A method and device for measuring angular velocity based on power exponent vortex beam and a medium

Abstract

This invention belongs to the field of rotational motion technology and relates to a method, device, and medium for measuring angular velocity based on a power-law vortex beam. The method involves modulating the power-law vortex beam to achieve zero relative phase between its various orbital angular momentum modes, thereby obtaining the normalized complex amplitudes of the target power-law vortex beam and its various orbital angular momentum modes. The target power-law vortex beam is then irradiated onto the surface of a rotating object to obtain the rotational Doppler effect spectrum data of the scattered light field, thereby obtaining the rotational Doppler effect spectrum intensity of the scattered light field at each frequency under the rotational angular frequency of the rotating object. Based on the modulation function of the rotating object on the target power-law vortex beam, the normalized complex amplitudes of each spiral mode in the spiral spectrum of the rotating object are obtained. Based on the normalized complex amplitudes of the orbital angular momentum modes, the normalized complex amplitudes of the spiral modes, and the rotational Doppler effect spectrum intensity of the scattered light field, the rotational angular velocity of the rotating object is calculated.

Description

Technical Field

[0001] This invention relates to the field of rotational motion technology, and in particular to a method, apparatus, and computer-readable storage medium for measuring angular velocity based on a power-law vortex beam. Background Technology

[0002] Rotational motion is widespread in various physical phenomena and engineering applications, and its accurate measurement is of great significance for fields such as industrial manufacturing, aerospace, and biomedicine. However, traditional angular velocity measurement methods are often limited by accuracy, stability, or applicability. Therefore, exploring new angular velocity measurement technologies is particularly important.

[0003] Currently, numerous studies on the application of structured light with various models for rotational speed detection have been conducted, including Laguerre-Gaussian (LG), Bessel-Gaussian (BG), and Perfect Optical Vortex (POV) beams. Specifically, when light illuminates the surface of a rotating object, the object's rotation interacts with the vortex phase of the light field, causing a frequency shift in the reflected or scattered echo light. This shift is called the rotational Doppler shift. Since the frequency shift has a clear quantitative relationship with the object's rotational speed and the topological charge of the structured light, the object's rotational speed can be calculated by subsequently acquiring the echo signal using components such as a single-photon avalanche detector array, performing a Fourier transform on the signal to obtain the frequency shift value. However, the radial intensity distribution of the LG beam is strongly coupled with the topological charge number, and higher-order modes are easily affected by diffraction and noise interference during propagation, resulting in spectral broadening and signal energy dispersion, which in turn destroys the discriminability of the frequency shift signal and reduces the sensitivity of angular velocity measurement. Although the BG beam has self-healing and diffraction-free characteristics, its energy utilization rate is low, and signal attenuation occurs in strong scattering or turbulent environments. Its anti-interference performance is insufficient, affecting the accuracy of angular velocity measurement. Although the ring radius of the POV beam is decoupled from the topological charge number, the ring radius of the beam can be adjusted independently to adapt to objects of different sizes on the north side, while maintaining the topological charge number to maintain frequency shift sensitivity and thus ensure the accuracy of angular velocity measurement, its generation usually depends on complex optical components, resulting in a large measurement system size and high cost, which limits miniaturization and integrated applications.

[0004] In summary, existing structured light-based angular velocity measurement methods suffer from low angular velocity measurement accuracy and the need for complex optical devices to generate the structured beam used for angular velocity measurement. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of low angular velocity measurement accuracy and the need for complex optical devices to generate the structured beam used to measure angular velocity in the existing structured light-based angular velocity measurement methods.

