Method and system for measuring angular acceleration of rotating object based on fractional Fourier transform

Abstract

The invention relates to a method and a system for measuring angular acceleration of a rotating object based on fractional Fourier transform, and the method comprises the following steps: a detection light beam irradiates the rotating object, and the rotating object modulates the detection light beam to generate a scattered light signal; a scattered light signal on the surface of the rotating object is obtained and subjected to photoelectric conversion to obtain a linear frequency modulation electric signal, namely a time-varying signal; applying different transformation orders to the time-varying signal to carry out fractional Fourier transform, and converting the time-varying signal from a time domain to a fractional domain; determining an optimal transformation order in the fractional domain through a peak search algorithm; and obtaining the angular acceleration of the rotating object according to the corresponding relation between the fractional Fourier transform order and the angular acceleration based on the optimal transform order. According to the method, the fractional Fourier transform is introduced, and the optimal transform order is determined through the peak search algorithm, so that the energy focusing characteristic and the anti-noise capability of the signal are remarkably improved, and non-contact high-precision measurement of the uniformly accelerated rotating object is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of angular acceleration measurement, and in particular to a method and system for measuring the angular acceleration of a rotating object based on fractional-order Fourier transform. Background Art

[0002] Rotational motion is a very common form of motion in nature and engineering. From the rotation of celestial bodies and microorganisms to high-speed rotating machinery in industry, the high-speed rotation of bullets and artillery shells in flight in the defense sector, and the rotation of unstable spacecraft, all involve the measurement of rotational motion. Angular velocity, as an important parameter describing the speed of rotational motion, has been widely studied and applied in its measurement technology. However, angular acceleration, as a key parameter describing the rate of change of rotational motion, is equally important in engineering practice. For example, accurate measurement of angular acceleration is required for analyzing the dynamic performance of mechanical systems and controlling the attitude adjustment of aircraft.

[0003] At present, the Rotational Doppler Effect (RDE) is one of the important research directions in the field of light field manipulation for measuring the angular velocity of rotating objects. RDE describes the frequency change phenomenon produced when a structured light beam carrying orbital angular momentum (OAM) interacts with a rotating object. Unlike the traditional Doppler effect, the frequency offset of RDE is directly related to the rotational angular velocity of the object and the topological charge (TC) of the light beam, providing a new technical means for non-contact measurement of rotating objects. Since Allen et al. first proposed the OAM characteristics of vortex beams in 1992, RDE has gradually become a research hotspot in the fields of optical sensing, precision measurement and quantum communication. However, the existing technology still has many shortcomings in using RDE to measure angular acceleration.

[0004] Although many advances have been made in the study of RDE, its application is mainly concentrated on the measurement of angular velocity of uniformly rotating objects. For the measurement of angular acceleration, the existing technology mainly adopts the principle of short-time Fourier transform (STFT). The short-time Fourier transform obtains the local characteristics of the signal in time and frequency by dividing the signal into multiple short time periods and performing Fourier transform on each time period. Specifically, the short-time Fourier transform uses a sliding window function to segment the signal, and then performs Fourier transform on the signal in each window to obtain the spectrum information of the time period, and finally accumulates all time periods to observe the frequency changes of the entire time period. In this way, the change of signal frequency over time can be revealed, which is suitable for analyzing non-stationary signals whose frequency changes over time.

[0005] However, the short-time Fourier transform has obvious defects when processing the echo signal of the angular acceleration object. Due to its fixed window length, it is impossible to accurately extract both high-frequency and low-frequency components at the same time, resulting in severe spectrum broadening and signal energy dispersion. In addition, the method has weak resistance to noise, especially in strong noise or turbulent environments, where signal features are easily submerged by noise, further reducing the measurement accuracy. For example, in high-temperature turbulence or strong noise environments, the spectrum broadening of the RDE signal is aggravated, and the traditional Fourier transform has difficulty in effectively extracting signal features due to its fixed frequency resolution. These limitations restrict the application of existing technologies in complex environments and make it difficult to meet the needs of high-precision measurement of angular acceleration.

[0006] Therefore, there is an urgent need for a method and system for measuring the angular acceleration of a rotating object based on fractional-order Fourier transform to address the shortcomings of the existing technology. Summary of the Invention

[0007] To this end, the technical problem to be solved by the present invention is to overcome the problem of insufficient signal processing capability of short-time Fourier transform in complex environments in the prior art, and to provide a method and system for measuring the angular acceleration of a rotating object based on fractional-order Fourier transform. By introducing the fractional-order Fourier transform and determining the optimal transformation order through a peak search algorithm, the energy focusing characteristics and anti-noise capability of the signal are significantly improved, thereby realizing non-contact, high-precision measurement of uniformly accelerated rotating objects.

