A spin precession decoupling measurement method based on a rotating Doppler signal

Abstract

The application relates to a spin precession decoupling measurement method based on a rotating Doppler signal. The method first analyzes the modulation characteristics of a rotating Doppler signal of a spin-precession compound rotating motion target according to the rotating Doppler effect of vortex light; second, superposition state vortex light is used as a detection carrier to act on the spin-precession compound rotating target; finally, the fluctuation period and the average value of the time-frequency spectrum of a signal are extracted through time-frequency analysis of a target echo signal, and then the spin angular velocity and the precession angular velocity of the target are obtained. The application realizes decoupling measurement of spin precession, obtains the overall rotating motion parameters of a space rotating target, widens the application range of the rotating Doppler effect, and has a wide application prospect.

Description

Technical Field

[0001] This invention mainly relates to the fields of optics, photoelectric conversion, and signal processing, especially techniques and methods for phase modulation and time-frequency analysis of light beams. Background Technology

[0002] The technical background of this invention is mainly the Doppler effect. Its basic principle is that when the wave source has relative motion with respect to the observer, the frequency of the wave received by the observer will change. When the two are relatively close, the frequency received by the observer will increase, and vice versa. The change in frequency usually has a clear mathematical relationship with the relative velocity between the wave source and the observer. Based on this, the relative velocity between the two can be calculated according to the frequency difference between the received wave and the transmitted wave.

[0003] The Doppler effect applies to both mechanical and electromagnetic waves. Light waves, as a type of electromagnetic wave, can also exhibit the Doppler effect. The classic optical Doppler effect can be expressed by the following equation:

[0004] (1)

[0005] in This represents the frequency difference between the frequency received by the object and the frequency emitted by the light source. Indicates the frequency of the light source, This represents the relative velocity between the object and the light source. Represents the speed of light in the medium. The angle between the relative velocity direction between the light source and the receiver and the direction of light wave propagation is represented by the Doppler frequency shift expression when the relative motion between the light source and the receiver is not perpendicular to the direction of light wave propagation. When the relative motion direction is perpendicular to the direction of light wave propagation, the Doppler frequency shift is 0, that is, no Doppler effect is generated.

[0006] However, the Doppler effect can also occur when a beam of light with a transverse phase distribution is in relative motion perpendicular to the direction of light propagation. Generally, assuming the light source and the photodetector are located at the same point, when a beam of light with a transverse phase distribution illuminates a moving particle, the light wave received by the photodetector can be expressed by the following equation:

[0007] (2)

[0008] in Let be the complex amplitude of the light wave at the source. , , ( ) represents the three coordinate components of a moving particle in a Cartesian coordinate system. For wave vector, This is the original angular frequency of the light wave. Let be the transverse phase distribution function of the light wave. The frequency of the received light wave can be represented by the phase change rate, which, in the above equation, is:

[0009] (3)

[0010] The frequency difference between the original light wave frequency and the frequency of the light wave is:

[0011] (4)

[0012] in, For Hamiltonian operators, Let be the transverse velocity component of the moving particle. The first term is the same as in formula (1), which is the linear Doppler frequency shift. The second term is related to the transverse phase distribution of the light wave and the transverse velocity component of the particle. This indicates that a Doppler frequency shift can also be generated when the particle moves perpendicular to the direction of beam propagation.

[0013] In 1992, Allen et al. proposed a space-structured beam carrying orbital angular momentum (OAM). Such beams can be collectively referred to as vortex beams, and their main characteristic is a helical transverse phase distribution. In polar coordinates, the general expression for a vortex beam is:

[0014] (5)

[0015] in Let be the amplitude of the electric field. l The topological charge number can be understood as the number of times the phase of a light beam changes from 0 to 2π within its cross-section. Each photon in such a beam carries a charge. The OAM has a transverse phase distribution function as follows: The intensity and phase distribution of the vortex beam are as follows: Figure 2 As shown in (a) and (b). If a particle propagates along the axis of the light beam... z If the axis is the center of rotation and the motion is circular with an angular velocity of Ω, then the second term in formula (4) can be expressed as follows:

[0016] (6)

[0017] This is the expression for the rotating Doppler effect of a vortex beam, proposed and experimentally verified by Padgett et al. at the University of Glasgow in 2013. Since the frequency of light waves is generally too high to be directly measured, beat frequency is usually used to examine the frequency change of the beam. A simple method is to use a superposition of vortex beams with the same topological charge but opposite directions, whose intensity and phase distribution are as follows: Figure 2 As shown in (c) and (d), the actual measured frequency is twice the value calculated by equation (6). Summary of the Invention

[0018] The technical problem solved by this invention is as follows: For targets rotating in space, such as gyroscopes, space satellites, and warheads, when subjected to external rotational forces, they exhibit not only spin motion but also precession motion, which together constitute the overall rotational motion of the target. To accurately acquire the motion parameters of targets undergoing combined spin and precession rotational motion, this invention proposes a spin-precession decoupling measurement method based on the vortex optical rotational Doppler effect. This method utilizes the subtle modulation characteristics of the rotational Doppler frequency shift introduced by precession, and employs time-frequency analysis to extract the precession angular velocity and spin angular velocity of the target separately, thereby obtaining the target's motion parameters more accurately and reconstructing the target's motion characteristics. This method is simple and clear in principle, easy to implement, requires no complex scientific instruments, and has broad application prospects in the measurement of micro-motions of highly sensitive rotating objects.

