CN112557690A - Object movement speed measuring method based on polarization grating Doppler effect - Google Patents
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- G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
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Abstract
The invention relates to a method for measuring the movement velocity of an object based on the Doppler effect of a polarization grating, which is based on the optical characteristics of the polarization grating, theoretically expounds the Doppler effect generation mechanism of the polarization grating, proposes a method for obtaining linearly polarized light with beat frequency characteristics by superposing +/-1-order diffracted light of the polarization grating, obtains the expression of signal light through theoretical derivation, obtains the average movement velocity by carrying out fast Fourier transform on the signal, obtains the characteristic that the movement velocity of the polarization grating changes along with time by carrying out time-frequency analysis on the signal by adopting short-time Fourier transform, and can obtain the movement information of the object by fixedly connecting the polarization grating and a moving object. The research realizes the measurement of the linear motion speed and the acceleration of the motion grating, and has potential significance for the further development of the optical heterodyne detection and laser frequency shift technology.
Description
Technical Field
The invention mainly relates to the fields of optics, physics, signal processing and the like, in particular to short-time Fourier transform in an optical beat technology and time-frequency analysis.
Technical Field
Polarized light is light in which the electric vector vibrates in a fixed manner with respect to the direction of propagation. According to the track formed by the tail end of the electric vector in the light transmission process, the polarized light is mainly divided into linearly polarized light, circularly polarized light, elliptically polarized light and partially polarized light. If the track is a line in the process of propagation, the track is linearly polarized light; if the tail end track of the electric vector is circular or elliptical on a plane perpendicular to the propagation direction, the tail end track of the electric vector is called circularly polarized light or elliptically polarized light; if the vibration of the electric vector is dominant in a certain direction during the propagation process, the polarized light is called partial polarized light. The polarization grating is an instrument capable of selectively splitting light according to the polarization characteristics of incident light, and the diffraction phenomenon of the polarization grating and the polarization state of diffracted light are different for incident light with different polarization states.
The existing laser spectrum range is 3.8 multiplied by 1014Hz～7.9×1014Hz, which is 10 for the currently used photodetectors (response time)-12s) the change in instantaneous frequency cannot be detected, so that the problem that the high-frequency signal cannot be measured can be solved by reducing the signal frequency by adopting the beat technology. The principle of optical beat is to superimpose two beams of light with a certain frequency difference together, so as to obtain the frequency difference and the frequency sum signal of the two beams of light, and the frequency sum of the two beams of light belongs to a high-frequency signal, which cannot be measured by a photoelectric detector, so that the signal measured by the detector is the frequency difference signal of the two beams of light.
The basic idea of short-time Fourier transform is to view the non-stationary process as the superposition of a series of short-time stationary signals, the short-time property can be realized by windowing the signals in time, and the Fourier transform is performed on the signals in the window to obtain the time-varying frequency spectrum of the signals, thereby obtaining the variation rule of the signal frequency along with the time.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the prior article researches that the Doppler effect of a common grating is utilized to realize the accurate measurement of the movement speed of the grating and the analysis of the vibration of the grating, and a polarization grating is different from the diffraction mode of the common grating and can generate diffracted light with different polarization states according to the different polarization states of incident light, and when the incident light is circularly polarized light, the diffracted light can also generate the defect level phenomenon, so that the traditional measurement method cannot be suitable for the measurement of the movement speed of the polarization grating. The method designs a diffraction light superposition light path aiming at the diffraction characteristic of the polarization grating and the polarization characteristic of the diffraction light, and realizes the object motion speed measurement based on the Doppler effect of the polarization grating for the first time.