[0008] In a first aspect, to solve the above technical problems, the present invention provides a method for measuring the angular acceleration of a rotating object based on fractional-order Fourier transform, comprising the following steps:

[0009] S1: The vortex beam serves as a probe beam to illuminate a rotating object, which modulates the probe beam to generate a scattered light signal.

[0010] S2: Acquire scattered light signals from the surface of a rotating object;

[0011] S3: performing photoelectric conversion on the acquired scattered light signal to obtain a linear frequency modulated electrical signal, i.e., generating a time-varying signal;

[0012] S4: applying different transformation orders to the time-varying signal to perform fractional Fourier transform, converting the time-varying signal from the time domain to the fractional domain;

[0013] S5: Determine the optimal transform order α in the fractional domain through the peak search algorithm opt ;

[0014] S6: Based on the optimal transformation order α opt , according to the correspondence between the fractional Fourier transform order and angular acceleration, the angular acceleration of the rotating object is obtained.

[0015] In one embodiment of the present invention, the specific method for obtaining the scattered light signal on the surface of the rotating object in step S2 is as follows:

[0016] S21. Establish an angular velocity model of a rotating object, and based on the angular velocity model, construct a modulation function for describing the rotation of the object;

[0017] S22. Multiply the electric field intensity of the vortex beam by the modulation function to obtain a scattered light signal scattered by the surface of the rotating object.

[0018] In one embodiment of the present invention, the position of the vortex beam in the cylindrical coordinate system is The expression of the electric field intensity E(r,φ) at is as follows:

[0019]

[0020] Where E0 is the amplitude of the electric field, ω0 is the LG waist radius, is the corresponding Laguerre polynomial, l is the topological charge, p is the radial quantum number, f is the optical frequency, t is the time, is the phase structure of the beam, and exp(-i2πft) is the actual related phase factor.

[0021] In one embodiment of the present invention, the expression of the angular velocity model Ω(t) of the rotating object is as follows:

[0022]

[0023] Where Ω0 is the initial angular velocity of the rotating object, and a(t) is the angular acceleration. When a(t) is greater than 0, it indicates that the object is rotating at an accelerated speed, and when it is less than 0, it indicates that the object is rotating at a decelerated speed.

[0024] In one embodiment of the present invention, the modulation function of the object rotation The expression is:

[0025]

[0026] Among them, A n (r) is the nth-order normalized complex amplitude, satisfying ∑|A n (r)| 2 =1, Ω(t) represents the angular velocity at any time t.

[0027] In one embodiment of the present invention, the scattered light signal scattered by the surface of the rotating object The expression is as follows:

[0028]

[0029] in, is the modulation function of the object rotation; is the incident light electric field;

[0030] When the vortex beam is a superposition of positive and negative topological charges,

[0031]

[0032] l is the topological charge; B(r) is the weight of different OAM mode components in the light source, f is the optical frequency, and n is the mode order associated with the vortex beam.

[0033] In one embodiment of the present invention, in step S3, the scattered light signal is photoelectrically converted by a photodetector. The total light intensity collected within a unit interface of the photodetector is the time-varying signal generated by the accelerated motion. The expression of the time-varying signal is:

[0034]

[0035] Among them, I(t) is the total light intensity collected within the unit interface of the photoelectric detector at time t, Cn is a constant, i is an imaginary unit, and i 2 =-1, f0 is the initial frequency of the signal, μ is the modulation frequency, which indicates the rate at which the frequency changes with time.

[0036] In one embodiment of the present invention, in step S5, the optimal transform order α is determined in the fractional domain by using a peak search algorithm. opt The specific methods are as follows:

[0037] S51: Parameter initialization setting, setting α0 = 0, step size = Δα, and the selection of Δα satisfies the constraint that nΔα = 2 is an integer, and the number of iterations k = 0;

[0038] S52: Apply fractional order α to the time-varying signal in sequence k =α0+kΔα(k=1,2,...,n) to perform fractional Fourier transform, and use the fast linear interpolation algorithm to generate the transformation results corresponding to each fractional order

[0039] S53: Compare the n transformation results numerically to determine the optimal order corresponding to the maximum value

[0040] S54: reduce the step size Δα′=Δα / 2;

[0041] S55: Comparison and If the size Then determine whether the number of iterations k exceeds the preset maximum number of iterations k max ; Otherwise, increase the number of iterations k=k+1 and return to step S53;

[0042] S46: When the number of iterations k exceeds the preset maximum number of iterations k max When , the optimal transformation order α is output opt and Otherwise, increase the number of iterations k=k+1 and return to step S53.

