An object inclination angle measurement method based on continuous change of ellipticity optical vortex

Abstract

This invention relates to a method for measuring the tilt angle of an object based on optical vortices with continuously varying ellipticity. First, the rotational Doppler frequency shift mechanism of vortexes with different ellipticities is elucidated. Then, a set of vortex beams with continuously varying ellipticity is prepared by adjusting the beam intensity and phase using a complex amplitude modulation method. These beams are sequentially irradiated onto a rotating object, and the echo signals are received. Subsequently, the rotational Doppler time-frequency spectrum is obtained using time-frequency analysis. Theoretical analysis shows that when the ellipticity of the vortex beam and the tilt angle of the object satisfy a corresponding relationship, the spectral broadening is minimized and the signal amplitude is maximized. Therefore, the optimal ellipticity of the beam and the object tilt angle can be determined based on the time-frequency spectrum changes. This method requires a simple detection system, is easy to operate, and can accurately measure the tilt angle of an object, thus having great application potential in telemetry.

Description

Technical Field

[0001] This invention relates to the fields of light field manipulation and optical detection technology, specifically to a method for measuring the tilt angle of an object based on an optical vortex with continuously varying ellipticity. Background Technology

[0002] In 1992, Allen first proposed that, in addition to spin angular momentum, vortex beams possess another momentum dimension: orbital angular momentum, and proved that the orbital angular momentum of each photon in a vortex light field is... ,in For topological load number, To reduce Planck's constant. Subsequently, vortex beams carrying orbital angular momentum attracted widespread attention from researchers, demonstrating enormous application potential from microparticle manipulation and rotational detection to astrometry. Due to the unique phase distribution of vortex beams, they are highly sensitive to rotational angular velocities or angular accelerations perpendicular to the beam propagation direction, causing a frequency shift known as the rotational Doppler effect. Since its inception, the rotational Doppler effect has been the subject of extensive research, ranging from non-coaxial rotational Doppler effects to the detection of geometric features of rotating objects. Optical vortices also play a crucial role in micro-displacement measurement and decoupling of complex motions. Nevertheless, currently, it is still impossible to extract much information about the relative pose of an object from the rotational Doppler frequency shift.

[0003] In traditional radar detection, the presence and overall orientation of a target can only be identified based on the linear Doppler frequency shift of the object. However, it cannot clearly identify the specific features and attitude of the target. Although traditional optical imaging can identify the target's position and attitude relatively clearly, its effective range is limited and it is greatly affected by weather. Therefore, there is an urgent need for a telemetry method that can clearly characterize the attitude of an object. Summary of the Invention

[0004] In view of this, the present invention proposes a method for measuring the tilt angle of an object based on an optical vortex with continuously varying ellipticity, which can realize the long-distance accurate measurement of the tilt angle of a rotating object.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for measuring the tilt angle of an object based on an optical vortex with continuously varying ellipticity is proposed. First, a geometric model of an elliptical vortex beam probing a tilted object is established, revealing the rotational Doppler frequency shift mechanism related to the object's tilt angle and the ellipticity of the vortex beam under tilt conditions. Then, the beam phase is adjusted using a complex amplitude modulation method to obtain a set of elliptical optical vortex holograms with continuously varying ellipticity, which are sequentially loaded onto a spatial light modulator. A linearly polarized beam is then used to illuminate this device to obtain an optical vortex with continuously varying ellipticity. After interacting with the object, the echo time-domain signal is received, and after time-frequency transformation, the rotational Doppler time spectrum is obtained. Based on the time spectrum of the signal and the rotational Doppler frequency shift expression of the elliptical vortex beam, the ellipticity of the vortex beam corresponding to the narrowest frequency shift is obtained. Finally, the object's tilt angle is calculated based on the correspondence between the tilt angle and the ellipticity of the optical vortex at this point.

[0007] In this process, the ellipticity of the optical vortex is controlled by coordinate transformation to obtain a set of optical vortex holograms with fixed ellipticity intervals and regular changes. These holograms are then sequentially loaded onto a spatial light modulator, and the device is irradiated with linearly polarized light to prepare a set of vortex beams with different ellipticities.

