Dynamic displacement measurement method of uniform and non-uniform surfaces using carrier optical vortex interferometer

Abstract

The invention discloses a method for measuring dynamic uniform and non-uniform surface displacement using a carrier optical vortex interferometer. The method adopts a high-order vortex beam with concentric rings of different radii as a detection beam for dynamic surface displacement measurement, and utilizes a chopper to convert the two-dimensional interference pattern into a one-dimensional time domain signal. When no surface displacement occurs on the measured surface, a carrier frequency signal is obtained by Fourier transforming the carrier signal. When uniform surface displacement occurs on the measured surface, a Doppler frequency shift is generated in the Fourier spectrum of the one-dimensional time domain signal, and the surface displacement velocity is obtained by locating the Doppler frequency shift. When non-uniform surface displacement occurs on the measured surface, a split Doppler frequency shift is generated in the Fourier spectrum of the one-dimensional time domain signal, and the surface displacement velocity corresponding to the radius of each concentric ring of the vortex beam is obtained by locating the Doppler peak frequency. The surface displacement profile at any moment is obtained by integrating the velocity with time, thereby realizing the measurement of dynamic surface displacement.

Description

Technical Field

[0001] The present invention relates to the field of photoelectric measurement technology, and in particular to a method for dynamic measurement of uniform and non-uniform surface displacements using a carrier optical vortex interferometer. The method is applied to the dynamic detection of uniform and non-uniform axisymmetric surface displacements in mechanical and thermal physics dynamics, and realizes displacement measurement from nanometer to micrometer levels in optical systems. Background Art

[0002] Nanoscale to micrometer-scale surface displacements are common in dynamic micromechanical and thermophysical processes, such as force-induced mechanical surface displacements and laser-induced thermoelastic surface displacements. Achieving high-precision, high-resolution dynamic displacement measurements at the nanometer to micrometer scale is crucial for understanding these dynamic processes. Laser interferometry, a displacement measurement tool with nanometer-scale resolution, plays a significant role in dynamic displacement measurements of uniform surfaces. However, conventional laser interferometers utilize a fundamental-mode Gaussian beam as the probe light, limiting their application in non-uniform surface displacement measurement scenarios.

[0003] Unlike the uniform phase of traditional Gaussian beams, vortex beams have a spiral phase structure, carrying orbital angular momentum. This spiral phase creates a central phase singularity, resulting in a hollow intensity distribution. These characteristics provide new degrees of freedom for beam manipulation and light field analysis. Therefore, vortex beams have significant potential applications in many fields, including optical measurement, particle manipulation, optical communications, quantum information processing, and super-resolution microscopy.

[0004] Introducing vortex beams into a laser interferometer, known as an optical vortex interferometer, provides a new technical approach for dynamic displacement measurement. Optical vortex interferometers utilize the coaxial coherent superposition of conjugate vortex beams to produce a petal-shaped interference pattern. The phase shift caused by surface displacement causes the petal-shaped fringes in the two-dimensional interference pattern to rotate in the azimuthal direction. By precisely measuring the rotation angle of the petals, the phase is inverted, resulting in the surface displacement.

[0005] Currently, the preferred method for phase inversion in optical vortex interferometers is to capture petal-shaped interference patterns with pixelated array detectors, determine the petal centroid position using image processing algorithms, and invert the phase by measuring the rotation angle of the centroid in the azimuthal direction. However, in practical applications, the centroid method is difficult to obtain accurate and stable measurement results due to the distortion of the petal intensity profile and the performance differences of the centroid positioning algorithm. The image correlation algorithm calculates the rotation angle by calculating the correlation coefficient between two adjacent rotated petal-shaped interference patterns. This method has a certain ability to resist random noise, but is sensitive to sudden environmental changes (such as airflow disturbances and mechanical vibrations). The feasibility of the centroid method and image correlation algorithm is based on the rotational invariance of the petal-shaped interference pattern caused by uniform surface displacement. In the case of non-uniform surface displacement, the petals in the interference pattern have different rotation angles and rotation speeds, resulting in stretching and deformation of the petals, which greatly reduces the feasibility of phase inversion using the centroid method and image correlation method. In addition, the centroid method and image correlation method are based on pixelated image morphological operations, and the phase inversion accuracy is inevitably limited by the pixel resolution of the array detector. Summary of the Invention

[0006] In order to avoid the shortcomings of the above-mentioned existing technologies, the present invention provides a carrier optical vortex interferometer dynamic uniform and non-uniform surface displacement measurement method, overcomes the limitations of traditional pixelated image morphological operations on phase inversion accuracy, and expands the traditional optical vortex interferometer from uniform surface displacement measurement to axisymmetric non-uniform surface dynamic displacement measurement.

