A method for optimizing a rotational Doppler signal based on nonholonomic vortex light correction

Abstract

The application relates to a rotating Doppler signal optimization method based on non-complete vortex light correction. Non-complete vortex beams are very common in actual rotating Doppler speed measurement, can be used for obtaining object parameters or carrying out rotating Doppler basic research, but the mode purity of the non-complete vortex beams is reduced due to diffraction in transmission, and the experimental results are affected. Based on the diffraction characteristics of vortex beams, a rotating Doppler signal optimization method based on non-complete vortex light correction is provided. First, a superposition state vortex light distribution carrying positive and negative topological charges is subjected to phase offset angles with equal size and opposite direction, and a corrected vortex beam is obtained. After transmitting for a certain distance, the deflection of the light beam can compensate the influence of diffraction, improve the mode purity, and improve the signal-to-noise ratio of the echo signal. The method is flexible and simple to operate, can effectively overcome the influence of diffraction, improve the speed measurement accuracy and speed detection distance, and has great application value in remote sensing detection.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of based on non-complete vortex light correction Rotational Doppler signal optimization method.The present application relates to holographic calculation, spatial light modulation, optical detection field, by changing the phase angle offset of non-complete vortex light beam with opposite topological charge, prepare the non-complete vortex light beam that is not completely superimposed after correction, detect rotating object after free propagation for a distance, overcome the defect that the orbital angular momentum mode purity is reduced due to diffraction in process, improve the signal-to-noise ratio of echo signal received by detector, improve the precision of rotational speed measurement, this method is simple to operate, flexible and convenient, it has greater application value in rotational Doppler remote sensing rotational speed measurement. TECHNICAL BACKGROUND

[0002] Vortex beam is a kind of special structure light beam with helical phase wave front, since it carries orbital angular momentum, it has been widely used in particle manipulation, optical communication, astronomical measurement and many other fields.In the field of light and matter interaction, the rotational Doppler effect of vortex beam is extremely sensitive to the rotational motion of the object, and has great advantages in rotational speed measurement.Non-complete vortex beam, as a special modulation mode of vortex beam, has unique advantages in measuring some characteristics of rotating objects, so it has attracted widespread attention from researchers.In 2006, Hamazaki et al. measured the profile of complete vortex beam by introducing asymmetry defects, i.e. using non-complete vortex beam to realize direct observation of Guoy phase shift and explore the influence of positive and negative topological charge on Guoy phase shift.In 2021, Qiu Song et al. also used non-complete vortex beam to realize direct measurement of the tilt angle of Poynting vector.In 2019, Li Xinzhong's research group of Henan University of Science and Technology proposed a new type of vortex beam with two or more different topological charges, i.e. grafted vortex beam, which can flexibly control the size and direction of local orbital angular momentum while keeping the intensity unchanged.These studies show that non-complete vortex beam has great application value in actual rotational speed measurement and experimental research.

[0003] However, due to its own characteristics and the effect of diffraction during transmission, the beam rotates obviously, and when using superposition state non-complete vortex beam to detect rotating objects, the vortex beams with opposite topological charges rotate in different directions, which destroys the superposition property, reduces the orbital angular momentum mode purity, and makes the echo signal spread wider and the signal-to-noise ratio lower.Therefore, in the process of preparing hologram of superposition state non-complete vortex beam, the phase offset angle of vortex beams with opposite topological charges is opposite and the same in size, and the corrected superposition state non-complete vortex beam is obtained, which overcomes the influence of beam rotation caused by diffraction during transmission, improves the orbital angular momentum mode purity, and improves the signal-to-noise ratio of rotational Doppler signal, so that the rotational speed measurement accuracy and detection distance are greatly improved.

[0004] In the aspect of beam preparation, a reflective spatial light modulator is used to generate a vortex beam, and the phase and amplitude of the vortex beam can be flexibly controlled through complex amplitude modulation. The correction method in this paper can flexibly change the phase angle distribution of the incomplete vortex beam, and the operation is convenient and the effect is relatively significant, which can achieve good signal optimization effect. SUMMARY

[0005] The technical problem solved by the present application is: In view of the defects that the non-complete superposition state vortex beam is misaligned due to its own characteristics and the influence of diffraction during transmission, which reduces the signal-to-noise ratio of the rotating Doppler signal, a rotating Doppler signal optimization method based on non-complete vortex light correction is proposed. By changing the phase angle distribution of the probe beam, the signal-to-noise ratio of the echo signal is improved. The method is simple to operate, flexible and effective, and greatly improves the rotation speed measurement accuracy and detection distance.

[0006] The solution of the present application is:

[0007] The present application relates to a rotating Doppler signal optimization method based on non-complete vortex light correction:

[0008] (1) First, change the phase angle distribution of the superposition state non-complete vortex beam, so that the vortex beams with opposite topological charge numbers rotate the same phase angle clockwise and counterclockwise, respectively, to obtain non-complete vortex beams that do not completely overlap. The beam is used to detect a rotating object at a certain distance, and the influence of diffraction is overcome in the process. Then, the intensity value of the echo signal is received by the photoelectric detector, and after filtering and Fourier transform on the computer, the corrected rotating Doppler signal is obtained. By comparing with the detection result of the non-corrected superposition state non-complete vortex beam, it is found that the signal-to-noise ratio is obviously improved.

