Precise angular displacement measurement device and method using vortex light and plane wave interference

Abstract

The application discloses a precise angular displacement measurement method of vortex light and plane wave interference, and an optical interference system is built based on a Mach-Zehnder interference structure. When the relative positions of a to-be-measured plane mirror and a reference plane mirror are no longer parallel, off-axis interference occurs when two light beams reflected by the to-be-measured plane mirror and the reference plane mirror meet again, and a strip interference pattern with a bifurcation structure in the middle and equidistantly distributed around the area is generated. When the to-be-measured plane mirror produces a slight angular displacement, the optical path difference between the two reflected light beams changes, and the interference pattern also changes correspondingly. The interference pattern contains relevant information such as the size and direction of the tilt angle change of the to-be-measured plane mirror. A CCD camera is used to collect the interference patterns of the plane mirror at different positions respectively, and through further image processing and calculation of the interference patterns, the fringe spacing and the tilt angle of the interference fringes can be obtained, and then the size and direction of the angular displacement change of the to-be-measured plane mirror can be obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of photoelectric detection, in particular to a device and method for detecting the direction and size of the deflection angle of a plane mirror by measuring the fork direction and the change of the fringe spacing of the interference fringes based on the interference of vortex light and plane wave. BACKGROUND

[0002] Vortex light refers to a light beam with a spiral wave front structure, and the wave front advances in a spiral manner around the propagation direction during propagation. Vortex light beams have a phase singularity at the center, so the central light intensity is zero, and the light intensity is distributed in a ring shape. The biggest feature of vortex light compared with ordinary light is that the phase of vortex light is distributed in a spiral shape around the singularity perpendicular to the propagation direction. The unique structure makes vortex light widely used in the research fields of optical communication, optical measurement and microparticle manipulation. With the increasing demand for the measurement accuracy of angular displacement in precision measurement, the measurement method of angular displacement is also required to be higher and higher. The optical angular displacement measurement method is concerned due to its high accuracy, and the application range of angular displacement measurement is also more and more extensive, involving many fields. The optical angular displacement measurement methods mainly include autocollimation method, optical internal reflection method, circular grating method and laser interference method, etc. The existing interference measurement method is based on the Michelson interferometer structure and uses Gaussian beam interference for measurement, and generates stripes with uniform thickness and stripe-shaped distribution of light and dark alternation. The accuracy of this measurement method is mainly determined by the optical path difference of the two beams, which is an indirect measurement method and introduces displacement measurement error. The interference fringes of ordinary light have no obvious characteristics, and only the size of the angular displacement can be judged according to the interference fringes, and the specific direction of the change of the angular displacement cannot be judged. SUMMARY

[0003] In view of the above problems, the present application combines the Mach-Zehnder interferometer structure and proposes an angular displacement measurement device and method based on the interference of vortex light and plane wave and application, and a parallel light tube is introduced on the other side of the optical path to measure the angular displacement of the plane mirror as a comparison, which improves the reliability and measurement accuracy of the system, and aims to solve the problem of simultaneous measurement of the direction and size of the angular displacement.

[0004] The beneficial effects of the present application include:

[0005] The present application converts the measurement of the pose of the plane mirror, i.e. the size and direction of the tilt angle, into the measurement of the fringe spacing and fork direction of the interference pattern based on the interference of vortex light and plane wave, which increases the stability and anti-interference of the system, is suitable for the measurement of the pose change of optical elements on the optical platform, and meets the testing requirements of micro-optics, microelectronics and other fields with high precision. BRIEF DESCRIPTION OF DRAWINGS

[0006] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0007] Figure 1 The optical interference system structure schematic diagram of the present application,

[0008] Figure 2 The vortex light and plane wave interference pattern of the present application,

[0009] Figure 3 The inclination angle θ and azimuth angle γ relationship schematic diagram of the present application after beam deflection,

[0010] Figure 4 The plane wave (l1=0) and vortex light beam (l2=2) off-axis interference pattern of the present application changing the inclination angle θ,

[0011] Figure 5 The plane wave (l1=0) and vortex light beam (l2=2) off-axis interference pattern of the present application changing the azimuth angle γ,

[0012] Figure 6 The working flow chart of the measurement system of the present application,

[0013] Figure 7 The rotation principle diagram of the plane mirror of the present application,

[0014] Figure 8 The inclination angle and interference fringe spacing relationship principle diagram,

[0015] Figure 9 The interference fringe pattern of vortex light and plane wave when γ=0.25π. DETAILED DESCRIPTION

[0016] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings.