[0006] To solve the above-mentioned technical problems, the present invention provides a method for measuring angular velocity based on a power-law vortex beam, comprising: Modulate the power-law vortex beam so that the relative phase between each order of orbital angular momentum modes is 0, and obtain the normalized complex amplitude of the target power-law vortex beam and its order of orbital angular momentum modes. Irradiate the surface of a rotating object with a target power-law vortex beam and obtain the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object. Based on the modulation function of the rotating object on the target power-law vortex beam, the normalized complex amplitude of each order of spiral mode in the spiral spectrum of the rotating object is obtained. The scattered light field is measured to obtain the rotational Doppler effect spectrum data of the scattered light field, thereby obtaining the rotational Doppler effect spectrum intensity of the scattered light field at each frequency under the rotational angular frequency of the rotating object. The rotational angular velocity of the rotating object is calculated based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the normalized complex amplitudes of the spiral modes of each order in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field.

[0007] Preferably, the rotational angular velocity of the rotating object is calculated based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the normalized complex amplitudes of the spiral modes of each order in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field, including: Based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power exponential vortex beam, the first radial integral term of the autocorrelation function of the orbital angular momentum spectrum of the target power exponential vortex beam is constructed. Based on the normalized complex amplitude of each order of spiral mode in the spiral spectrum of a rotating object, the second radial integral of the autocorrelation function of the spiral spectrum of a rotating object is constructed. Based on the rotational Doppler effect spectral intensity of the scattered light field at various frequencies at the rotational frequency of the rotating object, which is equal to the product of the first radial integral term and the second radial integral term, the rotational angular frequency of the rotating object is calculated, and thus the rotational angular velocity of the rotating object is obtained.

[0008] Preferably, the rotational Doppler effect spectral intensity of the scattered light field at various frequencies under the rotational frequency of the rotating object is expressed as: , in, This indicates that the rotational angular frequency of the rotating object is... At that time, frequency The spectral intensity of the scattered light field at that location due to the rotational Doppler effect; Indicates the topological charge number; It is a positive integer; Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode.

[0009] Preferably, the normalized complex amplitudes of each order orbital angular momentum mode in the target power-law vortex beam are expressed as: , in, Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; This represents the field amplitude of the target power-law vortex beam.

[0010] Preferably, the modulation function of the rotating object on the target power-law vortex beam is expressed as: , in, The modulation function representing the power-law vortex beam of the target object by the rotating object; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; Represents the imaginary unit; Represents azimuth coordinates; It represents the angular frequency of rotation of a rotating object; The modulation function representing the power-law vortex beam of the rotating object with respect to the target is in The time-varying term of time.

[0011] Preferably, the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object is expressed as: , in, This represents the scattered light field after the target power-law vortex beam is scattered by the surface of a rotating object; The modulation function representing the power-law vortex beam of the target object by the rotating object; , This represents the optical field of the normalized target power-law vortex beam. Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode. Represents the imaginary unit. Represents azimuth coordinates; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; It represents the angular frequency of rotation of a rotating object; The modulation function representing the power-law vortex beam of the rotating object with respect to the target is in The time-varying term of time.

[0012] Preferably, the power-law vortex beam is modulated so that the relative phase between each order of orbital angular momentum mode is 0, including: The field amplitude of the power-law vortex beam is modulated to change the amplitude and relative phase of each order orbital angular momentum mode in the power-law vortex beam until the relative phase between each order orbital angular momentum mode is 0.

[0013] Preferably, a power-law vortex beam is generated using a pure phase spatial light modulator.

[0014] The present invention also provides an angular velocity measuring device based on a power-law vortex beam, comprising: The incident light modulation module is used to modulate the power-law vortex beam so that the relative phase between each order of orbital angular momentum modes is 0, thereby obtaining the normalized complex amplitude of the target power-law vortex beam and its each order of orbital angular momentum modes. The scattered light field acquisition module is used to irradiate the surface of a rotating object with a target power-law vortex beam and acquire the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object. The modulation parameter acquisition module is used to obtain the normalized complex amplitude of each order of spiral mode in the spiral spectrum of the rotating object based on the modulation function of the rotating object on the target power-law vortex beam. The scattered light field measurement module is used to measure the scattered light field and obtain the rotational Doppler effect spectrum data of the scattered light field, thereby obtaining the rotational Doppler effect spectrum intensity of the scattered light field at each frequency under the rotational angular frequency of the rotating object. The rotational angular velocity calculation module is used to calculate the rotational angular velocity of a rotating object based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the normalized complex amplitudes of the spiral modes of each order in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field.