The technical solution of the invention is as follows: the invention relates to a method for measuring the movement speed of an object based on the Doppler effect of a polarization grating, wherein a measuring device comprises a Laser (Laser), a spatial Filter (Filter), a diaphragm (AP), a convex Lens (Lens1), a polaroid (P), a plane mirror (M1), a Polarization Grating (PG), a lambda/4 wave plate (lambda/4 WP), a plane mirror (M2), a plane mirror (M3), a plane mirror (M4), a Beam Splitter (BS), a Photoelectric Detector (PD) and an oscilloscope (oscilloscope). Firstly, a beam of linearly polarized light is incident to a polarization grating to ensure that the diffracted light has two stages of +1 stage and-1 stage, wherein the +1 stage is left-handed circularly polarized light, the-1 stage is right-handed circularly polarized light, the two beams of diffracted light are respectively changed into two beams of linearly polarized light with the same polarization direction through a lambda/4 wave plate, and finally, the linearly polarized light is changed into beat frequency linearly polarized light through superposition of a beam splitter, and the fundamental frequency of the laser is set as f0Doppler shift is Δ f, wave number is k, and distance traveled by +1 st order diffracted light is z1The distance traveled by the-1 st order diffracted light is z2Then, the expression of the beat signal is:
the obtained signal is subjected to fast Fourier transform to obtain a signal spectrogram
There will be a distinct peak where v is the velocity of motion and d is the grating constant of the polarization grating. Because the frequency shift is in direct proportion to the speed theoretically, the value of the frequency shift changes along with the change of the speed of the polarization grating, when the polarization grating does variable-speed motion or vibration, a spectrogram generated by performing Fast Fourier Transform (FFT) on a signal forms certain broadening at the position of a Doppler frequency shift signal, and the spectrogram cannot reflect complete motion information only by analyzing. The method adopts short-time Fourier transform (STFT) to carry out time-frequency analysis on the signal, can obtain the change condition of the movement speed of the polarization grating along with time, further can analyze the acceleration and vibration condition of the polarization grating, and can fixedly connect the polarization grating with the object to be measured for measurement when measuring the movement state of the object.
The principle of the invention is as follows:
(1) diffraction of polarization gratings
The polarization grating is a polarization instrument for selectively splitting light based on the polarization state of incident light, and the polarization characteristics of +1 order and-1 order diffracted lights can be changed by controlling the polarization state of the incident light.
FIG. 1 shows the diffraction condition of light beams with different polarization states after being incident on a polarization grating, as shown in FIG. 1(a), when the incident light is linearly polarized light or unpolarized light, the polarization grating simultaneously has +1 st-order and-1 st-order diffracted lights, the +1 st-order is left-handed circularly polarized light, and the-1 st-order is right-handed circularly polarized light; in fig. 1(b), when the incident light is right-handed circularly polarized light, only +1 st order diffracted light is left-handed circularly polarized light; in FIG. 1(c), when the incident light is left circularly polarized light, only-1 st order diffracted light is left circularly polarized light; when the incident light is elliptically polarized light, the +1 order and-1 order diffracted lights exist at the same time, and the light intensity ratio of the two-stage diffracted light beams is related to the ellipticity of the incident light.
In fact, the actual polarization grating has +1 st order diffracted light and other orders diffracted light except for small light intensity, and generally, the sum of the energy of the diffracted light of the other orders is less than 4%.
(2) Doppler effect of polarization grating
As shown in FIG. 2, assume a bundle of planar light waves at an angle θiIncident on the polarization grating at an angle thetamDiffraction, the incident light wave front A and the diffracted light wave front B intersect at the point O, and the polarization grating with the grating constant d makes a translational motion with the speed v along the direction shown in the figure, for the reference frame Ox in the figure, the light path is static relative to the reference frame, and the polarization grating makes a translational motion along the negative direction of the x axis relative to the reference frame. Therefore, at time t, the distance ON from the point O to the nth slit of the grating is:
x＝nd-vt (1)
the distance between the planes a and B where a ray passes through point N is:
l＝x(cosθi+cosθm) (2)
according to the Doppler effect principle, the Doppler shift of the diffracted light can be obtained as follows:
the condition for forming interference enhancement after light passes through the polarization grating is that the optical path difference of diffracted light of adjacent slits is integral multiple of wavelength, namely:
d(cosθi+cosθm)＝mλ (4)
where m is the diffraction order and λ is the wavelength. The joint type (3) and the formula (4) are obtained:
thus, when the polarization grating is moved, the angular frequency ω of the +1 st order diffracted light diffracted toward the moving direction1Comprises the following steps:
ω1＝2π(f0+Δf) (6)
and the angular frequency omega of the-1 st order diffracted light biased to the opposite direction of motion2Comprises the following steps:
ω2＝2π(f0-Δf) (7)
(3) beat frequency signal generation principle
In order to ensure that the light has + 1-order and-1-order circularly polarized diffracted lights after passing through the polarization grating, the light beam emitted by the laser needs to be processed into linearly polarized light by the polarizer and then passes through the moving polarization grating.