[0019] The technical solution of this invention is: to invent a spin precession decoupling measurement method based on rotational Doppler signals. Its core is to utilize the modulation characteristics of the rotational Doppler frequency shift by the scattering points on the surface of an object undergoing spin-precession composite motion. Under spin-precession composite motion conditions, the linear velocity of the scattering points on the object's surface is affected not only by spin but also by precession, thus causing the rotational Doppler frequency shift to change over time. When the propagation axis of the superimposed vortex beam coincides with the object's precession axis, the modulation of the rotational Doppler signal by the scattering points on the object's surface manifests as a sinusoidal fluctuation of the rotational Doppler frequency shift over time. The fluctuation period T is the precession period, and the frequency center value M is the rotational Doppler frequency shift value corresponding to the spin angular velocity. By performing time-frequency analysis on the echo signal, the above two characteristic values ​​can be extracted from the time-frequency spectrum, thereby achieving decoupling measurement of the object's spin-precession composite motion parameters. The detection process mainly includes: First, in the vortex light preparation subsystem, a laser generates a beam of ordinary laser light, which is modulated into a superimposed vortex beam with a helical phase distribution by means of a spatial light modulator or vortex waveplate; second, the superimposed vortex beam is expanded and collimated and then irradiated onto the surface of a rotating object, with the beam propagation axis coinciding with the precession axis of the rotating object; next, a scattered light receiving system composed of lenses and photodetectors is used to collect the scattered light from the object surface and convert it into an electrical signal; finally, an analog-to-digital converter such as an oscilloscope or data acquisition card is used to sample the electrical signal and input it into a computer for further time-frequency analysis. The spin angular velocity and precession angular velocity of the object are obtained by extracting the fluctuation period and average value of the signal's time spectrum.

[0020] The principle of this invention is:

[0021] (1) Rotational Doppler effect

[0022] As can be seen from the analysis in the technical background, the topological charge number of a bundle is... lThe frequency shift produced by a vortex beam illuminating a single rotating target can be expressed as ,in The change in frequency ω is the rotational angular velocity.

[0023] The expression for a beam of vortex light in polar coordinates can be written as:

[0024] (7)

[0025] in , , In polar coordinates, Let be the amplitude of the electric field. l For topological load number, It is the angular frequency of the light wave. Let be the time interval, and its transverse phase distribution function be: .

[0026] For a target exhibiting a combined spin and precession rotation, the velocity of its surface scattering points is determined not only by the spin angular velocity but also by the precession angular velocity, such as... Figure 3 The diagram shown illustrates the detection of a target undergoing combined spin-precession motion using a vortex beam. The beam propagation axis coincides with the precession axis, with the precession center at M and the rotation center at O. A Cartesian coordinate system is established with M as the origin. Let the target's precession angular velocity be Ω1 and its spin angular velocity be Ω2. Due to the scattering characteristics of the object's surface and the magnitude of the light field, not all scattered light signals from all points in the light field can be received by the photodetector; only scattered light from a small region of the light field can be received. This small region is called the strong scattering point. Let there be a strong scattering point A on the light spot, with the phase angle of point A in the coordinate system being... The radius of the light spot is At a certain moment, the object's rotation center O precesses to a position in the coordinate system with a phase angle of θ. φ The position can be obtained from the relationship between the phase angle and the precession angular velocity of O. , t For time, based on the relevant parameters and geometric relationships shown in the figure, we have:

[0027] (8)

[0028] The velocity of scattering point A is determined by both its rotational angular velocity and precession angular velocity at that moment. According to equation (8), the velocity of point A can be calculated by the following formula:

[0029] (9)

[0030] in For vectors The model, For vectors The phase angle. Substituting the velocity at point A and the transverse phase distribution function of the vortex beam into equation (6), the rotational Doppler frequency shift generated at scattering point A is obtained as:

[0031] (10)

[0032] As can be seen from the above equation, the rotational Doppler frequency shift varies with time as a cosine function, its fluctuation period is the same as the precession period, and its average value is the same as the rotational Doppler frequency shift caused by the spin angular velocity. When a superposition vortex beam is used as the probe light, the generated Doppler frequency shift is twice the aforementioned Doppler frequency shift.