[0017] Figure 1 The optical interference system structure schematic diagram of the present application, Figure 6 The working flow chart of the measurement system of the present application, Figure 6 and Figure 1 The precise angular displacement measurement device of vortex light and plane wave interference of the present application is described as follows:

[0018] The measuring device of the application comprises a computer, a PI control system, an optical interference system and an image acquisition system, wherein the optical interference system is an angular displacement measurement system based on the interference of vortex light and plane wave based on the structure of a Mach-Zehnder interferometer, and the specific structure is,

[0019] The He-Ne laser with a wavelength of 632.8 nm is included, the laser beam generated by the He-Ne laser is incident on the lens group composed of the first lens (L1) and the second lens (L2) after being reflected by the first plane mirror (M1) to perform collimation and beam expansion, and then enters the first beam splitter prism (BS1) to be divided into two beams, which are transmitted light and reflected light, wherein the transmitted light passes through the second beam splitter prism (BS2), and then passes through the third lens (L3) to adjust the size of the vortex light spot radius, and then is incident on the second plane mirror (M2), the light beam is reflected by the second plane mirror (M2) and returns to the second beam splitter prism (BS2), and then is reflected by the second beam splitter prism (BS2) and incident on the fourth beam splitter prism (BS4), and then is received by the CCD camera of the image acquisition system after being reflected by the fourth beam splitter prism (BS4);

[0020] The other reflected light entering the first beam splitter prism (BS1) is reflected by the first beam splitter prism (BS1) and then incident on the spiral phase plate (SPP) to generate vortex light carrying orbital angular momentum, and the generated vortex light carrying orbital angular momentum passes through the third beam splitter prism (BS3) and then is incident on the third plane mirror (M3), the light reflected by the third plane mirror (M3) is reflected by the third beam splitter prism (BS3) again and then is incident on the fourth beam splitter prism (BS4), and the two beams meet again on the fourth beam splitter prism (BS4) to interfere, when the second plane mirror (M2) and the third plane mirror (M3) exist at a small angle relative to each other, the two beams reflected by them interfere off-axis to generate interference fringes with a bifurcated structure in the central region and an equal-interval structure in other regions, and the interference fringe pattern is as shown in Figure 2

[0021] It is installed on a motion mirror base with a PiezoMike driver, which is used in cooperation with a piezoelectric inertial driver (PI), and the driver is controlled by computer software to make the measured plane mirror produce a small angular displacement around the x direction and the y direction relative to the optical axis (z axis) direction, which are denoted as alpha and beta respectively.

[0022] ​The second plane mirror (M2) is a double polished plane mirror, which is installed on a moving mirror base with a PiezoMike driver, and is used with a piezoelectric inertial driver (PI). The driver is controlled by computer software to make the measured plane mirror produce a small angle displacement in the x-axis direction and y-axis direction relative to the optical axis (z-axis) direction, which are denoted as α and β respectively. That is, the tilt angle of the plane mirror is changed, and then the tilt angle θ and azimuth angle γ of the reflected light relative to the incident light are changed, which are related to the optical axis direction as shown in Figure 3 wherein θ is the tilt angle of the reflected vortex beam relative to the incident beam, which is defined as the angle between the wave vector k and the positive direction of the z-axis, and γ is the angle between the projection of the wave vector k in the xoy plane and the positive direction of the x-axis.

[0023] The other side of the second plane mirror (M2) is provided with a collimator, which measures the angle displacement of the second plane mirror (M2) controlled by the piezoelectric inertial driver (PI), and compares the two measured tilt angles to evaluate the accuracy of the optical interference measurement.

[0024] The PI control system is a piezoelectric inertial driver.

[0025] When the vortex light with a topological charge number |l| interferes with a plane wave, a bifurcation number |l|+1 bifurcation fringe will be generated at the center of the vortex beam, and the edge region is an interference fringe with equal interval. When the tilt direction of the plane mirror is unchanged and only the size is changed, the fringe spacing of the interference fringe will change accordingly as shown in Figure 4 The larger the beam tilt angle θ is, the denser the fringe is. When the size of the tilt angle is unchanged and only the tilt direction of the plane mirror is changed, that is, the azimuth angle γ changes, the bifurcation direction of the interference fringe will change accordingly as shown in Figure 5 The azimuth angle γ has a one-to-one correspondence with the bifurcation direction. Therefore, by image processing the received interference pattern, the fringe spacing and the bifurcation direction of the fringe can be obtained, the size of the tilt angle of the measured plane mirror can be obtained from the relationship between the fringe spacing and the tilt angle, and the tilt direction of the measured plane mirror can be determined according to the bifurcation direction of the fringe, that is, the detection of the pose of the plane mirror is realized.

