CN111965378B - Vortex rotation based object rotating speed measuring method under any incidence condition - Google Patents
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Abstract
The invention relates to a method for measuring the rotating speed of an object under any incident condition based on vortex rotation. Vortex light is a special light field with a helical wavefront and the rotational doppler effect is the optical shift caused by a rotating object. Firstly, preparing a superposition vortex optical rotation by using a spatial light modulator; secondly, irradiating the superposed vortex light to any position on the rotating flat plate object through a light beam collimation and filtering system; and finally, detecting the light intensity information of the reflected light by using a photoelectric detector and inputting the light intensity information into an oscilloscope for spectrum analysis. And obtaining the rotating speed of the flat object according to the frequency shift signal displayed by the oscilloscope. The method has the advantages of simple light path, strong flexibility and higher precision, and can measure the rotating speed of an object under any incident condition.
Description
Technical Field
The invention relates to a method for measuring the rotating speed of an object under any incidence condition based on vortex rotation, which can obtain the rotating angular velocity of the object by measuring vortex light frequency shift signals caused by a rotating object. The method can measure the rotation speed of an object under any incident condition of vortex light, belongs to the field of vortex light detection, and can be applied to measurement of the rotation motion of the object.
Technical Field
Vortex light is a light field with a helical wavefront and a particular intensity distribution, and laguerre gaussian light is a typical vortex rotation. In recent years, eddy optical rotation has attracted much attention because of its wide application value in the fields of optical manipulation, optical communication, optical micro-measurement, and the like. The phenomenon of swirling in the optical field was originally discovered by Boivin, Dow and Wolf in 1967 near the focal plane of the lens stack. In 1973, Bryngdahl first developed an exploration of experimental methods for preparing vortex light. In 1979 Vaughan and Willets successfully produced vortex rotation using a continuous laser. Yu, Bazgenov V in 1990 accomplished the preparation of vortex optical rotations for the first time using a grating method.
The phase of the vortex rotation contains the angular phase factor
Wherein l is the topological charge number of the orbital angular momentum of the vortex light,
is the azimuth; each photon carries
The orbital angular momentum of (a) is,
the angular phase factor is a Planck constant, and indicates that in the propagation process of the vortex optical rotation, if the vortex optical rotation propagates around the optical axis for a period, the wave front just rotates around the optical axis for a circle, and the phase correspondingly changes by 2 pi l; the center of the helical phase is a phase singularity where the phase is uncertain and the optical field amplitude is zero, thus forming a hollow dark kernel at the center of the optical field. At present, vortex light is widely applied in the fields of optical micro-control, high-dimensional quantum state, remote sensing of angular velocity of an object by utilizing a rotary Doppler effect and the like.
The doppler effect is commonly present in various types of waves, and in sound waves, it appears that when a sound source is close to a human ear, the heard sound becomes sharp due to the increase of frequency; when the sound waves are far from the human ear, the heard sound becomes muffled as the frequency decreases. In the field of electromagnetic waves, the doppler effect is similar to that of sound waves, and this principle is also used by electromagnetic wave speed measuring radars used on highways. This phenomenon still exists in the visible frequency range. The doppler effect in the classical optical band can be represented by:
where Δ f represents the frequency difference between the frequency received by the detector and the light source, and f 0 Representing the frequency of the light source, v representing the relative speed of movement between the object and the light source, and c representing the speed of light in the medium.
The laguerre gaussian beam is a typical vortex rotation and is a set of solutions to the paraxial wave equation in a cylindrical coordinate system where vortex light can be expressed as:
E(r,θ,t)＝Af(r)exp[i(ωt-lθ)] (2)
in the formula, E represents the electric field intensity, r represents the polar diameter in the cylindrical coordinate, θ represents the polar angle in the cylindrical coordinate, t represents the light wave propagation time, a represents the amplitude, f (r) is a laguerre gaussian function, i is an imaginary number unit, ω represents the angular wave number, l is the topological charge of the orbital angular momentum of the vortex light, and the light intensity distribution is shown in fig. 2.
The vortex rotation has spiral phase distribution, the energy density vector of the vortex rotation is not coincident with the propagation direction, a certain included angle is formed, and the energy density vector is the poynting vector. According to the meaning of the poynting vector, its direction is perpendicular to the wave front of the light beam. For a linearly polarized Laguerre-Gaussian beam, the included angle between the poynting vector and the propagation axis of the beam is alpha, and the size of the included angle satisfies the requirement
sinα＝lλ/2πr (3)
Wherein l represents the topological charge number, lambda represents the optical wavelength, pi is the circumference ratio, and r is the radius of the vortex light beam. Sin α may be approximated as α when α is of the order of milliradians in size.