[0007] The present invention adopts the following technical solutions to solve the technical problems:

[0008] The characteristics of the carrier optical vortex interferometer dynamic uniform and non-uniform surface displacement measurement method of the present invention are:

[0009] A high-order vortex beam with concentric rings of different radii is used as a probe beam for dynamic surface displacement measurement. The probe beam and a reference beam are coaxially coherently superimposed to generate a two-dimensional interference pattern with petal-shaped vortices. The reference beam is a high-order vortex beam conjugated with the probe beam. The two-dimensional interference pattern is modulated by a chopper to convert it into a one-dimensional time-domain signal.

[0010] When no surface displacement occurs on the measured surface, the one-dimensional time domain signal is a carrier signal, and a carrier frequency signal is obtained by Fourier transforming the carrier signal;

[0011] When the measured surface undergoes uniform surface displacement, the two-dimensional interference pattern rotates as a whole due to the uniform phase shift, and the Fourier spectrum of the one-dimensional time domain signal produces a Doppler frequency shift relative to the carrier frequency signal. The surface displacement velocity is obtained by locating the Doppler frequency shift.

[0012] When non-uniform surface displacement occurs on the measured surface, petals at different radii of the two-dimensional interference pattern produce different rotation speeds due to different phase shifts, and the Fourier spectrum of the one-dimensional time domain signal produces a split Doppler frequency shift, and the Doppler peak frequency corresponds to the radius of each concentric ring in the vortex beam; the surface displacement velocity corresponding to the radius of the vortex beam ring is obtained by locating the Doppler peak frequency based on the carrier frequency signal;

[0013] The surface displacement profile at any moment is obtained by integrating the velocity over time, thus realizing the measurement of dynamic surface displacement.

[0014] The carrier optical vortex interferometer dynamic uniform and non-uniform surface displacement measurement method of the present invention is also characterized in that the high-order vortex light beams of concentric rings with different radii are at least two concentric rings with different radii.

[0015] The carrier optical vortex interferometer dynamic uniform and non-uniform surface displacement measurement method of the present invention is also characterized in that the high-order vortex beam is a Laguerre-Gaussian beam or a Bessel beam.

[0016] The characteristics of the carrier optical vortex interferometer dynamic uniform and non-uniform surface displacement measurement method of the present invention are: the measurement system is constructed as follows:

[0017] A laser beam with a set wavelength emitted by a laser transmitter is expanded by a beam expander and then introduced into a spatial light modulator through a first beam splitter, and a high-order vortex beam is generated by the spatial light modulator;

[0018] The high-order vortex beam is split into two vortex beams by a second beam splitter, one of which serves as a detection beam and the other as a reference beam; the detection beam reaches the measured surface through a third beam splitter and is reflected by the measured surface into a fourth beam splitter; the reference beam is reflected by a reflector and combined with the output light of the fourth beam splitter, so that the two vortex beams undergo odd and even reflections, respectively, to form a conjugate, and the conjugate vortex beams are coaxially coherently superimposed to produce a two-dimensional interference pattern showing a petal-shaped vortex;

[0019] A detection system consisting of an optical chopper, a lens and a point detector is provided to convert the two-dimensional interference pattern into a one-dimensional time domain signal.

[0020] The carrier optical vortex interferometer dynamic uniform and non-uniform surface displacement measurement method of the present invention is also characterized in that a high-order vortex beam for optimizing vortex beam imaging is arranged between the first beam splitter and the second beam splitter to enter the 4f system, and the 4f system is composed of two lenses with equal focal lengths and a variable aperture.

[0021] Compared with the existing technology, the beneficial effects of the present invention are embodied in:

[0022] 1. The carrier optical vortex interferometer of the present invention converts a two-dimensional petal-shaped interference pattern into a one-dimensional time-domain signal, namely a carrier, through a chopper and a point detector, and obtains the carrier frequency through frequency domain analysis. The dynamic displacement of the uniform surface produces a Doppler frequency shift relative to the carrier frequency. The uniform surface displacement velocity can be obtained by locating the Doppler frequency shift, and the surface dynamic displacement can be obtained by integrating the velocity over time, eliminating the limitations of traditional pixelated image morphology operations.

