CN116222435A - Device and method for measuring precise angular displacement by vortex rotation and plane wave interference - Google Patents
Device and method for measuring precise angular displacement by vortex rotation and plane wave interference Download PDFInfo
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract
The invention discloses a precise angular displacement measuring method for vortex light and plane wave interference, which is characterized in that an optical interference system is built based on a Mach-Zehnder interference structure, when the relative positions of a plane mirror to be measured and a reference plane mirror are no longer parallel, off-axis interference can occur when two light beams reflected by the plane mirror to be measured meet again, and a strip-shaped interference pattern with a bifurcation structure in the middle and equidistant distribution in surrounding areas is generated. When the plane mirror to be measured generates small angular displacement, the optical path difference between the two reflected light beams is changed, and the interference pattern also correspondingly changes, wherein the interference pattern contains the relevant information such as the size and the direction of the change of the inclination angle of the plane mirror to be measured. The CCD camera is used for respectively collecting interference patterns of the plane mirror at different positions, and the fringe spacing and the inclination angle of the interference fringes can be obtained by further image processing and calculation of the interference patterns, so that the size and the direction of the angle change of the plane mirror to be detected are obtained.
Description
Technical Field
The invention relates to the field of photoelectric detection, in particular to a device and a method for detecting the direction and the size of a deflection angle of a plane mirror to be detected based on the change of the direction of an interference fringe fork and fringe spacing of vortex rotation and plane wave interference.
Background
Vortex light refers to a light beam having a helical wavefront structure, which progresses in a helical fashion around the propagation direction during propagation. The vortex beam has phase singular point in the center, so that the central light intensity is zero, the light intensity is distributed in a ring shape, and compared with the common light, the vortex beam has the greatest characteristic that the vortex rotation phase is distributed in a spiral shape around the singular point along the direction perpendicular to the propagation direction. The unique structure makes vortex light widely used in the research fields of optical communication, optical measurement, particle manipulation and the like. Along with the increasing requirements of the measurement precision of the diagonal displacement in the precision measurement, the measurement method of the diagonal displacement also provides the increasing requirements. Optical-based angular displacement measurement methods are attracting attention due to their high precision, and angular displacement measurement is also increasingly used in a wide range of applications, involving many fields. The optical angular displacement measuring method mainly comprises an auto-collimation method, an optical internal reflection method, a circular grating method, a laser interferometry method and the like, the existing interferometry method is mostly based on a Michelson interferometer structure to measure by utilizing Gaussian beam interferometry, stripes with uniform thickness and stripe-shaped distribution are generated, the light and shade phases are alternately arranged, the accuracy of the measuring method is mostly determined by the optical path difference of two beams of light, and the measuring method is an indirect measuring method, so that displacement measuring errors are introduced. The interference fringes of the common light have no obvious characteristics, the size of the angular displacement can be judged only according to the interference fringes, and the specific direction of the angular displacement change cannot be judged in an omnibearing manner.
Disclosure of Invention
Aiming at the problems, the invention combines a Mach-Zehnder interferometer structure, provides an angular displacement measuring device, an angular displacement measuring method and an application based on vortex rotation and plane wave interference, introduces a collimator on the other side of a light path and simultaneously measures the angular displacement of a plane mirror as comparison, improves the reliability and the measuring precision of a system, and aims to solve the problem that the direction and the magnitude of the angular displacement are measured simultaneously.
The beneficial effects of the invention include:
the invention converts the measurement of the pose of the plane mirror, namely the magnitude and direction of the inclination angle into the measurement of the fringe spacing and the fork opening direction of the vortex rotation and plane wave interference patterns, increases the stability and the anti-interference performance of the system, is suitable for the measurement of the pose change of the optical element on the optical platform, and meets the test requirements of the fields of micro-optics, micro-electronics and the like with higher precision.