Since eddy rotation has the property that the pointing vector does not coincide with the direction of propagation, the pointing vector can be decomposed into two components along the direction of propagation of the light beam and perpendicular to the direction of propagation of the light beam. According to the Doppler effect principle, the eddy rotation has the capability of detecting the inward movement along the light beam propagation direction and the direction perpendicular to the light beam propagation direction. A single rotational movement is then exactly a movement in the beam propagation section, especially when the beam propagation direction coincides with the object rotation axis, then the rotating object has only a movement in the beam section. The Doppler effect of any scattering point on the surface of the object in this case can be expressed as:
in the formula, omega represents the rotation angular velocity of an object, l represents the topological charge number of vortex light, and pi is the circumferential rate.
When the light intensity information of the reflected light is detected by using the photoelectric detector and is input into the oscilloscope for spectrum analysis, the frequency of the light beam is too high to be directly measured, and the frequency change of the light beam can be detected by adopting a beat frequency mode. The beat frequency is the frequency shift generated by the rotary Doppler effect, which is obtained by detecting the frequency difference of two coherent lights after the interference of two coherent lights in space.
Two beams of coherent light with the same light intensity in the space are respectively expressed as:
and
wherein E 1 And E 2 Representing the electric field strength of two light waves, A 0 Indicates the light intensity, w 1 And w 2 Representing the angular frequencies of the two light waves, t representing the light wave propagation time,
and
showing the phase change of the two light waves caused by the initial phase and the propagation distance of the light waves. At the photodetector, the light intensity after the interference of the two beams can be expressed as:
the frequency of the vortex rotation is 10 14 Magnitude, far fromBeyond the response frequency of the photodetector, the term of the double frequency in equation (5) will become a dc component in the spectrum analysis, and the difference frequency term is within the response range of the photodetector, which can be effectively displayed in the spectrum. Therefore, the frequency variation of the light beam is checked by adopting a beat frequency mode, and the detection is usually carried out by adopting a superposed vortex light beam with the same topological charge number and opposite sign, so that the generated Doppler frequency shift is twice of the calculated value of the formula (4).
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problem that the object rotating speed is difficult to measure under any incidence condition by utilizing vortex optical rotation at present, a method for measuring the object rotating speed under any incidence condition based on the vortex optical rotation is provided. The method has the advantages of simple light path and strong flexibility, and can measure the rotation speed of the object under the conditions that an included angle exists between a vortex light propagation axis and an object rotating shaft and a transverse displacement exists between a light spot center and an object rotation center.
The technical solution of the invention is as follows:
the invention relates to a method for measuring the rotating speed of an object under any incident condition based on vortex rotation, which mainly comprises the following steps:
(1) and preparing a hologram of the superposed vortex optical rotation by utilizing a multi-parameter joint regulation and control technology, loading the hologram into a spatial light modulator, and irradiating linear polarization Gaussian light to the spatial light modulator to prepare the superposed vortex optical rotation.
(2) And (3) the superimposed vortex light passes through a light beam collimation and filtering system and then is irradiated on a rotating object at will, and the light intensity information of the reflected light is detected by using a photoelectric detector and is input into an oscilloscope for spectrum analysis. The rotation speed of the object can be obtained according to the frequency shift signal displayed by the oscilloscope, as shown in figure 1.
The principle of the invention is as follows:
the Laguerre Gaussian beam is a typical vortex rotation, is a group of solutions of paraxial wave equations in a cylindrical coordinate system, and the inclined vector direction of the Laguerre Gaussian beam forms an included angle with the propagation direction, and can be used for detecting the rotation angular velocity of an object.
The rotational doppler effect of vortex rotation is similar to the linear doppler effect of ordinary planar light waves. When relative motion exists between a light source of the common plane light wave and an object, a certain difference exists between the frequency emitted by the light source and the frequency received by the object, the magnitude of the difference is in direct proportion to the relative motion speed between the light source and the object, and the linear motion speed of the object can be detected according to the principle. For vortex rotation, the wave line direction and the light beam propagation direction have a certain included angle, and the direction perpendicular to the light beam propagation direction also has a component, so that the rotating Doppler frequency shift is generated.
