A signal enhancement method based on the rotational Doppler effect of multi-ring vortex beams

Abstract

The present application relates to a kind of signal enhancement methods based on the rotational Doppler effect of multi-ring vortex light beam.In actual telemetry,light beam divergence,atmospheric turbulence and other factors can lead to echo signal signal-to-noise ratio reduction,which brings difficulties to the rotational detection,pose measurement and other based on vortex light beam.To solve this problem,an enhanced signal method based on the rotational Doppler effect of multi-ring vortex light beam is proposed.First,prepare the hologram of multi-ring vortex light beam,then generate multi-ring vortex light using spatial light modulator;Second,use the light beam to detect rotating objects and process the echo signal to obtain the rotational Doppler shift,compared with the rotational Doppler spectrum obtained by single-ring light beam,signal-to-noise ratio is significantly improved.The method is simple to operate,low in experimental device requirements,and flexible in control,which can greatly improve the signal-to-noise ratio of scattered signal and has great application value in the telemetry of rotating objects.

Description

Technical fields:

[0001] This invention relates to a signal enhancement method based on the rotating Doppler effect of multi-ring vortex beams. The invention relates to fields such as holographic computing and light-object interaction. By preparing multi-ring vortex beams of different types carrying the same topological charge as a light source to detect rotating objects, the probability of target acquisition can be improved, the frequency domain amplitude of the echo signal can be increased, the detection distance can be increased, and the application range of rotational speed measurement can be expanded. Technical Background

[0002] Since the discovery of the orbital angular momentum of vortex beams, this unique structured beam has attracted widespread attention from scholars both domestically and internationally, demonstrating significant application potential in multiple fields. Similar to the polarization, amplitude, and phase of a beam, orbital angular momentum is another momentum dimension of a vortex beam. However, unlike the spin angular momentum of the beam, the number of orbital angular momentum modes is not limited to ±1 and can expand infinitely. Different orbital angular momentum modes are orthogonal to each other, theoretically forming an infinite Hilbert space. Compared to other dimensions of the beam, orbital angular momentum has a much larger controllable space and has already been applied to numerous fields such as optical manipulation, quantum communication, and remote sensing.

[0003] Especially in the field of rotation measurement, vortex beams have received increasing attention. In 1998, J. Courtial et al. proved that a beam carrying orbital angular momentum, rotating at an angular velocity Ω, produces a frequency shift of lΩ, where l represents the topological charge of the vortex beam. This was the first demonstration that in addition to the linear Doppler frequency shift, a rotational Doppler frequency shift also exists. In 2013, Lavery et al. first used a superposition state vortex beam to detect a real rotating object, obtaining the rotational Doppler frequency shift. In 2021, Qiu Song et al. from Ren Yuan's research group achieved a composite decoupling of linear and rotational motion based on the rotational Doppler effect. However, most micro-motion measurements based on the rotational Doppler effect of vortex beams require the beam to be aligned with the object's axis of rotation. When the two are offset or tilted, the rotational Doppler spectrum will broaden, and the signal-to-noise ratio will decrease, which is not conducive to long-distance detection and the engineering of rotating target measurement. Increasing the effective receiving power of the scattered light is very important. Although increasing the laser power is an intuitive and convenient option, the power of the laser cannot be too high due to the energy tolerance of the optical modulation device. Therefore, it is necessary to seek new methods to enhance the amplitude of echo signals. Summary of the Invention

[0004] The technical solution of this invention addresses the problems of reduced optical echo signal-to-noise ratio and low measurement accuracy in rotating object measurement applications based on the rotating Doppler effect, caused by misalignment between the optical axis and the object's rotation axis, long detection distance, and atmospheric turbulence interference. A signal enhancement method based on the rotating Doppler effect of a multi-ring vortex beam is proposed. This method designs a superimposed multi-ring vortex beam. By increasing the number of rings, the power of the detection beam is increased while maintaining the laser's output power, and the beam coverage area is also increased. Using this beam to detect rotating objects significantly improves the echo signal-to-noise ratio and increases the remote measurement distance of rotational speed. This method features a simple optical path, low operational difficulty, flexibility, and ease of use, greatly promoting the engineering application of rotational measurements based on the rotating Doppler effect of vortex beams.

