Method and system for simultaneous measurement of transverse vibration and angular dithering of a Hermite-Gaussian beam

Abstract

The application provides a method and system for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam, comprising: expanding a Gaussian light source, and modulating a phase diagram corresponding to the Hermite-Gaussian beam on a spatial light modulator; passing the Hermite-Gaussian beam through a pre-selection, separating horizontal polarization components and vertical polarization components of the beam, perceiving vibration and jitter of a perception unit, and converting the transverse vibration and jitter, and passing the polarization state of the beam through a post-selection; and making the beam incident on the spatial light modulator, modulating a phase diagram corresponding to a projection measurement base for transverse vibration signals and angular jitter signals, converting the projection measurement transverse vibration and angular jitter signals into light intensity information, measuring the light intensity and converting it into a voltage signal, and inputting the voltage signal into a spectrum analyzer to demodulate amplitudes and frequencies of the transverse vibration signals and the angular jitter signals.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of vibration measurement, in particular to a method and system for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam. BACKGROUND

[0002] In the field of vibration measurement, the transverse vibration or angular jitter of a sensing element can generally be measured by laser interference or light position sensing, but it is very difficult to simultaneously measure the transverse vibration and angular jitter of a mechanical part in practical engineering applications, for example:

[0003] 1. In the field of laser measurement, the transverse vibration of a mechanical part will cause a displacement signal of the transverse spatial position of a light beam, and the angular jitter of the mechanical part will cause a shift signal of the transverse momentum space of the light beam, and a traditional Gaussian profile laser beam cannot distinguish between the two types of signals.

[0004] 2. The measurement method based on laser interference converts both vibration and jitter signals into phase or frequency shift signals of the laser, and cannot distinguish between the two types of signals to be measured.

[0005] 3. The measurement method based on light position sensing cannot distinguish between the two types of signals, transverse vibration and angular jitter, and the detection bandwidth is limited.

[0006] Patent document CN105203200A discloses a steel wire rope transverse vibration signal measurement device, method and transverse vibration monitoring method, and specifically discloses that the sensing light curtains emitted by two groups of light curtain type laser displacement sensors are perpendicular to each other, and the planes of the two groups of light curtains are parallel and are arranged in an upper and lower interval. The steel wire simultaneously and vertically passes through the two groups of light curtains to obtain displacement signals in the x and y directions when the steel wire rope vibrates transversely. The measurement device includes two groups of light curtain type laser displacement sensors and a bracket, the sensing light curtains emitted by the two groups of sensors are perpendicular to each other, and the planes of the two groups of light curtains are parallel and are arranged in an upper and lower interval. The monitoring method is to measure the vibration displacement signal by using the steel wire rope transverse vibration displacement signal measurement method, process the vibration displacement signal to obtain the vibration amplitude and vibration frequency, compare with the preset value to determine the crisis prevention. However, the present application only solves the accurate measurement of transverse vibration, and cannot simultaneously realize the accurate measurement of the two types of signals, transverse vibration and angular jitter. SUMMARY

[0007] In view of the defects in the prior art, the purpose of the present application is to provide a method and system for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam.

[0008] According to the method for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam provided by the present application, the method comprises the following steps:

[0009] Step S1: expanding a Gaussian light source, modulating a phase pattern corresponding to an Hermite-Gaussian light beam on a spatial light modulator, and filtering the outgoing light;

[0010] Step S2: passing the Hermite-Gaussian light beam through pre-selection, separating the horizontal polarization component and the vertical polarization component of the light beam, perceiving the vibration and the jitter of the perception unit, converting the lateral vibration and the jitter, and post-selecting the polarization state of the light beam;

[0011] Step S3: inputting the light beam after the vibration and the jitter perception to the spatial light modulator, modulating a phase pattern corresponding to the projection measurement base of the lateral vibration signal and the angular jitter signal, and receiving the outgoing light at the rear focal point of the lens using a fiber tail fiber;

[0012] Step S4: converting the projection measurement lateral vibration and the angular jitter signal into light intensity information, measuring the light intensity and converting it into a voltage signal, inputting it into a spectrum analyzer, and demodulating the amplitude and the frequency of the lateral vibration signal and the angular jitter signal.

[0013] Preferably, in the step S1:

[0014] After expanding the Gaussian light source, the light beam is incident to the spatial light modulator A and modulates a phase pattern corresponding to an n-order Hermite-Gaussian light beam on the spatial light modulator A, and a high-purity n-order Hermite-Gaussian light source is generated after the outgoing light passes through a 4-f filtering system;

[0015] The phase pattern corresponding to the n-order Hermite-Gaussian light beam is obtained by numerical calculation, specifically:

[0016] The light beam distribution input to the spatial light modulator A is denoted as wherein is the light beam amplitude intensity distribution input to the spatial light modulator A, is the spatial phase distribution of the input light beam; the phase pattern loaded on the spatial light modulator A is denoted as H A (x, y); the light beam distribution output by the spatial light modulator A is wherein ψ n (x, y) is the light field distribution of the n-order lateral Hermite-Gaussian light beam, is the light beam amplitude intensity distribution output by the spatial light modulator A, is the spatial phase distribution of the light beam output by the spatial light modulator A;

[0017] The relative phase is wherein is the phase of the blazed grating loaded on the spatial light modulator A;

[0018] The relative amplitude is

[0019] The phase pattern corresponding to the n-order Hermite-Gaussian beam loaded on the spatial light modulator A is as follows:

[0020]

[0021] wherein is the inverse function of the first-order Bessel function.

[0022] Preferably, the 4-f filtering system, in particular,

[0023] A Fourier lens with a focal length of f1 is placed behind the spatial light modulator A, and a pinhole is placed behind the Fourier lens at f1. The light beam modulated by the spatial light modulator A is focused at the pinhole after passing through the Fourier lens. Since the phase pattern is additionally provided with a blazed grating, the focal points on the image plane are periodically arranged in the horizontal direction. The first-order diffraction light spot is filtered out by the pinhole, and another lens with a focal length of f2 is placed behind at f2 to output the n-order Hermite-Gaussian beam with high purity. The spatial distribution state of the Hermite-Gaussian beam is denoted as |n>, and the symbol |·> represents the Dirac right vector, and |n> = ∫∫dxdyψ n (x, y) |x, y>.

[0024] Preferably, in the step S2,

[0025] The polarization state of the Hermite-Gaussian beam is selected as 45-degree linearly polarized light by pre-selection. In the vibration and jitter sensing module, the horizontal polarization component H light and the vertical polarization component V light of the light beam are separated by an interferometer. The vibration and jitter of the sensing element are sensed on the light path of the horizontal polarization component, and the transverse vibration is converted into the transverse spatial displacement of the light beam, and the jitter is converted into the transverse momentum shift of the light beam. The polarization state of the light beam is post-selected, so that the transverse vibration signal and the angular jitter signal are completely modulated on the spatial mode of the Hermite-Gaussian beam.

[0026] The polarization state of the light beam is selected as 45-degree linearly polarized light by pre-selection, in particular,

[0027] The Hermite-Gaussian beam generated by the spatial light modulator A and the 4-f filtering system is incident to a G-L prismatic polarizer with an optical axis along the horizontal direction. After passing through a half-wave plate with an optical axis at an angle of 22.5° with the horizontal plane, the polarization state of the output light beam is pre-selected as:

[0028]

[0029] wherein i represents the pre-selected state, H represents the horizontal polarization light, and V represents the vertical polarization light.

[0030] The transverse vibration is converted into the transverse spatial displacement of the light beam, and the jitter is converted into the transverse momentum shift of the light beam, in particular.