[0008] First, a geometric model for detecting tilted objects using an elliptical vortex beam is established. Second, the rotational Doppler frequency shift mechanism related to the object's tilt angle and the ellipticity of the vortex beam under tilted conditions is revealed, namely:

[0009]

[0010] in Represents the rotational Doppler frequency shift. Represents ellipticity. Represents the topological charge number. Represents rotational speed. Represents the tilt angle. Represents azimuth. Represents the angular velocity vector of a rotating object exist Projection of the surface and The angle between the axes is measured by continuously scanning the rotating object using an optical vortex beam with a regular variation in ellipticity, and receiving the echo time-domain signal using a photodetector. Then, using a time-frequency transformation method, the rotating Doppler time spectrum is obtained. Combining the expressions for the rotating Doppler frequency shift of the elliptical vortex beam and the object's tilt angle and beam ellipticity, the object's tilt angle is obtained, where the object's tilt angle (… When matching the beam ellipticity, the corresponding time in the time-frequency diagram is ( The relationship between the angle of inclination and the object's tilt can be expressed as: , This corresponds to the time when the rotating Doppler spectrum is narrowest. It is the initial time of a set of beam scanning cycles. It is the hologram switching interval. It is the ellipticity interval of the probe beam.

[0011] Beneficial effects

[0012] (1) Improved the measurement accuracy of the tilt angle of the object and expanded the application range of tilt angle measurement. Compared with optical imaging methods that are greatly affected by weather and have limited distance, this method can significantly increase the working distance, and at the same time improve the measurement accuracy of the tilt angle of the object by reducing the ellipticity interval.

[0013] (2) The method requires simple equipment, easy optical path construction, and low operation difficulty. Only time-frequency analysis of the echo signal is needed to complete the measurement of the tilt angle of the object. At the same time, the elliptical vortex hologram used for detection is easy to make, and only the relevant parameters need to be modified.

[0014] (3) This method has a wide range of applications, a large angle measurement range, and good robustness. Only one set of optical vortices with regular changes in ellipticity is needed. For rotating objects with different tilt angles, there is no need to change the hologram or experimental device. Moreover, the measurement conditions are under tilted illumination conditions, so the application range is relatively wide. Attached Figure Description

[0015] Figure 1 This is a flowchart of the object tilt angle measurement method based on continuously varying ellipticity optical vortex according to the present invention.

[0016] Figure 2 This is a diagram of the optical path experimental setup for measuring the tilt angle of an object according to the present invention.

[0017] Figure 3 This is a schematic diagram of the rotating Doppler effect of the elliptical vortex beam under tilted conditions according to the present invention.

[0018] Figure 4 This is a structural diagram of the invention, which uses an optical vortex with continuously varying ellipticity to detect rotating objects.

[0019] Figure 5 These are the experimental measurement results of this invention. Figure 5 In the middle (a), the received echo time-domain signal is shown. Figure 5 (b) is the middle (b) Figure 5 (a) Rotational Doppler time spectrum after time-frequency transformation. Figure 5 (c) is the pair Figure 5 (b) The result after time-frequency spectrum filtering. Figure 5 (d) is the extraction Figure 5 The result of fitting the upper edge of the time spectrum in (c). Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] The principle of this invention is:

[0022] Vortex beams refer to a type of beam with a spiral phase. Structured beams, among which the Laguerre-Gaussian mode beam is the most common, can be written in cylindrical coordinates as follows:

[0023] (1)

[0024] in Using cylindrical coordinates, Represents the complex amplitude coefficient. Represents the Laguerre function, Represents the topological charge number. Represents radial sections, The wave number has a magnitude of , The wavelength of the light beam. Represents the distance of transmission The waist radius at that point can be expressed as: , It is the wavefront radius of curvature, which can be expressed as , Let be the Ruili radius. According to the transformation... and cylindrical coordinate system Transform to a spatial rectangular coordinate system After performing coordinate scaling operations, the elliptical vortex beam can be written as...

[0025] (2)

[0026] in Represents ellipticity, defined as the minor axis of the ellipse. Divide by the major axis ,Right now Based on elliptical polar coordinate system

[0027] (3)

[0028] Equation (2) can be written as

[0029] (4)

[0030] From equation (4), it can be seen that the spatial variation phase of the elliptical optical vortex is ,in This is the azimuth angle in an elliptical coordinate system. In a circular coordinate system, the azimuth angle... It can be represented as Therefore, the relationship between the azimuth angles in the two coordinate systems is: Therefore, the phase gradient of the elliptical optical vortex for,

[0031] (5)