Drawings
In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic diagram of an optical interference system according to the present invention;
FIG. 2 is a vortex rotation and plane wave interference pattern of the present invention;
FIG. 3 is a diagram showing the relationship between the tilt angle θ and the azimuth angle γ after the beam deflection according to the present invention;
FIG. 4 shows a plane wave (l) of the present invention with the tilt angle θ changed 1 =0) and vortex beam (l 2 =2) off-axis interference pattern;
FIG. 5 shows a plane wave (l) with a changed azimuth angle gamma 1 =0) and vortex beam (l 2 =2) off-axis interference pattern;
FIG. 6 is a flow chart of the operation of the measurement system of the present invention;
FIG. 7 is a rotational schematic diagram of a planar mirror of the present invention;
FIG. 8 is a schematic diagram of tilt angle versus fringe spacing;
fig. 9γ=0.25pi, which is an interference fringe pattern of vortex rotation and plane wave.
Detailed Description
The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings.
Fig. 1 is a schematic structural diagram of an optical interference system according to the present invention, fig. 6 is a working flow chart of a measuring system according to the present invention, and referring to fig. 6 and fig. 1, a precise angular displacement measuring device for interference of vortex light and plane wave according to the present invention is described as follows:
the measuring device 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 measuring system based on the interference of vortex rotation and plane wave of a Mach-Zehnder interferometer structure, and the specific structure is that,
the system comprises a He-Ne laser with wavelength of lambda=632.8 nm, wherein a laser beam generated by the He-Ne laser is incident to a lens group formed by a first plane mirror (M1) and a second lens (L2) for collimation and beam expansion, enters a first beam splitter prism (BS 1) and is divided into two beams of light to be transmitted light and reflected light, the transmitted light is transmitted through the second beam splitter prism (BS 2), the size of a vortex light spot radius is regulated by a third lens (L3) and then is incident on the second plane mirror (M2), the beam is reflected by the second plane mirror (M2) and then is returned to a second beam splitter prism (BS 2), and is reflected by the second beam splitter prism (BS 2) and then is incident on a fourth beam splitter prism (BS 4), and the reflected light is received by a CCD camera of an image acquisition system;
the other beam of reflected light entering the first beam splitting prism (BS 1) is reflected by the first beam splitting prism (BS 1) and then enters the Spiral Phase Plate (SPP) to generate vortex light carrying orbital angular momentum, the generated vortex light carrying orbital angular momentum enters the third plane reflecting mirror (M3) after passing through the third beam splitting prism (BS 3), the light reflected by the third plane reflecting mirror (M3) is reflected again by the third beam splitting prism (BS 3) and then enters the fourth beam splitting prism (BS 4), the two beams of light interfere when meeting again on the fourth beam splitting prism (BS 4), when a small angle exists between the second plane reflecting mirror (M2) and the third plane reflecting mirror (M3), the two beams of light reflected by the second plane reflecting mirror (M2) are interfered off-axis, a center area is formed with a forked structure, interference fringes with other areas being equidistant, the interference patterns are collected and received by the CCD camera of the image collecting system, and the interference patterns are shown in the figure 2;
the piezoelectric inertial drive is arranged on a base of the moving reflector with a Piezo Mike driver, the base is matched with the piezoelectric inertial driver (PI), and the driver is controlled by computer software to enable the plane mirror to be tested to generate tiny angular displacement along the x direction and the y direction and the direction of an optical axis (z axis), and the tiny angular displacement is respectively marked as alpha and beta.
The second plane mirror (M2) is a plane mirror with double polished surfaces and is arranged on a moving mirror base with a Piezo Mike driver, the base is matched with a piezoelectric inertia driver (PI), and the driver is controlled by computer software to enable the plane mirror to be detected to generate tiny angular displacement with the direction of an optical axis (z axis) around the direction of an x axis and the direction of a y axis, and the tiny angular displacement is respectively marked as alpha and beta. I.e., changing the tilt angle of the mirror and thus the tilt angle θ and azimuth angle γ of the reflected light with respect to the incident light, the relationship with the optical axis direction is shown in fig. 3. Wherein θ is the inclination angle of the reflected vortex beam relative to the incident beam, defined as the angle between the wave vector k and the positive z-axis direction, and γ is the angle between the projection of the wave vector k in the xoy plane and the positive x-axis direction.
The other side of the second plane reflecting mirror (M2) is provided with a collimator, the angular displacement of the second plane reflecting mirror (M2) controlled by the piezoelectric inertia driver (PI) is measured, and the results of the two measurement dip angles are compared, so that the accuracy of optical interferometry can be evaluated.