[0031] In the vibration and dithering sensing module, the horizontal polarization component H light and the vertical polarization component V light of the light beam are separated by a Mach-Zehnder interferometer with a polarization beam splitter, the vibration and dithering of the sensing element are sensed in the light path of the horizontal polarization component, the transverse vibration amplitude of the sensing element is d, and the angular dithering amplitude is The transverse spatial displacement of the light beam caused by the transverse vibration is d, and the transverse momentum offset of the light beam caused by the angular dithering is Where k = 2π / λ is the wave number of the light beam, λ is the central wavelength of the light source, and the sensing process is represented as:

[0032]

[0033] Where is the Pauli operator acting on the polarization state, is the momentum operator acting on the light beam, representing the transverse position translation, is the position operator acting on the light beam, representing the transverse momentum offset, is the unit matrix; the input state of the interferometer is denoted as: |Ψ in > = |i>|ψ i >, where |ψ i > = |n> represents the initial spatial mode of the light beam; the output state of the interferometer is denoted as:

[0034]

[0035] Preferably, the post-selection, in particular:

[0036] The light beam exiting the interferometer passes through a quarter-wave plate with an optical axis at about 45° to the horizontal direction, compensating for the constant phase difference between the two polarization components in the interferometer, and then passes through a half-wave plate with an optical axis at about angle to the horizontal direction, and then passes through a Glan-Taylor polarizing prism with an optical axis along the horizontal direction, and the polarization state of the output light beam is post-selected as:

[0037]

[0038] Where ε is the post-selection angle;

[0039] The transverse vibration signal d and the angular dithering signal are completely modulated on the spatial mode of the Hermite-Gaussian light beam, in particular:

[0040] The light beam after post-selection can be denoted by the state vector as:

[0041]

[0042] Where

[0043]

[0044] A w is a weak value, where d « 1, The spatial mode of the light beam after the post-selection is denoted as:

[0045]

[0046] where, is the spatial distribution variance of the fundamental Gaussian beam, i.e. 2σ0 = w0 is the beam waist radius of the fundamental Gaussian beam, and the spatial mode is:

[0047]

[0048]

[0049] and respectively carry the transverse vibration signal d and the angular jitter signal

[0050] Preferably, in the step S3:

[0051] The light beam after the vibration and jitter sensing process is incident on a second spatial light modulator B, and a phase diagram corresponding to the projection measurement bases designed in the application for the transverse vibration signal and the angular jitter signal is modulated thereon. After the exit light passes through a Fourier lens, it is received at the focal point behind the lens using a fiber tail fiber, realizing the reception of the projection measurement light intensity.

[0052] The projection measurement bases for the transverse vibration signal and the angular jitter signal are specifically:

[0053] In order to be able to directly demodulate the transverse vibration signal and the angular jitter signal, the following two non-orthogonal projection bases are designed:

[0054]

[0055]

[0056] so that and are respectively orthogonal to and When the light beam is projected and measured using the projection bases , the light intensity projection probability obtained by the measurement end is:

[0057]

[0058] The projection probability of the light intensity obtained by the measurement end can be calculated by: The transverse vibration signal can be directly demodulated from the projection light intensity on the projection base. When the projection measurement is performed on the light beam, the projection probability of the light intensity obtained by the measurement end is:

[0059]

[0060] The angular vibration signal can be directly demodulated from the projection light intensity on the projection base.

[0061] Preferably, the phase diagram corresponding to the projection measurement base is specifically:

[0062] When the phase diagram corresponding to the projection measurement base is calculated, let wherein is the two-dimensional spatial wave function distribution corresponding to the projection measurement base, and the amplitude intensity and the spatial phase are and The input light beam is parallel light, Let the relative phase be wherein

[0063] is the phase of the blazed grating loaded on the second spatial light modulator B; Let the relative amplitude be

[0064] The phase diagram corresponding to the projection measurement base is:

[0065] The phase diagram corresponding to the projection measurement base is:

[0066]

[0067] The phase diagram corresponding to the projection measurement base is: The projection measurement of the transverse vibration signal d is realized; the phase diagram corresponding to the projection measurement base is: let The phase diagram corresponding to the projection measurement base is: The projection measurement of the angular vibration signal is realized.

[0068] Preferably, the receiving of the projection measurement light intensity is realized by using the fiber tail fiber, and specifically:

[0069] A Fourier lens is used behind the spatial light modulator B to perform Fourier transform on the projection light field, and the distribution of the projection measurement light field to be modulated on the spatial light modulator is denoted as ψ M (x, y), the light field input into the second spatial light modulator B is ψ f (x, y), and the final state |ψ​​​f The corresponding two-dimensional light field distribution is transformed into a transformed light field at the back focal length of the Fourier lens, and then directly received at the center of the transformed light field by a single-mode optical fiber, and the receiving efficiency of the single-mode optical fiber is represented as

[0070]

[0071] where |<ψ M |ψ f | 2 is the projection probability of the final state of the light beam on the projection measurement basis |ψ M |

[0072] When the projection measurement is performed using the projection measurement basis |ψ , the projection measurement light intensity received by the single-mode optical fiber is:

[0073]

[0074] The transverse vibration signal d is directly demodulated from the projection light intensity; when the projection measurement is performed using the projection measurement basis |ψ , the projection measurement light intensity received by the single-mode optical fiber is:

[0075]

[0076] The angular jitter signal is directly demodulated from the projection light intensity. The projection measurement light intensity corresponding to the transverse vibration and angular jitter signals is amplified by a factor related to the Hermite-Gaussian spatial mode number n.

[0077] Preferably, in the step S4:

[0078] The projection measurement transverse vibration and angular jitter signals are converted into light intensity information, the light intensity is measured by an avalanche photodiode detector, and is converted into a voltage signal, which is input into a spectrum analyzer to demodulate the amplitudes and frequencies of the transverse vibration and angular jitter signals.

[0079] Step S4.1: The projection measurement light intensity received by the single-mode optical fiber is input into an avalanche photodiode detector for measurement, and is converted into a voltage signal.

[0080] After the projection measurement light intensity received by the single-mode optical fiber is input into the avalanche photodiode detector, it is converted into a photoelectric current signal through avalanche amplification, and the photoelectric current signal is converted into a voltage signal through amplification by a transimpedance amplifier built-in the avalanche photodiode detector, and the size of the voltage signal is proportional to the received light intensity, V det ∝I det .

[0081] ​Step S4.2: input the voltage signal of the avalanche photodiode detector into the spectrum analyzer to demodulate the amplitudes and frequencies of the transverse vibration signal and the angular jitter signal.

[0082] According to the application, a transverse vibration and angular jitter simultaneous measurement system of a Hermite-Gaussian beam is provided, and the transverse vibration and angular jitter simultaneous measurement method of the Hermite-Gaussian beam is executed, and the system comprises:

[0083] Module M1: expand the Gaussian light source, modulate the corresponding phase diagram of the Hermite-Gaussian beam on the spatial light modulator, and let the outgoing light pass through the filtering system;

[0084] Module M2: pass the Hermite-Gaussian beam through pre-selection, separate the horizontal polarization component and the vertical polarization component of the light beam, perceive the vibration and jitter of the perception unit, convert the transverse vibration and jitter, and perform post-selection on the polarization state of the light beam;

[0085] Module M3: after the vibration and jitter perception, the light beam is incident to the spatial light modulator, the phase diagram corresponding to the projection measurement base of the transverse vibration signal and the angular jitter signal is modulated, and the outgoing light is received by the fiber tail at the rear focal point of the lens;

[0086] Module M4: convert the projection measurement transverse vibration and angular jitter signal into light intensity information, measure the light intensity and convert it into a voltage signal, input it into the spectrum analyzer, and demodulate the amplitudes and frequencies of the transverse vibration signal and the angular jitter signal.

[0087] Compared with the prior art, the application has the following beneficial effects:

[0088] 1. Compared with the existing transverse vibration or angular jitter measurement scheme, the application can simultaneously realize accurate measurement of both transverse vibration and angular jitter signals in one system;

[0089] 2. The application is based on laser sensing technology and can perform non-contact measurement;

[0090] 3. The application uses a Hermite-Gaussian light source to improve the measurement accuracy of transverse vibration and angular jitter with the mode number of the Hermite-Gaussian beam;

[0091] 4. The application combines the weak value amplification technology to effectively resist the detection power saturation of the avalanche photodiode detector;

[0092] 5. The transverse vibration and angular jitter signals are demodulated by the projection measurement light intensity detected by the avalanche photodiode, and a larger detection bandwidth can be achieved;

[0093] 6. The measurement end of the application only needs a spatial light modulator to realize projection measurement, and the implementation is convenient. BRIEF DESCRIPTION OF DRAWINGS

[0094] Other features, objects, and advantages of the application will become more apparent from the following detailed description of non-limiting embodiments thereof, when read in conjunction with the accompanying drawings:

[0095] Figure 1 Structure diagram for the new method of simultaneous measurement of transverse vibration and angular jitter based on Hermite-Gaussian beams in the application;

[0096] Figure 2 Structure diagram for the new method of simultaneous measurement of transverse vibration and angular jitter based on Hermite-Gaussian beams in the application;

[0097] Figure 3 Structure diagram for the new method of simultaneous measurement of transverse vibration and angular jitter based on Hermite-Gaussian beams in the application; Spectrum measurement results at the corresponding phase diagram;

[0098] Figure 4 Structure diagram for the new method of simultaneous measurement of transverse vibration and angular jitter based on Hermite-Gaussian beams in the application; Spectrum measurement results at the corresponding phase diagram.