In order to superpose the two polarized lights, the two-stage diffracted lights pass through the lambda/4 wave plate respectively to be changed into linearly polarized lights, and then the two lights are superposed at a Beam Splitter (BS) through the reflection of a plane mirror. Assuming that electric vectors of the two diffracted stages of circularly polarized light before being incident on the wave plate are respectively as follows:
+ 1-stage left-handed circularly polarized light
-1 order right-handed circularly polarized light
Wherein A is amplitude, k is wave number, z0Is the distance traveled by the beam (the same distance traveled by the two-stage diffracted light before striking the waveplate), ω1、ω2Respectively, the angular frequency of the two-level light.
Defining the fast axis direction of the wave plate corresponding to the +1 st order light as the polarization component y direction, adjusting the fast axis directions of the two wave plates to make the polarization directions of the emergent light the same, i.e. making the phase of the y direction component of the +1 st order diffracted light lag behind the x direction component
The phase of the y-direction of the 1 st order diffracted light is advanced with respect to the x-direction component
The electric vector of the two-stage light after reflection by the plane mirror and BS is:
in the above formula, the first and second carbon atoms are,z1、z2respectively, the distances traveled by +/-1-level light after reflection are obtained by arranging the formula into a resultant vector:
the two beams of light are superposed and arranged to obtain the following expression:
the following equations (6) and (7) can be obtained:
ω1+ω2＝4πf0 (15)
ω1-ω2＝4πΔf (16)
substituting the formulas (15) and (16) into the formula (14) to obtain:
as can be seen from equation (5), in equation (17):
it can be seen that the latter cosine term of equation (17) carries a doppler shift term, which is equivalent to performing amplitude modulation based on the original frequency light to form a beat frequency. The frequency spectrum of the signal is shown in
There is a distinct peak, and since the frequency shift is theoretically proportional to the velocity, the value varies with the velocity of the polarization grating.
(4) Time-frequency analysis of signals
As can be seen from equation (18), the doppler shift is proportional to the movement velocity of the polarization grating. Because the size of the displacement table bearing the polarization grating is limited, the motion of the polarization grating must have an acceleration process and a deceleration process, and the time-varying signals are not suitable for being analyzed only by adopting Fast Fourier Transform (FFT). In order to obtain the characteristic of the change of the speed of the polarization grating along with the time, the time-frequency analysis is carried out by adopting short-time Fourier transform (STFT) to observe the change of Doppler frequency shift along with the time.
The basic formula of the short-time fourier transform is:
wherein x is signal data obtained by experiment, g*(τ -t) is the complex conjugate function of the window function g (τ -t). For this experiment, since the oscilloscope used is a digital oscilloscope, the acquired signal x (t) is a set of vectors, and the short-time fourier transform performed on the computer needs to be discretized, the discretized short-time fourier transform formula is:
wherein, N is the moving step length of the window function in the time domain, M is the length for carrying out local discrete Fourier transform, and M is a time point.
The selection of the STFT parameters affects the time resolution and the frequency resolution, and too low resolution affects the readability of the time-frequency diagram, so that the appropriate STFT parameters need to be selected according to the characteristics of the data.
Setting the length information intercepted in the time domain as L, and when L is larger than M, generating the phenomenon of frequency spectrum leakage due to the time domain part which cannot be analyzed; when L < M, the window function intercepts insufficient signals, resulting in excessive transformation, and the part without data will be zero-padded on the computer, so generally, L is selected as M, i.e. how many are intercepted, and how many are analyzed.
For the step length N, the step length N cannot exceed the window function length L, and if the step length N exceeds the window function length L, a part of signals cannot be analyzed; and when N is less than L, although the part of repeated analysis is provided, more analysis time periods are increased, and more detailed time-frequency information can be provided.
The overlap point number novelap is directly related to the detail degree of time-frequency information provided by short-time Fourier transform, and the analysis result is influenced to a certain extent when the numerical value is too large or too small. According to the analysis mode of short-time Fourier transform, the three variables have a fixed relation, namely:
N＝L-noverlap (21)
the step length N has the following inequality:
1≤N≤L (22)
the inequality relationship between the number of overlapping points novelap and the window function length L can be obtained according to equations (21) and (22):
0≤noverlop≤L-1 (23)
thus, three parameter relations of the window function length L, the stepping length N and the overlap point number novelap, which influence the time resolution and the frequency resolution, are obtained, and through the inequality relation, a Hamming window is selected in an experiment, the window function length L is 256, the overlap point number novelap is 250, and the stepping length N is 6, so that a clear time-frequency diagram can be obtained. The time-frequency analysis and the formula (18) can obtain the change situation of the speed along with the time.