The PI control system is a piezoelectric inertia driver.
When vortex light with the topological charge number of |l| interferes with plane waves, a bifurcation fringe with the bifurcation number of |l|+1 is generated at the center of the vortex light beam, and the fringe area is an interference fringe distributed at equal intervals. When the inclination direction of the plane mirror is unchanged and only the size is changed, the fringe spacing of the interference fringes changes correspondingly, as shown in fig. 4, and the larger the beam inclination angle theta, the denser the fringes are. The inclination angle is kept unchanged, and only the inclination direction of the plane mirror is changed, namely when the azimuth angle gamma is changed, the fork direction of the interference fringes is correspondingly changed, as shown in fig. 5, and the azimuth angle gamma and the fork direction have a one-to-one correspondence. Therefore, the fringe spacing and the direction of the fringe bifurcation opening can be obtained by carrying out image processing on the received interference pattern, the inclination angle of the plane mirror to be detected can be obtained according to the relationship between the fringe spacing and the inclination angle, and the inclination direction of the plane mirror to be detected can be judged according to the direction of the fringe bifurcation, namely the pose detection of the plane mirror can be realized.
The measuring method of the invention is described below with reference to the other figures:
the light beam emitted by the He-Ne laser is converted into vortex light beam carrying orbital angular momentum by a Spiral Phase Plate (SPP), the spiral phase plate with different topological charges is selected to generate vortex rotation with different topological charges, and the number of the topological charges and the bifurcation number of the plane wave interference pattern can be correspondingly changed when the topological charges are different. The phase of vortex light beam is spirally distributed, when no phase wave front is overlapped, the vortex light propagates along the positive direction of z axis, and the electric field complex amplitude E 1 The abbreviation on the z=0 plane is shown as 1:
wherein: i is the imaginary unit;
the phase representing the eddy-current rotation, also called optical phase; e (E) 0 、l 1 Beam amplitude and topological charge number of vortex light E1, and topological charge number l 1 At 0, the vortex light becomes a plane wave. When the vortex band has inclined wave front phase, the vortex band propagates along the positive direction of the z-axis, and the complex amplitude E of the electric field 2 Shorthand on the z=0 plane is shown in fig. 2:
wherein: l (L) 2 For vortex light E 2 Topology charges of (a); k is the magnitude of the wave vector; gamma is an azimuth angle, and is defined as an included angle between the projection of 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 z-axis direction.
When E is 1 And E is connected with 2 Two light beamsWhen interference occurs at the observation plane with z=0, the interference superposition light intensity I of the two is shown in formula 3:
wherein k (xcos gamma+ysin gamma) sin theta term represents phase change superimposed on the wavefront during beam propagation; l=l 2 -l 1 The difference between the topological charges of the two beams determines the branching number of fringes in the interference pattern.