[0099] Figure 2 In the application:

[0100] 1 is a single-frequency laser light source;

[0101] 2 is a beam expander;

[0102] 3 is a spatial light modulator;

[0103] 4 is a lens;

[0104] 5 is a pinhole;

[0105] 6 is a mirror;

[0106] 7 is a G-L polarization prism;

[0107] 8 is a half-wave plate;

[0108] 9 is a polarization beam splitter;

[0109] 10 is a mirror driven by a single PZT;

[0110] 11 is a mirror driven by two PZTs;

[0111] 12 is a polarizer;

[0112] 13 is a beam splitter;

[0113] 14 is a quarter-wave plate;

[0114] 15 is a single-mode optical fiber;

[0115] 16 is an avalanche photodiode detector;

[0116] 17 is a spectrum analyzer. DETAILED DESCRIPTION

[0117] The application will be described in detail below with specific examples. The following examples will help those skilled in the art to further understand the application, but do not limit the application in any form. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the application. These are within the scope of protection of the application.

[0118] Example 1

[0119] The application relates to simultaneous measurement of micro lateral vibration and angular jitter, and particularly relates to a micro lateral vibration and angular jitter simultaneous measurement process based on a Hermite-Gaussian light beam.

[0120] The application provides a new method for simultaneously measuring lateral vibration and angular jitter based on a Hermite-Gaussian light beam, which comprises a Hermite-Gaussian light source generation module, a vibration and jitter sensing module, a projection measurement module, an electrical module and a data processing module. The Hermite-Gaussian light source generation module is used to generate a high-order Hermite-Gaussian light source. The vibration and jitter sensing module is used to detect and sense the lateral vibration and angular jitter of a sensing element, and convert the lateral vibration and angular jitter into a lateral spatial displacement signal and a lateral momentum offset signal of the light beam. In the module, a weak value amplification technology is further introduced through post-selection to further amplify the weak vibration and jitter signals and improve the noise resistance of the system. The projection measurement module is used to demodulate the weak vibration and jitter signals into light intensity signals. The electrical module is used to convert the light signals into electrical signals to obtain measurement data and storage. The data processing module is used to analyze and process the measured data to calculate the vibration and jitter signal intensity and frequency of the sensing element. The application can realize the precise simultaneous measurement of lateral vibration and angular jitter by using the Hermite-Gaussian light beam and the weak value amplification technology, and the implementation scheme is simple and stable. Therefore, the method can effectively solve the simultaneous measurement and sensing problems of various types of parameters in optics and acoustics, and provides a practical new method for mechanical vibration detection, optical calibration and other related applications.

[0121] According to the application, a method for simultaneously measuring lateral vibration and angular jitter of a Hermite-Gaussian light beam is provided, as shown in Figures 1-4 , which comprises the following steps.

[0122] Step S1: expanding a Gaussian light source, modulating a phase diagram corresponding to a Hermite-Gaussian light beam on a spatial light modulator, and making the outgoing light pass through a filtering system.

[0123] Specifically, in the step S1, the phase diagram corresponding to the Hermite-Gaussian light beam is modulated on the spatial light modulator.

[0124] The Gaussian light source is expanded, and then is incident to the spatial light modulator A and modulates the phase pattern corresponding to the n-order Hermite-Gaussian light beam on the spatial light modulator A, and the outcoming light generates the n-order Hermite-Gaussian light source with high purity after passing through the 4-f filtering system;

[0125] The phase pattern corresponding to the n-order Hermite-Gaussian light beam is obtained by numerical calculation, and specifically is:

[0126] The light beam distribution input to the spatial light modulator A is denoted as Wherein is the light beam amplitude intensity distribution input to the spatial light modulator A, is the spatial phase distribution of the input light beam; the phase pattern loaded on the spatial light modulator A is denoted as H A (x, y); the light beam distribution output by the spatial light modulator A is Wherein ψn ( (x, y) is the light field distribution of the n-order transverse Hermite-Gaussian light beam, is the light beam amplitude intensity distribution output by the spatial light modulator A, is the spatial phase distribution of the light beam output by the spatial light modulator A;

[0127] The relative phase is Wherein is the phase of the blazed grating loaded on the spatial light modulator A;

[0128] The relative amplitude is

[0129] The phase pattern corresponding to the n-order Hermite-Gaussian light beam loaded on the spatial light modulator A is as follows:

[0130]

[0131] Wherein is the inverse function of the first Bessel function.

[0132] Specifically, the 4-f filtering system is specifically:

[0133] A Fourier lens with a focal length of f1 is placed at f1 behind the spatial light modulator A, and a small hole is placed at f1 behind the Fourier lens. The light beam modulated by the spatial light modulator A is focused at the small hole after passing through the Fourier lens. Since the phase pattern is additionally provided with a blazed grating, the focusing points on the image plane are periodically arranged in the horizontal direction. The first-order diffraction light spot is filtered out by using the small hole, and another lens with a focal length of f2 is placed at f2 behind the lens. The n-order Hermite-Gaussian light beam with high purity is output; the spatial distribution state of the Hermite-Gaussian light beam is denoted as |n>, the symbol |·> represents the Dirac right vector, and |n> = ∫∫dxdyψ n (x, y)|x, y>.

[0134] Step S2: passing the Hermite-Gaussian beam through a pre-selection, separating the horizontal polarization component and the vertical polarization component of the beam, perceiving the vibration and the wobble of the perception element, converting the lateral vibration and the wobble, and post-selecting the polarization state of the beam;

[0135] Specifically, in the step S2:

[0136] passing the Hermite-Gaussian beam through the pre-selection to select the polarization state of the beam as 45-degree linearly polarized light, in the vibration and wobble perception module, using an interferometer to separate the horizontal polarization component H light and the vertical polarization component V light of the beam, perceiving the vibration and the wobble of the perception element on the light path of the horizontal polarization component, and converting the lateral vibration into the lateral spatial displacement of the beam, and converting the wobble into the lateral momentum offset of the beam, and post-selecting the polarization state of the beam so that the lateral vibration signal and the angular wobble signal are completely modulated on the spatial mode of the Hermite-Gaussian beam;

[0137] the pre-selection of the beam selects the polarization state of the beam as 45-degree linearly polarized light, specifically:

[0138] the Hermite-Gaussian beam generated by the spatial light modulator A and the 4-f filtering system is incident to a G-L polarization prism with an optical axis along the horizontal direction, and the polarization state of the output beam is pre-selected as:

[0139]

[0140] wherein i represents the pre-selection state, H represents the horizontal polarization light, and V represents the vertical polarization light;

[0141] the conversion of the lateral vibration into the lateral spatial displacement of the beam and the conversion of the wobble into the lateral momentum offset of the beam are specifically:

[0142] in the vibration and wobble perception module, using a Mach-Zehnder interferometer with a polarization beam splitter to separate the horizontal polarization component H light and the vertical polarization component V light of the beam, perceiving the vibration and the wobble of the perception element on the light path of the horizontal polarization component, the lateral vibration amplitude of the perception element is d, and the angular wobble amplitude is the lateral spatial displacement of the beam caused by the lateral vibration is d, and the lateral momentum offset of the beam caused by the angular wobble is wherein k=2π / λ is the wave number of the beam, λ is the central wavelength of the light source, and the perception process is represented as:

[0143]

[0144] wherein is the Pauli operator acting on the polarization state, is the momentum operator acting on the beam, representing a transverse position translation, is the position operator acting on the beam, representing a transverse momentum shift, is the unit matrix; the input state of the interferometer is denoted as: in > = |i> |ψ i >, where |ψ i > = |n> represents the initial spatial mode of the beam; the output state of the interferometer is denoted as:

[0145]

[0146] Specifically, the post-selection, in particular:

[0147] The beam exiting the interferometer passes through a quarter wave plate with its optical axis at about 45° to the horizontal, compensating for the constant phase difference between the two polarization components in the interferometer, and then through a half wave plate with its optical axis at about angle to the horizontal, and then through a Glan-Taylor polarizer with its optical axis along the horizontal, the polarization state of the output beam is post-selected to be:

[0148]

[0149] where ε is the post-selection angle;