[0026] The measurement method of the present application is described as follows in combination with other drawings:

[0027] The light beam emitted by the He-Ne laser is converted into a vortex beam carrying orbital angular momentum by a spiral phase plate (SPP). Different topological charge number spiral phase plates can be selected to generate vortex light with different topological charge numbers, and the bifurcation number of the interference pattern will change accordingly when the topological charge number is different. The phase of the vortex beam is distributed in a spiral shape. When there is no phase wavefront superposition, the vortex light propagates along the positive direction of the z-axis, and the electric field complex amplitude E1 in the z=0 plane is shown in formula 1:

[0028]

[0029] where i is the imaginary unit; denotes the phase of the vortex light, also known as optical phase; E0, l1are the beam amplitude and topological charge of the vortex light E1, respectively, and when the topological charge l1is 0, the vortex light becomes a plane wave. When the vortex light has a tilted wavefront phase, it propagates along the positive direction of the z-axis, and the electric field complex amplitude E2in the z = 0 plane is simply shown as formula 2:

[0030]

[0031] where l2is the topological charge of the vortex light E2; k is the magnitude of the wave vector; γ is the azimuth angle, defined as the angle between the projection of the wave vector k in the xoy plane and the positive direction of the x-axis; θ is the tilt angle, defined as the angle between k and the positive direction of the z-axis.

[0032] When E1and E2two beams interfere at the z = 0 observation plane, the interference superposition intensity I of the two beams is shown as formula 3:

[0033]

[0034] where the k (x cos γ + y sin γ) sin θ term represents the phase change superimposed on the wavefront during beam propagation; l = l2-l1is the difference between the topological charges of the two beams, which determines the number of bifurcations of the fringes in the interference pattern.

[0035] When the propagation direction of the incident beam does not change, the plane mirror is adjusted to have a rotation angle of α, and the tilt angle between the reflected beam and the incident beam changes to θ, as shown in the principle Figure 7 , the plane mirror rotation reflection relationship is shown as formula 4:

[0036] θ = 2α (4)

[0037] In the case of complete alignment of the built optical path, the two plane mirrors are in parallel relative to each other. When the plane mirror produces an angular displacement, the vortex light and the plane wave undergo off-axis interference. At this time, the interference condition is similar to the case of equal-thickness interference of two plane waves based on the Mach-Zehnder interference structure, and the relative position between the double-side polished plane mirror and the ordinary plane mirror is no longer parallel, but there is a wedge angle consistent with the tilt angle of the plane mirror as shown in Figure 8 , there is an optical path difference between the two beams as shown in formula 5 and formula 6:

[0038]

[0039]

[0040] where n is the refractive index, h is the thickness between two plates, λ is the wavelength of light, Δ is the optical path difference between two beams of light, m is a positive integer, and represents the interference fringe order, The term is the half-wave loss due to the light ray from the optically thin medium to the optically thick medium. Formulas 5 and 6 represent the bright and dark fringes in the interference pattern, respectively, and thus the thicknesses of the bright and dark fringes are represented by formulas 7 and 8, respectively:

[0041] h = (2m - 1)λ / 4n (7)

[0042] h = mλ / 2n (8)

[0043] The difference Δh between the thicknesses corresponding to adjacent bright (dark) fringes is represented by formula 9:

[0044] Δh = h m+1 - h m = λ / 2n (9)

[0045] where h m and h m+1 represent the thicknesses corresponding to the m and m+1 orders of interference fringes, respectively; the difference between the thicknesses of adjacent bright and dark fringes is the same, and Figure 8 the spacing Δs between two adjacent bright (dark) fringes is represented by formula 10:

[0046] Δs = Δh / sinα = λ / (2nsinα) (10)

[0048] When the propagation medium of the light beam is air, the refractive index n = 1, and since the deflection angle α is very small, much smaller than 1°, sinα ≈ α, and the fringe spacing of the generated interference fringes is represented by formula 11:

[0049] Δs = λ / 2α = λ / θ (11)

[0050] Similarly, when the plane mirror to be measured is deflected about the y axis by an angle β, and since the structure is symmetrical, θ = 2β, and thus the fringe spacing is represented by formula 12:

[0051] Δs = λ / 2β = λ / θ (12)

