A laser radar rotating Doppler correction method based on elliptical vortex beam

Abstract

This invention relates to a rotational Doppler correction method for lidar based on an elliptical vortex beam. Vortex beams with structural phase are highly sensitive to rotation and can be used for precise measurement of rotational speed. However, when the vortex beam emitted by the lidar does not coincide with the axis of rotation of the object, the rotational Doppler spectrum broadens, reducing the signal-to-noise ratio (SNR), which greatly limits the application scenarios of vortex lidar. To address this problem, a rotational Doppler correction method for lidar based on an elliptical vortex beam is proposed. First, an elliptical vortex beam is prepared by adjusting the intensity and phase distribution of the vortex beam using complex amplitude modulation. By using an elliptical vortex beam with appropriate ellipticity to detect a tilted rotating object, the rotational Doppler broadening effect can be almost completely offset, improving the SNR of the frequency domain signal. This method is simple to operate, flexible and controllable, has high redundancy, and can greatly increase the detection range, showing great promise for applications in telemetry.

Description

Technical Field

[0001] This invention relates to the fields of lidar and light-matter interaction technology, and specifically to a lidar rotational Doppler correction method based on an elliptical vortex beam. Background Technology

[0002] Rotational motion is very common in real life, but accurately measuring the rotational speed of an object is a very difficult and important problem. Vortex beams are a type of beam with a helical phase wavefront, carrying a helical phase term. Special structure beam, in which Represents the topological charge number. These are azimuth coordinates. This is an imaginary number. Unlike the linear Doppler effect in the radial direction used in traditional radar, the rotational Doppler effect refers to the sensitivity of vortex beams to the rotational motion of objects, causing a frequency shift in the echo. Therefore, in the field of light-matter interaction, vortex beams are extremely sensitive to the rotational motion of objects, giving them a significant advantage in measuring the rotational speed of objects. In 2013, Lavery et al. first achieved the measurement of the rotational speed of a real object using a superposition-state vortex beam.

[0003] However, most current research on rotational speed measurement is conducted under the condition that the optical axis coincides with the object's rotation axis. Since this condition is difficult to meet in reality, Qiu Song et al. studied the rotational Doppler effect under non-coaxial conditions. Their research showed that when a vortex beam is incident at an angle onto a rotating object, the corresponding rotational Doppler spectrum broadens. When the tilt angle is too large, the spectral broadening effect intensifies, the amplitude of the effective signal decreases, and it gradually gets submerged in noise, making it impossible to extract the object's rotational speed. Moreover, in actual measurements, misalignment with the rotating object is very common. Therefore, improving the signal-to-noise ratio of the rotational Doppler signal and increasing the accuracy of rotational speed measurement under tilt conditions is a pressing problem that needs to be solved. Summary of the Invention

[0004] In view of this, the present invention proposes a rotating Doppler correction method for lidar based on an elliptical vortex beam, which can improve the signal-to-noise ratio of lidar echo signals under tilt detection conditions.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A rotating Doppler correction method for lidar based on an elliptical vortex beam is proposed. First, a tilted Doppler frequency shift model based on the elliptical vortex beam is established. Then, the elliptical vortex beam required for lidar detection is prepared using complex amplitude modulation and coordinate transformation. Subsequently, the beam is used to detect a tilted rotating object. The scattered light from the object is received by a photodetector to obtain the time-domain signal. Finally, the time-domain signal is processed by Fourier transform to obtain the corrected rotating Doppler spectrum.

[0007] In this method, the intensity and phase distribution of the superimposed vortex beam are adjusted by using complex amplitude modulation and coordinate transformation to prepare superimposed elliptical vortex beam holograms with different ellipticities. These holograms are then loaded onto a spatial light modulator, illuminated with linearly polarized light, and spatially filtered to obtain a superimposed elliptical vortex beam with an ellipticity corresponding to the tilt angle of the object.

[0008] First, a tilting rotational Doppler frequency shift model for an elliptical vortex beam was established:

[0009] , Represents the rotational Doppler frequency shift. Represents ellipticity, defined as the minor axis of the ellipse. Divide by the major axis , Represents the topological charge number. Represents rotational speed. Represents azimuth. The tilt angle is represented by the elliptical vortex beam that was prepared. Then, the tilted rotating object is detected by the prepared elliptical vortex beam. The corrected rotating Doppler spectrum is obtained by performing a Fourier transform on the received time-domain signal.

[0010] Beneficial effects

[0011] (1) This scheme is simple to design and easy to control. Based on the original vortex-based lidar detection scheme, no additional optical path and devices are required. Only the phase hologram loaded onto the spatial light modulator needs to be changed to modulate the elliptical vortex detection source required by the lidar. At the same time, the elliptical vortex beam is easy to prepare. By modifying a single parameter, elliptical vortex beams with different ellipticity can be prepared.