[0043] In one embodiment of the present invention, the relationship between the fractional Fourier transform order and the angular acceleration in step S3 is expressed as follows:

[0044]

[0045] Where α is the fractional Fourier transform order, a is the angular acceleration, and l is the topological charge.

[0046] In a second aspect, in order to solve the above technical problems, the present invention provides a rotating object angular acceleration measurement system based on fractional-order Fourier transform, comprising:

[0047] A rotor, used to place the rotating object to be measured;

[0048] a light source for generating a tunable laser beam;

[0049] A beam expander, used for expanding the laser beam generated by the light source;

[0050] a polarization unit comprising a half-wave plate and a polarizer, wherein the half-wave plate is used to convert the light beam from the light source unit into circularly polarized light; and the polarizer is used to convert the circularly polarized light into horizontally polarized light;

[0051] A spatial light modulator receives the horizontally polarized light emitted by the polarizer and loads holograms with different superimposed phases to generate a variety of petal-shaped structured detection lights;

[0052] electric heating plates for generating thermally induced turbulence;

[0053] Photodetector, used to capture light signals scattered by rotating objects and convert them into electrical signals;

[0054] The beam splitter splits the light beam into two parts, one part hits the rotating object and continues to propagate, and the other part is reflected to the photodetector;

[0055] a signal processing unit, configured to perform fractional Fourier transform processing on the electrical signal converted by the photodetector, and to use a peak search algorithm to determine the optimal transform order to calculate the angular acceleration of the rotating object;

[0056] Output unit, used to display or transmit the calculated angular acceleration.

[0057] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0058] (1) The present invention can optimally focus the energy of the linear frequency modulation signal within a specific narrow band in the fractional domain through the adaptive order adjustment characteristics of the fractional Fourier transform. This method significantly improves the detectable threshold of the peak signal-to-noise ratio and the input signal-to-noise ratio; it can maintain stable measurement even in a high-temperature turbulent environment, breaking through the limitation of traditional methods that can only measure angular velocity, and realizing non-contact high-precision measurement of uniformly accelerated rotating objects, significantly reducing the error of acceleration measurement.

[0059] (2) The peak search algorithm of the present invention can dynamically adjust the step size when adaptively scanning the optimal order of the fractional order, thereby significantly improving the computational efficiency while ensuring computational accuracy. This algorithm can quickly locate the approximate range of the optimal order in the global search phase and further accurately optimize it in the local search phase, ensuring efficient operation in different environments and conditions.

[0060] (3) The present invention does not require complex optical path modulation and can achieve high-precision measurement only by real-time monitoring of the signal-to-noise ratio, which significantly reduces the system complexity and experimental cost. Compared with traditional measurement methods, the measurement optical path of the present invention is simpler, more convenient to operate, and easy to implement. It has good engineering application prospects and can adapt to the angular acceleration measurement needs of rotating objects in various complex environments, providing a more efficient and reliable measurement method for related applications in industry, national defense and other fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings, wherein

[0062] Figure 1 Flowchart of a method for measuring angular acceleration of a rotating object based on fractional Fourier transform in a preferred embodiment of the present invention;

[0063] Figure 2 A flow chart for determining the optimal transformation order for the peak search algorithm of the present invention;

[0064] Figure 3 Schematic diagram of the optical path for measuring the angular acceleration of a rotating object in the present invention;

[0065] Figure 4 Schematic diagram of the time-frequency-space domain of the fractional-order Fourier transform of the present invention;

[0066] Figure 5 (a) Angular acceleration measurements of rotating objects under different topological loads under acceleration;

[0067] Figure 5 (b) is the measured angular acceleration of the rotating object under different topological loads under deceleration;

[0068] Figure 6 The signal-to-noise ratios detected by fractional Fourier transform analysis and short-time Fourier analysis for turbulent environments at different temperatures;

[0069] Figure 7 (a) Comparison of accelerations detected by fractional Fourier transform analysis and short-time Fourier transform analysis in a turbulent environment at 100°C;

[0070] Figure 7 (b) Comparison of accelerations detected by fractional-order Fourier transform analysis and short-time Fourier transform analysis in a turbulent environment at 200°C;

[0071] Figure 7 (c) Comparison of accelerations detected by fractional-order Fourier transform analysis and short-time Fourier transform analysis in a turbulent environment at 300°C;

[0072] Explanation of the accompanying drawings in the specification: 1. Light source; 2. Beam expander; 3. Half-wave plate; 4. Polarizer; 5. Spatial modulator; 6. Hot plate; 7. Beam splitter; 8. Photodetector; 9. Rotor. DETAILED DESCRIPTION

[0073] 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 the present invention and implement it. However, the embodiments are not intended to limit the present invention.

