular momentum is divided into a reference beam and a measurement beam by a beam splitter, the reference beam passes through a second corner cube prism and a Dove prism and returns to the beam splitter, and the topological charge of the returned reference beam changes from a positive number to a negative number; the measurement beam becomes an m-th order diffracted light after being diffracted by the reflection grating, the m-th order diffracted light enters the first corner cube prism and returns to the reflection grating, and after secondary diffraction, returns to the beam splitter; the measurement beam and the reference beam undergo conjugate interference at the beam splitter, forming a petal-shaped interference pattern, and obtaining a reference conjugate interference image;

[0008] (3) After the reflection grating moves, repeat steps (1) and (2) to obtain the measured conjugate interference image, compare it with the reference conjugate interference image, demodulate the rotation angle of the conjugate interference image, and calculate the displacement of the reflection grating in the plane and out of the plane.

[0009] Furthermore, the measuring beam is diffracted by the reflection grating to become the mth order diffracted light. The mth order diffracted light is emitted at a diffraction angle α and is incident on the first corner cube prism. The diffraction angle α is

[0010] α=arcsin(mλ / d)

[0011] Wherein, the diffraction order m is an integer not equal to 0, λ is the wavelength of the linearly polarized laser, and d is the grating pitch of the reflection grating. Further, in step (1), the light field E of the light beam with orbital angular momentum l (r,θ) is

[0012] E l (r,θ)=R l (r)exp(ilθ)

[0013] Among them, R l (r) represents the radial distribution of the light field, r represents the distance from the center of the light beam to a certain point, that is, the radial coordinate, l represents the number of topological charges of the light beam with orbital angular momentum, θ represents the azimuth angle of the light beam with orbital angular momentum rotating around the optical axis, and i represents the imaginary unit, which is used to express the phase term in the light field.

[0014] Furthermore, in step (2), the light field E of the reference beam re (r,θ) is

[0015] E re (r,θ)=R -l (r)exp(-ilθ)

[0016] The light field E of the measuring beam me (r,θ) is

[0017]

[0018] in, and They represent the phase difference of the measurement beam caused by the in-plane and out-of-plane displacement of the reflection grating. The resulting interference light intensity expression is:

[0019]

[0020] Wherein, Δx is the in-plane displacement of the reflection grating, Δz is the out-of-plane displacement of the reflection grating, λ is the wavelength of the linearly polarized laser, d is the grating pitch of the reflection grating, and α is the diffraction angle.

[0021] Furthermore, the displacement of the reflection grating in the plane and out of the plane in step (3) is

[0022]

[0023] Where Δθ is the rotation angle of the conjugate interference image.

[0024] Furthermore, when the reflection grating undergoes in-plane displacement, the change in the phase of the measurement beam depends on the Doppler shift of the reflection grating.

[0025] Furthermore, when the grating undergoes out-of-plane displacement, the phase change of the measurement beam depends on the change in its optical path and the Doppler shift of the reflected grating.

[0026] The displacement measurement system based on orbital angular momentum beam conjugate interferometry of the present invention comprises:

[0027] a laser for generating linearly polarized laser light;

[0028] Light field control module, used to convert linearly polarized light into a beam with orbital angular momentum;

[0029] A beam splitter is used to split the vortex beam into a reference beam and a measurement beam, and combine the returned reference beam and the measurement beam after secondary diffraction to generate conjugate interference;

[0030] a second corner cube prism, used for changing the direction of the reference beam so as to make it return along a reverse path;

[0031] Dove prism, used to change the topological charge of the reference beam from positive to negative;

[0032] A reflection grating, used for diffracting incident light to obtain m-th order diffracted light;

[0033] The first corner cube is used to return the m-th order diffracted light to the reflection grating for secondary diffraction;

[0034] The image acquisition and processing module is used to acquire the petal-shaped interference pattern formed by conjugate interference.

[0035] Furthermore, the light field control module includes an optical attenuator, an optical beam expander, a quarter wave plate and a vortex wave plate.

[0036] Preferably, the wavelength λ of the linearly polarized laser output by the laser is smaller than the grating pitch d of the reflection grating, and the polarization ratio of the linearly polarized laser output by the laser is not less than 500:1.