[0012] (2) This method can significantly improve the signal-to-noise ratio of the rotating Doppler echo signal of the lidar, reduce the spectral broadening range, and improve the accuracy of rotational speed measurement. Under the more general condition of tilt, using an elliptical vortex beam lidar to detect rotating objects can overcome the problem of low signal-to-noise ratio caused by misalignment in traditional vortex beam detection, reduce the spectral broadening range of the rotating Doppler, greatly improve the signal-to-noise ratio, significantly increase the detection distance, and expand the application scenarios of vortex beam lidar.

[0013] (3) This scheme has great practical value and high redundancy. In actual lidar detection, tilted illumination is more common, and this scheme has a significant correction effect in tilted illumination. At the same time, even if the ellipticity of the lidar light source does not strictly correspond to the tilt angle of the object, within a certain fluctuation range, the elliptical vortex beam as the detection beam can still partially eliminate the spectral spread effect introduced by tilt, and improve the signal-to-noise ratio of the signal to a certain extent. Attached Figure Description

[0014] Figure 1 This is a flowchart of the non-coaxial rotating Doppler correction process for the elliptical vortex beam radar system of this invention.

[0015] Figure 2 This is a diagram of the experimental setup for using elliptical vortex light for rotational Doppler correction according to the present invention.

[0016] Figure 3 This is the geometric model for the elliptical vortex beam radar detection of the present invention.

[0017] Figure 4 The simulation results are for the echo rotation Doppler frequency shift of the lidar based on the elliptical vortex beam, according to an embodiment of the present invention. Figure 4 (a) Figure 4 (b) shows the beam ellipticity in order of magnitude. , Simulation results of time-rotational Doppler frequency shift.

[0018] Figure 5 The intensity distribution of superimposed elliptical vortex beams with different ellipticities is shown in the embodiments of the present invention.

[0019] Figure 6 The tilt angle of the object in this embodiment of the invention is... The results of radar echo rotation Doppler frequency shift for beams with different ellipticity. Figure 6 (a) Figure 6 (b) shows the topological charge of the vortex beam as... The object rotates at 50 Hz and its tilt angle is... Under the given conditions, the ellipticity of the probe beam is as follows: , The corresponding rotating Doppler spectrum.

[0020] Figure 7 The object tilt angle in this embodiment of the invention is... , At that time, the experimental measurement results. Figure 7 (a) Figure 7 In (b), the topological load number is... The object rotates at 50 Hz and its tilt angle is... Under the given conditions, the ellipticity of the probe beam is as follows: , The corresponding rotating Doppler spectrum; Figure 7 (c) Figure 7 (d) represents the angle of inclination of the object. Under the conditions, the ellipticity of the probe beam is as follows: , The corresponding rotating Doppler spectrum. Detailed Implementation

[0021] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] The principle of this invention is:

[0023] Consider a beam with spatial phase change The beam of light can be expressed as,

[0024] (1)

[0025] in Using rectangular coordinates, Represents time, The complex amplitude of the beam. For transmission distance, The radius of the basic mode waist, The wave number has a magnitude of , The wavelength of the light beam. This is an imaginary number. After target modulation and beat frequency processing, the frequency shift of the optical echo can be obtained from this beam. ,

[0026] (2)

[0027] in The frequency of the light beam, At the speed of light, For the object along The rotation speed of the axis, For the lateral phase gradient, Let be the velocity of the scattering particles in the transverse plane of the object. The first term in equation (2) represents the linear Doppler frequency shift, and the second term represents the transverse motion of the scattering particles, i.e., the frequency shift caused by motion perpendicular to the beam propagation direction. When the lidar detection beam is a vortex beam carrying a spiral phase, the second term is converted into a rotational Doppler frequency shift, i.e.,

[0028] (3)

[0029] Using ellipticity Topological charge number is The elliptical vortex beam detection rotational angular velocity is When two objects are tilted, their relative spatial positions are as follows: Figure 3 As shown. Defined as the minor axis of an ellipse Divide by the major axis ,Right now The center of the elliptical vortex beam illuminating the tilted object. A spatial rectangular coordinate system is established with the origin as the origin, the beam propagation direction as the z-axis, and the horizontal direction of the beam's transverse plane as the y-axis. A represents a scattering particle in the elliptical vortex beam's optical field. Representing the origin The vector to scattering particle A, the magnitude of which is the radius of the elliptical vortex beam. , Let be the angular velocity vector of the object, its direction being the normal vector of the plane rotating the object, and its magnitude being . . Vector Orthogonal decomposition along the coordinate axes, where and The included angle of the axis is . Let be the linear velocity at scattering point A.