[0074] Reference Figure 1 As shown, the present invention provides a method for measuring the angular acceleration of a rotating object based on fractional-order Fourier transform, comprising the following steps:

[0075] S1: The vortex beam serves as a probe beam to illuminate a rotating object, which modulates the probe beam to generate a scattered light signal.

[0076] S2: Acquire scattered light signals from the surface of a rotating object;

[0077] S3: performing photoelectric conversion on the acquired scattered light signal to obtain a linear frequency modulated electrical signal, i.e., generating a time-varying signal;

[0078] S4: applying different transformation orders to the time-varying signal to perform fractional Fourier transform, converting the time-varying signal from the time domain to the fractional domain;

[0079] S5: Determine the optimal transform order α in the fractional domain through the peak search algorithm opt ;

[0080] S6: Based on the optimal transformation order α opt, according to the correspondence between the fractional Fourier transform order and angular acceleration, the angular acceleration of the rotating object is obtained.

[0081] In one embodiment of the present invention, the specific method for obtaining the scattered light signal on the surface of the rotating object in step S2 is as follows:

[0082] S21. Establish an angular velocity model of a rotating object, and based on the angular velocity model, construct a modulation function for describing the rotation of the object;

[0083] S22. Multiply the electric field intensity of the vortex beam by the modulation function to obtain a scattered light signal scattered by the surface of the rotating object.

[0084] In one embodiment of the present invention, the position of the vortex beam in the cylindrical coordinate system is The expression of the electric field intensity E(r,φ) at is as follows:

[0085]

[0086] Where E0 is the amplitude of the electric field, ω0 is the LG waist radius, is the corresponding Laguerre polynomial, l is the topological charge, p is the radial quantum number, f is the optical frequency, t is the time, is the phase structure of the beam, and exp(-i2πft) is the actual related phase factor.

[0087] In one embodiment of the present invention, the expression of the angular velocity model Ω(t) of the rotating object is as follows:

[0088]

[0089] Where Ω0 is the initial angular velocity of the rotating object, and a(t) is the angular acceleration. When a(t) is greater than 0, it indicates that the object is rotating at an accelerated speed, and when it is less than 0, it indicates that the object is rotating at a decelerated speed.

[0090] In one embodiment of the present invention, the modulation function of the object rotation The expression is:

[0091]

[0092] Among them, A n (r) is the nth-order normalized complex amplitude, satisfying ∑|A n (r)| 2 =1, Ω(t) represents the angular velocity at any time t.

[0093] In one embodiment of the present invention, the scattered light signal scattered by the surface of the rotating object The expression is as follows:

[0094]

[0095] in, is the modulation function of the object rotation; is the incident light electric field;

[0096] The scattered light modulated by the rotating object contains many OAM components. Each mode carries a frequency shift after being modulated by the rotating object. However, these frequency changes are superimposed on the optical frequency and are close to the PHz level. The existing machine sampling rate cannot reach this level. Therefore, a vortex beam with superposition of positive and negative topological charges is selected as the detection beam, and then:

[0097]

[0098] l is the topological charge; B(r) is the weight of different OAM mode components in the light source, f is the optical frequency, and n is the mode order associated with the vortex beam.

[0099] The expression of the time-varying signal in this embodiment is:

[0100]

[0101] Where I(t) is the total light intensity collected within the unit interface of the photodetector at time t, Cn is a constant, i is an imaginary unit, and i 2 =1, f0 is the initial frequency of the signal, μ is the modulation frequency, which indicates the rate at which the frequency changes with time.

[0102] In this embodiment, the relationship between the fractional Fourier transform order α and the angular acceleration in step S3 is expressed as follows:

[0103]

[0104] Where α is the fractional Fourier transform order, a is the angular acceleration, and l is the topological charge.

[0105] The following is the scattered light signal scattered by the surface of a rotating object The specific process of deriving time-varying signals:

[0106] The total light intensity collected by the photodetector per unit interface can be expressed as:

[0107]

[0108] because If the object is in uniform motion, that is, a(t) = a is a constant.

