CN114754674A - Object rotation center positioning method based on conjugate superposition state vortex optical rotation - Google Patents
Object rotation center positioning method based on conjugate superposition state vortex optical rotation Download PDFInfo
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Abstract
The invention relates to an object rotation center positioning method based on conjugate superposition vortex rotation. The conjugate superposed vortex light comprises vortex light with two conjugate modes, can be prepared by combining a laser with a spatial light modulator, and the topological charge number and the radius of the light beam can be flexibly adjusted. A beam of collimated emitted conjugate superposition Laguerre-Gaussian beam vertically irradiates the surface of a rotating object, the frequency shift generated by reflected light is analyzed, the distance of the rotating center of the object from the center of the beam can be calculated, and the calculation precision can be controlled by adjusting the radius and the topological charge number of the beam; adjusting the light beam to resolve the distance at different positions can determine the position of the rotation center on the surface of the object; when the position of the light beam is adjusted to enable the frequency spectrum to generate a single signal, the rotation center of the object is coincided with the center of the light beam, and the calibration of the rotation center of the object can be realized. The method has the advantages of simple operation, flexible adjustment, high positioning precision and wide application range, and can be used for positioning the rotation center of an object.
Description
Technical Field
The invention relates to a method for positioning an object rotation center based on conjugate superposition state vortex optical rotation, which can determine the position of the object rotation center by measuring the distance between the center of a light beam of the conjugate superposition state vortex optical rotation and the object rotation center for multiple times, and can also realize the calibration of the object rotation center by adjusting the position of the light beam irradiated on the surface of the object. The method can be used for positioning the rotation center of an object and has important application value in the fields of mechanical processing and optical measurement.
Technical Field
Vortex light is a spatially structured light beam carrying Orbital Angular Momentum (OAM) with a helical phase factor
Where l is the orbital angular momentum topological charge number, also known as the mode number,
is the azimuth angle. Each photon in the beam carries
The orbital angular momentum of (a) is,
to approximate the planck constant, the phase factor indicates that in the propagation process of the eddy rotation, if the light beam propagates for a period, the wavefront rotates around the optical axis exactly once, and the phase changes by 2 pi l correspondingly. The center of the spiral phase factor is a phase singularity, the phase at the singularity is uncertain, and the light intensity is zero, so that the center of the light beam is a hollow dark core, and the light beam has annular intensity distribution. There are different kinds of eddy rotation, such as laguerre-gaussian beam, bessel-gaussian beam, round alley-gaussian beam, etc. The conjugate superposition state vortex light is vortex optical rotation simultaneously containing two conjugate modes (two topological charge numbers with opposite signs), and the topological charge number is | -l>+|+l>In the Laguerre-Gaussian (LG) mode, the intensity distribution is in a petal shape, the number of the petals is 2l, and the petals are uniformly distributed on a circle which takes the center of a light beam as the center of a circle.
Vortex rotation can be prepared by a variety of methods, and commonly used methods include a mode conversion method, a computer generated hologram method, a spatial light modulator method, a Q-plate method, and a matrix spiral phase plate method. Under the laboratory condition, the spatial light modulator method is commonly used, and the topological charge number, the radial pitch number and the radius of the light beam can be flexibly adjusted according to requirements. The phase type spatial light modulator controls the electric field to cause the change of the spatial phase of the liquid crystal display, thereby writing new information into the light wave and realizing the modulation of the light wave. For example, a holographic pattern of the LG light beam is prepared by a complex amplitude regulation and control technology and is loaded to a spatial light modulator, a linear polarization Gaussian beam is used for irradiating a liquid crystal display screen of the spatial light modulator, and emergent light comprises the LG light beam with a plurality of diffraction orders. Through spatial filtering, the first order diffracted light with higher quality and intensity can be selected.
Vortex rotation has a special hollow structure, and the beam radius is related to a plurality of factors. For example, a conjugate superposition Laguerre-Gaussian beam has a topological charge (| -l > + | + l >) and contains two conjugate modes (+ l and l) in equal proportion, which have a petal-shaped intensity distribution, and the intensity at the center of the beam is zero. The radius of the light beam is not only related to a Gaussian function in the complex amplitude of the light beam, but also influenced by parameters such as topological charge number, radial nodal number and the like, and also influenced by experimental operations such as beam expansion, collimation and the like. In the cross section of the light beam, the intensity distribution of each petal is rotationally symmetrical about the center of the light beam and follows Gaussian distribution, and the radius of a conjugate superposition state LG light beam is defined as: in the radial direction of the beam, the field amplitude decreases to a point 1/e of the outermost maximum to the beam center.