[0150] The transverse vibration signal d and the angular jitter signal are completely modulated on the spatial mode of the Hermite-Gaussian beam, in particular:

[0151] The beam after post-selection can be denoted by the state vector:

[0152]

[0153] where

[0154]

[0155] A w is a weak value, where d « 1, The spatial mode of the beam after post-selection is denoted as:

[0156]

[0157] where, is the spatial distribution variance of the fundamental mode Gaussian beam, i.e. 2σ0 = w0 is the waist radius of the fundamental mode Gaussian beam, and the spatial mode state:

[0158]

[0159]

[0160] and carries transverse vibration signal d and angular jitter signal

[0161] Step S3: the light beam after vibration and jitter sensing is incident to a spatial light modulator, and the phase diagram corresponding to the projection measurement base for the transverse vibration signal and the angular jitter signal is modulated, and the exit light is received by a fiber tail at the rear focal point of the lens;

[0162] Specifically, in the step S3:

[0163] The light beam after the vibration and jitter sensing process is incident to a second spatial light modulator B, and the phase diagram corresponding to the projection measurement base for the transverse vibration signal and the angular jitter signal designed in the application is modulated thereon, and the exit light is received by a fiber tail at the rear focal point of a Fourier lens, realizing the receiving of the projection measurement light intensity;

[0164] The projection measurement base for the transverse vibration signal and the angular jitter signal, specifically:

[0165] In order to be able to directly demodulate the transverse vibration signal and the angular jitter signal, the following two non-orthogonal projection bases are designed:

[0166]

[0167]

[0168] make and orthogonal to and When the light beam is projected and measured using the projection base , the light intensity projection probability obtained by the measurement end is:

[0169]

[0170] The transverse vibration signal can be directly demodulated by the projection light intensity on the projection base , and when the light beam is projected and measured using the projection base , the light intensity projection probability obtained by the measurement end is:

[0171]

[0172] The angular jitter signal can be directly demodulated by the projection light intensity on the projection base .

[0173] Specifically, the phase diagram corresponding to the projection measurement base, specifically:

[0174] When calculating the projection measurement basis The corresponding phase map is Where The projection measurement basis The corresponding two-dimensional spatial wave function distribution, whose amplitude intensity and spatial phase are And The input light beam is parallel light,

[0175] Let the relative phase be Where is the phase of the blazed grating loaded on the second spatial light modulator B;

[0176] Let the relative amplitude be

[0177] The projection measurement basis The corresponding phase map is

[0178]

[0179] Load the projection measurement basis The corresponding phase map on the second spatial light modulator B, realize the projection measurement of the transverse vibration signal d; the projection measurement basis The corresponding phase map, let Load the projection measurement basis The corresponding phase map on the spatial light modulator B, which can realize the projection measurement of the angular jitter signal .

[0180] Specifically, the use of a fiber tail fiber to receive, realize the reception of the projection measurement light intensity, specifically:

[0181] A Fourier lens is used behind the spatial light modulator B to perform Fourier transform on the projection light field, and the projection measurement light field distribution that the spatial light modulator hopes to modulate is denoted as ψ M (x, y), the light field input into the second spatial light modulator B is ψ f (x, y), the corresponding two-dimensional light field distribution of the beam final state |ψ f > after the perception process, the transformed light field is obtained at the back focal length of the Fourier lens, and then a single-mode optical fiber is used to directly receive at the center of the transformed light field, and the receiving efficiency of the single-mode optical fiber is represented as

[0182]

[0183] Where |<ψ M |ψ f >| 2 is the projection probability of the beam final state on the projection measurement basis |ψ M >.

[0184] When using the projection measurement basis The projection measurement light intensity received by the single-mode optical fiber when performing the projection measurement:

[0185]

[0186] The transverse vibration signal d is directly demodulated from the projection light intensity; When using the projection measurement basis The projection measurement light intensity received by the single-mode optical fiber when performing the projection measurement:

[0187]

[0188] The angular jitter signal is directly demodulated from the projection light intensity The projection measurement light intensity corresponding to the transverse vibration and angular jitter signals is amplified by a factor related to the Hermite-Gaussian spatial mode number n .

[0189] Step S4: converting the projection measurement transverse vibration and angular jitter signals into light intensity information, measuring the light intensity and converting it into a voltage signal, inputting it into a spectrum analyzer, and demodulating the amplitudes and frequencies of the transverse vibration and angular jitter signals.

[0190] Specifically, in the step S4:

[0191] The projection measurement transverse vibration and angular jitter signals are converted into light intensity information, the light intensity is measured using an avalanche photodiode detector, and is converted into a voltage signal, which is input into a spectrum analyzer to demodulate the amplitudes and frequencies of the transverse vibration and angular jitter signals.

[0192] Step S4.1: inputting the projection measurement light intensity received by the single-mode optical fiber into an avalanche photodiode detector for measurement, and converting it into a voltage signal;

[0193] After the projection measurement light intensity received by the single-mode optical fiber is input into the avalanche photodiode detector, it is converted into a photoelectric current signal through avalanche amplification, and the photoelectric current signal is converted into a voltage signal through amplification by a transimpedance amplifier built into the avalanche photodiode detector, the size of which is proportional to the received light intensity, V det ∝I det .

[0194] Step S4.2: inputting the voltage signal of the avalanche photodiode detector into a spectrum analyzer to demodulate the amplitudes and frequencies of the transverse vibration and angular jitter signals.

[0195] Embodiment 2:

[0196] Embodiment 2 is a preferred example of Embodiment 1, which more specifically illustrates the present application.

[0197] The application also provides a system for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam, which can be implemented by performing the flow steps of the method for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam, that is, the method for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam can be understood as a preferred embodiment of the system for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam by those skilled in the art.

[0198] According to the application, a system for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam is provided, and the method for simultaneously measuring transverse vibration and angular jitter of a Hermite-Gaussian beam is performed, comprising:

[0199] Module M1: expanding a Gaussian light source, modulating a corresponding phase diagram of a Hermite-Gaussian beam on a spatial light modulator, and filtering the outgoing light;

[0200] Module M2: passing the Hermite-Gaussian beam through pre-selection, separating the horizontal polarization component and the vertical polarization component of the light beam, perceiving the vibration and jitter of the perception unit, converting the transverse vibration and jitter, and post-selecting the polarization state of the light beam;

[0201] Module M3: inputting the light beam after vibration and jitter perception to a spatial light modulator, modulating a corresponding phase diagram of a projection measurement base for a transverse vibration signal and an angular jitter signal, and receiving the outgoing light at a rear focal point of a lens using a fiber tail fiber;

[0202] Module M4: converting the projection measurement transverse vibration and angular jitter signal into light intensity information, measuring the light intensity and converting it into a voltage signal, inputting the voltage signal into a spectrum analyzer, and demodulating the amplitude and frequency of the transverse vibration signal and the angular jitter signal.

[0203] Embodiment 3:

[0204] Embodiment 3 is a preferred example of Embodiment 1, which more specifically illustrates the application.

[0205] In view of the defects in the prior art, the application aims to provide a new method for simultaneously measuring weak transverse vibration and angular jitter based on a Hermite-Gaussian beam, which is suitable for systems that require to identify the transverse vibration and angular jitter of a perception unit and have high requirements on measurement accuracy.

[0206] According to the application, a new method for simultaneously measuring transverse vibration and angular jitter based on a Hermite-Gaussian beam is provided, comprising:

[0207] Step 1: After expanding, the Gaussian light source is incident to a spatial light modulator and modulates the phase pattern corresponding to the n-order Laguerre-Gaussian beam on the spatial light modulator, and the output light generates a high-purity n-order Laguerre-Gaussian light source after passing through a 4-f filtering system;

[0208] Step 2: The Laguerre-Gaussian beam is selected by the front selection to be a 45-degree linearly polarized light, and in the vibration and jitter sensing module, the horizontal polarization component (H light) and the vertical polarization component (V light) of the light beam are separated by an interferometer, the vibration and jitter of the sensing unit are sensed on the light path of the horizontal polarization component, the transverse vibration is converted into the transverse spatial displacement of the light beam, and the jitter is converted into the transverse momentum offset of the light beam, and then the polarization state of the light beam is selected by the rear selection, so that the transverse vibration signal and the angular jitter signal are completely modulated on the spatial mode of the Laguerre-Gaussian beam;

[0209] Step 3: The light beam after the vibration and jitter sensing process is incident to a second spatial light modulator, and the phase pattern corresponding to the projection measurement base for the transverse vibration signal and the angular jitter signal designed in the application is modulated on the spatial light modulator, and the output light is received by a fiber tail fiber at the rear focal point of a Fourier lens after passing through the Fourier lens, so as to realize the reception of the projection measurement light intensity;

[0210] Step 4: The projection measurement transverse vibration and angular jitter signal is converted into light intensity information, the light intensity is measured by using an avalanche photodiode detector and converted into a voltage signal, which is input into a spectrum analyzer to demodulate the amplitude and frequency of the transverse vibration signal and the angular jitter signal.