[0109]

[0110] Simplify I(t), set t2-t1=t, set the starting frequency Frequency conversion factor So far, it is deduced that the linear frequency modulation signal generated by the accelerated motion of the rotating object is

[0111]

[0112] The above formula is the time-varying signal generated by accelerated motion. It can be found that its frequency changes linearly with time. The instantaneous frequency increases or decreases uniformly from the starting value during the pulse duration, and appears as a linear function curve in the frequency domain. Therefore, this signal is a standard linear frequency modulation signal. This signal achieves high-resolution detection by expanding the bandwidth, while maintaining a long transmission time to improve energy efficiency, effectively solving the problem of the mutual constraint between detection range and accuracy in traditional pulse radar.

[0113] The following is the specific process of fractional Fourier transform decomposition of a time-varying signal when a vortex beam with superimposed positive and negative topological charges is used as a detection beam:

[0114] As a one-dimensional linear transformation, the fractional Fourier transform can gradually transition the signal from the time domain to the frequency domain, or any fractional domain between the two. This characteristic gives the fractional Fourier transform a unique advantage in processing non-stationary signals (such as linear frequency modulation signals). The formula of the fractional Fourier transform is as follows:

[0115]

[0116] Among them, B α (u, t) is the kernel function of the fractional Fourier transform, u and t represent the time axis before and after the transformation, respectively, and α is the order of the fractional order, ranging from 0 to 4, which corresponds to the time-frequency rotation angle of the fractional space changing from 0° to 360°, as shown in Figure 4 shown.

[0117] in,

[0118] Transform kernel Represents the rotation angle of the time-frequency plane around the origin. It can be found that the transformation kernel of the fractional Fourier transform is a set of modulation frequency cotφ, initial frequency -ucotφ, and complex amplitude A φ The chirp signal is the orthogonal complete basis of the fractional Fourier transform. For the linear frequency modulation signal, cot(φ) = cot(φ + π). Therefore, the period of α is further compressed by 2, and the angle φ is changed, which corresponds to different orders of the fractional Fourier transform.

[0119] Substitute the time-varying signal I(t) formula (6) into the fractional Fourier transform formula (10) to calculate, and we get

[0120]

[0121] The integral is an integral of the variable t, which includes the linear term 2t(f0-ucscφ) and the quadratic term t 2 (μ + cotφ), by adjusting the order α so that μ = -cotφ, f0 = ucscφ. After eliminating the first and second terms, since there is no function related to t inside the integral, the integral sign can be removed, and the final result is:

[0122]

[0123] The above result is a non-zero term, and not satisfying the conditions of μ = -cotφ, f0 = ucscφ will result in the infinite integral being 0, that is, the result of the fractional Fourier transform is similar to a delta function, which responds to a maximum value only under certain conditions.

[0124] In this embodiment, a fast linear interpolation algorithm is used to generate the transformation result corresponding to each fractional order. Its computational efficiency O(NlogN) is comparable to that of the fast Fourier algorithm, and it can achieve higher operational freedom for the fractional Fourier transform.

[0125] In step S5, when the peak search algorithm is used to determine the optimal transform order in the fractional domain, the peak search algorithm is combined with the fractional Fourier transform, such as Figure 2 The flowchart of this algorithm is shown, and the specific steps are as follows:

[0126] S51: Parameter initialization setting, setting α0 = 0, step size = Δα, and the selection of Δα satisfies the constraint that nΔα = 2 is an integer, and the number of iterations k = 0;

[0127] S52: Apply fractional order α to the time-varying signal in sequence k =α0+kΔα(k=1,2,...,n) to perform fractional Fourier transform, and use the fast linear interpolation algorithm to generate the transformation results corresponding to each fractional order

[0128] S53: Compare the n transformation results numerically to determine the optimal order corresponding to the maximum value

[0129] S54: reduce the step size Δα′=Δα / 2;

[0130] S55: Comparison and If the size Then determine whether the number of iterations k exceeds the preset maximum number of iterations k max ; Otherwise, increase the number of iterations k=k+1 and return to step S53;

[0131] S46: When the number of iterations k exceeds the preset maximum number of iterations k max When , the optimal transformation order α is output opt and Otherwise, increase the number of iterations k=k+1 and return to step S53.

[0132] It should be noted that: during initialization, an iteration counter k=0 needs to be created, and a storage matrix needs to be pre-allocated to save the transformation results of each order; according to the periodic characteristics of the fractional Fourier transform FrFT, the constraint condition of nΔα=2 is strictly satisfied to ensure that the order is fully covered within the period [0,2). Since the smaller the step size Δα is set, the more subdivided the order of the fractional Fourier transform is, the parameter setting needs to balance the calculation accuracy and efficiency. When Δα is reduced, the order resolution is improved but the calculation amount is reduced. 2 Growth, so the adaptive step size strategy is adopted in this embodiment.