[0033] (2) Extraction of spin precession velocity based on rotating Doppler time spectrum

[0034] Based on the time-varying characteristics of the rotating Doppler frequency shift analyzed in (1), a superposition-state vortex beam is used to detect a spin-precessing composite rotating target. The optical axis coincides with the precession axis. A scattered light receiver is used to receive the scattered light signal and perform photoelectric conversion. After sampling the converted electrical signal, a short-time Fourier transform is performed, and the resulting time spectrum is as follows: Figure 4 As shown, the precession angular velocity and spin angular velocity of the target can be obtained by extracting the period T and the average frequency M of the spectral fluctuations.

[0035] Main advantages of the invention

[0036] (1) This method has a simple structure and is easy to implement.

[0037] (2) This method has high reliability and accuracy in detecting a combined spin-precession rotating object, and can obtain the spin velocity and precession velocity of the object in one measurement, which greatly simplifies the measurement of motion parameters of objects with this rotational motion characteristic.

[0038] (3) This method is still applicable under extreme conditions such as high-speed rotation. This device uses laser as the detection medium, which has a long transmission distance, fast response speed, and is less affected by the environment, and has broad application prospects. Attached Figure Description

[0039] Figure 1 This is a flowchart of the method.

[0040] Figure 2 The diagram shows the intensity and phase distribution of the vortex beam.

[0041] Figure 3 This is a schematic diagram of the motion of the scattering point under the combined conditions of spin precession and spin-induced motion.

[0042] Figure 4 This is a time-frequency analysis diagram of the echo signal; Detailed Implementation Plan

[0043] This invention uses superimposed vortex light as a detection carrier, and the specific implementation steps are as follows:

[0044] This method mainly includes a vortex light preparation subsystem, a scattered light receiving subsystem, and a photoelectric signal processing subsystem.

[0045] First, in the vortex light preparation subsystem, a regular laser beam is generated by a laser, and then modulated into a superimposed vortex beam with a spiral phase distribution by means of a spatial light modulator or vortex waveplate.

[0046] Secondly, the superimposed vortex beam is expanded and collimated before being irradiated onto the surface of the rotating object, with the beam propagation axis coinciding with the precession axis of the rotating object;

[0047] Next, a scattered light receiving system consisting of lenses and photodetectors is used to collect the scattered light from the object's surface and convert it into an electrical signal;

[0048] Finally, the electrical signal is sampled and input into a computer using a digital-to-analog converter such as an oscilloscope or data acquisition card for further time-frequency analysis. The spin angular velocity and precession angular velocity of the object are obtained by extracting the fluctuation period and average value of the signal's time spectrum.

[0049] The contents not described in detail in this invention are existing technologies known to those skilled in the art.

Claims

1. A spin precession decoupling measurement method based on rotating Doppler signals, characterized in that: Using a vortex beam preparation device to generate a topological charge of ± l A superposition-state vortex beam is incident on the surface of a composite rotating object with a precession angular velocity of Ω1 and a rotation angular velocity of Ω2, with the beam propagation axis coinciding with the object's precession axis. A scattered light receiver collects the scattered beam from the object's surface and performs photoelectric conversion. Time-frequency analysis is performed on the obtained photoelectric signal. Based on the variation of the rotational Doppler frequency shift with time under the combined spin and precession rotational motion, the fluctuation period T and center value M of the time spectrum are extracted. The results are then calculated using the formulas T = 2π / Ω1 and M = ... l Ω2 / π, and simultaneously calculate the target's precession angular velocity and rotation angular velocity.

2. The spin precession decoupling measurement method based on rotating Doppler signals according to claim 1, characterized in that, This method utilizes the modulation characteristics of the scattering points on the surface of an object undergoing spin-precession composite motion to influence the rotational Doppler frequency shift. Under the condition of spin-precession composite motion, the linear velocity of the scattering points on the object's surface is affected not only by the spin but also by the precession, thus causing the rotational Doppler frequency shift to change over time. Instead of performing a single spectral analysis on the echo signal, this method performs time-frequency analysis. Based on the fluctuation period and frequency center value of the time-frequency spectrum, the measured values ​​of the object's spin-precession motion parameters are obtained simultaneously, achieving decoupled measurement of spin-precession.

3. The spin precession decoupling measurement method based on rotating Doppler signals according to claim 1, characterized in that, When the propagation axis of the superimposed vortex beam coincides with the precession axis of the object, the modulation of the rotating Doppler signal by the scattering points on the object's surface is as follows: the rotating Doppler signal oscillates sinusoidally with time, the oscillation period T is the precession period 2π / Ω1, and the center value of the oscillation frequency M is the rotating Doppler frequency shift value corresponding to the spin angular velocity. l Ω2 / π.

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