[0037] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: 1. The method of the present invention can effectively realize out-of-plane and in-plane displacement measurement without changing the optical configuration. The measurement results are traced back to the grating pitch of the stable reflection grating rather than the laser wavelength, which can effectively reduce the interference of environmental factors such as temperature changes and vibrations, greatly improve the environmental adaptability of the measurement system, and provide higher measurement accuracy in complex environments; 2. The method of the present invention can be used under conditions where the ambient temperature changes greatly. Its measurement accuracy depends on the accuracy of the grating itself, and the measurement repeatability depends on the thermal conductivity of the grating scale; 3. The method of the present invention uses circular angle subdivision rather than phase interpolation to subdivide the interference signal. The circumference provides a natural reference of 360°, which reduces the influence of the interference signal quality on the effectiveness of phase interpolation subdivision and greatly improves the measurement accuracy; 4. The structure of the system of the present invention is simple and compact, the optical path adjustment is convenient and easy to operate, and without changing the optical configuration, it can effectively realize two-dimensional measurement of grating out-of-plane and in-plane displacement at low cost, and can be widely used in high-end equipment manufacturing, semiconductor industry, precision measurement and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a structural diagram of the system of the present invention;

[0039] Figure 2 Schematic diagram of the petal-shaped interference pattern when m is -1 and l is 1 with an in-plane / out-of-plane displacement of 50 nm;

[0040] Figure 3 Schematic diagram of the petal-shaped interference pattern when m is -1, l is 2, and the in-plane / out-of-plane displacement is 50 nm. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings.

[0042] like Figure 1 The displacement measurement system based on orbital angular momentum beam conjugate interference of the present invention includes:

[0043] Laser 1, for generating linearly polarized laser light;

[0044] Light field control module, used to convert linearly polarized light into a beam with orbital angular momentum;

[0045] A beam splitter 6 is used to split the vortex beam into a reference beam and a measurement beam, and combine the returned reference beam and the measurement beam after secondary diffraction to generate conjugate interference;

[0046] A second corner cube prism 9 is used to change the direction of the reference beam so that it returns along a reverse path;

[0047] A dove prism 10, used to change the topological charge of the reference beam from positive to negative;

[0048] The reflection grating 7 is used to diffract the incident light to obtain the mth order diffracted light;

[0049] The first corner cube prism 8 is used to return the m-th order diffracted light to the reflection grating for secondary diffraction;

[0050] The image acquisition and processing module 11 is used to acquire the petal-shaped interference pattern formed by conjugate interference.

[0051] The light field manipulation module includes an optical attenuator 2, a beam expander 3, a quarter-wave plate 4, and a vortex wave plate 5. Laser 1 uses a helium-neon laser, and image acquisition and processing module 11 uses a CCD image sensor. The linearly polarized laser light output by helium-neon laser 1 has a polarization ratio greater than 500:1, and the wavelength λ of the linearly polarized laser light is less than the grating pitch d of the reflection grating. After attenuation by the optical attenuator 2, the linearly polarized laser light is adjusted by the beam expander 3 to a size compatible with the CCD image sensor. After passing through the quarter-wave plate 4, it becomes circularly polarized light. This light is then converted by the vortex wave plate 5 into a beam with orbital angular momentum (OAM beam), referred to as an OAM(+1) beam. The OAM(+1) beam is split into a reference beam and a measurement beam by a beam splitter 6. The measurement beam is perpendicularly incident on the reflection grating 7. The mth-order diffracted light enters the first corner cube prism 8 and returns to the reflection grating. After secondary diffraction, it returns along the original optical path, carrying phase information related to the grating displacement. After passing through the second corner cube prism 9, the reference beam returns along the reverse path, where its topological charge l is converted from positive to negative by the Dove prism 10, transforming the OAM(+l) beam into an OAM(-l) beam. The measurement and reference beams undergo conjugate interference at the beam splitter, forming a petal-shaped interference pattern that is detected by the CCD image sensor. Subsequent filtering and cross-correlation analysis enable two-dimensional detection of both in-plane and out-of-plane displacements of the grating.

[0052] The displacement measurement method based on orbital angular momentum beam conjugate interferometry of the present invention comprises the following steps:

[0053] (1) The linearly polarized laser output by the laser passes through the light field control module to obtain a beam with orbital angular momentum, which is called an OAM (+l) beam.

[0054] Assume that the light field E of the generated beam with orbital angular momentum is l(r,θ) is

[0055] E l (r,θ)=R l (r)exp(ilθ)

[0056] Among them, R l (r) represents the radial distribution of the light field, r represents the distance from the center of the light beam to a certain point, that is, the radial coordinate, l represents the number of topological charges of the light beam with orbital angular momentum, θ represents the azimuth angle of the light beam with orbital angular momentum rotating around the optical axis, and i represents the imaginary unit, which is used to express the phase term in the light field.