[0133] When implementing the transformation, a discretization method is used: α is applied to the time-varying signal I(t) in sequence. k =α0+kΔα(k=0,1,...,n-1)(k=1,1,...,n)-order fractional Fourier transform, and generate the transformation result by linear interpolation fast algorithm Each transformation order corresponds to a specific time-frequency plane rotation angle θ=απ / 2, achieving optimal aggregation of signal energy on the time-frequency plane.

[0134] In the coarse search stage, the global extreme value detection algorithm is used, that is, the transformation results of n transformation results are transformed Compare the modulus values ​​and locate the optimal order corresponding to the maximum peak At this time, a fine search window (α m -Δα, α m +Δα), compress the step size to Δα'=Δα / 2 and then m The process adopts a dynamic adjustment strategy, that is, after each iteration, the search interval is adaptively shrunk according to the newly detected peak position, and the shortened step size is updated to output the fitted α and Further through the relationship between order α and μ0 To calculate the acceleration.

[0135] The present invention also provides a system for measuring the angular acceleration of a rotating object based on fractional-order Fourier transform, comprising:

[0136] The rotor 9 is used to place the rotating object to be measured;

[0137] Light source 1, for generating a tunable laser beam;

[0138] A beam expander 2, used for expanding the laser beam generated by the light source;

[0139] a polarization unit comprising a half-wave plate 3 and a polarizer 4, wherein the half-wave plate 3 is used to convert the light beam from the light source unit into circularly polarized light; and the polarizer 4 is used to convert the circularly polarized light into horizontally polarized light;

[0140] The spatial light modulator 5 receives the horizontally polarized light emitted by the polarizer 4 and loads holograms with different superimposed phases to generate a variety of petal-shaped structured detection lights;

[0141] The electric heating plate 7 is used to generate thermal turbulence;

[0142] A photodetector 8, for capturing light signals scattered by the rotating object and converting them into electrical signals;

[0143] The beam splitter 7 splits the light beam into two parts, one part is irradiated onto the rotating object and continues to propagate, and the other part is reflected to the photodetector 8;

[0144] a signal processing unit for performing fractional Fourier transform processing on the electrical signal converted by the photodetector 8 and using a peak search algorithm to determine the optimal transform order to calculate the angular acceleration of the rotating object;

[0145] Output unit, used to display or transmit the calculated angular acceleration.

[0146] In this example, a pure amplitude spatial light modulator (SLM) was used to generate the searchlight beam. The SLM had a pixel size of 1920 x 1080 pixels and a pixel size of 8 μm. A PDA10A2 photodetector was used. A TBS2000B oscilloscope was connected to the photodetector, which stored the waveforms and processed the frequency information using MATLAB software.

[0147] like Figure 3 As shown, the laser beam first passes through the beam expander 2 and the half-wave plate 3, then adjusts the polarization state through the polarizer 4, and then enters the spatial light modulator 5 to load the hologram to generate a vortex beam. The vortex beam is irradiated onto the rotating rotor 9, and the rotor 9 modulates the beam to generate scattered light carrying angular acceleration information. After the scattered light passes through the electric heating plate 7, it is split into two parts by the beam splitter 7. One part continues to propagate, and the other part is reflected to the photodetector 8. The optical signal detected by the photodetector 8 is then converted into an electrical signal for the subsequent signal processing unit. The signal processing unit determines the optimal transformation order of the fractional Fourier transform in the fractional domain through the peak search algorithm, and optimally focuses the energy of the linear frequency modulation signal within a specific narrow band in the fractional domain. Finally, the angular acceleration is calculated through the correspondence between the transformation order and the angular acceleration of the rotating object.

[0148] To verify the feasibility of fractional Fourier transform (FrRDE) analysis in acceleration and deceleration measurement, the heating plate needs to be turned off (to room temperature). The experiment uses vortex beams with topological charge l = ±3, l = ±4, l = ±5, and l = ±6 for accuracy verification. For each topological charge and acceleration setting, ten sets of data are collected. The measurement results are as follows: Figure 5 As shown, Figure 5 (a) and 5(b) represent acceleration and deceleration conditions, respectively. The solid line represents the theoretical value, the dots are the mean of ten measurements, and the error bars represent the standard deviation. In this scheme, the data acquisition time for each set of data is 5.55 seconds, and the y-axis corresponds to the measurement value (equal to 21a). The maximum measurement error of acceleration is 1.3404%, and the maximum standard deviation is 0.015; the maximum measurement error of deceleration condition is 1.3733%, and the maximum standard deviation is 0.014. The error mainly comes from the inaccuracy of the optimal fractional-order fitting, which affects the accurate calculation of the speed change process. Increasing the number of iterations and reducing the scan step size can improve the accuracy to a certain extent, but it will increase the computer computing load.