[0052] The direction of the fringes is related to the azimuth angle γ, which is determined by the deflection of the plane mirror to be measured about the x axis or the y axis. The angle φ between the bifurcation direction of the interference fringes and the x axis direction is represented by formula 13 in combination with formula 3:

[0053] φ = π / 2 - γ (13)

[0054] When the bifurcation direction changes according to a clockwise rotation, it has a certain relationship with the azimuth angle. When γ = 0.25π, the bifurcation of the interference fringes is such that the angle φ between the bifurcation direction and the positive x-axis is 0.25π. The bifurcation of the interference fringes is as follows: Figure 9 As shown, the interference between vortex light and plane wave generates a bifurcated structure in the central region, while other edge regions exhibit equally spaced interference fringes. In the interference image, the azimuth angle γ determines the direction of the bifurcations, the beam tilt angle θ determines the fringe spacing, and |l| affects the number of bifurcations in the image. By processing the interference fringe pattern received by the CCD camera, the fringe spacing and bifurcation direction are obtained, thus yielding the magnitude and direction of the tilt angle of the plane mirror under test. The selected plane mirror under test is a double-polished mirror. A collimator is used on the other side to simultaneously measure the angular displacement of the mirror as a comparative experiment. This method demonstrates high accuracy in measuring the angular displacement of the plane mirror and can serve as a standard for optical interferometry measurements, further emphasizing its measurement accuracy.

[0055] Utilizing the characteristics of interference between vortex light and plane waves, and combining this with a Mach-Zehnder interferometer structure, a non-contact optical angular displacement measurement system was designed. This system transforms the measurement of the angular displacement of optical elements into the measurement of the spacing and bifurcation direction of the interference fringe pattern. Since traditional dual-plane-wave interference patterns do not have bifurcation fringes, when the plane mirror under test is tilted, causing a change in azimuth angle γ of π, the angle change in the tilt direction of the interference fringes is also π. In this case, it is impossible to determine the specific tilt direction of the interference fringes, and consequently, the specific tilt direction of the plane mirror. This method can measure the tilt direction simultaneously with the magnitude of the tilt angle, offering a significant advantage. This invention realizes an optical element angular displacement measurement system with strong anti-interference capabilities and high resolution.

[0056] The Mach-Zehnder interference system is one of the most widely used optical precise measurement systems, and its main feature is that the relative tilt angle of the plane mirrors in the two arms is changed, the plane mirror angle change causes the optical path difference between the two beams, and the interference fringes generated when the two beams meet again change, and the change of the interference fringes can reflect the size and tilt direction of the tilt angle change. Using a traditional laser light source, a large number of interference fringes will be generated in the interference fringes, the focusing on the measured surface is not accurate enough, and the phase jump fuzzy problem is caused. The bright and dark fringe pattern generated by interference is greatly disturbed by external noise, and the stability is poor. In the application, a frequency stabilized He-Ne laser (λ=632.8nm) is applied, and an optical interference system is built based on the Mach-Zehnder interference structure. When the light beams reflected by the two plane mirrors meet again, off-axis interference occurs, a strip interference pattern with bifurcation structure in the middle and equal interval distribution around is generated, when a small angular displacement of one of the plane mirrors occurs, the optical path difference between the two reflected light beams changes, and the interference pattern also changes accordingly. The interference pattern contains information such as the size and direction of the tilt angle change of the plane mirror. The CCD camera is used to collect the interference patterns of the plane mirror at different positions, and through further image processing and calculation of the interference patterns, the fringe spacing can be obtained, and then the size of the angular displacement of the plane mirror can be obtained. When the tilt direction of the plane mirror changes, the fork direction of the interference pattern can be used to determine the specific tilt direction of the plane mirror. This method converts the measurement of the angular displacement of the measured plane mirror into the change of the fringe in the interference pattern, and analyzes the size and fork direction of the fringe to obtain information such as the size and direction of the tilt angle change of the plane mirror. The selected plane mirror is a double-side polished plane mirror, and the other side is measured by a high-precision collimator. The tilt angle measurement results of the two methods are compared, and the accuracy of the optical interference measurement method can be evaluated.

[0057] The above is only the preferred embodiment of the present application, but the protection scope of the present application is not limited to this. Any changes or replacements within the scope of the present application disclosed in the present application can be easily thought by those skilled in the art, and should be covered in the protection scope of the present application. Therefore, the protection scope of the present application should be limited by the protection scope of the claims.