[0015] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method for measuring the angular velocity of a power-law vortex beam.

[0016] The angular velocity measurement method based on power-law vortex beams provided in this application has the following advantages: Because power-law vortex beams exhibit a distinct symmetry structure after focusing, this symmetry allows the scattered light from the surface of a rotating object to form a stable modulation signal. This results in a single, stable characteristic peak in the Doppler shift signal of the scattered light, which, combined with the parameters of the power-law vortex beam, allows for the inference of the rotating object's angular velocity. Based on this, this application innovatively pioneers a new application of structured beams in angular velocity measurement by introducing power-law vortex beams to control the light field distribution. By adjusting the radial geometry of the vortex beam using power-law parameters, efficient extraction of angular velocity information from rotating objects is achieved. Furthermore, by modulating the power-law vortex beam to ensure that the relative phase of each orbital angular momentum mode is zero, modes with different topological charges form a coherent superposition, avoiding inversion. The increased charge number addresses the issue of radial intensity dispersion in the beam, concentrating signal energy and reducing diffraction loss during propagation. This improves the sensitivity of angular velocity measurement. Furthermore, it ensures that the Doppler effect spectrum of the scattered light field obtained from the rotating object is identical to the spectrum of the target power-law vortex beam, ignoring the influence of relative phase between orbital angular momentum modes. This simplifies the relationship between the intensity of the Doppler effect spectrum of the scattered light field and the modulation functions of the target power-law vortex beam and the rotating object under test. Therefore, the actual rotational angular velocity of the rotating object can be deduced by measuring the intensity of the rotational Doppler effect spectrum of the scattered light field, enabling quantitative detection of angular velocity. In addition, the power-law vortex beam can be generated using only a pure phase spatial light modulator, eliminating the need for complex optical components and reducing the complexity of the angular velocity measurement system. Attached Figure Description

[0017] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein: Figure 1 A flowchart illustrating the angular velocity measurement method based on a power-law vortex beam provided in this application embodiment; Figure 2The simulated power-law light intensity and phase diagram provided in this application embodiment; wherein, Figure 2 In the figure, (a) represents the phase of the beam in the source plane when the topological charge number l=2, and the intensity and phase of the focused beam in the focal plane. Figure 2 (b1) represents the phase of the beam in the source plane when the topological charge number l=3, and the intensity and phase of the focused beam in the focal plane. Figure 2 (b2) represents the phase of the beam in the source plane and the intensity and phase of the focused beam in the focal plane when the topological charge number l=4. Figure 2 (b3) represents the phase of the beam in the source plane and the intensity and phase of the focused beam in the focal plane when the topological charge number l=5. Figure 3 The autocorrelation spectrum product and Doppler effect spectrum of incident light and rotating object provided in the embodiments of this application; wherein, Figure 3 In the diagram, (a) represents the product of the radial integral of the autocorrelation function of the orbital angular momentum spectrum of the incident light and the radial integral of the autocorrelation function of the orbital angular momentum spectrum of the rotating object. Figure 3 (b) in the figure represents the simulated rotational speed. The Doppler effect spectrum obtained at that time; Figure 4 This is a simulation diagram of a power-law vortex beam rotating Doppler velocimeters provided in an embodiment of this application; wherein, Figure 4 (a1) in the image represents the intensity simulation image of the light source and the object when the object's symmetry k=1 and the light source's topological charge l=3. Figure 4 (a2) in the image represents the simulated intensity images of the light source and the object when the object's symmetry k=2 and the light source's topological charge l=3. Figure 4 (a3) in the image represents the intensity simulation of the light source and the object when the object's symmetry k=3 and the light source's topological charge l=3. Figure 4 In this context, (b1) is the product of the autocorrelation function of the light source and the autocorrelation function of the object corresponding to (a1). Figure 4 In (b2), the product of the autocorrelation function of the light source and the autocorrelation function of the object corresponding to (a2) is given. Figure 4 In the equation (b3), the product of the autocorrelation function of the light source and the autocorrelation function of the object corresponding to (a3) ​​is given. Figure 4 In this context, (c1) represents the simulated Doppler effect spectrum corresponding to the rotational speed measurement of (a1). Figure 4 In this context, (c2) represents the simulated Doppler effect spectrum corresponding to the rotational speed measurement in (a2). Figure 4 (c3) in the figure is the simulated Doppler effect spectrum of the rotational speed measurement corresponding to (a3). Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0019] Please see Figure 1 , Figure 1 The diagram shows a flowchart of an angular velocity measurement method based on a power-law vortex beam provided in an embodiment of this application. The method specifically includes: S10: Modulate the power-law vortex beam so that the relative phase between each order of orbital angular momentum modes is 0, and obtain the normalized complex amplitude of the target power-law vortex beam and its order of orbital angular momentum modes.