[0149] To further account for the effects of a turbulent environment, this embodiment employs a hot plate 7 to generate thermally induced turbulence in the laboratory. The hot plate device is 320 mm long and 200 mm wide, with the beam propagation path maintaining a vertical spacing of 21.5 mm from the hot plate surface. Figure 6 The signal-to-noise ratios detected by the fractional-order Fourier analysis in this embodiment and the traditional short-time Fourier analysis in turbulent environments at different temperatures are shown. It can be noted that the signal-to-noise ratio obtained by the fractional-order Fourier analysis in this embodiment is one order of magnitude higher than that of the traditional method, which is consistent with the theoretical prediction and provides a guarantee for accurate measurement.

[0150] Figure 7The detection accuracy test results of the two methods at 100°C, 200°C and 300°C were compared, and each data point represents the result of a sampling time of 5.55 seconds. The results show that under turbulence at 100°C, the measurement errors of the two methods are similar, with the result of the patented method being 6.487±0.028Hz / s and the traditional method being 6.488±0.047Hz / s (standard deviation in brackets); when the temperature rises to 200°C and 300°C, the advantages of the method proposed in this patent are significantly improved. In short-time Fourier analysis, strong turbulence leads to increased spectrum broadening, and the projection of the spectrum on each component in the frequency domain tends to be averaged, resulting in a serious decrease in spectral resolution. Fractional-order Fourier analysis can stably extract time-frequency-space information and effectively eliminate nonlinear frequency modulation terms caused by interference factors such as noise and turbulence. Specific data show that at 200°C, the measurement error of fractional-order Fourier analysis is 6.475±0.027Hz / s, and that of short-time Fourier transform is 6.469±0.103Hz / s; at 300°C, the error of fractional-order Fourier analysis is 6.472±0.032Hz / s, while the error of short-time Fourier transform increases to 6.428±0.169Hz / s.

[0151] Figure 5 、 Figure 6 and Figure 7 The experimental results confirm the theoretical prediction: regardless of the presence of atmospheric turbulence in the transmission path, fractional Fourier analysis can stably maintain the time-frequency information of scattered light. This proves that the robustness of the present invention is sufficient to effectively resist the negative effects of noise and turbulent atmosphere.

[0152] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0153] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 a process or multiple processes and / or boxes Figure 1A system that specifies the functions of a box or boxes.

[0154] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction system that is implemented in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0155] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0156] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for measuring the angular acceleration of a rotating object based on fractional Fourier transform, characterized in that: The following steps are involved: S1: The vortex beam serves as a probe beam to illuminate a rotating object, which modulates the probe beam to generate a scattered light signal. S2: Acquire scattered light signals from the surface of a rotating object; S3: performing photoelectric conversion on the acquired scattered light signal to obtain a linear frequency modulated electrical signal, i.e., generating a time-varying signal; S4: applying different transformation orders to the time-varying signal to perform fractional Fourier transform, converting the time-varying signal from the time domain to the fractional domain; S5: Determine the optimal transform order α in the fractional domain through the peak search algorithm opt ; S6: Based on the optimal transformation order α opt , according to the correspondence between the fractional Fourier transform order and angular acceleration, the angular acceleration of the rotating object is obtained.

2. The method for measuring angular acceleration of a rotating object based on fractional Fourier transform according to claim 1, wherein: The specific method for obtaining the scattered light signal on the surface of the rotating object in step S2 is as follows: S21. Establish an angular velocity model of a rotating object, and based on the angular velocity model, construct a modulation function for describing the rotation of the object; S22. Multiply the electric field intensity of the vortex beam by the modulation function to obtain a scattered light signal scattered by the surface of the rotating object.

3. The method for measuring the angular acceleration of a rotating object based on fractional Fourier transform according to claim 2, wherein: the position of the vortex beam in the cylindrical coordinate system is The expression of the electric field intensity E(r,φ) at is as follows: in, E0 is the amplitude of the electric field, ω0 is the LG beam waist radius, is the corresponding Laguerre polynomial, l is the topological charge, p is the radial quantum number, f is the optical frequency, t is the time, is the phase structure of the beam, and exp(-i2πft) is the actual related phase factor.