[0032] To further illustrate the rotating Doppler effect of an elliptical vortex beam, a schematic diagram of the rotating Doppler effect of an elliptical vortex beam under inclined conditions is established, as follows: Figure 3 As shown. The central ellipse represents the intensity distribution of the incident elliptical optical vortex projected onto the rotating object. A spatial rectangular coordinate system is established with the center of this elliptical vortex as the origin, the beam propagation direction as the z-axis, and the horizontal direction of the beam's transverse plane as the y-axis. Take any scattering point 'a' within the beam spot... Representing the origin The vector to scattering particle a, The angular velocity vector has a magnitude of . Represents the tilt angle of an object. Projection and The included angle of the axis is . Let be the linear velocity at scattering point a. Based on the elliptical coordinate system represented by equation (3) and... Figure 3 From the geometric relationships in the diagram, we can obtain...

[0033] (6)

[0034] in The azimuth angle is in a circular coordinate system. Let be the ellipticity. Therefore, the expression for the linear velocity of point a can be derived as follows:

[0035] (7)

[0036] in,

[0037] (8)

[0038] Finally, the rotational Doppler shift of different elliptical vortex beams under misalignment conditions can be written as,

[0039] (9)

[0040] in Represents the rotational Doppler frequency shift. Represents ellipticity. Represents the topological charge number. Represents rotational speed. Represents the tilt angle. Represents azimuth. Represents the angular velocity vector of a rotating object exist Projection of the surface and The angle between the axes. From formula (9), it can be seen that when the major axis of the elliptical vortex beam is aligned with the direction of the object's tilt, i.e. At that time, the ellipticity of the elliptical optical vortex corresponds strictly to the tilt angle of the object, that is, it satisfies the condition. At that time, the rotating Doppler frequency shift formula degenerates into In other words, the rotating Doppler spectrum does not broaden, and when the beam ellipticity does not correspond to the object's tilt angle, the ellipticity... and As the difference between them increases, the spectrum broadens more severely, and the signal amplitude gradually decreases, becoming submerged in noise.

[0041] Based on this variation law, a set of elliptic optical vortices with continuously varying ellipticity is used to detect rotating objects. Optical echoes within at least one period are received. A schematic diagram of using elliptic optical vortices with continuously varying ellipticity to detect rotating objects is shown in Figure 4. Then, the rotational Doppler frequency spectrum can be obtained through time-frequency analysis. Since the ellipticity of the probe beam is related to the switching time, and time is related to the rotational Doppler frequency shift in the time-frequency spectrum, the correlation between the ellipticity and the rotational Doppler frequency shift can be obtained. When the ellipticity strictly corresponds to the tilt angle of the object, the rotational Doppler spectrum hardly widens, and the signal amplitude is at its maximum in the time-frequency domain. The tilt angle at this time (…) ) and the corresponding time ( The relationship between ) can be represented as,

[0042] (10)

[0043] This corresponds to the time when the rotating Doppler spectrum is narrowest. It is the initial time of a cycle. It is the hologram switching interval, and It is the ellipticity interval of the elliptical optical vortex. This method allows for the simultaneous determination of the object's tilt angle and the optimal ellipticity of the light beam.

[0044] This invention measures the tilt angle of an object based on an optical vortex with continuously varying ellipticity. Specifically, the object of implementation is an optical vortex and a tilted, rotating object. The specific implementation steps are as follows:

[0045] The overall flowchart for measuring the tilt angle of an object based on an optical vortex with continuously varying ellipticity is as follows: Figure 1 As shown in Figure 3, the geometric model of an elliptical vortex beam for detecting an inclined object is first established during the measurement. The elliptical vortex beam is positioned with its center at the center. A spatial rectangular coordinate system is established with the origin as the origin, the beam propagation direction as the z-axis, and the horizontal direction of the beam's transverse plane as the y-axis. An arbitrary scattering point 'a' within the beam spot is then considered. Representing the origin The vector to scattering particle a, The angular velocity vector has a magnitude of . Represents the tilt angle of an object. Projection and The included angle of the axis is . Let be the linear velocity at scattering point a. A rotational Doppler frequency shift expression based on elliptical optical vortices with respect to the object tilt angle and beam ellipticity is derived, i.e. in Represents azimuth. Represents ellipticity. represent exist Projection of the surface and The included angle of the axis, Represents the topological charge number. Represents rotational speed. This represents the tilt angle.