For a flat object with constant rotation speed, when vortex light is vertically incident to the center of the object, the rotation Doppler effect generates a unique frequency shift signal; when vortex light randomly enters a flat object, namely an included angle exists between a vortex light propagation axis and an object rotating shaft, and a transverse displacement exists between a light spot center and an object rotating center, a frequency shift signal is widened.
Due to oblique illumination, the vortex spot on the object surface will change from circular to elliptical shape, as shown in fig. 3. Taking the average value of the inner diameter and the outer diameter of the vortex light actually measured in the experiment as the radius r of the vortex light, establishing two coordinate systems which are respectively a light beam coordinate system O-xyz and a light spot coordinate system O '-xyz, and enabling a conversion matrix from the light spot coordinate system to the light beam coordinate system to be O' O ＝M x -gamma, gamma being the angle between the axis of rotation of the object and the axis of propagation of the light beam.
In the beam coordinate system O-xyz, the poynting vector is at x 0 The direction at a point may be expressed as
On the cross section of the light beam, the direction of the poynting vector of any point A around the optical axis is as follows:
where θ is the angular distance between the A point and the x axis, and the matrix M z And (theta) represents a rotation matrix of the space coordinate system rotating theta around the z axis, r is the average radius of the vortex light beam, l is the topological charge number of the vortex light, and lambda is the wavelength of the vortex light.
In the spot coordinate system O' -xyz, the angular velocity vector of the rotation of the object is
The projection point of the point A on the light spot is A'. The Q coordinate of the center of the rotating shaft of the object is (0, -d,0), the A' coordinate is (rcos theta, rsec gamma sin theta, 0), and then
The velocity vector of A' is:
in the formula, Ω is the rotation angular velocity of the object, r is the average radius of the vortex beam, γ is the angle between the propagation axis of the beam and the rotation axis of the object, and θ is the angular distance between the a' point and the x axis.
The direction of the poynting vector does not change along the direction of the optical axis during the transmission process of the vortex rotation, namely the direction of the poynting vector of the point A and the point A' is the same. In the spot coordinate system, the poynting vector of the point a' is:
in the formula (I), the compound is shown in the specification,
poynting vector at A' point, M x (-gamma) is a rotation matrix of a space coordinate system rotating gamma angle around the negative direction of an x axis, l represents topological charge number, lambda represents optical wavelength, pi represents circumferential rate, r represents the average radius of a vortex light beam, theta represents the included angle between a certain point and the x axis, gamma represents the included angle between a vortex optical rotation propagation axis and the rotating shaft of an object,
the doppler shift caused by the vortex light at point a' is then:
in the formula, Δ f represents the frequency shift of a certain point on a light spot, l represents the topological charge number, λ represents the light wavelength, π is the circumferential rate, Ω represents the rotation angular velocity of an object, θ represents the angle between a certain point and the x-axis, γ represents the angle between the vortex rotation propagation axis and the rotation axis of an object, d represents the lateral displacement between the center of a light spot and the rotation center of an object, f represents the frequency of the vortex rotation, and c represents the propagation velocity of light in vacuum.
In order to rotate the doppler shift frequency,
is a linear doppler shift.
When the superimposed vortex light beam is used, the linear frequency shift is offset, the rotational frequency shift is doubled, and the frequency shift displayed in the spectrum of the scattered light signal is as follows:
extracting 3 characteristic frequency values:
in the formula (I), the compound is shown in the specification,
Δf π 、
respectively indicate that theta in the frequency spectrum is respectively
π，
Corresponding frequency values, l represents the topological charge number, λ represents the optical wavelength, π is the circumferential ratio, Ω representsThe angular velocity of the object rotation, theta represents the angle between a certain point on the light spot and the x axis, gamma represents the angle between the vortex optical rotation propagation axis and the rotating shaft of the object, r represents the average radius of the vortex light beam, and d represents the transverse displacement between the center of the light spot and the rotating center of the object.
The angular velocity of rotation of the object can be obtained from equation (11):
the scheme of the invention has the main advantages that:
(1) the light path is concise, other requirements for building the light path are not required, the operation is simple, and the use is convenient.
(2) The method has wide application range and strong flexibility, and can measure the rotating speed of an object under any incident condition.
(3) The response speed is fast, the real-time is good, the light wave is used as a detection medium, the propagation speed is fast, and the fast measurement of the rotating speed of the object can be realized by combining the frequency spectrum analysis.