Drawings
FIG. 1 shows diffraction patterns of light beams with different polarization states after being incident on a polarization grating, wherein (a) the light beams are linearly polarized or unpolarized and (b) the light beams are rightwards circularly polarized and (c) the light beams are leftwards circularly polarized;
FIG. 2 is a view of a light beam passing through a moving polarization grating;
FIG. 3 shows velocity v1Time signal analysis, (a) a signal spectrogram and (b) a signal time-frequency graph;
FIG. 4 shows velocity v2Time signal analysis, (a) a signal spectrogram and (b) a signal time-frequency graph;
FIG. 5 shows velocity v3Velocity v of time signal spectrogram (a)3Time signal spectrogram, (b) velocity v3Time-frequency diagram with acceleration process, (c) enlarged diagram of acceleration process, (d)Velocity v3A time-frequency diagram with a deceleration process, (e) an enlarged diagram of the deceleration process;
FIG. 6 is an experimental set-up;
detailed description of the preferred embodiments
In consideration of the limitation of the load weight of the linear displacement table and the reduction of the preset speed of the displacement table caused by the load weight, the polarization grating is clamped by a self-made portable support table and is arranged on the linear displacement table, the stepping distance and the stepping speed of the displacement table are controlled by a computer, and the experimental light path is shown in fig. 6.
1. Filtering and polarizing
A solid Laser (Laser) emits a Laser beam with the wavelength of 532nm, the Laser beam firstly passes through a spatial Filter (Filter), and a diffracted central circular light spot is selected through an Aperture (AP), so that stray light in emergent light of the Laser is removed. The position of the convex Lens (Lens1) is adjusted to collimate the filtered light beam.
In order to ensure that the polarization grating diffracts incident light into two-stage circularly polarized light, collimated light beams need to be changed into linearly polarized light through a polarizing plate (P), and meanwhile, in order to make the light path compact and fully utilize the experiment table, a plane mirror (M1) is arranged in the light path to reflect the light beams at right angles.
2. Diffraction and superposition
Linearly polarized light passing through the polarizing plate is diffracted by a Polarization Grating (PG) moving in the direction shown in the figure, the diffracted light takes two stages of +/-1 grade, the two stages generate Doppler frequency shifts with equal magnitude and opposite directions due to the movement of the polarization grating, and the 0 grade and other secondary large light spots are not related to the experiment, so the 0 grade and other secondary large light spots are shielded or scattered, and are not shown in the figure. In order to superpose the light beams to form beat frequency, the +/-1 order light respectively passes through a lambda/4 wave plate (lambda/4 WP), and the directions of fast axes of the two wave plates are adjusted, so that the two beams of diffracted light are changed into linearly polarized light with the same polarization direction.
Three plane mirrors M2, M3 and M4 are arranged according to the positions shown in the figure, and the angle of the plane mirror M4 is adjusted, so that the + 1-level light is reflected by the plane mirror M4 and impinges on a beam splitting cube (BS); and simultaneously adjusting the plane mirrors M2 and M3 to ensure that-1-level light is superposed and superposed with + 1-level light on the BS after being reflected twice by the two plane mirrors M2 and M3, and a superposed light signal is captured by a Photoelectric Detector (PD) and displayed and collected by an oscilloscope (oscilloscope).
3. Data processing
By performing fast Fourier transform on the signal, the spectrogram can be found in
The peak value appears and is accompanied with broadening, and the center frequency is extracted to obtain the average speed of movement; and performing short-time Fourier transform on the signal, selecting proper STFT parameters to obtain a signal time-frequency diagram with good time-frequency resolution, and further analyzing to obtain the condition that the polarization grating speed changes along with time.
Respectively setting the average speed of the displacement table as v1＝3.33×10-2m/s and v2＝2.57×10-2m/s, according to the formula (18), the Doppler shifts are theoretically obtained as Δ f19523.8Hz and Δ f27346.93 Hz. When the polarization grating is respectively at different speeds v1And v2In motion, the echo signal is subjected to fast fourier transform, as can be seen from fig. 3(a) and 4(a), the spectrograms of which are at the theoretical value Δ f1And Δ f2Broadening occurs nearby. In order to obtain the change of the movement speed of the polarization grating along with the time, the time-frequency graphs shown in fig. 4(b) and fig. 6(b) can be obtained by using short-time fourier transform.