[0020] S20: Irradiate the surface of the rotating object with the target power-law vortex beam and obtain the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object.

[0021] S30: Based on the modulation function of the rotating object on the target power-law vortex beam, obtain the normalized complex amplitude of each order of spiral mode in the spiral spectrum of the rotating object.

[0022] S40: Measure the scattered light field to obtain the rotational Doppler effect spectrum data of the scattered light field, thereby obtaining the rotational Doppler effect spectrum intensity of the scattered light field at each frequency under the rotational angular frequency of the rotating object.

[0023] S50: The rotational angular velocity of the rotating object is calculated based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the normalized complex amplitudes of the spiral modes of each order in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field.

[0024] Specifically, step S50 includes: S500: Based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the first radial integral term of the autocorrelation function of the orbital angular momentum spectrum of the target power-law vortex beam is constructed.

[0025] S501: Based on the normalized complex amplitude of each order of spiral mode in the spiral spectrum of a rotating object, construct the second radial integral of the autocorrelation function of the spiral spectrum of a rotating object.

[0026] S502: Based on the rotational Doppler effect spectral intensity of the scattered light field at each frequency under the rotational frequency of the rotating object, which is equal to the product of the first radial integral term and the second radial integral term, the rotational angular frequency of the rotating object is calculated, and thus the rotational angular velocity of the rotating object is obtained.

[0027] Specifically, compared with traditional vortex beams with uniform phase variation... (Where i represents the imaginary unit, and l represents the topological load number,) Compared to azimuth coordinates, the electric field of a power-law vortex beam with Gaussian amplitude distribution in the source plane (z=0) is... It can be represented as: , in, Represents polar coordinates in the source plane. Radial coordinates, These are azimuth coordinates. The waist radius is Represents the remainder function. For topological load number, The power of the spiral phase, power series It can be an integer or a fraction, when the parameter At that time, the power-law vortex beam will degenerate into a traditional vortex beam.

[0028] When a power-law vortex beam is focused by a thin Fourier lens, it exhibits a symmetrical radial geometry on the focal plane, similar to a Laguerre-Gaussian beam. The shape of this radial geometry can be freely modulated by adjusting the topological charge value, such as... Figure 2 The diagram shown is a simulated power-law light intensity and phase diagram provided in an embodiment of this application; wherein, Figure 2 In the figure, (a) represents the phase of the beam in the source plane when the topological charge number l=2, and the intensity and phase of the focused beam in the focal plane. Figure 2 (b1) represents the phase of the beam in the source plane when the topological charge number l=3, and the intensity and phase of the focused beam in the focal plane. Figure 2 (b2) represents the phase of the beam in the source plane and the intensity and phase of the focused beam in the focal plane when the topological charge number l=4. Figure 2 (b3) represents the phase of the beam in the source plane when the topological charge number l=5, and the intensity and phase of the focused beam in the focal plane; from Figure 2 As can be seen, the power-law vortex beam exhibits a very obvious symmetrical structure after focusing. This symmetry allows the scattered light from the surface of the rotating object to form a stable modulation signal, resulting in a single and stable characteristic peak in the Doppler frequency shift signal of the scattered light from the surface of the rotating object. By combining the parameters of the power-law vortex beam, the rotational angular velocity of the rotating object can be deduced.