[0211] Preferably, the phase pattern corresponding to the n-order Laguerre-Gaussian beam in step 1 is obtained by numerical calculation, specifically:

[0212] The light beam distribution input into the spatial light modulator A is denoted as wherein is the amplitude intensity distribution of the light beam input into the spatial light modulator A, is the spatial phase distribution of the input light beam, and i is the imaginary symbol. The phase pattern loaded on the spatial light modulator A is denoted as H A (x, y). The output light beam distribution of the spatial light modulator A is wherein ψ n (x, y) is the light field distribution of the n-order transverse Laguerre-Gaussian beam that we want to obtain, and the amplitude intensity and the spatial phase are denoted as and

[0213] The relative phase is denoted as wherein is the blazed grating phase loaded on the spatial light modulator A.

[0214] The relative amplitude is denoted as

[0215] The phase pattern corresponding to the n-order Hermite-Gaussian beam loaded on the spatial light modulator A is given by the formula

[0216]

[0217] wherein is the inverse function of the first-order Bessel function.

[0218] Preferably, the 4-f filtering system in step 1 is specifically:

[0219] A Fourier lens with a focal length of f1 is placed behind the spatial light modulator A, and a pinhole is placed behind the Fourier lens at f1. The light beam modulated by the spatial light modulator is focused at the pinhole after passing through the Fourier lens. Due to the addition of the blazed grating on the phase pattern, the focal points on the image plane will be periodically arranged in the horizontal direction. The first-order diffraction light spot is filtered out by the pinhole, and another lens with a focal length of f2 is placed behind at f2 to output the n-order Hermite-Gaussian beam with high purity. The spatial distribution state of the Hermite-Gaussian beam can be denoted as |n>, and the symbol |·> represents the Dirac right vector, and

[0220] |n>=∫∫dxdyψ n (x, y) |x, y>

[0221] Preferably, the polarization state of the light beam is selected to be 45-degree linearly polarized light by the front selection in step 2, which is specifically:

[0222] The Hermite-Gaussian beam generated by the spatial light modulator and the 4-f filtering system is incident to a G-L prisms with the optical axis along the horizontal direction, and the polarization state of the output light beam is front-selected to be:

[0223]

[0224] wherein i represents the front-selected state, H represents horizontal polarization light, and V represents vertical polarization light.

[0225] Preferably, the transverse vibration is converted into the transverse spatial displacement of the light beam, and the dithering is converted into the transverse momentum shift of the light beam in step 2, which is specifically:

[0226] In the vibration and dithering sensing module, the horizontal polarization component (H light) and the vertical polarization component (V light) of the light beam are separated by using a Mach-Zehnder interferometer with a polarization beam splitter. The vibration and dithering of the sensing element are sensed on the light path of the horizontal polarization component. The transverse vibration amplitude of the sensing element is d, and the angular dithering amplitude is The lateral spatial displacement of the beam caused by lateral vibration is d, and the lateral momentum shift of the beam caused by angular jitter is... Where k = 2π / λ is the wavenumber of the beam, and λ is the center wavelength of the light source, this sensing process can be represented by the evolution operator as follows:

[0227]

[0228] in For Pauli operators acting on polarization states, Let be the momentum operator acting on the beam, representing the lateral position translation. Here, represents the position operator acting on the beam, indicating the lateral momentum shift. Let |Ψ| be the identity matrix. The input state of the interferometer can be denoted as: |Ψ| in > = |i> |ψ i >, where |ψ i > = |n> represents the initial spatial mode of the beam. Therefore, the output state of the interferometer can be denoted as:

[0229]

[0230] Preferably, the subsequent selection in step 2 specifically refers to:

[0231] The beam emitted from the interferometer is passed through a quarter-wave plate whose optical axis is at approximately 45° to the horizontal to compensate for the constant phase difference between the two polarization components in the interferometer. It then passes through another plate whose optical axis is at approximately 45° to the horizontal. A half-wave plate with an angle of 1 / 2 is passed through a Glan Taylor polarizing prism with its optical axis in the horizontal direction, and the polarization state of the output beam is subsequently selected as follows:

[0232]

[0233] Where ε is the post-selection angle, 0.05 < ε < 1.

[0234] Preferably, the lateral vibration signal d and the angular jitter signal mentioned in step 2 are... It is completely modulated onto the spatial mode of the Hermitian beam, specifically:

[0235] The available state vector of the beam after selection is denoted as:

[0236]

[0237] in

[0238]

[0239] As a weak value, we consider both lateral vibration and angular jitter to be weak signals, i.e., d << 1. Thus, the spatial mode of the light beam after the post-selection can be recorded as:

[0240]

[0241] where is the spatial distribution variance of the fundamental Gaussian light beam, i.e. 2σ0=w0 is the waist radius of the fundamental Gaussian light beam, and the spatial mode state:

[0242]

[0243]

[0244] respectively carry the transverse vibration signal d and the angular jitter signal However, and are not orthogonal, which means that directly using the state and to project the light beam after the sensing process, the projection intensity on and cannot directly demodulate the transverse vibration signal d and the angular jitter signal

[0245] Preferably, the projection measurement bases for the transverse vibration signal and the angular jitter signal in step 2 are specifically:

[0246] In order to be able to directly demodulate the transverse vibration signal and the angular jitter signal, in the present application, the following two non-orthogonal projection bases are designed:

[0247]

[0248]

[0249] so that they are respectively orthogonal to and When the projection base is used to project the light beam for measurement, the projection probability of the light intensity obtained at the measurement end is:

[0250]

[0251] only related to the transverse vibration signal d, i.e. the transverse vibration signal can be directly demodulated by the projection intensity on the projection base When the projection base is used to project the light beam for measurement, the projection probability of the light intensity obtained at the measurement end is:

[0252]

[0253] only related to the angular jitter signal The angular vibration signal can be demodulated directly by the projection light intensity on the projection base .

[0254] Preferably, the phase map corresponding to the projection measurement base in step 2 is specifically:

[0255] When calculating the phase map corresponding to the projection measurement base , let where is the two-dimensional spatial wave function distribution corresponding to the projection measurement base , the amplitude intensity and spatial phase of which are denoted as and Here, the preset input light beam is parallel light, i.e.

[0256] Let the relative phase be where is the phase of the blazed grating loaded on the second spatial light modulator.

[0257] Let the relative amplitude be

[0258] Thus, the phase map corresponding to the projection measurement base is given by the formula

[0259]

[0260] . By loading the phase map corresponding to the projection measurement base on the second spatial light modulator, the projection measurement of the transverse vibration signal d can be realized. Similarly, the phase map corresponding to the projection measurement base is also given by the above method, only let By loading the phase map corresponding to the projection measurement base on the second spatial light modulator, the projection measurement of the angular vibration signal can be realized.

[0261] Preferably, the receiving of the projection measurement light intensity in step 2 is realized by using a fiber tail fiber, specifically:

[0262] A Fourier lens is used behind the second spatial light modulator to perform Fourier transform on the projection light field, and let the projection measurement light field distribution that the spatial light modulator hopes to modulate be ψ M (x, y) (i.e., the loaded phase map is the phase map corresponding to the projection measurement base | ψ M >), and the light field input into the second spatial light modulator is ψ f (x, y), i.e., the light beam final state | ψ f after the perception process.The corresponding two-dimensional light field distribution is transformed into a transformed light field at the back focal length of the Fourier lens (first-order diffraction position), and then directly received at the center of the transformed light field through a single-mode optical fiber. Since the mode field diameter of the single-mode optical fiber is much smaller than the size of the transformed light field, the receiving efficiency of the single-mode optical fiber can be expressed as

[0263]

[0264] where |<ψ M |ψ f >| 2 is exactly the projection probability of the final state of the light beam on the projection measurement basis |ψ M .