[0057] (2) The light beam with orbital angular momentum is divided into a reference beam and a measurement beam by a beam splitter. The reference beam passes through a second corner cube prism and a Dove prism and returns to the beam splitter. The topological charge of the returned reference beam changes from a positive number to a negative number. The measurement beam becomes an m-th order diffracted light after being diffracted by the reflection grating. The m-th order diffracted light enters the first corner cube prism and returns to the reflection grating. After secondary diffraction, it returns to the beam splitter. The measurement beam and the reference beam undergo conjugate interference at the beam splitter to form a petal-shaped interference pattern, and a reference conjugate interference image is obtained.

[0058] The measuring beam is diffracted by the reflection grating and becomes the mth order diffracted light. The mth order diffracted light is emitted at a diffraction angle α and is incident on the first corner cube prism. The diffraction angle α is

[0059] α=arcsin(mλ / d)

[0060] Wherein, the diffraction order m is an integer not equal to 0, λ is the wavelength of the linearly polarized laser, and d is the grating pitch of the reflection grating.

[0061] The OAM beam in the measurement optical path undergoes two m-order diffractions after passing through the reflective diffraction grating and the first corner cube prism. The OAM beam in the reference optical path undergoes two m-order diffractions after passing through the Dove prism. The topological charge number remains unchanged but the sign is opposite. re and measurement optical path E me The light field expression can be simplified as:

[0062] E re (r,θ,z)=R -l (r)exp(-ilθ)

[0063]

[0064] in, and is the phase difference of the measurement beam caused by the in-plane and out-of-plane displacement of the grating.

[0065] At the beam splitter, the measuring beam and the reference beam undergo conjugate interference, and the expression for the interference light intensity is:

[0066]

[0067] (3) After the reflection grating moves, repeat steps (1) and (2) to obtain the measured conjugate interference image, compare it with the reference conjugate interference image, demodulate the rotation angle of the conjugate interference image, and calculate the displacement of the reflection grating in the plane and out of the plane.

[0068] When the grating undergoes an in-plane displacement Δx, the phase change of the measurement beam caused by the two m-order diffraction is caused by the grating Doppler effect. It can be expressed as

[0069]

[0070] When the grating undergoes an out-of-plane displacement Δz, the phase change of the measuring beam is It is mainly caused by the grating Doppler effect and the optical path change of the beam, which can be expressed as

[0071]

[0072] When the phase of the measurement beam changes, the petal-shaped interference pattern with 2l petals rotates as its phase changes. Therefore, after demodulating the rotation angle Δθ from the petal-shaped interference pattern, the in-plane displacement and out-of-plane displacement of the grating can be expressed as:

[0073]

[0074] If the laser wavelength λ used is 632.8nm, and the grating pitch d is 833.333nm. Through theoretical calculations, it can be known that when the diffraction order m is -1 and the topological charge number l is 1, the conjugate petals rotate 1° corresponding to an in-plane displacement of 2.313nm and an out-of-plane displacement of 1.067nm. The preferred CCD image sensor resolution of the present invention is 2592*1944, and the single pixel size is 2.2um. Arctan (1 / 972) = 0.058°, it can be obtained that the theoretical resolution of the in-plane displacement measurement is about 0.133nm, and the theoretical resolution of the out-of-plane displacement measurement is about 0.062nm. If the performance of the CCD image sensor is improved, such as achieving an angular resolution of 0.01°, when l is 1, the measurement resolution of the in-plane displacement is 23pm, and the measurement resolution of the out-of-plane displacement is 11pm.

[0075] like Figure 2As shown in the figure, when m is -1 and l is 1, the interference pattern is obtained when the in-plane and out-of-plane displacement is 50 nm. When the in-plane displacement is 50 nm, the petals rotate 21.614°, and when the out-of-plane displacement is 50 nm, the petals rotate 46.886°. At the same time, the rotation direction of the petals reflects the direction of movement.

[0076] like Figure 3 As shown in the figure, when m is -1 and l is 2, the interference pattern is obtained when the in-plane and out-of-plane displacement is 50 nm. When the in-plane displacement is 50 nm, the petals rotate 10.807°, and when the out-of-plane displacement is 50 nm, the petals rotate 23.443°. At the same time, the rotation direction of the petals reflects the direction of movement.