[0029] Furthermore, any vortex beam can be represented as an orthogonal superposition of a series of integer-order orbital angular momentum beams. Therefore, the electric field intensity of a power-law vortex beam focused on the focal plane is... It can be represented as: , in, For topological load number, For field amplitude, by changing It can simultaneously modulate the amplitude and relative phase of each orbital angular momentum mode beam in the structured beam, corresponding to the clipping of the orbital angular momentum amplitude spectrum and the orbital angular momentum phase spectrum, respectively.

[0030] Therefore, step S10 specifically includes: A power-law vortex beam is generated using a pure phase spatial light modulator. The field amplitude of the power-law vortex beam is modulated to change the amplitude and relative phase of each orbital angular momentum mode in the power-law vortex beam until the relative phase between each orbital angular momentum mode is 0.

[0031] Specifically, by modulating the relative phase between each order of orbital angular momentum modes to be 0, the Doppler effect spectrum of the final scattered light field can be made to be exactly the same as the spectrum of the target power-law vortex beam. By ignoring the influence of the relative phase between the orbital angular momentum modes, the relationship between the intensity of the Doppler effect spectrum of the scattered light field and the modulation function of the target power-law vortex beam and the rotating object can be simplified. This allows for a more direct deduction of the actual rotational angular velocity of the rotating object, enabling quantitative detection of the angular velocity.

[0032] Specifically, the normalized complex amplitudes of each order orbital angular momentum mode in the target power-law vortex beam are expressed as: , in, Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; This represents the field amplitude of the target power-law vortex beam.

[0033] Specifically, when a light beam illuminates a rotating object with a rough surface, its phase is modulated in the scattered light. The modulation function of the rough surface can be expressed as: ， Furthermore, when the object rotates at an angular frequency Upon rotation, the modulation function acquires an additional time-varying term. Therefore, the modulation function of the rotating object with respect to the target power-law vortex beam is expressed as: , in, The modulation function representing the power-law vortex beam of the rotating object on the target; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; Represents the imaginary unit; Represents azimuth coordinates; It represents the angular frequency of rotation of a rotating object; The modulation function representing the power-law vortex beam of a rotating object with respect to a target is in The time-varying term of time.

[0034] Furthermore, the scattered light field is represented as the product of the amplitude of the target power-law vortex beam and the modulation function of the rotating object. Specifically, the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object is represented as follows: , in, This represents the scattered light field after the target power-law vortex beam is scattered by the surface of a rotating object; The modulation function representing the power-law vortex beam of the rotating object on the target; , This represents the light field of the normalized target power-law vortex beam.

[0035] Furthermore, the rotational Doppler effect spectrum at the rotational angular frequency of the rotating object is At that time, frequency The intensity at that point can be expressed as: , in, , , It is a positive integer. express The complex conjugate, express .

[0036] From the above rotational Doppler effect spectrum at frequency As can be seen from the intensity formula, the orbital angular momentum amplitude spectrum and the orbital angular momentum phase spectrum jointly determine the distribution and relative magnitude of the peaks in the rotating Doppler effect spectrum. However, in this application, after modulating the power-law vortex beam in step S10, the resulting target power-law vortex beam has no relative phase between its various orbital angular momentum modes, and the phase of each orbital angular momentum mode is related to the topological charge number. The linear correlation means that the spectrum of the rotating Doppler effect is exactly the same as the spectrum of the target power-law vortex beam, at which point the frequency... The intensity of the rotational Doppler effect spectrum at a given location can be simplified to the following form: , in, This indicates that the rotational angular frequency of the rotating object is... At that time, frequency The spectral intensity of the scattered light field at that location due to the rotational Doppler effect; Indicates the topological charge number; It is a positive integer; Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode.