[0046] Secondly, the ellipticity of the light is modulated using complex amplitude modulation and coordinate transformation, and the beam ellipticity range is designed to be... , interval is In actual detection, the ellipticity interval can be adjusted according to actual requirements. This set contains 34 optical vortex holograms with different ellipticities. They are sequentially displayed on a spatial light modulator, and a series of elliptical vortex beams with continuously varying ellipticities are obtained by irradiation with linearly polarized light. The object rotation speed is set to 50Hz, the object tilt angle to 45 degrees, and the beam topological charge is... The cycle period of this set of elliptical optical vortices is set to 1.65s, meaning the display time for each hologram is 0.02s. The experimental optical path for measuring the object's tilt angle is shown in Figure 2. The laser beam is first modulated into a horizontally polarized beam by a polarizer. After passing through a beam expander and collimator system composed of lens 1 and lens 2, it illuminates a spatial light modulator loaded with a set of elliptical vortex beam holograms. A spatial filtering system composed of lenses and apertures selects the desired optical vortex. After passing through a reflector and beam splitter, it is split into two paths. One beam is focused by a lens and received by a camera to detect the spot quality. The other beam illuminates an object with a tilt angle of... Rotation speed is The light scattered from the object is focused by a lens and received by a photodetector, then converted into a time-domain signal for acquisition. In the experiment, echo signals from the object were collected over a period of 2 seconds. The received echo time-domain signal is shown in Figure 5(a). The signal was then processed using a short-time Fourier transform to obtain the time spectrum of the Doppler signal, as shown in Figure 5(b). Figure 5As can be seen in (b), the rotating Doppler band first contracts and then broadens with time or the ellipticity of the beam, and the signal energy in the frequency domain is strongest at the narrowest point of the band. This is consistent with the theoretical analysis. To further measure the optimal ellipticity, [further analysis is needed]. Figure 5 The time-frequency signal in (b) is filtered, and the result is as follows: Figure 5 As shown in (c). Because the Short Time Fourier Transform (STFT) spectrum is affected by factors such as window length, sampling time, and sampling frequency, it is difficult to obtain the object's tilt angle and beam ellipticity as accurately as theoretical analysis. Therefore, the contour of the upper edge of the time spectrum is extracted, and trigonometric functions are used to fit the contour to obtain the minimum value of the curve, which corresponds to the narrowest RDE spectrum, as shown in (c). Figure 5 As shown in (d). The corresponding time is 0.818s, and the ellipticity of the SERV is 0.74, according to the formula... The calculated tilt angle of the object was 42.05 degrees, with a corresponding measurement error of 6.5%. This experimental result proves that this method can achieve accurate measurement of the tilt angle of an unknown target.

[0047] The contents not described in detail in this invention are existing technologies known to those skilled in the art.

Claims

1. A method for measuring the tilt angle of an object based on an optical vortex with continuously varying ellipticity, characterized in that: First, the ellipticity of the optical vortex is controlled. Through coordinate transformation and scaling, a set of optical vortex holograms with regularly varying ellipticity is obtained. These holograms are sequentially loaded onto a spatial light modulator, and a set of vortex beams with continuously varying ellipticity is prepared by irradiation with linearly polarized light. The prepared vortex beams are then used to sequentially scan and irradiate a rotating target. The rotating target modulates the frequency of the elliptical vortex beams, generating a rotational Doppler frequency shift. The echo time-domain signal is received using a photodetector, and after processing using time-frequency analysis, the rotational Doppler time spectrum is obtained. Based on the time spectrum, the time corresponding to the narrowest frequency shift in the time-varying spectrum is obtained. Combining this with the relationship between the tilt angle and the time, the object's tilt angle is obtained. A geometric model for detecting tilted objects with elliptical vortex beams is established, illustrating the relationship between the object's tilt angle, the ellipticity of the vortex beam, and the rotational Doppler frequency shift under tilted conditions. in Represents the rotational Doppler frequency shift. Represents ellipticity. Represents the topological charge number. Represents rotational speed. Represents azimuth. Represents the angular velocity vector of a rotating object exist Projection of the surface and The angle between the axes was determined; an expression was established relating the time in the time spectrum of the echo signal to the object's tilt angle. , This corresponds to the time when the rotating Doppler spectrum is narrowest. It is the initial time of a cycle. It is the hologram switching interval, and It is the ellipticity interval of the probe beam. This represents the tilt angle; the tilt angle of an object can be obtained by using the time corresponding to the frequency in the time spectrum.

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