It can be found that the doppler frequency shift fluctuates around the theoretical value with time, which is a phenomenon that the time-frequency diagram fluctuates due to the vibration phenomenon in the moving process caused by the unstable movement of the displacement table, and the vibration can generate a modulation effect on the echo signal.
In order to analyze the acceleration and deceleration process of the polarization grating on the translation stage, the average speed of the motion of the polarization grating is set as v3＝6×10-2m/s, theoretical value of frequency shift Δ f3From fig. 5(a), it can be seen that the spectrogram spreads around the theoretical value of 17.14 kHz. Firstly, analyzing signals of the polarization grating accelerated to a uniform speed process. The time-frequency diagram of the signal is shown in FIG. 5(b), and after the amplification and acceleration process, the addition thereof can be found according to FIG. 5(c)The speed process is a uniform acceleration motion, acceleration a1＝23.00m/s2。
FIG. 5(d) shows a time-frequency analysis diagram of the signal from constant speed to deceleration, wherein the acceleration at the deceleration stage is a obtained by calculation2＝22.56m/s2。
Claims (3)
1. A method for measuring the moving speed of an object based on the Doppler effect of a polarization grating is characterized in that: the Laser comprises a Laser (Laser), a spatial Filter (Filter), a diaphragm (AP), a convex Lens (Lens1), a polaroid (P), a plane mirror (M1), a Polarization Grating (PG), a lambda/4 wave plate (lambda/4 WP), a plane mirror (M2), a plane mirror (M3), a plane mirror (M4), a Beam Splitter (BS), a Photoelectric Detector (PD) and an oscilloscope (oscilloscope).
2. The method for measuring the moving speed of an object based on the Doppler effect of the polarization grating as claimed in claim 1, wherein: one beam of linearly polarized light is made to pass through a moving polarization grating to produce two beams of circularly polarized light with certain frequency difference, the +1 st order is left circularly polarized light, the-1 st order is right circularly polarized light, the two beams of diffracted light are superposed via lambda/4 wave plate, beam splitter and other optical devices to become beat frequency linearly polarized light, and the base frequency of the laser is set to be f0Doppler shift is Δ f, wave number is k, and distance traveled by +1 st order diffracted light is z1The distance traveled by the-1 st order diffracted light is z2When the electric vector of light is E, time is t, the motion velocity is v, and the grating constant of the polarization grating is d, the signal measured by the oscilloscope can be represented as:
performing fast Fourier transform on the signal, wherein the spectrogram of the signal is
There will be a distinct peak where the average velocity of the object can be obtained by extracting the center frequency.
3. The method for measuring the moving speed of an object based on the Doppler effect of the polarization grating as claimed in claim 1, wherein: the frequency shift is in direct proportion to the speed, so that the value of the frequency shift changes along with the change of the speed of the polarization grating, the frequency shift is expressed as the broadening of a signal in a frequency spectrum, the time-frequency analysis is carried out on the signal by adopting short-time Fourier transform, the change condition of the motion speed of the polarization grating along with the time can be obtained, and the acceleration and vibration information of the polarization grating can be further obtained.
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| CN113030513A (en) * | 2021-05-25 | 2021-06-25 | 欧梯恩智能科技(苏州)有限公司 | Diffraction type silicon light acceleration sensor |
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| CN106597001A (en) * | 2017-01-12 | 2017-04-26 | 北京理工大学 | Rotator angular velocity detection method and apparatus capable of removing the influence of obstacles |
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| US4470696A (en) * | 1981-10-14 | 1984-09-11 | Systems Research Laboratories, Inc. | Laser doppler velocimeter |
| WO1987001496A1 (en) * | 1985-09-09 | 1987-03-12 | Forso^/Gsanla^Eg Riso^/ | Method and apparatus for measuring the rotary movement of objects, especially the rotary velocity of a rotating body and the vorticity in a flowing medium |
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| CN113030513A (en) * | 2021-05-25 | 2021-06-25 | 欧梯恩智能科技(苏州)有限公司 | Diffraction type silicon light acceleration sensor |
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Application publication date: 20210326 |