[0265] Therefore, when the projection measurement is performed using the projection measurement basis |ψ , the projection measurement light intensity received by the single-mode optical fiber is

[0266]

[0267] The transverse vibration signal d can be directly demodulated from the projection light intensity. When the projection measurement is performed using the projection measurement basis |ψ , the projection measurement light intensity received by the single-mode optical fiber is

[0268]

[0269] The angular jitter signal can be directly demodulated from the projection light intensity. In addition, in the measurement scheme of the present application, the projection measurement light intensities corresponding to the transverse vibration and angular jitter signals are both amplified by a factor related to the Hermite-Gaussian spatial mode number n.

[0270] Preferably, the step 4 comprises the following steps:

[0271] Step 401: inputting the projection measurement light intensity received by the single-mode optical fiber into an avalanche photodiode detector for measurement and converting it into a voltage signal;

[0272] Step 402: inputting the voltage signal of the avalanche photodiode detector 16 into a spectrum analyzer 17 to demodulate the amplitudes and frequencies of the transverse vibration signal and the angular jitter signal.

[0273] Preferably, the voltage signal converted in step 401 is specifically:

[0274] After the projection measurement light intensity received by the single-mode optical fiber is input into the avalanche photodiode detector, it is converted into a photocurrent signal through avalanche amplification. The photocurrent signal is converted into a voltage signal through amplification by a transimpedance amplifier built-in the avalanche photodiode detector, and its size is proportional to the received light intensity, i.e. V​det ∝I det .

[0275] Example 4:

[0276] Example 4 is a preferred example of Example 1 to more specifically illustrate the present application.

[0277] In this embodiment, there are deployed a Hermite-Gaussian light source generation module, a vibration and jitter sensing module, a projection measurement module, an electrical module and a data processing module; the Hermite-Gaussian light source generation module is used to generate a high-order Hermite-Gaussian light source; the vibration and jitter sensing module is used to detect and sense the transverse vibration and angular jitter of the sensing element, and convert them into transverse spatial displacement signals and transverse momentum offset signals of the light beam, in which module a weak value amplification technique is further introduced through post-selection to further amplify the weak vibration and jitter signals and improve the noise immunity of the system; the projection measurement module is used to demodulate the weak vibration and jitter signals into light intensity signals; the electrical module is used to convert the light signals into electrical signals to obtain measurement data and store them; the data processing module is used to analyze and process the measured data to calculate the vibration and jitter signal intensity and frequency of the sensing element.

[0278] Specifically, the new method for simultaneously measuring transverse vibration and angular jitter based on Hermite-Gaussian light beams includes the following steps:

[0279] Step A1: After expanding the Gaussian light source of the single-frequency laser 1 through the expander 2, it is incident to the spatial light modulator 3A;

[0280] Step A2: Modulate the phase pattern corresponding to the n-order Hermite-Gaussian light beam on the spatial light modulator 3A, specifically:

[0281] Let the light beam distribution input to the spatial light modulator 3A be wherein is the light beam amplitude intensity distribution input to the spatial light modulator 3A, is the input light beam spatial phase distribution. The phase pattern loaded on the spatial light modulator 3A is denoted as H A (x, y). The output light beam distribution of the spatial light modulator 3A is wherein ψ n (x, y) is the light field distribution of the n-order transverse Hermite-Gaussian light beam that we want to obtain, and the amplitude intensity and spatial phase are denoted as and

[0282] Let the relative phase be wherein is the blazed grating phase loaded on the spatial light modulator 3A.

[0283] Let the relative amplitude be

[0284] The phase pattern corresponding to the n-order Hermite-Gaussian beam loaded on the spatial light modulator A is given by the formula

[0285]

[0286] where J1 -1 [·] is the inverse function of the first-order Bessel function.

[0287] Step A3: The exit light of the spatial light modulator 3A generates a high-purity n-order Hermite-Gaussian light source after passing through the 4-f filtering system, specifically:

[0288] A Fourier lens 4A with a focal length of f1 is placed at f1 behind the spatial light modulator 3A, and a pinhole 5 is placed at f1 behind the Fourier lens 4A. The light beam modulated by the spatial light modulator will be focused at the pinhole 5 after passing through the Fourier lens 4A. Due to the addition of the blazed grating on the phase pattern, the focal points on the image plane will be periodically arranged in the horizontal direction. The first-order diffraction light spot is filtered out using the pinhole 5, and a lens 4B with a focal length of f2 is placed at f2 behind the exit light beam. A high-purity n-order Hermite-Gaussian beam is generated. The spatial distribution state of the Hermite-Gaussian beam can be denoted as |n>, and the symbol |·> represents the Dirac right arrow, and

[0289] |n> = ∫∫dxdyψ n (x, y) |x, y>

[0290] Step B1: The polarization state of the Hermite-Gaussian beam is selected to be 45-degree linearly polarized light by pre-selection, specifically:

[0291] The Hermite-Gaussian beam generated by the spatial light modulator and the 4-f filtering system is incident to a G-L polarization prism 7A with its optical axis along the horizontal direction, and then passes through a half-wave plate 8A with an optical axis at an angle of 22.5° with the horizontal plane. The polarization state of the output light beam is pre-selected as:

[0292]

[0293] where i represents the pre-selected state, H represents horizontal polarization light, and V represents vertical polarization light.

[0294] Step B2: In the vibration and dither perception module, the horizontal polarization component (H light) and the vertical polarization component (V light) of the light beam are separated using a Mach-Zehnder interferometer with a polarization beam splitter 9. The vibration and dither of the perception unit are perceived on the light path of the horizontal polarization component, and the lateral vibration is converted into the lateral spatial displacement of the light beam, and the dither is converted into the lateral momentum shift of the light beam, specifically:

[0295] In this example, the sensing element is a mirror 11 driven by two PZTs, and the two PZTs are arranged in parallel to apply a transverse vibration signal and an angular dithering signal to the mirror simultaneously. In the horizontal polarization component light path, a transverse vibration signal with amplitude d and an angular dithering signal with amplitude are applied to the mirror 11 by the two PZTs simultaneously, the transverse spatial displacement of the light beam caused by the transverse vibration signal is d, and the transverse momentum shift of the light beam caused by the angular dithering signal is where k = 2π / λ is the wave number of the light beam, and λ is the central wavelength of the light source. The sensing process can be represented by an evolution operator as follows:

[0296]

[0297] where is a Pauli operator acting on the polarization state, is a momentum operator acting on the light beam, representing a transverse position translation, is a position operator acting on the light beam, representing a transverse momentum shift. The input state of the interferometer can be recorded as: in > = |i>|ψ i >, where |ψ i > = |n> represents the initial spatial mode of the light beam. Thus, the output state of the interferometer can be recorded as:

[0298]

[0299] In this example, a polarizer 12A with an optical axis along the horizontal direction is placed in the horizontal polarization component light path of the Mach-Zehnder interferometer, and a polarizer 12B with an optical axis along the vertical direction is placed in the vertical polarization component light path to improve the polarization purity of the light beam in the interferometer. In addition, the mirror 11 driven by a single PZT is driven by a feedback signal amplified by a phase-locked amplifier to stabilize the relative phase of the two light paths of the interferometer.

[0300] Step B3: Then the polarization state of the light beam is post-selected so that the transverse vibration signal d and the angular dithering signal are completely modulated on the spatial mode of the Hermite-Gaussian light beam, specifically:

[0301] The light beam emitted by the interferometer passes through a quarter-wave plate 14 with an optical axis at about 45° to the horizontal direction to compensate for the constant phase difference between the two polarization components in the interferometer, and then passes through a half-wave plate 8B with an optical axis at about angle to the horizontal direction, and then passes through a Glan-Taylor polarizing prism 7B with an optical axis along the horizontal direction, and the polarization state of the output light beam is post-selected as:

[0302]

[0303] where ε is the post-selection angle, in this example ε = 5°.