[0023] 2. The present invention uses high-radial-order vortex light with multiple concentric rings to expand the optical vortex interferometer to the measurement scenario of the dynamic displacement of axisymmetric non-uniform surfaces; the high-radial-order vortex light has an intensity distribution of concentric rings with different radii, causing the Doppler shift to split into multiple frequency peaks, each frequency peak corresponding to a ring radius. By locating multiple frequency peaks, the surface displacement velocity at different radii can be obtained, and the dynamic displacement profile of the axisymmetric non-uniform surface can be obtained by integrating the velocity over time, thereby expanding the traditional optical vortex interferometer from uniform surface displacement measurement to axisymmetric non-uniform surface dynamic displacement measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 This is the optical principle diagram of the measurement method of the present invention.

[0025] Figure 2 The carrier and the interference pattern after cutting as well as the carrier spectrum are obtained when there is no surface displacement on the measured surface.

[0026] Figure 3 These are the time domain signals and frequency spectra at different chopper angular velocities when the measured surface undergoes uniform surface displacement and the displacement velocity is constant.

[0027] Figure 4 The time domain signals and time-frequency diagrams at different chopper angular velocities are shown when the measured surface undergoes uniform surface displacement and the displacement speed is non-constant.

[0028] Figure 5 is the intensity distribution of the Laguerre-Gaussian beam and the velocity distribution of the corresponding non-uniform axisymmetric surface displacement.

[0029] Figure 6 It is the time domain signal of the displacement of the non-uniform axisymmetric surface and the interference pattern before being modulated by the chopper, the time domain signal spectrum at different chopper angular velocities, and the theoretical and inverted Doppler frequency shift and frequency difference.

[0030] Figure 7 It is the time domain signal spectrum, Doppler peak frequency difference and relative error between theoretical and inverted values ​​of non-uniform axisymmetric surface displacement at different surface displacement velocities.

[0031] Figure 8It is the time domain signal and time-frequency diagram of the measured surface when non-uniform axisymmetric surface displacement and non-constant surface displacement velocity occur and the radial index is different.

[0032] Numbers in the figure: 1 laser emitter, 2 spatial light modulator, 3 first beam splitter, 4 4f system, 5 second beam splitter, 6 reflecting mirror, 7 third beam splitter, 8 fourth beam splitter, 9 optical chopper, 10 lens, 11 point detector, 12 measured surface. DETAILED DESCRIPTION

[0033] The method for measuring the dynamic uniform and non-uniform surface displacement using the carrier optical vortex interferometer of this embodiment is as follows:

[0034] A high-order vortex beam with concentric rings of varying radii is used as the probe beam for dynamic surface displacement measurement. The vortex beam is a Laguerre-Gaussian or Bessel beam with multiple concentric rings. The probe beam and a reference beam are coaxially coherently superimposed to produce a two-dimensional interferogram of petal-shaped vortices. The reference beam is a high-order vortex beam conjugated to the probe beam. A chopper is used to modulate the two-dimensional interferogram and convert it into a one-dimensional time-domain signal.

[0035] When the measured surface does not undergo surface displacement, the one-dimensional time domain signal is the carrier signal, and the carrier frequency signal is obtained by Fourier transforming the carrier signal;

[0036] When the measured surface undergoes uniform surface displacement, the two-dimensional interference pattern rotates as a whole due to the uniform phase shift, and the Fourier spectrum of the one-dimensional time domain signal produces a Doppler frequency shift relative to the carrier frequency signal. The surface displacement velocity is obtained by locating the Doppler frequency shift.

[0037] When non-uniform surface displacement occurs on the measured surface, the petals at different radii of the two-dimensional interference pattern produce different rotation speeds due to different phase shifts. The Fourier spectrum of the one-dimensional time domain signal produces a split Doppler frequency shift, and the Doppler peak frequency corresponds to the radius of each concentric ring in the vortex beam. The surface displacement velocity corresponding to the radius of the vortex beam ring is obtained by locating the Doppler peak frequency based on the carrier frequency signal.

[0038] The surface displacement profile at any moment is obtained by integrating the velocity over time, thus realizing the measurement of dynamic surface displacement.

[0039] In specific implementation, the corresponding technical measures also include:

[0040] The high-order vortex beams of concentric rings with different radii are at least two concentric rings with different radii.

[0041] The high-order vortex beam is a Laguerre-Gaussian beam or a Bessel beam.