[0005] The technical solution of this invention is:

[0006] This invention relates to a signal enhancement method based on the rotating Doppler effect of a multi-ring vortex beam:

[0007] (1) First, multiple vortex beams with the same topological charge are combined and superimposed vortex beams with different ring numbers are prepared by complex amplitude modulation method. Then, the beams are arbitrarily irradiated onto a rotating object. A photodetector is used to receive the scattered light and sample the time-domain signal. The time-domain signal is transformed into a frequency-domain rotating Doppler spectrum with significantly improved signal-to-noise ratio by using a frequency-domain transformation tool. It can be found that as the number of rings increases, the signal-to-noise ratio of the scattered signal from the target and the intensity of the vortex beam continuously increase.

[0008] (2) In rotational Doppler signal measurement, the optical axis does not need to be strictly aligned with the object's rotation axis. Detection in any pose can improve the signal-to-noise ratio. For example, the frequency shift generated after modulation by the rotating target under lateral conditions is... Where f represents the rotational Doppler frequency shift, l is the topological charge of the vortex beam, Ω represents the target rotational speed, r is the distance from the center of the vortex beam to each scattering point, d represents the distance between the target rotation axis and the vortex beam axis, θ represents the azimuth angle, and the frequency shift under tilt conditions is... Where γ is the tilt angle of the object, under these two conditions, the amplitude of the broadened rotating Doppler spectrum is significantly improved when using a multi-ring vortex beam to detect rotating objects.

[0009] (3) In terms of the preparation of multi-ring vortex beams. The probe beam is no longer the single-ring vortex beam used in traditional detection, but a composite vortex beam with multiple rings in a superposition state. The present invention uses a spatial light modulator to prepare the required beam. First, the radius and intensity distribution of the vortex beam are modulated to obtain a hologram of the multi-ring vortex beam. Then, a linearly polarized Gaussian beam is used to illuminate the spatial light modulator loaded with the hologram, and the first order in the diffraction order is selected as the probe light source.

[0010] The principle of this invention is:

[0011] The complex amplitude expression of a vortex beam in cylindrical coordinates can be written as...

[0012]

[0013] in λ is the azimuth angle, r is the radius, z is the propagation distance, k is the wavenumber (λ / 2π), and l is the topological charge number. represents the complex amplitude, and i represents the imaginary number. A multi-ring vortex beam is a composite of multiple vortex beams with different radii, and its expression can be written as ,

[0014]

[0015] in Let be the complex amplitude of the nth vortex beam, and N be the number of rings in the multi-ring vortex beam. Taking the Laguerre-Gaussian beam and the perfect vortex beam as examples respectively, their expressions can be written as follows:

[0016]

[0017] in Represents a cylindrical coordinate system, w z Let p be the beam radius at a propagation distance of z, and let p and l represent the radial number of nodes and the topological charge, respectively. To associate Laguerre polynomials, R z Let be the radius of curvature of the wavefront, expressed as: In the formula k is the wave number, expressed as k = 2π / λ. w represents the halo width of the perfect vortex beam, and r1 represents the radius of the perfect vortex beam. According to formula (2), the expressions for their respective composite multi-ring vortex beams are as follows:

[0018]

[0019] When using a multi-ring vortex beam to detect a rotating object, a rotational Doppler effect occurs, similar to the linear Doppler effect, causing a change in the beam frequency. Several situations exist when using a Laguerre-Gaussian beam for rotational speed detection. When the vortex beam's optical axis is aligned with the object's center of rotation, the presence of orbital angular momentum creates an angle between the Poynting vector and the beam propagation axis: sinα = lλ / 2πr, where r represents the vortex beam radius, l is the topological charge, and the rotational speed is set to Ω. Based on the rotational Doppler effect, the expression relating the frequency shift Δf to the topological charge and rotational speed is obtained:

[0020]

[0021] Where λ represents the beam wavelength, c represents the beam, f0 = c / λ represents the beam frequency, and v represents the linear velocity of the object. When there is a lateral offset d, according to the scattering point model, the linear velocity v = Ωr1 of each point on the object is decomposed into two directions: the tangential and radial directions along the vortex ring. The velocity component in the tangential direction modulates the light frequency, and r1 represents the distance from a point on the object to the center of rotation. The final rotational Doppler frequency shift is:

[0022]

[0023] Where r2 is the radius of the vortex halo, defined as the distance between the point from the beam center to the central axis when the beam amplitude drops to 1 / e of the amplitude on the central axis, d is the lateral offset value, and θ represents the azimuth angle.