[0304] The post-selected beam can be denoted by the state vector:

[0305]

[0306] where

[0307]

[0308] is weak, here we consider both the transverse vibration and the angular jitter as weak signals, i.e. d « 1, Thus, the spatial mode of the post-selected beam can be denoted by:

[0309]

[0310] where is the spatial distribution variance of the fundamental Gaussian beam, i.e. 2σ0= w0is the waist radius of the fundamental Gaussian beam, the spatial mode state:

[0311]

[0312]

[0313] carries the transverse vibration signal d and the angular jitter signal However, and are not orthogonal, which means that directly using the state and to project the post-sensed beam, the transverse vibration signal d and the angular jitter signal and cannot be directly demodulated from the projected intensity on the

[0314] Step C1: the post-sensed beam is incident on the spatial light modulator 3B, and the phase pattern corresponding to the projection measurement bases designed for the transverse vibration signal and the angular jitter signal in the present application is modulated on the spatial light modulator 3B, specifically

[0315] In order to directly demodulate the transverse vibration signal and the angular jitter signal, in the present application, the following two non-orthogonal projection bases are designed:

[0316]

[0317]

[0318] so that they are respectively orthogonal to and Orthogonal. When using projection basis The projection probability of light intensity obtained by the measurement end when performing projection measurement on the light beam is

[0319]

[0320] Only related to the transverse vibration signal d, that is, the transverse vibration signal can be directly demodulated by the projection light intensity on the projection basis When using projection basis The projection probability of light intensity obtained by the measurement end when performing projection measurement on the light beam is

[0321]

[0322] Only related to the angular vibration signal , that is, the angular vibration signal can be directly demodulated by the projection light intensity on the projection basis

[0323] The projection measurement basis and The corresponding phase diagram generation method is similar to step A2. When calculating the corresponding phase diagram of the projection measurement basis , let where is the two-dimensional spatial wave function distribution corresponding to the projection measurement basis , and the amplitude intensity and spatial phase are denoted as and Here, the preset input light beam is parallel light, that is,

[0324] Let the relative phase be where is the phase of the blazed grating loaded on the spatial light modulator 3B.

[0325] Let the relative amplitude be

[0326] Therefore, the corresponding phase diagram of the projection measurement basis is given by the formula

[0327]

[0328] . Load the corresponding phase diagram of the projection measurement basis on the spatial light modulator 3B, and the projection measurement of the transverse vibration signal d can be realized. Similarly, the corresponding phase diagram of the projection measurement basis is also given by the above method, only let Load the corresponding phase diagram of the projection measurement basis on the spatial light modulator 3B, and the projection measurement of the angular vibration signal can be realized.​

[0329] Step C2: the exit light of the spatial light modulator 3B is received by a fiber tail after passing through a Fourier lens, so as to realize the receiving of the projection measurement light intensity, specifically:

[0330] A Fourier lens 4C is used behind the spatial light modulator 3B to perform Fourier transform on the projection light field, and the projection measurement light field distribution expected to be modulated on the spatial light modulator 3B is denoted as ψ M (x, y) (i.e. the loaded phase diagram corresponds to the projection measurement basis | ψ M >), and the light field input into the spatial light modulator 3B is ψ f (x, y), i.e. the two-dimensional light field distribution corresponding to the beam final state | ψ f > after the sensing process, and the transformed light field is obtained at the back focal length (the first-order diffraction position) of the Fourier lens 4C, and then received directly at the center of the transformed light field by a single-mode optical fiber 15. Since the mode field diameter of the single-mode optical fiber 15 is much smaller than the size of the transformed light field, the receiving efficiency of the single-mode optical fiber 15 can be expressed as

[0331]

[0332] where | < ψ M | ψ f > | 2 is exactly the projection probability of the beam final state on the projection measurement basis | ψ M >.

[0333] Therefore, when the projection measurement is performed using the projection measurement basis | ψ , the projection measurement light intensity received by the single-mode optical fiber is

[0334]

[0335] The transverse vibration signal d can be directly demodulated from the projection light intensity. Therefore, when the projection measurement is performed using the projection measurement basis | ψ

[0336]

[0337] The angular vibration signal can be directly demodulated from the projection light intensity. In addition, in the measurement scheme of the present application, the projection measurement light intensities corresponding to the transverse vibration and angular vibration signals are both amplified by a factor related to the Hermite Gaussian spatial mode number n.

[0338] Step D1: the projection measurement light intensity received by the single-mode optical fiber 15 is input into an avalanche photodiode detector 16 for measurement, and converted into a voltage signal, specifically:​

[0339] The projected measurement light intensity received by the single-mode fiber 15 is converted into a photoelectric current signal after being input into the avalanche photodiode detector 16, and the photoelectric current signal is converted into a voltage signal after being amplified by a transimpedance amplifier built in the avalanche photodiode detector 16, and the size of the voltage signal is proportional to the received light intensity, that is, V det ∝I det .

[0340] In step D2, the voltage signal of the avalanche photodiode detector 16 is input into the spectrum analyzer 17 to demodulate the amplitudes and frequencies of the transverse vibration signal and the angular jitter signal, specifically:

[0341] In this example, by applying sinusoidal signals with an amplitude of 1 V, a relative phase of 4°, and a frequency of 2 kHz to the two PZTs on the two PZT-driven mirrors 11, a transverse vibration signal with an amplitude d = 15.55 nm and an angular jitter signal with an amplitude of 0.5 nm are simultaneously modulated on the sensing element, and the frequencies of the vibration and jitter signals are both 2 kHz. By displaying the projection measurement basis corresponding phase diagram on the spatial light modulator 3B, the frequency spectrum measurement results under different orders of Hermite-Gaussian light sources can be obtained, as shown in FIG. 6, and the size and frequency of the corresponding transverse vibration signal can be demodulated accordingly. Figure 3 By displaying the projection measurement basis corresponding phase diagram on the spatial light modulator 3B, the frequency spectrum measurement results under different orders of Hermite-Gaussian light sources can be obtained, as shown in FIG. 7, and the size and frequency of the corresponding angular jitter signal can be demodulated accordingly. Figure 4

[0342] In the description of the present application, it should be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0343] ​Those skilled in the art know that, in addition to implementing the system, device and each module thereof provided by the present application in the form of pure computer readable program code, the same program can also be implemented in the form of logic gate, switch, special integrated circuit, programmable logic controller and embedded microcontroller, etc. by logically programming the method steps. Therefore, the system, device and each module thereof provided by the present application can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures in the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing methods and structures in the hardware component.

[0344] The specific embodiments of the present application are described above. It needs to be understood that the present application is not limited to the specific embodiments described above, and various changes or modifications can be made by those skilled in the art within the scope of the claims, which does not affect the essential content of the present application. The embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily without conflict.

Claims

1. A method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam, characterized in that, include: Step S1: Expand the Gaussian light source beam, modulate the phase diagram corresponding to the Hermitian Gaussian beam on the spatial light modulator, and the outgoing light passes through the filtering system; Step S2: The Hermigasaurus beam is pre-selected to separate the horizontal and vertical polarization components of the beam, the vibration and jitter of the sensing element are sensed, the transverse vibration and jitter are converted, and the beam polarization state is post-selected. Step S3: The beam after vibration and jitter sensing is incident on the spatial light modulator to modulate the phase diagram corresponding to the projection measurement base for the lateral vibration signal and the angular jitter signal. The outgoing light is received by an optical fiber pigtail at the focal point behind the lens. Step S4: Convert the projected transverse vibration and angular jitter signals into light intensity information, measure the light intensity and convert it into a voltage signal, input it into a spectrum analyzer, and demodulate the amplitude and frequency of the transverse vibration and angular jitter signals. In step S2: The Hermetic Gaussian beam is pre-selected to be linearly polarized at 45 degrees. In the vibration and jitter sensing module, an interferometer is used to separate the horizontal polarization component H and the vertical polarization component V of the beam. The vibration and jitter of the sensing element are sensed in the optical path of the horizontal polarization component. The transverse vibration is converted into the transverse spatial displacement of the beam, and the jitter is converted into the transverse momentum shift of the beam. The polarization state of the beam is post-selected so that the transverse vibration signal and the angular jitter signal are completely modulated onto the spatial mode of the Hermetic Gaussian beam. The beam is pre-selected to have its polarization state set to 45-degree linearly polarized light, specifically: A Hermigaussian beam generated by a spatial light modulator A and a 4-f filter system is incident on a Glan Taylor polarizing prism with its optical axis along the horizontal direction. The beam then passes through a prism with its optical axis perpendicular to the horizontal plane. For a half-wave plate with an included angle, the polarization state of the output beam is preselected as follows: in, Indicates the pre-selection state. Indicates horizontally polarized light. Indicates vertically polarized light; The process of converting lateral vibration into lateral spatial displacement of the light beam and dithering into lateral momentum shift of the light beam specifically involves: In the vibration and jitter sensing module, a Mach-Zehnder interferometer with a polarization beam splitter is used to separate the horizontal polarization component (H-beam) and the vertical polarization component (V-beam) of the light beam. Vibration and jitter of the sensing element are sensed along the optical path of the horizontal polarization component. The transverse vibration amplitude of the sensing element is... The angular jitter amplitude is The lateral spatial displacement of the light beam caused by the lateral vibration is The lateral momentum shift of the beam caused by angular jitter is ,in The wavenumber of the beam. The center wavelength of the light source is represented as: in , For Pauli operators acting on polarization states, Let be the momentum operator acting on the beam, representing the lateral position translation. Here, represents the position operator acting on the beam, indicating the lateral momentum shift. The identity matrix is ​​denoted as: The input state of the interferometer is denoted as: ,in The initial spatial mode of the beam is represented; the output state of the interferometer is denoted as: 。 2. The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam according to claim 1, characterized in that, In step S1: The Gaussian light source is expanded and then incident on spatial light modulator A, where it is modulated. The phase diagram corresponding to the Hermitian beam shows that the emitted light, after passing through a 4-f filter system, generates a high-purity beam. Hermigaussian light source; The The phase diagram corresponding to the Hermitian beam was obtained through numerical calculation, specifically as follows: Let the beam distribution input to spatial light modulator A be denoted as... ,in The amplitude intensity distribution of the beam input to spatial light modulator A. The spatial phase distribution of the input beam; the phase diagram loaded on the spatial light modulator A is denoted as... The output beam distribution of spatial light modulator A is as follows: ,in for The optical field distribution of a transverse Hermitian Gaussian beam. The amplitude and intensity distribution of the output beam from spatial light modulator A. The spatial phase distribution of the output beam of spatial light modulator A; Relative phase is ,in It is the phase of the blazed grating loaded on the spatial light modulator A; Relative amplitude is ; Loaded on spatial light modulator A The phase diagram corresponding to the Hermitian beam is as follows: in It is the inverse function of the first-order Bessel function.