[0037] As can be seen from the simplified formula, the rotational Doppler effect spectrum of the scattered light field is the product of the radial integral of the autocorrelation function of the orbital angular momentum spectrum of the target power-law vortex beam and the radial integral of the autocorrelation function of the spiral spectrum of the rotating object. Therefore, by experimentally measuring the intensity of the rotational Doppler effect spectrum of the scattered light field, the rotational angular velocity of the rotating object can be calculated by reverse calculation using this formula.

[0038] For example, such as Figure 3 The image shown is a spectrum of the autocorrelation spectrum product and Doppler effect of the incident light and the rotating object provided in an embodiment of this application; wherein, Figure 3 In the diagram, (a) represents the product of the radial integral of the autocorrelation function of the orbital angular momentum spectrum of the incident light and the radial integral of the autocorrelation function of the orbital angular momentum spectrum of the rotating object. Figure 3 (b) in the figure represents the simulated rotational speed. The Doppler effect spectrum obtained at that time.

[0039] from Figure 3 As can be seen, the weighting ratios at the peaks of the autocorrelation product spectrum and the rotating Doppler effect spectrum obtained from the speed measurement simulation are basically consistent. The first significant peak appears at m=3 in the autocorrelation product spectrum, which should correspond to the frequency of the rotating Doppler effect spectrum at m=3. The peaks at that location correspond to the peaks shown in the figure. The rotational speed of the rotating object can be calculated from this. The results are consistent with the simulation settings.

[0040] To verify the feasibility of the aforementioned angular velocity measurement method based on a power-law vortex beam, this application embodiment also conducted relevant simulations using MATLAB software. The simulations used a power-law vortex beam with a beam waist of 0.5 mm, a wavelength of 532 nm, a topological charge of 3, and a power-law exponent of 2 as the incident beam. Multiple simulations were performed using rotating objects with different symmetries, yielding the following results: Figure 4 The rotating Doppler velocimetry results shown are as follows, Figure 4 (a1) in the image represents the intensity simulation image of the light source and the object when the object's symmetry k=1 and the light source's topological charge l=3. Figure 4 (a2) in the image represents the intensity simulation of the light source and the object when the object's symmetry k=2 and the light source's topological charge l=3. Figure 4 (a3) in the image represents the simulated intensity images of the light source and the object when the object's symmetry k=3 and the light source's topological charge l=3. Figure 4 In this context, (b1) is the product of the autocorrelation function of the light source and the autocorrelation function of the object corresponding to (a1). Figure 4 In this context, (b2) is the product of the autocorrelation function of the light source and the autocorrelation function of the object corresponding to (a2). Figure 4 In (b3), the product of the autocorrelation function of the light source and the autocorrelation function of the object corresponding to (a3) ​​is given. Figure 4 In this context, (c1) represents the simulated Doppler effect spectrum corresponding to the rotational speed measurement of (a1). Figure 4 In this context, (c2) represents the simulated Doppler effect spectrum corresponding to the rotational speed measurement in (a2). Figure 4 (c3) in the figure is the simulated Doppler effect spectrum of the rotational speed measurement corresponding to (a3).

[0041] in, Figure 4 The horizontal axis of (b1), (b2), and (b3) in the figure represents the autocorrelation value obtained by mode decomposition, and the vertical axis represents the relative weight of the mode. Specifically, the rotational speed of the rotating object can be obtained by dividing the frequency corresponding to the significant peak in the rotational Doppler effect spectrum by the index m of the same peak in the autocorrelation product spectrum.

[0042] from Figure 4 As can be seen from the simulation of velocity measurement of objects and light sources under different degrees of symmetry, the weight ratios at the peaks of the spectral images of the rotating Doppler effect obtained by the product of the autocorrelation function and the rotational speed measurement simulation are basically the same, indicating that the angular velocity measurement method based on the power exponential vortex beam proposed in this application is feasible.

[0043] Based on the power-law vortex beam-based angular velocity measurement method provided in the above embodiments, this application also provides an angular velocity measurement device based on a power-law vortex beam, which specifically includes: The incident light modulation module is used to modulate the power-law vortex beam so that the relative phase between each order of orbital angular momentum modes is 0, thereby obtaining the normalized complex amplitude of the target power-law vortex beam and its order of orbital angular momentum modes.