When the propagation direction of the incident beam is unchanged, and the rotation angle of the plane mirror is adjusted to be alpha, the inclination angle between the reflected beam and the incident beam is changed to be theta, the principle is shown in fig. 7, and the rotation reflection relationship of the plane mirror is shown in formula 4:
θ＝2α (4)
in the case of perfect alignment of the built light path, the two plane mirrors are relatively in parallel. When the plane mirror generates angular displacement, the vortex rotation interferes with the plane wave off-axis. The interference condition at this time is similar to the condition that two beams of plane waves based on Mach-Zehnder interference structures are subjected to equal-thickness interference, the relative positions of the plane mirrors subjected to double-sided polishing and the common plane mirrors are not parallel, a wedge angle consistent with the inclination angle of the plane mirrors exists, as shown in fig. 8, and an optical path difference exists between the two beams of light, as shown in the formulas 5 and 6:
wherein n is refractive index, h is thickness between two plates, lambda is wavelength of light, delta is optical path difference between two beams of light, m is positive integer, representing interference fringe order,
the term is the half-wave loss due to light going from the optically sparse medium to the optically dense medium. Equation 5 represents the bright fringes in the interference pattern and equation 6 represents the dark fringes, so that the thicknesses of the bright and dark fringes are respectively shown in equations 7 and 8:
h＝(2m-1)λ/4n (7)
h＝mλ/2n (8)
the difference Δh between the thicknesses of the adjacent light (dark) patterns is shown in formula 9:
Δh＝h m+1 -h m ＝λ/2n(9)
in the formula, h m And h m+1 Respectively representing the thickness corresponding to m and m+1 level interference fringes; the difference between the thicknesses of the adjacent bright and dark fringes is the same, and the interval deltas between two adjacent bright (dark) fringes is shown in formula 10 in fig. 8:
Δs＝Δh/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 and is much smaller than 1 °, sin α≡α, the fringe spacing of the generated interference fringes is as shown in formula 11:
Δs＝λ/2α＝λ/θ (11)
similarly, when the plane mirror to be measured deflects around the y axis, the deflection angle is β, and because of its structural symmetry, the stripe pitch is shown in formula 12:
Δs＝λ/2β＝λ/θ (12)
the fringe direction is related to the azimuth angle gamma, which is determined by the deflection of the mirror under test around the x-axis direction or the y-axis direction. The angle phi between the bifurcation direction and the x-axis direction of the interference fringe is shown in formula 13 by combining formula 3:
φ＝π/2-γ (13)
when the bifurcation direction changes according to the rule of clockwise rotation, a certain relation is formed between the bifurcation direction and the azimuth angle, when gamma=0.25pi, the bifurcation condition of the interference bar is that the included angle phi=0.25pi between the bifurcation direction and the positive direction of the x axis at the moment, and the bifurcation condition of the interference bar is shown in fig. 9, so that vortex light and plane wave are interfered to generate a central area with a bifurcation structure, and other edge areas are equidistant interference fringes. In the interference image, the azimuth angle gamma determines the direction of the branching mouth of the interference fringes, the beam inclination angle theta determines the fringe spacing of the interference fringes, and the I influences the branching number of the interference fringes of the image. And (3) performing image processing on the interference fringe pattern received by the CCD camera to obtain fringe spacing and a fork direction, and obtaining the angle and the inclination direction corresponding to the inclination of the plane mirror to be detected. The plane mirror to be measured is a plane mirror with polished two sides, the other side of the plane mirror is used for measuring the angular displacement of the plane mirror by the collimator as a comparison experiment, the method has higher precision for measuring the angular displacement of the plane mirror, and the method can be used as a standard of an optical interferometry method for researching the measurement precision.
By utilizing the characteristics of vortex rotation and plane wave interference, a non-contact optical angular displacement measurement system is designed by combining a Mach-Zehnder interference structure, and the measurement of the angular displacement of an optical element is converted into the measurement of the interference fringe pattern pitch and the fringe bifurcation direction. Because the fringe pattern of the traditional dual plane wave interference does not have bifurcation fringes, when the plane mirror to be detected is inclined to enable the variation of the azimuth angle gamma to be pi, the angle variation of the inclined direction of the interference fringe is pi, at the moment, the specific inclined direction of the interference fringe cannot be judged, and the specific inclined direction of the plane mirror cannot be judged. The method can measure the inclination angle and realize the measurement of the inclination direction at the same time, and has certain advantages. The invention realizes an optical element angular displacement measurement system with strong anti-interference capability and higher resolution.