Claims

1. A precision angular displacement measurement device of vortex light and plane wave interference, characterized in that, It comprises a computer, a PI control system, an optical interference system and an image acquisition system, wherein the optical interference system is an angular displacement measurement system based on Mach-Zehnder interferometer structure and plane wave interference, and the specific structure is as follows: The He-Ne laser with wavelength of 632.8nm is used, and the laser beam generated by the He-Ne laser is reflected by the first plane mirror M1 and then enters the lens group composed of the first lens L1 and the second lens L2 for collimation and beam expansion, and then enters the first beam splitter BS1 and is divided into two beams, which are transmitted light and reflected light, wherein the transmitted light passes through the second beam splitter BS2, is adjusted by the third lens L3 to adjust the size of the vortex light spot radius, and then enters the second plane mirror M2, and the light beam is reflected by the second plane mirror M2 and returns to the second beam splitter BS2, and then is reflected by the second beam splitter BS2 and enters the fourth beam splitter BS4, and then is received by the CCD camera of the image acquisition system after being reflected by the fourth beam splitter BS4; The other reflected light entering the first beam splitter BS1 is reflected by the first beam splitter BS1 and then enters the spiral phase plate SPP to generate vortex light carrying orbital angular momentum, and the generated vortex light passes through the third beam splitter BS3 and then enters the third plane mirror M3, and the light reflected by the third plane mirror M3 is reflected by the third beam splitter BS3 again and then enters the fourth beam splitter BS4, and the two beams meet again on the fourth beam splitter BS4 and interfere, and when the second plane mirror M2 and the third plane mirror M3 have a small angle relative to each other, the two beams reflected by them interfere off-axis, and an interference pattern with a bifurcated structure in the central region and equidistant interference fringes in other regions is generated, which is collected and received by the image acquisition system CCD camera; The second plane mirror M2 is a double-side polished plane mirror and is installed on a moving mirror base with a PiezoMike driver, and the base is used in cooperation with the piezoelectric inertia driver PI, and the driver is controlled by the computer software to make the measured plane mirror produce a small angular displacement around the x-axis direction and the y-axis direction, which are denoted as alpha and beta respectively, that is, by changing the tilt angle of the measured plane mirror and then changing the tilt angle theta and the azimuth angle gamma of the reflected light relative to the incident light, wherein theta is the tilt angle of the reflected vortex light beam relative to the incident light beam, which is defined as the angle between the wave vector k and the positive direction of the z-axis, and gamma is the angle between the projection of the wave vector k in the xoy plane and the positive direction of the x-axis.

2. The precision angular displacement measurement device of claim 1, wherein, The other side of the second plane mirror M2 is provided with a collimator, which is used to measure the angular displacement of the second plane mirror M2 controlled by the piezoelectric inertia driver PI, and the results of the two kinds of tilt angle measurement are compared to evaluate the accuracy of the optical interference measurement.

3. The precision angular displacement measurement device of claim 1, wherein, The PI control system is a piezoelectric inertia driver.

4. A method for measuring the precision angular displacement measurement device of vortex light and plane wave interference as claimed in any one of claims 1-3, characterized in that, The precise angular displacement measurement method comprises the following steps: An angular displacement measurement system based on Mach-Zehnder interferometer structure and plane wave interference is built; The light beams reflected by the second plane mirror M2 and the third plane mirror M3 meet again at the fourth beam splitter BS4, and off-axis interference occurs, thus generating a strip interference pattern with a bifurcated structure in the middle and an equal-interval distribution around the pattern; when one of the plane mirrors produces an angular displacement, the optical path difference between the two reflected light beams changes, and the interference pattern also changes accordingly; the interference pattern contains the size and direction information of the tilt angle change of the plane mirror; A CCD camera is used to collect the interference patterns when the plane mirror is at different positions; Through further image processing and calculation on the interference patterns, the fringe spacing is obtained, and then the size of the angular displacement of the plane mirror is obtained; When the tilt direction of the plane mirror changes, the size and direction of the tilt angle change of the plane mirror are obtained by analyzing the size of the fringe spacing and the direction of the bifurcation.