[0030] To clearly explain the mechanism of the tilting rotational Doppler effect in an elliptical vortex beam, the rotational Doppler frequency shift caused by the object's scattering points was analyzed. In fact, the total rotational Doppler frequency shift of the echo signal caused by the object's rotation is the sum of the frequency shifts at each scattering point. Based on the vector relationships in the coordinate system, it can be deduced that... , and The relationship between them

[0031] (4)

[0032] Based on the geometric relationships in the diagram and combined with equation (4), we can derive...

[0033] (5)

[0034] Therefore, the expression for the linear velocity of point A can be derived as follows:

[0035] (6)

[0036] Compared to traditional vortex beams, the phase distribution of elliptical vortex beams is as follows: Its phase gradient can be written as,

[0037] (7)

[0038] Therefore, the rotational Doppler shift under misalignment conditions can be written as,

[0039] (8)

[0040] in For ellipticity, For topological load number, For the tilt angle of the object, For the object's rotational speed, The azimuth angle is given by equation (8). It can be seen from equation (8) that under tilted conditions, after the interaction between the elliptical vortex beam and the matter, the rotational Doppler frequency shift carried by the optical echo is not only related to the rotational speed of the object and the topological charge of the elliptical vortex beam, but also to the ellipticity of the elliptical vortex beam and the spatial pose of the object. This provides a powerful method for correcting the broadening of the rotational Doppler frequency shift caused by the misalignment of the object using the parameters of the vortex beam itself. When the ellipticity strictly corresponds to the tilt angle of the object, i.e., the condition is satisfied... The formula for the rotational Doppler shift of an elliptical vortex beam degenerates into: This means that the rotational Doppler spectrum does not broaden, achieving correction of the rotational Doppler signal under tilted conditions. To clearly illustrate the correction effect of the elliptical vortex beam, the beam topological charge is set to... The object rotates at 50 Hz, and the object's tilt angle is... The ellipticity of the beams are respectively , Simulation results of echo rotation Doppler frequency shift based on elliptical vortex radar were obtained, such as... Figure 4 As shown, Figure 4 In the middle (a), the ellipticity is... Simulation results of time-rotational Doppler frequency shift. Figure 4 In (b), the ellipticity of the beam is... Simulation results of the rotating Doppler frequency shift. It can be seen that under actual tilt conditions, using an elliptical vortex lidar detection system with appropriate ellipticity can theoretically completely overcome the defects of reduced signal-to-noise ratio and spectral broadening caused by non-ideal conditions, making the rotating Doppler frequency shift appear as a single peak.

[0041] This invention optimizes the rotating Doppler signal of a lidar system based on an elliptical vortex beam. The specific implementation steps are as follows:

[0042] First, a geometric model of the scattering points based on an elliptical vortex beam lidar was established, as follows: Figure 3 As shown, the center of the elliptical vortex beam illuminating the tilted object. A spatial rectangular coordinate system is established with the origin as the origin, the beam propagation direction as the z-axis, and the horizontal direction of the beam's transverse plane as the y-axis. A represents a scattering particle in the elliptical vortex beam's optical field. Representing the origin The vector to scattering particle A has a magnitude equal to the radius of the elliptical vortex beam. Let be the angular velocity vector of the object, its direction being the normal vector of the plane rotating the object, and its magnitude being . . Vector Orthogonal decomposition along the coordinate axes, where and The included angle of the axis is . Let be the linear velocity at scattering point A. The formula for the rotational Doppler frequency shift of an elliptical vortex beam under inclined illumination conditions is derived, i.e. ,in Represents ellipticity, defined as the minor axis of the ellipse. Divide by the major axis , Represents the topological charge number. Represents rotational speed. Represents azimuth. This represents the tilt angle.