The Mach-Zehnder interference system is one of the most widely applied optical precise measurement systems, and is mainly characterized in that the inclination angle of one of the plane mirrors of the arm is changed, the plane mirrors of the two-arm light path generate relative inclination angles, the angle change of the plane mirrors causes the two light beams to have optical path difference, interference fringes generated when the two light beams meet again can change, and the change of the interference fringes can reflect the information such as the change of the inclination angle, the inclination direction and the like. The conventional laser source is used, a large amount of miscellaneous patterns exist in the generated interference fringes, the focusing on the measured surface is not accurate enough, and the problem of phase jump blurring is further generated. The fringe pattern with alternately bright and dark generated by interference is greatly interfered by external noise, and the stability is poor. In the invention, a frequency stabilization He-Ne laser (lambda=632.8nm) is applied, an optical interference system is built based on a Mach-Zehnder interference structure, off-axis interference occurs when light beams reflected by two plane mirrors meet again, a strip-shaped interference pattern with a bifurcation structure in the middle and equidistant distribution around is generated, when one plane mirror generates small angular displacement, the optical path difference between the two reflected light beams changes, the interference pattern also changes correspondingly, and the interference pattern contains the related information such as the change of the inclination angle of the plane mirror, the direction and the like. The CCD camera is used for respectively collecting interference patterns of the plane mirror at different positions, and the fringe spacing can be obtained by further image processing and calculation of the interference patterns, so that the angular displacement of the plane mirror is obtained. When the inclination direction of the plane mirror changes, the specific inclination direction of the plane mirror can be judged by utilizing the fork opening direction of the interference pattern. According to the method, the measurement of the angular displacement of the plane mirror to be measured is converted into the problem of fringe variation in the interference pattern, and the information such as the magnitude and the direction of the inclination angle variation of the plane mirror is obtained by analyzing the magnitude of the fringe spacing and the direction of the fork. The plane mirror is selected as a plane mirror with double-sided polishing, the other side is measured by a collimator with higher precision, and then the results of the two measurement inclinations are compared, so that the precision of the optical interferometry method can be evaluated.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (5)
1. The utility model provides a vortex light and plane wave interference's accurate angular displacement measuring device which characterized in that, includes computer, PI control system, optical interference system and image acquisition system, wherein, optical interference system structure is the angular displacement measuring system that vortex rotation and plane wave interfered based on Mach-Zehnder interferometer structure, and specific structure is:
the system comprises a He-Ne laser with wavelength of lambda=632.8nm, wherein a laser beam generated by the He-Ne laser is reflected by a first plane reflector (M1) and then is incident on a lens group consisting of a first lens (L1) and a second lens (L2), collimated and expanded, enters a first beam-splitting prism (BS 1) and then is divided into two beams of light to be transmitted light and reflected light, wherein the transmitted light passes through the second beam-splitting prism (BS 2), is incident on the second plane reflector (M2) after the size of the radius of a vortex light spot is regulated by a third lens (L3), is reflected by the second plane reflector (M2), is reflected by the second beam-splitting prism (BS 2) and then is incident on a fourth beam-splitting prism (BS 4), and is received by a CCD camera of an image acquisition system after being reflected by the fourth beam-splitting prism (BS 4);
the other beam of reflected light entering the first beam splitting prism (BS 1) is reflected by the first beam splitting prism (BS 1) and then enters the Spiral Phase Plate (SPP) to generate vortex light carrying orbital angular momentum, the generated vortex light enters the third plane reflecting mirror (M3) after passing through the third beam splitting prism (BS 3), the light reflected by the third plane reflecting mirror (M3) is reflected again by the third beam splitting prism (BS 3) and then enters the fourth beam splitting prism (BS 4), the two beams of light interfere when meeting again on the fourth beam splitting prism (BS 4), when a small angle exists between the second plane reflecting mirror (M2) and the third plane reflecting mirror (M3), the two beams of light reflected by the second plane reflecting mirror (M2) are interfered off-axis, a center area is formed with a forked structure, other areas are equidistant interference fringes, and interference patterns are collected and received by a CCD camera of an image collecting system;
the second plane mirror (M2) is a plane mirror with double polished surfaces and is arranged on a moving mirror base with a Piezo Mike driver, the base is matched with a piezoelectric inertia driver (PI), and the driver is controlled by computer software to enable the plane mirror to be detected to generate tiny angular displacement with the direction of an optical axis (z axis) around the direction of an x axis and the direction of a y axis, and the tiny angular displacement is respectively marked as alpha and beta. Namely, the inclination angle of the plane mirror to be measured is changed so as to change the inclination angle theta and the azimuth angle gamma of the reflected light relative to the incident light, wherein theta is the inclination angle of the reflected vortex light beam relative to the incident light beam, the inclination angle is defined as the included angle between the wave vector k and the positive direction of the z axis, and gamma is the included angle between the projection of the wave vector k in the xoy plane and the positive direction of the x axis.