[0044] The scattered light field acquisition module is used to irradiate the surface of a rotating object with a target power-law vortex beam and acquire the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object.

[0045] The modulation parameter acquisition module is used to obtain the normalized complex amplitude of each order of spiral modes in the spiral spectrum of the rotating object based on the modulation function of the target power-law vortex beam by the rotating object.

[0046] The scattered light field measurement module is used to measure the scattered light field and obtain the rotational Doppler effect spectrum data of the scattered light field, thereby obtaining the rotational Doppler effect spectrum intensity of the scattered light field at each frequency under the rotational angular frequency of the rotating object.

[0047] The rotational angular velocity calculation module is used to calculate the rotational angular velocity of a rotating object based on the normalized complex amplitude of each orbital angular momentum mode in the target power-law vortex beam, the normalized complex amplitude of each order of spiral modes in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field.

[0048] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method for measuring the angular velocity of a power-law vortex beam.

[0049] This application innovatively pioneers the application of new structured beams in angular velocity measurement by introducing a power-law vortex beam to control the light field distribution. By adjusting the radial geometry of the vortex beam using the power-law parameter, it achieves efficient extraction of angular velocity information of rotating objects, thus expanding the available structured beams for angular velocity measurement. Specifically, by utilizing the inherent spatial phase distribution of a power-law vortex beam, its orbital angular momentum characteristics can directly map the angular velocity information of the target object during rotation. This avoids the complex phase superposition process required by traditional Laguerre-Gaussian beams in velocity measurement, simplifying the signal extraction process and improving efficiency. Simultaneously, by controlling the spatial structure of the beam through power-law parameters, energy is concentrated in a specific radius region. While maintaining the orbital angular momentum characteristics, this effectively overcomes the problem of the main loop radius of higher-order Laguerre-Gaussian beams significantly increasing with topological charge, thereby improving the sensitivity and signal-to-noise ratio of weak signal detection. Even in complex environments or long-distance measurements, this method maintains a high signal-to-noise ratio and stable spectral lines, achieving high-precision angular velocity measurement. It overcomes the limitations of existing structured light modes in terms of anti-interference capability, measurement accuracy, and system feasibility, providing an innovative solution for non-contact, high-precision angular velocity detection in complex environments.

[0050] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0051] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0052] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0053] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0054] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for measuring angular velocity based on a power-law vortex beam, characterized in that, include: Modulate the power-law vortex beam so that the relative phase between each order of orbital angular momentum modes is 0, and obtain the normalized complex amplitude of the target power-law vortex beam and its order of orbital angular momentum modes. Irradiate the surface of a rotating object with a target power-law vortex beam and obtain the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object. Based on the modulation function of the rotating object on the target power-law vortex beam, the normalized complex amplitude of each order of spiral mode in the spiral spectrum of the rotating object is obtained. The scattered light field is measured to obtain the rotational Doppler effect spectrum data of the scattered light field, thereby obtaining the rotational Doppler effect spectrum intensity of the scattered light field at each frequency under the rotational angular frequency of the rotating object. The rotational angular velocity of the rotating object is calculated based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the normalized complex amplitudes of the spiral modes of each order in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field.

2. The angular velocity measurement method based on a power-law vortex beam according to claim 1, characterized in that, Based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the normalized complex amplitudes of the spiral modes of each order in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field, the rotational angular velocity of the rotating object is calculated, including: Based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power exponential vortex beam, the first radial integral term of the autocorrelation function of the orbital angular momentum spectrum of the target power exponential vortex beam is constructed. Based on the normalized complex amplitude of each order of spiral mode in the spiral spectrum of a rotating object, the second radial integral of the autocorrelation function of the spiral spectrum of a rotating object is constructed. Based on the rotational Doppler effect spectral intensity of the scattered light field at various frequencies at the rotational frequency of the rotating object, which is equal to the product of the first radial integral term and the second radial integral term, the rotational angular frequency of the rotating object is calculated, and thus the rotational angular velocity of the rotating object is obtained.