[0009] (2) In the aspect of non-complete vortex beam correction, according to the detection distance and the topological charge number of the beam, the complex amplitude modulation method is used to control the vortex beams with opposite topological charge numbers in the detection beam to deflect the same angle value in the clockwise and counterclockwise directions, respectively, to obtain the corrected non-complete vortex beam hologram. Then, the beam with Gaussian distribution after beam expansion and collimation is used to irradiate the hologram, and the first-order diffraction light with good light intensity and mode purity is selected as the corrected non-complete vortex beam required for detection.

[0010] (3) In terms of rotating Doppler signal measurement, orbital angular momentum mode spectrum decomposition is used to obtain the orbital angular momentum spectrum of the non-complete vortex beam. The corresponding rotating Doppler signal is theoretically analyzed. Then, the distance between the spatial light modulator and the object being detected is fixed, and the object is illuminated by the corrected superposition state non-complete vortex beam. The scattered light is collected by a photodetector and transformed to obtain the corrected rotating Doppler signal. By comparison, it can be found that the signal-to-noise ratio is significantly improved.

[0011] The principle of this invention is:

[0012] A non-perfect vortex beam, as a part of a perfect vortex beam, can be simply understood as a beam with partial intensity and phase distribution obtained by blocking the perfect vortex beam. The general expression for a perfect vortex beam is:

[0013] (1)

[0014] in It is the azimuth angle. The radius is represented by z, and the propagation distance is z. The wave number represents the wave number, and its magnitude is , Represents the topological charge number. Let z represent the complex amplitude at a distance z. As part of a complete vortex beam, the electric field expression of a non-perfect vortex beam can be written as:

[0015] (2)

[0016] in Represents the starting angle of a non-complete vortex beam. Represents the central angle of a fan-shaped, incomplete vortex beam. This is a step function. When a vortex beam illuminates a rotating object, according to the rotational Doppler effect, the rotating object modulates the incident light, producing a rotational Doppler frequency shift, as shown in Figure 2(a). The Poynting vector represents the energy flow direction. As can be seen from Figure 2(b), the Poynting vector is not collinear with the propagation axis, and the angle between them is approximately... This results in a component of the rotational motion perpendicular to the beam propagation axis in the beam energy flow direction, which is consistent with the linear Doppler effect. The rotational Doppler effect of vortex light can be regarded as the superposition of the linear Doppler effects of each ray of light along the Poynting vector direction within the wavefront, thus deriving the expression for the rotational Doppler frequency shift:

[0017] (3)

[0018] in Represents the frequency of the vortex beam. Represents the wavelength of the light beam. The linear velocity representing a point on the plane of rotation. Represents the angular velocity of a rotating object. Represents the radius of the vortex beam. Represents the speed of light. Represents the topological charge number. The angle between the Poynting vector and the beam propagation axis is represented by equation (3). It can be seen from equation (3) that when the rotational speed of the object is fixed, the rotational Doppler frequency shift is proportional to the topological charge of the vortex beam itself. Theoretically, the topological charge of the prepared complete vortex beam is a single value. The topological charge of the incomplete vortex beam changes because the integrity of the beam is broken. Based on the standard Laguerre-Gaussian mode, the mode decomposition method can be used to decompose the incomplete vortex into series. The principle is as follows:

[0019] (4)

[0020] (5)

[0021] In the formula This represents a standard Laguerre-Gaussian beam. It is the amplitude related to the topological charge number and radial number of elements. Represents radial segments. The azimuth initiation angle of the incomplete vortex beam is set to... , The topological charge number is The mode decomposition of this non-holonomic vortex beam is performed using equations (4) and (5), and the amplitude intensities of different radial nodal orders are superimposed. , obtained only about The OAM spectrum, simulation results are as follows Figure 3 As shown.

[0022] from Figure 3 It can be seen that when using a non-holonomic vortex beam to detect a rotating object, the beam mode expands, which can be regarded as the superposition of multiple vortex beams with different topological charges. According to equation (3), the rotational Doppler frequency shift obtained by using this superimposed beam will be broadened. When this beam propagates in free space, due to the effects of Gouye phase shift and diffraction, the beam mode will be further broadened, and the rotational Doppler spectrum will be further broadened, resulting in a decrease in signal-to-noise ratio. However, by applying the same reverse rotation angle to vortex beams with opposite topological charges in advance, a corrected non-holonomic vortex beam is obtained as the detection source, such as... Figure 4 As shown, this can counteract the effects of diffraction, improve the mode purity of the superimposed incomplete vortex beam, make the frequency shift signal more concentrated, thereby improving the signal-to-noise ratio of the echo signal and increasing the beam detection distance.

[0023] The advantages of this solution compared to existing solutions are:

[0024] (1) This scheme is simple to operate, flexible and convenient. The phase angle and intensity modulation method of the beam is simple. Only the hologram loaded on the spatial light modulator needs to be replaced to complete the correction of the non-complete vortex beam. There is no need to adjust other optical path components, and the operation is convenient.