[0024] This invention uses different types of multi-ring superposition modes, namely Laguerre-Gaussian beams and perfect vortex beams, as the detection source to illuminate a rotating object, collects their respective optical echoes, and compares the rotational Doppler frequency shifts of multi-ring vortex beams with different ring numbers after frequency domain transformation, to obtain the rotational Doppler spectrum after the signal-to-noise ratio is significantly improved.

[0025] Compared with existing solutions, the main advantages of this invention are:

[0026] 1. Simple, convenient, and flexible in operation. No need to adjust the optical path; simply replace the hologram loaded onto the spatial light modulator to generate multi-ring beams and improve the intensity of the detection light source.

[0027] 2. Significantly improves the signal-to-noise ratio and detection range of the echo signal. By adopting a multi-ring vortex beam detection method, the signal-to-noise ratio of the rotating Doppler signal is improved, which has great practical value for applications such as pose measurement and pattern recognition based on the rotating Doppler effect.

[0028] 3. It is robust and applicable to a wide range of scenarios. Even if the beam does not fully illuminate the rotating object, the multi-ring beam can still improve the signal-to-noise ratio of the echo signal compared to the single-ring beam. It can be used even under misaligned or uncollimated conditions. Attached Figure Description

[0029] Figure 1 This is a flowchart of the multi-ring vortex beam detection process.

[0030] Figure 2 This is a schematic diagram of the detection optical path.

[0031] Figure 3 Intensity distribution diagrams for multi-ring Laguerre-Gaussian beams and multi-ring perfect vortex beams.

[0032] Figure 4 The rotating Doppler shift map obtained by multi-ring vortex beam detection under alignment conditions. Figure 4In the middle (a)-(d), the rotational Doppler spectra of a rotating object are obtained by a Laguerre Gaussian beam with 1 to 4 vortex rings under alignment conditions, respectively. Figure 4 In the middle (e)-(h), we see the rotating Doppler spectra obtained by probing rotating objects with a perfect vortex beam containing 1 to 4 vortex rings under aligned conditions.

[0033] Figure 5 This is a rotating Doppler shift map obtained by multi-ring vortex beam detection under misalignment conditions. Figure 5 (a)-(d) represent the rotational Doppler spectra obtained by probing rotating objects with a Laguerre Gaussian beam containing 1 to 4 vortex rings under misaligned conditions; Figure 5 In the middle (e)-(h), we see the rotating Doppler spectra obtained by probing rotating objects with a perfect vortex beam containing 1 to 4 vortex rings under misaligned conditions. Specific implementation plan:

[0034] This invention uses a multi-ring vortex beam as a detection source, and the target is a rotating object in space. The specific steps are as follows:

[0035] First, the phase and intensity distribution of the vortex beam were adjusted to design phase diagrams for superimposed multi-ring perfect and Laguerre-Gaussian vortex beams. Holograms of the multi-ring perfect vortex beam and the multi-ring Laguerre-Gaussian beam were then prepared using amplitude information and a blazed grating, respectively. The holograms were then loaded onto a spatial light modulator, and a linearly polarized laser was used to illuminate the spatial light modulator. An aperture was used to select the first-order diffracted light as the detection source. The required optical path for detection is as follows: Figure 1 As shown. In actual measurements, different types of multi-ring vortex beams can be prepared according to the measurement conditions, such as Bessel-Gaussian beams and Laguerre-Gaussian beams. Then, the multi-ring vortex beam is used to detect rotating objects in any pose. Under the same laser output power, the more rings, the larger the amplitude of the echo signal and the higher the signal-to-noise ratio. Taking multi-ring vortex beams with 1 to 4 rings as an example, the signal-to-noise ratio improvement effect brought by multi-ring vortex beam detection is illustrated.