When vortex light irradiates the surface of a rotating object, OAM carried by the light beam interacts with the rotating object, and the reflected light is subjected to frequency shift, which is called a rotating Doppler effect. Collecting reflected light for photoelectric conversion, sampling and fourier transforming the converted voltage signal, and obtaining a rotating doppler frequency shift spectrum, which generally consists of several discrete peak signals and is affected by many parameters, such as: topological charge number of the light beam, radius of the light beam, rotational frequency of the object, position of light beam irradiation, and the like. When other parameters are determined, the positions of the light beams irradiated on the surface of the object are different, and the obtained rotating Doppler frequency shift spectrum is also different, so that the position of the rotating object relative to the light beams can be calculated from the composition of the frequency shift spectrum, and the position of the rotating center of the object can be determined. Meanwhile, the rotary Doppler effect can also be used for measuring the spin frequency, the spin acceleration and the like of the object, and has important significance for measuring the rotary motion parameters.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the determination of the rotation center of an object is of great significance in the fields of machining, optical measurement and the like, and the currently common technology needs to additionally mount a device, such as a grating or a beam splitter, on the surface of the rotating object, but a non-cooperative target cannot normally mount the device. Aiming at the problem that the rotation center of the existing rotating object, particularly a non-cooperative rotating object, is difficult to position, a method for positioning the rotation center of the object based on conjugate superposition state vortex optical rotation is provided. The method is simple and convenient to operate, strong in flexibility and high in precision, devices do not need to be installed on the surface of an object, the rotating object is irradiated by the conjugate superposition state vortex light, the distance between the center of the light beam and the rotating center of the object can be calculated by receiving the reflected light, and the positioning of the rotating center of the object is realized.
The technical solution of the invention is as follows:
the invention relates to an object rotation center positioning method based on conjugate superposition vortex rotation, which mainly comprises the following steps:
(1) and preparing a conjugate stack-state Laguerre-Gaussian vortex optical rotation hologram by using a multi-parameter joint regulation and control technology, loading the hologram to a spatial light modulator, and irradiating the spatial light modulator with linearly polarized Gaussian light to prepare the conjugate stack-state Laguerre-Gaussian vortex optical rotation.
(2) The conjugate superposition Laguerre-Gaussian vortex optical rotation irradiates the surface of a rotating object after passing through a light beam collimation and filtering system, the light beam is parallel to the rotating shaft of the object as far as possible, reflected light is received for photoelectric conversion, the converted voltage signal is sampled and subjected to Fourier transform, and the frequency shift of the reflected light is analyzed.
(3) And adjusting the light beam, measuring the rotating Doppler frequency shift spectrum at least three non-collinear positions, resolving the distance between the center of the light beam and the rotating center of the object, and determining the position of the rotating center of the object by applying a three-circle positioning principle. The position of the light beam can also be continuously adjusted to reduce the number of signals in the rotating doppler frequency shift spectrum to one, and the center of the light beam coincides with the rotation center of the object, so that the position of the rotation center of the object can be calibrated, as shown in fig. 1.
The principle of the invention is as follows:
the laguerre-gaussian (LG) beam is the most commonly used beam in the research of the rotating doppler effect, and is a set of solutions of paraxial wave equations in a cylindrical coordinate system, which can be expressed as:
where E is the wave vector of the LG beam,
is a cylindrical coordinate, r is a polar diameter,
is polar angle, z is beam propagation distance, l is topological charge number, p is radial nodal number, zRIs the Rayleigh length, ωzIs the radius of the light beam and,
for the associative laguerre polynomial, k ═ 2 pi/λ is the angular wavenumber, λ is the wavelength of light, i is the imaginary unit, and pi is the circumferential ratio. When z is determined, (1) formula may be abbreviated as:
the conjugate-superimposed LG beam contains two conjugate modes in the same proportion, and can be expressed as:
the topological charge number is | -15>+|+15>For example, the intensity distribution of the stacked LG beam comprises 30 identical petals which are uniformly distributed on the cross section of the beam, and the intensity of each petal follows a gaussian distribution, as shown in fig. 2. The radius of the conjugate-superposition-state LG beam is 6mm, as defined by the radius of the beam.
When an LG light beam irradiates the surface of a rotating object, the reflected light undergoes a rotary Doppler shift (delta f)l) The size of which is related to the rotational frequency of the object and the OAM mode change of the beam. When the incident light mode is l, the object spin frequency is f, and the reflected light mode is m, the rotary Doppler shift is Δ fl(l-m) f. When the incident light is a conjugate superposition LG beam, the mode is | -l>+|+l>Then the two conjugate modes occur with frequency shifts of Δ flIs (l-m) f and Δ f-l(-l-m) f, the reflected light contains a rotational doppler shift of Δ fl-Δf-l. When the beam is incident perpendicularly to the center of the rotating object, the doppler shift spectrum contains only a single signal: Δ fl-Δf -l2 lf. When the center of the light beam is not coincident with the center of the rotating object, the Doppler frequency shift spectrum is broadened and comprises a plurality of discrete signals.