Drawings
FIG. 1 is a flow chart of object rotation speed measurement under any incidence condition based on vortex rotation;
FIG. 2 is a plot of a Laguerre Gaussian intensity profile;
FIG. 3 is a schematic view of a vortex light illuminating an object;
FIG. 4 is a graph of the intensity distribution of the vortex light in the superimposed state;
FIG. 5 is a schematic view of a vortex light measurement protocol at any incidence;
FIG. 6 is a graph of vortex optical measurement object spectra.
Detailed description of the preferred embodiments
The invention takes the superimposed vortex light as a detection medium, and an implementation object is a spatial light modulator, and the specific implementation steps are as follows:
firstly, preparing superposed vortex light and superposing blazed gratings by using a multi-parameter joint regulation and control technology to obtain a holographic pattern which can be accurately regulated and controlled, loading the holographic pattern to a spatial light modulator (6), generating stable Gaussian light by a laser generator (1), sequentially transmitting a linear polarizer (2) and a neutral density filter (3), then transmitting a light beam collimation system consisting of a lens (4) and a lens (5) to irradiate the spatial light modulator (6), carrying out complex amplitude modulation, then emitting light as superposed vortex optical rotation, and transmitting the superposed vortex optical rotation to a rotating object (10) after passing through a filtering system consisting of the lens (7), a diaphragm (8) and a lens (9). The reflected light from the object is received by the photodetector (11), and the light intensity signal is then converted into an electrical signal and transmitted to a spectrum analysis oscilloscope (12), as shown in fig. 5.
For example, a superimposed vortex light with a topological charge number of ± 15 is obliquely irradiated on a rotating object, a light beam propagation axis is coplanar with a rotating axis of the object, an included angle is 45 °, a transverse displacement between a light spot center and an object rotating center is 1mm, a vortex light average radius is 4mm, an object rotating speed is 314rad/s, and an obtained doppler spectrogram is shown in fig. 6. In the figure, the position of the first and second end faces,
Δf π ＝1746Hz、
combining the formula (12), the obtained object rotation speed Ω is 314.19rad/s, which is consistent with the actual rotation speed of the object.
In addition, the spatial light modulator limits the incident angle and power of the light beam, so the specific light path design is performed according to the actual conditions of a laboratory.
Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.
Claims (1)
1. A method for measuring the rotating speed of an object under any incidence condition based on vortex rotation is characterized by comprising the following steps: the vortex light is a special light field with a spiral wave front, and any incidence condition means that an included angle gamma can exist between the optical axis of vortex rotation and the rotating shaft of the flat object, and the transverse displacement d can exist between the center of a light spot and the rotating center of the object; firstly, preparing a superposed vortex optical rotation with topological charge number of +/-l by using a spatial light modulator method; secondly, irradiating the superposed vortex light to any position on the rotating flat plate object through a light beam collimation and filtering system; finally, use up lightThe electric detector detects the light intensity change of the reflected light and inputs the light intensity change into the oscilloscope for spectrum analysis; when the rotating shaft of the object and the propagation axis of vortex light are coplanar, the rotating angular velocity of the object is omega, the average radius of vortex light beams is r, the included angle between a scattering point and the minor axis of the elliptical light spot is theta, and the Doppler frequency shift delta f generated by the scattering point is as follows:
when theta is pi/2, pi, 3 pi/2, the corresponding rotary Doppler frequency shift values are respectively
The available object rotation speed:
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| CN112505345B (en) * | 2020-12-21 | 2022-09-09 | 中国人民解放军战略支援部队航天工程大学 | Target rotating speed measuring method based on discrete rotating Doppler frequency shift signal |
| CN112924397B (en) * | 2021-01-22 | 2022-10-14 | 中国人民解放军战略支援部队航天工程大学 | Target rotating speed and steering measurement method based on dual-frequency superposition state vortex optical rotation |
| CN112801917B (en) * | 2021-03-03 | 2023-11-17 | 南京大学 | Device and method for monitoring rotating object rotating speed and recovering image blurring based on Laguerre Gaussian mode |
| CN113238239B (en) * | 2021-05-11 | 2023-08-01 | 中国人民解放军战略支援部队航天工程大学 | Object rotating shaft relative distance measuring method based on incomplete vortex rotation |
| CN115963289B (en) * | 2023-03-01 | 2023-08-01 | 哈尔滨工业大学 | Transverse velocity measurement method and system based on dual-mode vortex beam |
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