[0042] In this embodiment, in order to realize the dynamic uniform and non-uniform surface displacement measurement of carrier optical vortex interferometer, a Figure 1 The measurement system shown is:

[0043] The laser beam with a set wavelength emitted by the laser transmitter 1 is expanded by the beam expander and then introduced into the spatial light modulator 2 through the first beam splitter 3, and the spatial light modulator 2 generates a high-order vortex beam;

[0044] The high-order vortex beam is divided into two vortex beams by the second beam splitter 5, one of which is used as a detection beam and the other as a reference beam; the detection beam reaches the measured surface 12 through the third beam splitter 7, and is reflected by the measured surface 12 into the fourth beam splitter 8; the reference beam is combined with the output light of the fourth beam splitter 8 after being reflected by the reflector 6, so that the two vortex beams undergo odd and even reflections respectively to form a conjugate. The second beam splitter 5, the beam reflector 6, the third beam splitter 7, and the fourth beam splitter 8 form an optical measurement system based on a Mach-Zehnder interferometer, and the conjugate vortex beams are coaxially coherently superimposed to produce a two-dimensional interference pattern of petal-shaped vortices;

[0045] A detection system consisting of an optical chopper 9, a lens 10 and a point detector 11 is provided to convert the two-dimensional interference pattern into a one-dimensional time domain signal.

[0046] In order to optimize high-quality vortex beam imaging and facilitate subsequent calibration of the radius of the concentric rings of the vortex beam, a high-order vortex beam is set between the first beam splitter 3 and the second beam splitter 5 to enter the 4f system 4.

[0047] The present invention can realize dynamic measurement of uniform and non-uniform displacement of measured surfaces from nanometer to micrometer level, and has wide applications in many fields such as mechanics and thermal physics dynamics.

[0048] The effectiveness of the method of the present invention is theoretically verified by the following process:

[0049] Probe beam electric field strength Characterized by formula (1):

[0050]

[0051] Reference beam electric field strength Characterized by formula (2):

[0052]

[0053] Probe beam amplitude A l,p (r) and reference beam A l,p (r) The amplitudes are equal and are represented by equation (3):

[0054]

[0055] In formula (1), formula (2) and formula (3):

[0056] The superscript a and superscript b represent the measurement beam and the reference beam respectively.

[0057] R, θ and z are used to represent the cylindrical coordinate parameters, and k is the wave number;

[0058] The radius w of the Gaussian beam at 1 / e is: Where w0 is the waist, z R is the Rayleigh distance;

[0059] is the related Laguerre polynomial, R=z[1+(z R / z) 2 ] is the radius of curvature of the wavefront at a distance z from the beam waist;

[0060] For the ancient phase shift,

[0061] is the phase shift caused by surface displacement, l is the topological charge, p is the radial order,

[0062] In this embodiment, the detection beam is a Laguerre-Gaussian beam with p>0, which has p+1 concentric rings with zero intensity on the axis.

[0063] The reference beam and the measurement beam converge and interfere, and after coaxial superposition, a daisy-petal-shaped interference pattern is generated. The light intensity I(r,θ) after the reference beam and the measurement beam converge and interfere is represented by formula (4):

[0064]

[0065] When the phase difference satisfies an integer multiple of 2π, the brightness is the brightest and the number of petals is 2l;

[0066] The two-dimensional interferogram is modulated by the chopper, and the chopper transmittance function T(θ,t) is represented by equation (5):

[0067]

[0068] In formula (5), Ω is the angular velocity of the chopper, and the number of blades of the chopper is 2l;

[0069] The transmittance function T(θ,t) is a square wave with a period of π / l and an angular frequency of 2lΩ. The interference pattern modulated by the chopper is collected by the lens. The total intensity of the interference light modulated by the chopper, I(t), is a function of time and is expressed by Equation (6):

[0070]

[0071] The collected petal-shaped interferogram is subjected to spectrum analysis according to the following two scenarios:

[0072] Scenario 1: Assuming the surface displacement is a uniform profile and the moving speed is v0, the phase shift for: Phase shift Substituting into equation (6), the interference light intensity I1(t) when the surface displacement speed is v0 is expressed by equation (7):

[0073]

[0074] The first integral in formula (7) Independent of time, the result is a constant, the second integral over the azimuth θ It is related to time. The frequency component of the total intensity of the interference light when the surface displacement velocity is v0 is observed from the Fourier transform of the time-varying term. The fundamental frequency H1(ω) of the interference light when the surface displacement velocity is v0 is represented by formula (8):

[0075]

[0076] In formula (8):

[0077] and ω represent Fourier transform and angular frequency, respectively;

[0078] Square wave integral term It is a triangle wave, written in Fourier series form, which contains infinite harmonics and the envelope form is sinc 2 Here, the first harmonic (m = 0) is used to locate the fundamental frequency. After Fourier transform, the negative frequency and DC component are ignored. The simplified fundamental frequency H1(ω) is represented by equation (9):

[0079]

[0080] δ is the Dirac function, is the angular frequency of the phase shift.