4. The method for measuring angular acceleration of a rotating object based on fractional Fourier transform according to claim 2, wherein: The expression of the angular velocity model Ω(t) of the rotating object is as follows: Where Ω0 is the initial angular velocity of the rotating object, and a(t) is the angular acceleration. When a(t) is greater than 0, it indicates that the object is rotating at an accelerated speed, and when it is less than 0, it indicates that the object is rotating at a decelerated speed.

5. The method for measuring angular acceleration of a rotating object based on fractional Fourier transform according to claim 4, wherein: The modulation function of the rotating object The expression is: Among them, A n (r) is the nth-order normalized complex amplitude, satisfying ∑|A n (r)| 2 =1, Ω(t) represents the angular velocity at any time t.

6. The method for measuring angular acceleration of a rotating object based on fractional Fourier transform according to claim 5, wherein: The scattered light signal scattered by the surface of the rotating object The expression is as follows: in, is the modulation function of the object rotation; is the incident light electric field; When the vortex beam is a superposition of positive and negative topological charges, l is the topological charge; B(r) is the weight of different OAM mode components in the light source, f is the optical frequency, and n is the mode order associated with the vortex beam.

7. The method for measuring angular acceleration of a rotating object based on fractional Fourier transform according to claim 6, wherein: In step S3, the obtained scattered light signal is subjected to photoelectric conversion to obtain a linear frequency modulated electrical signal, that is, a time-varying signal is generated. The expression of the time-varying signal is: Among them, I(t) is the total light intensity collected within the unit interface of the photoelectric detector at time t, Cn is a constant, i is an imaginary unit, and i 2 =-1, f0 is the initial frequency of the signal, μ is the modulation frequency, which indicates the rate at which the frequency changes with time.

8. The method for measuring angular acceleration of a rotating object based on fractional-order Fourier transform according to claim 1, wherein: In step S5, the optimal transformation order α is determined in the fractional domain by using a peak search algorithm. opt , the specific method is as follows: S51: Parameter initialization setting, setting α0 = 0, step size = Δα, and the selection of Δα satisfies the constraint that nΔα = 2 is an integer, and the number of iterations k = 0; S52: Apply fractional order α to the time-varying signal in sequence k =α0+kΔα(k=1,2,...,n) to perform fractional Fourier transform, and use the fast linear interpolation algorithm to generate the transformation results corresponding to each fractional order S53: Compare the n transformation results numerically to determine the optimal order corresponding to the maximum value S54: Reduce step size Δα '＝ Δα / 2; S55: Comparison and If the size Then determine whether the number of iterations k exceeds the preset maximum number of iterations k max ; Otherwise, increase the number of iterations k=k+1 and return to step S53; S56: When the number of iterations k exceeds the preset maximum number of iterations k max When , the optimal transformation order α is output opt and Otherwise, increase the number of iterations k=k+1 and return to step S53 until k exceeds the preset maximum number of iterations k max until.

9. The method for measuring angular acceleration of a rotating object based on fractional-order Fourier transform according to claim 1, wherein: The relationship between the fractional Fourier transform order and angular acceleration in step S3 is expressed as follows: Where α is the fractional Fourier transform order, a is the angular acceleration, and l is the topological charge.

10. A system for measuring the angular acceleration of a rotating object based on fractional-order Fourier transform, characterized in that: include: A rotor, used to place the rotating object to be measured; a light source for generating a tunable laser beam; A beam expander, used for expanding the laser beam generated by the light source; a polarization unit comprising a half-wave plate and a polarizer, wherein the half-wave plate is used to convert the light beam from the light source unit into circularly polarized light; and the polarizer is used to convert the circularly polarized light into horizontally polarized light; A spatial light modulator receives the horizontally polarized light emitted by the polarizer and loads holograms with different superimposed phases to generate a variety of petal-shaped structured detection lights; electric heating plates for generating thermally induced turbulence; Photodetector, used to capture light signals scattered by rotating objects and convert them into electrical signals; The beam splitter splits the light beam into two parts, one part hits the rotating object and continues to propagate, and the other part is reflected to the photodetector; a signal processing unit, configured to perform fractional Fourier transform processing on the electrical signal converted by the photodetector, and to use a peak search algorithm to determine the optimal transform order to calculate the angular acceleration of the rotating object; Output unit, used to display or transmit the calculated angular acceleration.

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