5. The method according to claim 4, wherein the method is characterized by, The calculation process of the relationship between the characteristic information of the interference pattern and the angular displacement change is as follows: The light beam emitted by the He-Ne laser passes through the spiral phase plate SPP to be converted into a vortex light beam carrying orbital angular momentum; different spiral phase plates with different topological charges are selected to generate vortex light with different topological charges; when the topological charges are different, the bifurcation number of the plane wave interference pattern also changes accordingly; The phase of the vortex light beam is distributed in a spiral shape; when there is no phase wave front superposition, the vortex light propagates in the positive direction of the z-axis, and the electric field complex amplitude E1 on the z=0 plane is shown in formula (1): where i is the imaginary unit; denotes the phase of the vortex light, also known as optical phase; E0, l1are the beam amplitude and the topological charge of the vortex light E1, respectively. When the topological charge l1is 0, the vortex light degenerates into a plane wave. When the vortex light has a tilted wavefront phase, along the positive direction of the z-axis, the electric field complex amplitude E2in the z=0 plane is simply shown as formula (2): In the formula, x and y are coordinate axes; l2 is the topological charge of the vortex light E2; k is the size of the wave vector; γ is the azimuth angle, defined as the included angle between the projection of the wave vector k in the xoy plane and the positive direction of the x-axis; θ is the inclination angle, defined as the included angle between k and the positive direction of the z-axis; When E1 and E2 interfere with each other at the z=0 observation plane, the interference superposition intensity I of the two beams is shown in formula (3): Wherein, the term k(xcosγ+ysinγ)sinθ represents the phase change of the wave front superimposed in the propagation process of the light beam; l=l2-l1 is the difference between the topological charges of the two light beams, which determines the bifurcation number of the fringes in the interference pattern; When the propagation direction of the incident light beam does not change, the second plane mirror M2 is adjusted to rotate around the x-axis by an angle α, the tilt angle between the reflected light beam and the incident light beam changes to θ, and the plane mirror rotation reflection relationship is shown in formula (4): θ=2α (4) Under the condition that the optical path is completely aligned, the second plane mirror M2 and the third plane mirror M3 are in a parallel state relative to each other; when the plane mirror produces an angular displacement, the vortex light and the plane wave produce off-axis interference; at this time, the interference condition is similar to the equal-thickness interference condition of the two plane waves based on the Mach-Zehnder interference structure; the relative position between the second plane mirror M2 and the third plane mirror M3 is no longer parallel, but there is a wedge angle consistent with the size of the tilt angle of the plane mirror; there is an optical path difference between the two light beams, as shown in formula (5) and formula (6): where n is the refractive index, h is the thickness between two plates, λ is the wavelength of light, Δ is the optical path difference between two beams of light, m is a positive integer, indicating the interference fringe order, The term is the half-wave loss due to the light ray from the optically thin medium to the optically dense medium; formula (5) represents the bright lines in the interference pattern, formula (6) represents the dark lines, and thus the thicknesses at the bright and dark lines are shown in formula (7) and formula (8), respectively: h=(2m-1)λ / 4n (7) h=mλ / 2n (8) The difference △h between the thicknesses corresponding to adjacent bright and dark fringes is shown in formula (9): Δh = h m+1 -h m = λ / 2n (9) where h m and h m+1 respectively represent the thickness corresponding to the m and m+1 order interference fringes; the difference between the thicknesses of adjacent bright and dark fringes is the same, and the spacing Δs between two adjacent bright and dark fringes is shown in formula (10): △s=△h / sinα=λ / (2nsinα) (10) When the propagation medium of the light beam is air, the refractive index n = 1, and since the deflection angle α is very small, much smaller than 1°, sin α ≈ α, the fringe spacing of the generated interference fringes is shown in equation (11) : △s = λ / 2α = λ / θ (11) Similarly, when the measured plane mirror is deflected around the y-axis, let the deflection angle be β, and since the structure is symmetrical, θ = 2β, then the fringe spacing is shown in equation (12) : △s = λ / 2β = λ / θ (12) The fringe direction is related to the azimuth angle γ, which is determined by the deflection of the measured plane mirror around the x-axis or y-axis. According to equation (3), the angle φ between the bifurcation direction of the interference fringes and the x-axis is shown in equation (13) : φ = π / 2 - γ (13) When the bifurcation direction rotates clockwise according to the law, it has a certain relationship with the azimuth angle. When γ = 0.25π, the bifurcation of the interference fringes is φ = 0.25π, which is the angle between the bifurcation direction and the positive direction of the x-axis. The central region of the interference fringes generated by vortex light and plane wave has a bifurcation structure, and the other edge regions have equidistant interference fringes. In the interference image, the azimuth angle γ determines the direction of the bifurcation of the interference fringes, the tilt angle θ determines the fringe spacing of the interference fringes, and |l| affects the number of bifurcations of the image interference fringes. By image processing the interference fringe pattern received by the CCD camera, the fringe spacing and bifurcation direction can be obtained, and the size and direction of the tilt angle of the measured plane mirror can be obtained.

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