2. The precise angular displacement measuring device of vortex light and plane wave interference according to claim 1, wherein a collimator is arranged at the other side of the second plane mirror (M2), the angular displacement of the second plane mirror (M2) controlled by the piezoelectric inertial drive (PI) is measured, and the results of the two measurement inclinations are compared to evaluate the accuracy of the optical interferometry.
3. The precise angular displacement measuring device of claim 1, wherein the PI control system is a piezoelectric inertial drive.
4. A method for measuring precise angular displacement by interference of vortex light and plane wave according to any one of claims 1-3, wherein the method for measuring precise angular displacement comprises the following steps:
constructing an angular displacement measurement system based on vortex rotation and plane wave interference of a Mach-Zehnder interferometer structure;
when the second plane reflector (M2) and the third plane reflector (M3) meet again, off-axis interference occurs, a strip-shaped interference pattern with a bifurcation structure in the middle and equidistant distribution around is generated, when one plane reflector generates angular displacement, the optical path difference between the two reflected lights changes, the interference pattern also changes correspondingly, and the interference pattern contains the information about the size, direction and the like of the inclination angle change of the plane reflector;
respectively acquiring interference patterns of the plane mirror at different positions by using a CCD camera;
further image processing and calculation are carried out on the interference pattern to obtain fringe spacing, and then the angular displacement of the plane reflector is obtained;
when the inclination direction of the plane mirror changes, the size and the direction of the inclination angle change of the plane mirror are obtained by analyzing the size of the stripe spacing and the direction of the fork opening.
5. The method for measuring the precise angular displacement of vortex light and plane wave interference according to claim 4, wherein the calculation of the relation between the characteristic information of the interference pattern and the angular displacement change comprises the following specific steps:
the light beam emitted by the He-Ne laser is converted into vortex light beam carrying orbital angular momentum through a Spiral Phase Plate (SPP), vortex rotation with different topological charges can be generated by selecting the spiral phase plate with different topological charges, and the topological charges and the bifurcation number of the plane wave interference pattern can be correspondingly changed when different;
the phase of vortex light beam is spirally distributed, when no phase wave front is overlapped, the vortex light propagates along the positive direction of z axis, and the electric field complex amplitude E 1 The abbreviation on the z=0 plane is shown as 1:
wherein: i is the imaginary unit;
the phase representing the eddy-current rotation, also called optical phase; e (E) 0 、l 1 Vortex lights E respectively 1 Beam amplitude and topological charge number of (2), topological charge number l 1 When 0, vortex light is degenerated into plane wave, when vortex light has inclined wave front phase, the vortex light propagates along positive direction of z axis, and electric field complex amplitude E 2 Shorthand on the z=0 plane is shown in fig. 2:
wherein: x and y are coordinate axes; l (L) 2 For vortex light E 2 Topology charges of (a); k is the magnitude of the wave vector; gamma is an azimuth angle, and is defined as an included angle between the projection of wave vector k in the xoy plane and the positive direction of the x axis; θ is the angle of inclination,the included angle between k and the positive direction of the z axis is defined;
when E is 1 And E is connected with 2 When two light beams interfere at the z=0 observation surface, the interference superposition light intensity I of the two light beams is shown as formula 3:
wherein k (xcos gamma+ysin gamma) sin theta term represents phase change superimposed on the wavefront during beam propagation; l=l 2 -l 1 The difference of topological charge numbers of the two beams of light is used for determining the branching number of fringes in the interference pattern;
when the propagation direction of the incident light beam is unchanged, and the second plane mirror (M2) is adjusted to rotate around the x axis by an angle alpha, the inclination angle between the reflected light beam and the incident light beam is changed to be theta, and the rotation reflection relation of the plane mirror is shown as a formula 4:
θ＝2α (4)