[0025] (2) This method can significantly improve the signal-to-noise ratio of the echo signal and increase the detection distance. By using a corrected superimposed state incomplete vortex beam to detect rotating objects, the defect of reduced beam mode purity caused by beam rotation due to diffraction and Gouye phase shift during beam propagation can be overcome, resulting in a significant improvement in the signal-to-noise ratio of the echo signal, which helps to improve the accuracy of rotational speed measurement or other object parameter acquisition.

[0026] (3) This scheme is highly practical and has a high fault tolerance rate. In remote sensing, the limit value of the rotation angle of a non-perfect vortex beam caused by diffraction is... Therefore, in practical long-distance measurements, vortex beams carrying two opposite topological charges can be directly applied clockwise and counterclockwise, respectively. The phase shift angle, when illuminating the surface of a rotating object, can almost completely cancel out the diffraction effect. Furthermore, even in close-range detection, applying a small phase shift correction angle can improve the signal-to-noise ratio of the echo signal to some extent. Attached Figure Description

[0027] Figure 1 Flowchart for rotating Doppler measurement with non-holoscopic vortex beam correction;

[0028] Figure 2 A schematic diagram of a vortex beam detecting a rotating object;

[0029] Figure 3 This is a decomposition diagram of a non-complete vortex beam mode;

[0030] Figure 4 The beam intensity distribution before and after correction at a certain distance;

[0031] Figure 5 Comparison of rotational Doppler signals before and after correction;

[0032] Figure 6 This is the experimental optical path diagram;

[0033] Figure 7 The diagram shows the intensity and phase distribution of the incomplete vortex beam before and after correction. Detailed Implementation Plan

[0034] This invention optimizes rotating Doppler signals based on nonholonomic vortex beam correction, and the application target is a nonholonomic vortex beam. The specific implementation steps are as follows:

[0035] First, phase angle correction is performed on the superposition-state non-holonomic vortex beam, especially for beams with positive topological charge. The vortex beam is deflected counterclockwise. ,for The vortex beam is deflected clockwise. The corrected vortex beam hologram is obtained. Combining formula (2), this paper uses the topological charge number... The starting azimuth angle is , Using a superimposed, non-perfect vortex beam as the detection source, the distance between the rotating object and the spatial light modulation is set to... Deflection angle The intensity and phase distribution of the corrected incomplete vortex beam are obtained as follows: Figure 5 As shown, the experimental optical path was constructed as follows: Figure 6 As shown, the Gaussian light emitted from the laser is expanded, collimated, and modulated into linearly polarized light before illuminating a spatial light modulator. Using a 4f system composed of lenses L3, AP, and L4, the first-order diffracted light is selected as the corrected incomplete vortex beam. This beam then passes through a semi-transparent mirror (BS) and illuminates a rotating object. The reflected light signal is focused by the BS and a convex lens onto an avalanche photodetector (APD). The scattered light is collected and converted into an electrical signal, which is then acquired by a data acquisition card and transmitted to a computer for data processing to obtain the rotational Doppler frequency shift. The resulting rotational Doppler signals before and after correction are shown below. Figure 7 As shown, the rotational Doppler spectrum broadened significantly before correction, with an average signal-to-noise ratio of -98.5 dB. After correction, the rotational Doppler spectrum broadened less, with an average signal-to-noise ratio of -88.5 dB. Figure 7 It is evident that using a corrected vortex beam to detect rotating objects significantly improves the signal-to-noise ratio of the echo signal and optimizes the signal quality. This contributes to improving the accuracy of rotational speed measurement and other parameter acquisition, while also increasing the detection range of the rotating Doppler. In practical telemetry, when the distance is too large, it can be directly set... .

[0036] The contents not described in detail in this invention are existing technologies known to those skilled in the art.

Claims

1. A method for optimizing rotating Doppler signals based on nonholonomic vortex optical correction, characterized in that: First, for the incomplete vortex beam, based on the detection distance and the topological charge of the beam, the complex amplitude modulation method is used to control the vortex beams with opposite topological charges in the incomplete vortex beam so that they deflect by the same angle value in the clockwise and counterclockwise directions, respectively. This yields a partially overlapping incomplete vortex beam and a hologram of the corrected incomplete vortex beam. Then, a Gaussian beam is used to illuminate this hologram, and the first-order diffracted light with good intensity and mode purity is selected as the corrected superimposed state incomplete vortex beam required for detection. This is then used to detect rotating objects. A photodetector is used to receive the scattered light and convert it into an electrical signal. A data acquisition card is used for sampling, and the optimized data spectrum is obtained after signal processing.

2. The method for optimizing rotating Doppler signals based on nonholonomic vortex optical correction according to claim 1, characterized in that: The limit value of the rotational azimuth angle due to diffraction in the propagation of a non-perfect vortex beam is... Therefore, when telemetry is performed on the target, the phase offset angle of the two vortex beams with opposite topological charges is directly set to . .

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