[0081] If v0=0, then the phase shift Equation (9) reveals the fundamental frequency f C is: f C =ω / 2π=lΩ / π, which is generated by the static petal-shaped interferogram modulated by the chopper. There is no time domain signal with surface displacement and the corresponding fundamental frequency f C They are called carrier and carrier frequency respectively.

[0082] If v0 is a non-zero constant, that is: Formula (9) shows that for f C= Doppler shift f = lΩ / π D =2v0 / λ.

[0083] If v0 is not a constant value, but a time-varying velocity v(t) is used to replace the original constant velocity v0, then Doppler shift f D (t) becomes: f D (t) = 2v(t) / λ. For this non-stationary signal, time domain analysis is required to locate the Doppler shift that varies with time.

[0084] Scenario 2: Assume that the surface displacement has a non-uniform axisymmetric surface displacement profile, and its moving speed is v(r j ).

[0085] Phase Shift for: r j is the discrete radius of camera pixel sampling j=0,1,2,...M, j is the sampling length of camera pixel sampling radius. Substitute into formula (6) to obtain the moving speed v(r j ) is represented by formula (10):

[0086]

[0087] The frequency H2(ω) obtained by Fourier transform of equation (10) is represented by equation (11):

[0088]

[0089] The Fourier term in equation (11) is the same as the Fourier transform term in equation (8). After applying partial integration and the first-order harmonic approximation to equation (11), and further ignoring negative frequencies and DC components as in equations (8) and (9), the frequency H2(ω) represented by equation (12) is obtained as:

[0090]

[0091] If v(r j ) at each radius r j is constant, and Equation (12) reveals that the Doppler frequency shift f D (r j )=2v(r j ) / λ at each r j Up-weighted This means that the spectral distribution given by Equation (12) looks identical to the intensity profile of a Laguerre-Gaussian beam. Therefore, if the intensity distribution of a Laguerre-Gaussian beam exhibits p+1 concentric rings, the spectrum will be split into p+1 Doppler peaks corresponding to the radii of the p+1 concentric rings of the Laguerre-Gaussian beam. Since the higher harmonics in the Fourier transform of ∫T(θ,t)dθ are neglected, the actual spectral distribution differs slightly from Equation (12), but the Doppler frequency splitting still exists, and the relationship to the frequency peak associated with the first harmonic remains unchanged.

[0092] If v(r j ) in r j It is not constant at each radius, that is, the velocity v(r j ,t) instead of v(r j ), the split Doppler frequency peak is f D (r j ,t)=2v(r j ,t) / λ, which is a time-dependent function. Similarly, time domain analysis is required to locate these time-varying frequency peaks.

[0093] By locating these Doppler frequency peaks, the displacement velocity of the measured surface at the corresponding radius and specific time can be obtained, and then the dynamic displacement change information of the measured surface can be obtained by integrating the velocity over time.

[0094] The measurement process and effects of the present invention are further demonstrated below with reference to the accompanying drawings.

[0095] When the measured surface undergoes uniform surface displacement, a vortex beam with a high radial order of a specific wavelength is used. In the present invention, the topological charge of the vortex beam is l=10, the radial index p=7, the angular velocity of the chopper is Ω=±10πrad / s, and the phase shift is The sampling rate is F S =400Hz. When the measured surface does not undergo surface displacement, the petal-shaped interference modulated by the chopper Figure 1 Straight is still, such as Figure 2 shown. Figure 2 Figure (a) shows the carrier and the interference pattern after cutting obtained when there is no surface displacement within 0.5 seconds. Figure 2 Figure (a) is the time domain carrier obtained by equation (6), showing the carrier obtained when there is no surface displacement, that is, the phase shift The figure shows the signal within 0.5 seconds, and also shows the cut interference pattern and the maximum, minimum and median intensity of the petal-shaped interference pattern. Figure 2 Figure (b) shows the carrier spectrum after the discrete Fourier transform of the carrier, which shows that the fundamental frequency is exactly at f after the discrete Fourier transform of the carrier. C= lΩ / π = 100Hz. The carrier frequency is independent of the chopping direction, where the Fourier transform shows infinite harmonics and the envelope form is sinc 2 .