Claims

1. A displacement measurement method based on orbital angular momentum beam conjugate interferometry, characterized in that: The following steps are involved: (1) The linearly polarized laser output by the laser passes through the light field control module to obtain a beam with orbital angular momentum; (2) The light beam with orbital angular momentum is divided into a reference beam and a measurement beam by a beam splitter, the reference beam passes through a second corner cube prism and a Dove prism and returns to the beam splitter, and the topological charge of the returned reference beam changes from a positive number to a negative number; the measurement beam becomes an m-th order diffracted light after being diffracted by the reflection grating, the m-th order diffracted light enters the first corner cube prism and returns to the reflection grating, and after secondary diffraction, returns to the beam splitter; the measurement beam and the reference beam undergo conjugate interference at the beam splitter, forming a petal-shaped interference pattern, and obtaining a reference conjugate interference image; (3) After the reflection grating moves, repeat steps (1) and (2) to obtain the measured conjugate interference image, compare it with the reference conjugate interference image, demodulate the rotation angle of the conjugate interference image, and calculate the displacement of the reflection grating in the plane and out of the plane.

2. The displacement measurement method based on orbital angular momentum beam conjugate interferometry according to claim 1, characterized in that: The measuring beam is diffracted by the reflection grating and becomes the mth order diffracted light. The mth order diffracted light is emitted at a diffraction angle α and is incident on the first corner cube prism. The diffraction angle α is α = arcsin (mλ / d) Wherein, the diffraction order m is an integer not equal to 0, λ is the wavelength of the linearly polarized laser, and d is the grating pitch of the reflection grating.

3. The displacement measurement method based on orbital angular momentum beam conjugate interferometry according to claim 1, characterized in that: In step (1), the light field E of the light beam with orbital angular momentum l (r,θ) is From l (r,θ)=R l (r)exp(ilθ) Among them, R l (r) represents the radial distribution of the light field, r represents the radial coordinate, that is, the distance from the center of the light beam to a certain point, l represents the number of topological charges of the light beam with orbital angular momentum, θ represents the azimuth angle of the light beam with orbital angular momentum rotating around the optical axis, and i represents the imaginary unit, which is used to express the phase term in the light field.

4. The displacement measurement method based on orbital angular momentum beam conjugate interferometry according to claim 1, characterized in that: In step (2), the light field E of the reference beam re (r,θ) is From re (r,θ)=R -l (r)exp(-ilθ) The light field E of the measuring beam me (r,θ) is in, and They represent the phase differences of the measurement beam caused by the in-plane and out-of-plane displacements of the reflection grating, respectively.

5. The displacement measurement method based on orbital angular momentum beam conjugate interferometry according to claim 1, characterized in that: The interference light intensity I formed in step (3) is Wherein, Δx is the in-plane displacement of the reflection grating, Δz is the out-of-plane displacement of the reflection grating, λ is the wavelength of the linearly polarized laser, d is the grating pitch of the reflection grating, and α is the diffraction angle.

6. The displacement measurement method based on orbital angular momentum beam conjugate interferometry according to claim 1, characterized in that: The displacement of the reflection grating in the plane and out of the plane in step (3) is: Where Δθ is the rotation angle of the conjugate interference image.

7. The displacement measurement method based on orbital angular momentum beam conjugate interferometry according to claim 1, characterized in that: When the reflection grating undergoes in-plane displacement, the change in the measurement beam phase depends on the Doppler shift of the reflection grating; When the grating is displaced out of plane, the phase change of the measurement beam depends on the change of its optical path and the Doppler shift of the reflected grating.

8. A displacement measurement system based on orbital angular momentum beam conjugate interferometry, characterized in that: include a laser for generating linearly polarized laser light; Light field control module, used to convert linearly polarized light into a beam with orbital angular momentum; A beam splitter is used to split the light beam with orbital angular momentum into a reference beam and a measurement beam, and combine the returned reference beam and the measurement beam after secondary diffraction to generate conjugate interference; a second corner cube prism, used for changing the direction of the reference beam so as to make it return along a reverse path; Dove prism, used to change the topological charge of the reference beam from positive to negative; A reflection grating, used for diffracting incident light to obtain m-th order diffracted light; The first corner cube is used to return the m-th order diffracted light to the reflection grating for secondary diffraction; The image acquisition and processing module is used to acquire the petal-shaped interference pattern formed by conjugate interference.

9. The displacement measurement system based on orbital angular momentum beam conjugate interferometry according to claim 8, characterized in that: The light field control module includes an optical attenuator, a light beam expander, a quarter wave plate and a vortex wave plate.

10. The displacement measurement system based on orbital angular momentum beam conjugate interferometry according to claim 8, characterized in that: The wavelength λ of the linearly polarized laser output by the laser is smaller than the grating pitch d of the reflection grating, and the polarization ratio of the linearly polarized laser output by the laser is not smaller than 500:1.

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