[0043] Secondly, an experimental setup for an elliptical vortex lidar detection system with rotational Doppler correction was designed, such as... Figure 2 As shown, firstly, a hologram of the corresponding elliptical vortex beam is prepared using the complex amplitude modulation method and loaded onto the spatial light modulator. After passing through a beam expander and collimator system composed of a polarizer and a lens, the laser beam enters the spatial light modulator, and the first-order diffracted elliptical vortex beam with the highest intensity is selected as the lidar source. The intensity distribution of elliptical vortex beams with different ellipticities is shown in the figure. Figure 5 As shown. The beam then passes through a reflector and illuminates the tilted, rotating object. The scattered light, after being focused by a convex lens, is received by a photodetector to obtain a time-domain echo signal. A personal computer is used for data processing and hologram creation. The specific flowchart of the non-coaxial rotating Doppler correction process based on the elliptical vortex beam radar system is shown below. Figure 1 As shown. In the experiment, the laser output power was set to 20.9 mW, and the topological charge of the vortex beam was... ellipticity is The rotating object rotates at a speed of 50 Hz and has a tilt angle of . Simultaneously, a traditional circular vortex beam lidar system is used to detect tilt angles of... Using a rotating object as a control group, after obtaining the time-domain signal, a Fourier transform is performed to obtain the object's tilt angle. At that time, the radar echo rotation Doppler frequency shift results for beams with different ellipticity are as follows: Figure 6 , Figure 6 (a) Figure 6 (b) shows the topological charge of the vortex beam as... The object rotates at 50 Hz and its tilt angle is... Under the conditions, the ellipticity of the probe beam is as follows: , The corresponding rotational Doppler spectrum. From Figure 6 It can be seen that when the object's tilt angle is... In the case of using ellipticity of When a circular vortex beam is used as the detection beam, the frequency spectrum is significantly broadened, and the peak frequency domain value of the Doppler echo signal is 0.004V. However, when an ellipticity of [missing value] is used... When the elliptical vortex beam detects an object, the frequency domain amplitude of the Doppler echo signal is 0.011V, approximately three times that before correction, and the rotating Doppler spectrum shows almost no broadening, proving the correctness of the rotating Doppler correction method for lidar based on the elliptical vortex beam. To further verify the generality of this method, the object tilt angle is... and At that time, the ellipticity of the elliptical vortex beam in the radar system was set to 1. and This was used to detect rotating objects, and the resulting rotating Doppler spectra were compared with those produced by a conventional circular vortex beam under the same conditions to obtain the object's tilt angle. , The experimental measurement results at that time are as follows Figure 7 As shown, where, Figure 7 (a) Figure 7 In (b), the topological load number is... The object rotates at 50 Hz and its tilt angle is... Under the conditions, the ellipticity of the probe beam is as follows: , The corresponding rotating Doppler spectrum; Figure 7 (c) Figure 7 (d) represents the angle of inclination of the object. Under the conditions, the ellipticity of the probe beam is as follows: , The corresponding rotating Doppler spectrum. It can be seen that the frequency domain peak value of the rotating Doppler signal generated by the elliptical vortex beam lidar detecting an object using appropriate ellipticity is increased by 0.006V and 0.003V respectively compared to the frequency domain peak value generated by the circular vortex beam, approximately twice that before correction, proving the generality of the method. The above experimental results show that, under inclined incident conditions, the rotating Doppler frequency shift correction method of lidar based on elliptical vortex beams can basically eliminate the spectral spread effect caused by tilt, greatly enhancing the signal strength of the rotating Doppler spectrum. It should be noted that, although when the tilt angle... and the ellipticity of the beam satisfy The method achieves the best correction effect, but when the tilt angle and ellipticity do not correspond, it can still optimize the rotating Doppler signal to a certain extent within a certain deviation range. Therefore, this method is highly practical, has a high fault tolerance rate, and has great application value in telemetry.

[0044] The contents not described in detail in this invention are existing technologies known to those skilled in the art.

Claims

1. A method for rotating Doppler correction of a lidar based on an elliptical vortex beam, characterized in that: First, an elliptical vortex beam required for lidar detection is prepared using complex amplitude modulation and coordinate transformation. Then, this beam is used to detect a tilted rotating object. The scattered light from the object is received by a photodetector to obtain a time-domain signal. Finally, the time-domain signal is processed by Fourier transform to obtain the corrected rotating Doppler spectrum. In this method, complex amplitude modulation and coordinate transformation are used to adjust the intensity and phase distribution of the superimposed vortex beams, thus preparing superimposed elliptical vortex beam holograms with different ellipticities. These holograms are then loaded onto a spatial light modulator, illuminated with linearly polarized light, and spatially filtered to obtain superimposed elliptical vortex beams with ellipticities corresponding to the object's tilt angle. The established tilt-rotation Doppler frequency shift model of the elliptical vortex beam is as follows: , Represents the rotational Doppler frequency shift. Represents ellipticity, defined as the minor axis of the ellipse. Divide by the major axis , Represents the topological charge number. Represents rotational speed. Represents azimuth. Represents the tilt angle; Secondly, the ellipticity obtained from the preparation is used as... The vortex beam detection tilt angle is For a rotating object, once the ellipticity and tilt angle are determined, the corrected rotational Doppler spectrum can be obtained by substituting the parameters into the formula based on the established rotational Doppler frequency shift model of the elliptical vortex beam. This is possible when the ellipticity and the object's tilt angle satisfy the following relationship: hour, Degenerate into If the corrected rotational Doppler spectrum is no longer broadened, the signal-to-noise ratio is improved compared to before correction.

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