in the case of perfect alignment of the constructed light path, the second plane mirror (M2) is in a parallel state with respect to the third plane mirror (M3). When the plane mirror generates angular displacement, the vortex rotation interferes with the plane wave off-axis. The interference situation is similar to the situation that two plane waves based on Mach-Zehnder interference structures are subjected to equal-thickness interference, the relative positions of the second plane mirror (M2) and the third plane mirror (M3) are not parallel any more, a wedge angle consistent with the inclination angle of the plane mirrors exists, and an optical path difference exists between the two light beams as shown in the formulas 5 and 6:
wherein n is refractive index, h is thickness between two plates, lambda is wavelength of light, delta is optical path difference between two beams of light, and m is positiveAn integer representing the number of interference fringe orders,
the term is the half-wave loss due to light going from the optically sparse medium to the optically dense medium; equation 5 represents the bright fringes in the interference pattern and equation 6 represents the dark fringes, so that the thicknesses of the bright and dark fringes are respectively shown in equations 7 and 8:
h＝(2m-1)λ/4n (7)
h＝mλ/2n (8)
the difference Δh between the thicknesses of the adjacent light (dark) patterns is shown in formula 9:
Δh＝h m+1 -h m ＝λ/2n (9)
in the formula, h m And h m+1 Respectively representing the thickness corresponding to m and m+1 level interference fringes; the difference in thickness between adjacent bright and dark fringes is the same, and the spacing deltas between two adjacent bright (dark) fringes is shown in equation 10:
Δs＝Δh/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 and is much smaller than 1 °, sin α≡α, the fringe spacing of the generated interference fringes is as shown in formula 11:
Δs＝λ/2α＝λ/θ (11)
similarly, when the plane mirror to be measured deflects around the y axis, the deflection angle is β, and because of its structural symmetry, the stripe pitch is shown in formula 12:
Δs＝λ/2β＝λ/θ (12)
the fringe direction is related to the azimuth angle gamma, which is determined by the deflection of the plane mirror to be measured around the x-axis direction or the y-axis direction. The angle phi between the bifurcation direction and the x-axis direction of the interference fringe is shown in formula 13 by combining formula 3:
φ＝π/2-γ (13)
when the bifurcation direction changes according to the rule of clockwise rotation, a certain relation is formed between the bifurcation direction and the azimuth angle, and when gamma=0.25pi, the bifurcation condition of the interference bar is that the included angle phi=0.25pi between the bifurcation direction and the positive direction of the x axis at the moment; the vortex rotation and plane wave interference generate interference fringes with a forked structure in a central area and equidistant other edge areas;
in the interference image, the azimuth angle gamma determines the direction of the branching mouth of the interference fringes, the inclination angle theta determines the fringe spacing of the interference fringes, and the I influences the branching number of the interference fringes of the image;
and (3) performing image processing on the interference fringe pattern received by the CCD camera to obtain fringe spacing and a fork direction, and obtaining the angle and the inclination direction corresponding to the inclination of the plane mirror to be detected.
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310237021.4A CN116222435A (en) | 2023-03-13 | 2023-03-13 | Device and method for measuring precise angular displacement by vortex rotation and plane wave interference |
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| CN202310237021.4A CN116222435A (en) | 2023-03-13 | 2023-03-13 | Device and method for measuring precise angular displacement by vortex rotation and plane wave interference |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117075354A (en) * | 2023-09-14 | 2023-11-17 | 上海交通大学 | Device for generating high contrast relativity vortex rotation and space wave front diagnosis method |
| CN117686008A (en) * | 2024-02-01 | 2024-03-12 | 广东海洋大学 | Fiber Bragg grating signal demodulation system and method based on image processing |
| CN117705304A (en) * | 2023-12-11 | 2024-03-15 | 中国地质大学（武汉） | Vortex beam topology charge number measuring system, method, device, equipment and medium |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117075354A (en) * | 2023-09-14 | 2023-11-17 | 上海交通大学 | Device for generating high contrast relativity vortex rotation and space wave front diagnosis method |
| CN117705304A (en) * | 2023-12-11 | 2024-03-15 | 中国地质大学（武汉） | Vortex beam topology charge number measuring system, method, device, equipment and medium |
| CN117686008A (en) * | 2024-02-01 | 2024-03-12 | 广东海洋大学 | Fiber Bragg grating signal demodulation system and method based on image processing |
| CN117686008B (en) * | 2024-02-01 | 2024-04-26 | 广东海洋大学 | Fiber Bragg grating signal demodulation system and method based on image processing |
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