This broadening effect can be described in terms of the mode expansion method of the beam. The OAM carried by the vortex light comprises a series of mutually orthogonal modes, such as-2, -1,0, +1, +2, and one or more modes can be carried by one vortex rotation, and the proportion of each mode determines the intensity and phase distribution of the vortex light beam. For example, a series of coaxial LG beams with different mode numbers are superposed according to a specific proportion, so that an LG beam with a lateral offset from the original beam can be generated. In turn, a beam of light that is laterally offset from the center of rotation of the object
Can be decomposed into a combination of LG beams coaxial with the axis of rotation of the object:
wherein A islIs the complex coefficient of each LG mode,
representing a single LG mode, r is the pole diameter,
is the polar angle, l is the topological charge number, and p is the radial pitch number. Due to the orthogonality between the modes, the inner product operation result of different modes is 0, then
All AlThe OAM spectrum is formed after normalization, and the characteristics of the OAM spectrum are mainly reflected in mode composition and the proportion of each mode. Under the condition that the offset distance between the center of the light beam and the rotation center of the object is constant, the topological charge number and the radius of the light beam determine the composition of the OAM spectrum. For one conjugate superposition state LG light beam, the transverse deviation of the light beam center and the object rotation center is 0.1mm, and the topological charge number is | -15>+|+15>The radius is 6mm, its OAM spectrum contains two parts, and the two parts are symmetric about 0, as shown in fig. 3.
The rotary doppler shift signal is mainly affected by each mode in the OAM spectrum, and the larger the proportion of the mode is, the higher the corresponding rotary doppler shift signal intensity is. Experimental rules show that when the specific gravity of a certain mode is greater than 2%, the corresponding rotating doppler frequency shift signal can be detected. Therefore, the mode with the specific gravity of more than 2% is the effective mode. Since the OAM spectrum contains two parts symmetrical about 0, the number (M) of any one part of the active modes is equal to the number (N) of the rotating doppler shift signals. When the topological charge number and the radius of the probe beam are determined, the number (M) of the modes is in proportion to the lateral deviation (d), and the proportional relation between M and d can be obtained by performing least square fitting on the proportional relation. When the topological charge of the beam is (| -15> + | +15> and the radius is 6mm, the ratio is M ═ 10.5d +2.05, as shown in fig. 4, since the number of rotating doppler shift signals is equal to the number of modes, i.e., M ═ N, the lateral shift can be resolved as d ═ N-2.05)/10.5.
The scheme of the invention has the main advantages that:
(1) the method is simple and convenient to operate, devices do not need to be installed on the surface of an object, only the conjugated stack state vortex light is irradiated to the surface of a rotating object, reflected light is collected and subjected to spectrum analysis, the offset distance between the center of the light beam and the rotation center of the object can be resolved, and the object rotation center can be positioned by resolving the offset distance in at least 3 different positions. The position of the light beam can be continuously adjusted, so that the number of signals in the rotary Doppler frequency shift spectrum is reduced to one, the center of the light beam is coincided with the rotation center of the object, and the position of the rotation center of the object can be calibrated.
(2) The technical scheme relies on the rotary Doppler effect, is suitable for objects with different rotating speeds, and the detection precision can be controlled through the topological charge number and the radius of the light beam.
Drawings
FIG. 1 is a flow chart of an object rotation center positioning operation based on conjugate stacking state vortex rotation;
FIG. 2 is a graph of the intensity distribution of an LG beam with topological charge numbers | -15> + | +15 >;
fig. 3 is an OAM composition diagram when the conjugate superimposed LG beam is laterally shifted;
FIG. 4 is a graph of the number of modes as a function of lateral offset;
FIG. 5 is a diagram of a positioning scheme of an object rotation center based on conjugate stacking vortex rotation;
FIG. 6 is a diagram of the positioning result of the object rotation center;
FIG. 7 is a diagram illustrating the calibration result of the object rotation center;
detailed description of the preferred embodiments
The invention takes conjugate superposition vortex light as a detection medium, and an implementation object is a rotating object, and the specific implementation steps are as follows:
firstly, a phase diagram of conjugate superimposed LG light beams is prepared and blazed gratings are superimposed to obtain a holographic pattern which can be accurately regulated and controlled, the holographic pattern is loaded to a spatial light modulator (6), stable Gaussian light is generated through a continuous laser (1), the stable Gaussian light sequentially penetrates through a linear polarizer (2) and a neutral density filter (3), the light is irradiated to the spatial light modulator (6) through a light beam collimation and expansion system consisting of a lens (4) and a lens (5), emergent light after complex amplitude modulation is conducted is conjugate superimposed LG light beams, and the conjugate superimposed LG light beams are irradiated to the surface of a rotating object (10) after passing through a spatial filtering system consisting of a lens (7), a diaphragm (8) and a lens (9). The reflected light from the surface of the object is received by the photodetector (11), the light intensity signal is converted into a voltage signal, and the voltage signal is input to an oscilloscope for fourier transform and spectral analysis, as shown in fig. 5.