[0036] The topological charge of the vortex beam was set to ±20, and the number of rings ranged from 1 to 4. The intensity distribution diagrams of the two sets of Laguerre-Gaussian beams and the perfect vortex beam with different numbers of rings are shown below. Figure 3 As shown in the figure. Multi-ring superposition Laguerre-Gaussian beams with ring numbers ranging from 1 to 4 and perfect vortex beams were used to probe rotating objects under collimation conditions. The experimental results are shown in the figure. Figure 4 As shown, Figure 4 In the middle (a)-(d), the rotational Doppler spectra of a rotating object are obtained by a Laguerre Gaussian beam with 1 to 4 vortex rings under alignment conditions, respectively. Figure 4In the figures (e)-(h), the rotational Doppler spectra obtained by probing a rotating object with a perfect vortex beam containing 1 to 4 vortex rings under aligned conditions are shown. The experimental results show that as the number of beam rings increases, the rotational Doppler amplitude of the echo signal continuously increases. Specifically, the echo amplitude of the 4-ring superposition Laguerre-Gaussian beam is 0.003V higher than that of a single ring, with an intensity increase of approximately 16 times; the echo amplitude of the 4-ring perfect beam is 0.0032V higher than that of a single ring, with an intensity increase of approximately 6.4 times. Subsequently, under misaligned conditions, with a beam radius of 2mm and a lateral displacement of 0.5mm, two types of beams were used to illuminate a rotating object. The experimental results are as follows: Figure 5 As shown, Figure 5 (a)-(d) represent the rotational Doppler spectra obtained by probing rotating objects with a Laguerre Gaussian beam containing 1 to 4 vortex rings under misaligned conditions; Figure 5 In the diagram, (e)-(h) represent the rotating Doppler spectra obtained by detecting rotating objects with a perfect vortex beam containing 1 to 4 vortex rings under misaligned conditions. It can be seen that the signal amplitude is significantly enhanced, indicating that using a multi-ring vortex beam as the detection source significantly improves the signal-to-noise ratio of the optical echo compared to a traditional single-ring vortex beam. This helps to increase the detection distance and has significant application value in the telemetry of rotating objects.

[0037] The contents not described in detail in this invention are existing technologies known to those skilled in the art.

Claims

1. A signal enhancement method based on the rotating Doppler effect of a multi-ring vortex beam, characterized in that: First, multiple vortex beams with the same topological charge but different radii are combined. Then, superimposed vortex beams with different ring numbers are prepared using the complex amplitude modulation method. These beams are then arbitrarily irradiated onto a rotating object. A photodetector is used to receive the scattered light and sample it to obtain a time-domain signal. Finally, a frequency-domain transformation tool is used to transform the time-domain signal into a frequency-domain rotating Doppler signal with a significantly improved signal-to-noise ratio.

2. The signal enhancement method based on the rotating Doppler effect of a multi-ring vortex beam according to claim 1, characterized in that: It is not necessary for the optical axis to be strictly aligned with the object's rotation axis; signal-to-noise ratio improvement can be achieved under any pose. The frequency shift produced by multi-ring vortex light illuminating a rotating target under lateral conditions can be expressed as... Where f represents the rotational Doppler frequency shift, l is the topological charge of the vortex beam, Ω represents the target rotational speed, r is the distance between the center of the vortex beam and each scattering point, d represents the distance between the target rotation axis and the vortex beam axis, and θ represents the azimuth angle. Under tilted conditions, the frequency shift can be expressed as... Where γ is the tilt angle of the object.

3. The signal enhancement method based on the rotating Doppler effect of a multi-ring vortex beam according to claim 1, characterized in that: The light source is no longer the single-ring vortex light used in traditional detection, but a composite vortex beam with multiple rings in a superposition state. This invention uses a spatial light modulator to prepare the required beam. First, the radius and intensity of the vortex beam are modulated and coaxially superimposed to obtain a hologram of the multi-ring vortex beam. Then, a linearly polarized Gaussian beam is used to illuminate the spatial light modulator loaded with the hologram, and the first order in the diffraction order is selected as the detection light source.

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