[0096] When the uniform surface moves at a constant speed v0 = 0.5 μm / s, Figure 3 Figure (a) shows the time domain signal of uniform surface displacement when v0 = 0.5 μm / s and Ω = 10πrad / s. Since the petal-shaped interferogram and the chopper rotate in the same direction, the time domain signal when Ω = 10πrad / s changes slowly relative to the carrier. Figure 3 The solid line part of Figure (a) is shown, and the dotted line part represents the carrier. Figure 3 Figure (b) shows the time domain signal of uniform surface displacement when v0 = 0.5 μm / s and Ω = -10πrad / s. If the chopper rotates in the opposite direction to the interference pattern, that is, when Ω = -10πrad / s, the time domain signal changes faster than the carrier. The time domain signal is as follows: Figure 3 As shown in Figure (b). Figure 3 Figure (c) is Figure 3 The spectrum of the time domain signal in (a) and (b) is shown in Figure 1. The discrete Fourier transform of the time domain signal leads to the C The positive Doppler shift f D =1.58Hz, for f C Negative Doppler shift f D =-1.58Hz. Similarly, when v0 = 0.5μm / s, the discrete Fourier transform of the time domain signal is f C The Doppler frequency shift f D =1.58Hz, which is consistent with the theoretical value f D =2v0 / λ, compared with the calculation, f D The small error is 2.8×10 -4 Hz, and its corresponding speed error value is v0=λf D / 2=0.088nm / s, this frequency estimation error is reasonable.

[0097] In the case of uniform surface displacement and non-uniform velocity, it is assumed that the uniform surface moves at a non-constant velocity v(t) = a×t = 5tμm / s, where the constant acceleration a = 5μm / s 2 . Figure 4 Figure (a) shows the time domain signal of uniform surface displacement when v(t) = a×t = 5tμm / s, Ω = 10πrad / s; Figure 4 Figure (b) shows the time domain signal of uniform surface displacement when v(t) = a×t = 5tμm / s and Ω = -10πrad / s. Figure 4 Figure (c) is Figure 4 (a) and (b) are time-frequency diagrams of the time domain signal. Figure 4 The solid line part in Figure (c) is the time-frequency diagram of synchronous compression wavelet transform based on Morlet wavelet, from which it is observed that the carrier frequency f C =100 Hz, corresponding to the linear up-chirp and down-chirp of Ω = -10πrad / s and Ω = 10πrad / s, respectively. Figure 4 Figure (d) is v(t) = a(t) × t = 2t 2 The time-frequency diagram of the time domain signal of uniform surface displacement at μm / s. When the speed of surface displacement is v(t)=a(t)×t=2t 2 μm / s, where acceleration a(t) = 2tμm / s 2 When the acceleration is non-constant, the quadratic up-chirp and down-chirp of Ω = -10πrad / s and Ω = 10πrad / s can be obtained in time-frequency representation, respectively, as shown in Figure 4 The solid line in Figure (d) shows that the maximum energy time-frequency ridge is extracted to obtain the Doppler frequency shift at a specific time point, and then the Inverse dynamic surface displacements.

[0098] When studying the measurement of non-uniform axisymmetric surface displacement under non-uniform surface displacement and constant speed, the present invention uses a surface with a Gaussian distribution to simulate the non-uniform axisymmetric surface displacement. At a constant speed, a vortex beam with p+1 concentric rings is used to illuminate the non-uniform axisymmetric surface. In order to make the vortex beam completely cover the area of ​​surface displacement, a high-order vortex beam with a higher radial order is selected, and p=10 is selected here. There is a phase shift caused by different surface movement speeds on the concentric circles of different radii. Before measurement, the power-weighted average radius r of each ring needs to be calculated. n Calibrate, radius r n Characterized by formula (13):

[0099]

[0100] The radius r j is the discrete radius of the Laguerre-Gaussian beam; M is the sampling length of the radius; I(r j ) is the intensity distribution of the Laguerre-Gaussian beam when l = 10. For a fixed radial order p, the waist radius ω0 of the Laguerre-Gaussian beam can be adjusted in equation (3) to adjust the lateral resolution of the surface displacement measurement determined by the radius position of the Laguerre-Gaussian beam. Figure 5 Figure (a) in the middle is the intensity distribution of a high-order Laguerre-Gaussian beam when l=10 and p=10. Figure 5 Figure (b) shows the velocity distribution of the corresponding non-uniform axisymmetric surface displacement, and the calibration radius is given by Figure 5 The dotted line indicates . Figure 5Figure (b) shows the velocity distribution of the non-uniform axisymmetric surface displacement at r = 0 mm and the non-uniform axisymmetric surface displacement velocity v0 = 1 μm / s, given by equation (14). Assuming that the velocity of the non-uniform axisymmetric surface displacement has a Gaussian distribution, the non-uniform axisymmetric surface displacement velocity v(r) is represented by equation (15):

[0101] v(r)=v0·exp(r 2 / σ 2 ) (14)

[0102] Where: σ=3mm, r=0mm, v0=1μm / s, such as Figure 5 As shown in Figure (b), according to the non-uniform axisymmetric surface displacement velocity given by formula (14), the theoretical velocity at the calibration radius is The corresponding theoretical Doppler frequency If the surface has an inclination angle or is laterally offset, points with the same radius will have different velocities.