For example, a spatial light modulator is used to produce a topological charge number (| -15)>+|+15>) And irradiating the laminated LG light beam onto the surface of the rotating object. The beam radius is 6mm and the object rotation frequency is 30Hz, rotating Doppler shift spectra are measured at 3 different positions (A, B, C), the distance between the beam center and the object rotation center is calculated according to the functional relationship between the number of frequency shift signals and the lateral shift, d1、d2、d3. The position of the center of rotation of the object can be determined according to the three-circle positioning principle, as shown in fig. 6. AB and BC are perpendicular to each other, and | AB | BC | 1 mm. Due to the resolving error, three circles intersect with each other to generate three intersection points, the overlapped area of the three circles is the positioning result, and S is the real position of the rotation center of the object. The maximum error of the positioning is 0.2mm, which is 3.33% of the radius of the light beam, which shows that the method can realize the positioning with higher precision.
In addition, the position of the light beam can be adjusted step by step, so that the number of signals in the rotating doppler frequency shift spectrum is gradually reduced, and when the frequency shift spectrum only contains one signal, the center of the light beam is coincident with the rotation center of the object, so that the calibration of the rotation center of the object can be realized, as shown in fig. 7. The positioning error is now 0.1mm, which is 1.67% of the beam radius.
The measurement error increases with increasing lateral offset, so the lateral offset should be determined within a certain range to ensure measurement accuracy, typically 25% of the beam radius. When the lateral offset is in this range, the accuracy of positioning and calibration can be adjusted by beam radius and topological charge. The larger the beam radius is, the smaller the topological charge number is, and the lower the precision is; the smaller the beam radius, the larger the topological charge number and the higher the accuracy.
In addition, the spatial light modulator limits the incident angle and power of the light beam to some extent, and the detection light beam should be parallel to the rotating shaft of the object as much as possible, so the specific light path design is carried out according to the actual conditions of the laboratory.
Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.
Claims (4)
1. An object rotation center positioning method based on conjugate superposition state vortex rotation is characterized in that: the method uses a conjugate superposition Laguerre-Gaussian beam as detection light, the beam irradiates the surface of a rotating object after being collimated, the included angle between the beam and the rotating shaft of the object is less than 10 degrees, reflected light is collected for photoelectric conversion, the rotating Doppler frequency shift generated by the reflected light is analyzed, the distance between the rotating center of the object and the center of the beam can be calculated by analyzing the components of frequency shift signals, the calculation precision can be controlled by adjusting the radius and the topological charge number of the beam, the position of the rotating center of the surface of the object can be determined by calculating the distance at different positions, and the position of the rotating center of the object can be calibrated by gradually adjusting the position of the beam until a single signal appears.
2. The method for positioning the rotation center of an object based on conjugate stacking state vortex rotation according to claim 1, wherein: the rotating Doppler frequency shift spectrum is generally composed of single or a plurality of discrete signals, the number of the signals and the distance of the rotating center of the object from the center of the light beam have a functional relation, the functional relation is influenced by the topological load number of the light beam and the radius of the light beam, the distance of the rotating center of the object from the center of the light beam can be calculated from the number of the signals, the distance can be calculated from at least three different positions by adjusting the light beam, and the position of the rotating center of the surface of the object can be determined.
3. The method for positioning the rotation center of an object based on conjugate stacking state vortex rotation according to claim 1, wherein: when the distance of the rotating center of the object deviating from the center of the light beam is calculated from the number of the rotating Doppler frequency shift signals, the distance is usually not more than 25% of the radius of the light beam, the calculating accuracy is influenced by the radius of the light beam and the topological charge number, the smaller the radius is, the larger the topological charge number is, the higher the measurement accuracy is, the larger the radius is, the smaller the topological charge number is, and the lower the measurement accuracy is.
4. The method for positioning the rotation center of an object based on conjugate stacking state vortex rotation according to claim 1, wherein: and adjusting different positions of the surface of the object irradiated by the light beam, recording the rotating Doppler frequency shift spectrum in real time to gradually reduce the number of signals, and when a single peak value appears, the center of the light beam is superposed with the rotating center of the object, so that the calibration of the rotating center position of the object is completed.
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