3. The angular velocity measurement method based on a power-law vortex beam according to claim 2, characterized in that, The rotational Doppler effect spectral intensity of the scattered light field at various frequencies at the rotational frequency of the rotating object is expressed as: ， in, This indicates that the rotational angular frequency of the rotating object is... At that time, frequency The spectral intensity of the scattered light field at that location due to the rotational Doppler effect; Indicates the topological charge number; It is a positive integer; Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode.

4. The angular velocity measurement method based on a power-law vortex beam according to claim 1, characterized in that, The normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam are expressed as follows: ， in, Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode; This represents the field amplitude of the target power-law vortex beam.

5. The angular velocity measurement method based on a power-law vortex beam according to claim 1, characterized in that, The modulation function of the rotating object on the target power-law vortex beam is expressed as: ， in, The modulation function representing the power-law vortex beam of the target object by the rotating object; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; Represents the imaginary unit; Represents azimuth coordinates; It represents the angular frequency of rotation of a rotating object; The modulation function representing the power-law vortex beam of the rotating object with respect to the target is in The time-varying term of time.

6. The angular velocity measurement method based on a power-law vortex beam according to claim 1, characterized in that, The scattered light field after the target power-law vortex beam is scattered by the surface of a rotating object is expressed as: ， in, This represents the scattered light field after the target power-law vortex beam is scattered by the surface of a rotating object; The modulation function representing the power-law vortex beam of the target object by the rotating object; , This represents the optical field of the normalized target power-law vortex beam. Indicates the target power-law vortex beam at a radius place Normalized complex amplitude of the orbital angular momentum mode. Represents the imaginary unit. Represents azimuth coordinates; Indicates the helical spectrum of a rotating object at the radius Place Normalized complex amplitude of the spiral mode; It represents the angular frequency of rotation of a rotating object; The modulation function representing the power-law vortex beam of the rotating object with respect to the target is in The time-varying term of time.

7. The angular velocity measurement method based on a power-law vortex beam according to claim 1, characterized in that, Modulating the power-law vortex beam to achieve a relative phase of 0 between each order of orbital angular momentum mode includes: The field amplitude of the power-law vortex beam is modulated to change the amplitude and relative phase of each order orbital angular momentum mode in the power-law vortex beam until the relative phase between each order orbital angular momentum mode is 0.

8. The angular velocity measurement method based on a power-law vortex beam according to claim 1, characterized in that, A power-law vortex beam is generated using a pure phase spatial light modulator.

9. An angular velocity measuring device based on a power-law vortex beam, characterized in that, include: The incident light modulation module is used to modulate the power-law vortex beam so that the relative phase between each order of orbital angular momentum modes is 0, thereby obtaining the normalized complex amplitude of the target power-law vortex beam and its each order of orbital angular momentum modes. The scattered light field acquisition module is used to irradiate the surface of a rotating object with a target power-law vortex beam and acquire the scattered light field after the target power-law vortex beam is scattered on the surface of the rotating object. The modulation parameter acquisition module is used to obtain the normalized complex amplitude of each order of spiral mode in the spiral spectrum of the rotating object based on the modulation function of the rotating object on the target power-law vortex beam. The scattered light field measurement module is used to measure the scattered light field and obtain the rotational Doppler effect spectrum data of the scattered light field, thereby obtaining the rotational Doppler effect spectrum intensity of the scattered light field at each frequency under the rotational angular frequency of the rotating object. The rotational angular velocity calculation module is used to calculate the rotational angular velocity of a rotating object based on the normalized complex amplitudes of the orbital angular momentum modes of each order in the target power-law vortex beam, the normalized complex amplitudes of the spiral modes of each order in the spiral spectrum of the rotating object, and the rotational Doppler effect spectral intensity of the scattered light field.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the angular velocity measurement method based on a power-law vortex beam as described in any one of claims 1 to 8.

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