[0103] Figure 6 Figure (a) shows the time domain signal of the displacement of a non-uniform axisymmetric surface when v0 = 1 μm / s, r = 0 mm, and Ω = -10πrad / s, as well as the interference pattern before shearing at t = 1, 3, 6, and 10 seconds. The figure shows that the signal envelope decreases in an oscillatory manner, indicating that it is composed of multiple frequency components. Due to the high degree of distortion and stretching of the petal-shaped fringes, the intensity of the interference pattern after passing through the chopper changes very little, and the signal change almost disappears after 10 seconds. Conventional fringe morphology operations can only observe for 2-3 seconds due to the large distortion of the petals, but the carrier optical vortex interferometer designed here can observe time domain signals for about 10 seconds, thus increasing the time span of dynamic measurement. Figure 6 Figure (b) is Figure 6 (a) The time domain signal spectrum when Ω = -10πrad / s and Ω = 10πrad / s, Figure 6 The dotted line in Figure (b) is the carrier frequency. Figure 6 The time domain signal spectrum on the right side of the dotted line in (b) shows that the Doppler frequency shift is split into p+1=11 peaks, corresponding to the different radii of the multiple rings of the vortex beam. Figure 6 As can be seen from Figure (b), the larger the radius, the smaller the corresponding speed and the smaller the Doppler shift. C The theoretical Doppler frequency peak can be obtained, that is, it can be used Get the velocity at the corresponding radius. Figure 6 Figure (c) shows the theoretical and inverted Doppler frequency peaks, i.e. and The relationship between the inverted Doppler shift and the theoretical Doppler shift is shown, and the two are in good agreement.

[0104] Frequency difference In the range of [-0.0277, 0.0106] Hz, as shown in Figure 6 (d). Figure 6 Figure (d) shows the frequency difference between the theoretical and inverted Doppler frequency peaks. The difference error between the two is affected by two factors: one is the frequency estimation error caused by the interval of discrete Fourier transform. The higher the frequency resolution, the more accurate the frequency estimation; the other is the discrete error in the spatial domain. In numerical studies, the light field and surface displacement are both discretely sampled in the spatial domain. Therefore, the intensity and radius of the Laguerre-Gaussian beam should correspond to the pixel index, which are both integers. However, the pixel index given in Equation (13) is usually a decimal, which leads to the inevitable discretization error in numerical studies. The higher the pixel resolution, the smaller the discretization error and the lower the computational efficiency. In practical applications, since the intensity distribution of the light field is continuous, the decimal obtained by Equation (13) is used as a sub-pixel interpolation to make the radius calibration and frequency estimation more accurate.

[0105] Since the lower the speed, the smaller the Doppler shift and the higher the requirement for frequency resolution, the sampling length should be increased by 2 times and 10 times at v0 = 0.1 μm / s and v0 = 0.5 μm / s, respectively, compared with v0 = 1 μm / s, to reduce the frequency estimation error. Figure 7 Figure (a) shows the time domain signal spectrum of the displacement of the non-uniform axisymmetric surface at r = 0 mm and v0 = 0.1, 0.5 μm / s and 1 μm / s. The dotted line represents the carrier frequency. Figure 7 The middle (b) figure shows the difference in Doppler frequency peaks at the corresponding radii when v0 = 0.1, 0.5 μm / s and 1 μm / s, where the right vertical axis represents the velocity difference, showing the difference between the theoretically estimated Doppler shift and the inverted Doppler shift when v0 = 0.1, 0.5 μm / s and the velocity is 1 μm / s, that is, The difference between the estimated velocity of the measured surface and the inverted value is given by Given, it is only scaled by multiples of λ / 2. Figure 7 Figure (c) shows the difference between the theoretical and inverted Doppler frequency peaks when v0 = 0.1, 0.5 μm / s and 1 μm / s. Figure 7 In Figure (c), the relative error of the inverted Doppler frequency is The surface displacement velocity error with the inverted |v rtr (r n )-v thr (r n )| / v thr (r n ) are on the same vertical axis. The results show that the relative errors of displacement velocities on different surfaces are consistent.