3. The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam according to claim 2, characterized in that: The 4-f filter system is specifically as follows: Behind spatial light modulator A Place a focal length at [location]. The Fourier lens, behind the Fourier lens A small aperture is placed at the image plane. The light beam modulated by the spatial light modulator A is focused at the aperture after passing through a Fourier lens. Because a blazed grating is added to the phase diagram, the focal points of the image plane are periodically arranged in the horizontal direction. The aperture filters out the light spot at the first-order diffraction point and stores it behind the image. Place another focal length at that location. The lens produces high purity output. A Hermitian beam; the spatial distribution of this Hermitian beam is denoted as... ,symbol Indicates Dirac's right arrow, and .

4. The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam according to claim 1, characterized in that: The subsequent selection specifically refers to: The beam emitted from the interferometer passes through an optical axis that is perpendicular to the horizontal direction. A quarter-wave plate is used to compensate for the constant phase difference between the two polarization components in the interferometer, passing through an optical axis perpendicular to the horizontal direction. A half-wave plate with an angle of 1 / 2 is passed through a Glan Taylor polarizing prism with its optical axis in the horizontal direction, and the polarization state of the output beam is subsequently selected as follows: in For later selection angle; The transverse vibration signal Angular jitter signal It is completely modulated onto the spatial mode of the Hermitian beam, specifically: The available state vector of the beam after selection is denoted as: in It is a weak value, where , The selected beam spatial mode is denoted as: in, Let Variance be the spatial distribution variance of the fundamental Gaussian beam, i.e. Let the beam waist radius be the fundamental Gaussian beam, and the spatial mode be: and They respectively carried lateral vibration signals and angular jitter signal .

5. The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam according to claim 1, characterized in that, In step S3: After the vibration and jitter sensing process, the light beam is incident on the second spatial light modulator B, and the phase diagram corresponding to the projection measurement basis for the transverse vibration signal and the angular jitter signal is modulated on it. After the outgoing light passes through a Fourier lens, it is received by an optical fiber pigtail at the focal point behind the lens to realize the reception of the projection measurement light intensity. The projection measurement base for the lateral vibration signal and the angular jitter signal is specifically as follows: To enable direct demodulation of lateral vibration and angular jitter signals, the following two non-orthogonal projection bases are designed: make and respectively with and Orthogonal, when using projection base When projecting a light beam, the probability of the light intensity projection obtained at the measuring end is: Able to project base The projected light intensity directly demodulates the transverse vibration signal when using a projection base. When projecting a light beam, the probability of the light intensity projection obtained at the measuring end is: Able to project base The projected light intensity is directly demodulated to obtain the angular jitter signal.

6. The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam according to claim 5, characterized in that: The phase diagram corresponding to the projection measurement base is specifically as follows: When calculating the projection measurement base When the corresponding phase diagram is given, let ,in For projection measurement base The corresponding two-dimensional spatial wave function distribution has amplitude intensity and spatial phase as follows: and ; The input beam is parallel light. , ; Let the relative phase be denoted as ,in It is the phase of the blazed grating loaded on the second spatial light modulator B; Let the relative amplitude be denoted as ; Projection measurement base The corresponding phase diagram is: Projection measurement base is loaded onto the second spatial light modulator B. The corresponding phase diagram enables the processing of lateral vibration signals. Projection measurement; projection measurement base The corresponding phase diagram, let Projection measurement base is loaded onto spatial light modulator B. The corresponding phase diagram can realize diagonal jitter signal. Projection measurement.

7. The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam according to claim 5, characterized in that: The use of fiber optic pigtail receivers to receive the light intensity for projection measurement is specifically as follows: A Fourier lens is used behind the spatial light modulator B to perform a Fourier transform on the projected light field. The desired projection measurement light field distribution on the spatial light modulator is denoted as... The input light field of the second spatial light modulator B is The final state of the beam after the sensing process The corresponding two-dimensional optical field distribution is transformed into a transformed optical field at the focal length behind the Fourier lens. This transformed optical field is then directly received at the center of the transformed optical field via a single-mode fiber. The receiving efficiency of the single-mode fiber is expressed as... in The final state of the beam in the projection measurement base Projection probability on; When using projection measurement base During projection measurement, the intensity of the projection measurement light received by the single-mode fiber is: The transverse vibration signal can be directly demodulated from the projected light intensity. When using a projection measurement base During projection measurement, the intensity of the projection measurement light received by the single-mode fiber is: The angular jitter signal is directly demodulated from the projected light intensity. The projected light intensity corresponding to the lateral vibration and angular jitter signals is obtained through the Hermetic Gaussian spatial mode number. Related factors Enlarge it.

8. The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam according to claim 1, characterized in that, In step S4: The lateral vibration and angular jitter signals are projected and converted into light intensity information. The light intensity is measured using an avalanche photodiode detector and converted into a voltage signal. This signal is then input into a spectrum analyzer to demodulate the amplitude and frequency of the lateral vibration and angular jitter signals. Step S4.1: Input the projected light intensity received by the single-mode fiber into the avalanche photodiode detector for measurement, and convert it into a voltage signal; The projected light intensity received by the single-mode fiber is input into the avalanche photodiode detector, where it is amplified by avalanche amplification and converted into a photocurrent signal. This photocurrent signal is then amplified by the transimpedance amplifier built into the avalanche photodiode detector and converted into a voltage signal, the magnitude of which is proportional to the received light intensity. ; Step S4.2: Input the voltage signal of the avalanche photodiode detector into the spectrum analyzer to demodulate the amplitude and frequency of the lateral vibration signal and the angular jitter signal.

9. A system for simultaneously measuring the transverse vibration and angular jitter of a Hermitian Gaussian beam, characterized in that, The method for simultaneously measuring the transverse vibration and angular jitter of a Hermitian beam as described in claim 1 includes: Module M1: Expands the Gaussian light source beam, modulates the phase diagram corresponding to the Hermitian Gaussian beam on the spatial light modulator, and the outgoing light passes through the filtering system; Module M2: The Hermetic Gaussian beam is pre-selected to separate the horizontal and vertical polarization components of the beam, senses the vibration and jitter of the sensing element, converts the transverse vibration and jitter, and performs post-selection on the beam polarization state. Module M3: The beam after vibration and jitter sensing is incident on the spatial light modulator, modulating the phase diagram corresponding to the projection measurement base for the lateral vibration signal and the angular jitter signal. The outgoing light is received by an optical fiber pigtail at the focal point behind the lens. Module M4: Converts the projected lateral vibration and angular jitter signals into light intensity information, measures the light intensity and converts it into a voltage signal, inputs it into a spectrum analyzer, and demodulates the amplitude and frequency of the lateral vibration and angular jitter signals.

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