[0106] Under non-uniform surface displacement and non-constant velocity, it is assumed that the non-uniform surface moves at a non-constant velocity v0(t) = a×t = 10tμm / s, where the constant acceleration a = 10μm / s 2 . Figure 8 Figure (a) shows the time domain signal of the displacement of the non-uniform axisymmetric surface when r = 0 mm, Ω = -10πrad / s, p = 10, and v0(t) = a×t = 10tμm / s. It can be seen from the oscillation envelope and the gradually increasing frequency that this is a multi-component linear chirp. Figure 8 Figure (b) is Figure 8 Figure (a) shows a high-resolution time-frequency diagram based on multi-synchronous compression. Due to the contrast of the time domain signals, the time-frequency diagram has strong energy before 0.1s, but the multiple frequency components are close together, making them difficult to distinguish. After 0.1s, the multiple frequency components gradually separate, but some frequency components are also missing. To observe multiple frequency components more clearly, the radial order can be reduced. Here, p = 10 is reduced to p = 5 to expand the frequency interval between adjacent frequency components, making the observation of multiple frequency components clearer. Figure 8 Figure (c) is the time-frequency diagram of the time domain signal when p=5. By using the best fit with the time-frequency ridge line, multiple frequencies of this period can be extracted, and then Get the dynamic surface displacement.

[0107] The above describes the specific embodiments of the present invention. Those skilled in the art may also make changes and modifications to the above embodiments, and some modifications and changes to the invention should also fall within the scope of protection of the claims of the present invention.

Claims

1. A method for measuring the displacement of dynamic uniform and non-uniform surfaces using a carrier optical vortex interferometer, characterized by: A high-order vortex beam with concentric rings of different radii is used as a probe beam for dynamic surface displacement measurement. The probe beam and a reference beam are coaxially coherently superimposed to generate a two-dimensional interference pattern with petal-shaped vortices. The reference beam is a high-order vortex beam conjugated with the probe beam. The two-dimensional interference pattern is modulated by a chopper to convert it into a one-dimensional time-domain signal. When no surface displacement occurs on the measured surface, the one-dimensional time domain signal is a carrier signal, and a carrier frequency signal is obtained by Fourier transforming the carrier signal; When the measured surface undergoes uniform surface displacement, the two-dimensional interference pattern rotates as a whole due to the uniform phase shift, and the Fourier spectrum of the one-dimensional time domain signal produces a Doppler frequency shift relative to the carrier frequency signal. The surface displacement velocity is obtained by locating the Doppler frequency shift. When non-uniform surface displacement occurs on the measured surface, petals at different radii of the two-dimensional interference pattern produce different rotation speeds due to different phase shifts, and the Fourier spectrum of the one-dimensional time domain signal produces a split Doppler frequency shift, and the Doppler peak frequency corresponds to the radius of each concentric ring in the vortex beam; the surface displacement velocity corresponding to the radius of the vortex beam ring is obtained by locating the Doppler peak frequency based on the carrier frequency signal; The surface displacement profile at any moment is obtained by integrating the velocity over time, thus realizing the measurement of dynamic surface displacement.

2. The method for measuring dynamic uniform and non-uniform surface displacement using a carrier optical vortex interferometer according to claim 1, wherein: The high-order vortex light beams of the concentric rings with different radii are at least two concentric rings with different radii.

3. The method for measuring dynamic uniform and non-uniform surface displacement using a carrier optical vortex interferometer according to claim 2, wherein: The high-order vortex beam is a Laguerre-Gaussian beam or a Bessel beam.

4. The method for measuring dynamic uniform and non-uniform surface displacement using a carrier optical vortex interferometer according to claim 1, wherein: Construct the measurement system as: A laser beam with a set wavelength emitted by a laser transmitter (1) is expanded by a beam expander and then introduced into a spatial light modulator (2) through a first beam splitter (3), and a high-order vortex beam is generated by the spatial light modulator (2); The high-order vortex beam is divided into two vortex beams by a second beam splitter (5), wherein one vortex beam is used as a detection beam and the other vortex beam is used as a reference beam; the detection beam reaches the measured surface via a third beam splitter (7) and enters a fourth beam splitter (8) after being reflected by the measured surface; the reference beam is combined with the output light of the fourth beam splitter (8) through the mirror reflection of the reflector (6), so that the two vortex beams undergo odd-numbered reflections and even-numbered reflections respectively to form a conjugate, and the conjugate vortex beams are coaxially coherently superimposed to generate a two-dimensional interference pattern in the form of a petal-shaped vortex; A detection system consisting of an optical chopper (9), a lens (10) and a point detector (11) is provided to convert the two-dimensional interference pattern into a one-dimensional time domain signal.

5. The method for measuring the displacement of a carrier optical vortex interferometer on a dynamic uniform and non-uniform surface according to claim 4, wherein: A high-order vortex beam for optimizing vortex beam imaging is arranged between the first beam splitter (3) and the second beam splitter (5) and enters a 4f system (4). The 4f system (4) is composed of two lenses with equal focal lengths and a variable aperture.

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