Micro-displacement measurement method based on conjugate vortex light interference on medium metasurface

Abstract

The invention discloses a micro-displacement measurement method based on conjugate vortex light interference on a dielectric metasurface, and relates to the technical field of optical micro-displacement measurement, and the method comprises the following steps: designing the dielectric metasurface through a numerical simulation mode; constructing a precise displacement measurement system based on conjugate vortex light interference by adopting a medium metasurface; acquiring interference intensity distribution images before and after the object moves by adopting a precision displacement measurement system; extracting the light intensity change of the interference intensity distribution image through multiple regions, and inverting a whole-course rotation angle; and calculating the micro-displacement according to the whole-course rotation angle. According to the method, the dielectric metasurface is designed through numerical simulation, stable vortex light with different topological charges can be generated, the whole-course rotation angle is inverted by combining the light intensity change of the multi-region extraction interference intensity distribution image, and the working range, the environmental adaptability and the measurement precision of micro-displacement measurement are improved.

Description

Technical Field

[0001] The present application relates to the field of optical micro-displacement measurement technology, and in particular to a micro-displacement measurement method based on conjugate vortex optical interference of a dielectric metasurface. Background Art

[0002] As vortex light research in optics deepens, its unique phase distribution has broad applications in measuring tiny displacements, making it crucial for precision machining, materials testing, medical diagnostics, and other fields. For example, in precision manufacturing, measuring tiny displacements on the surface of mechanical parts can be used to detect surface defects, wear, or assembly accuracy, thereby improving product quality. In materials science, measuring nanoscale displacements on a material's surface can assess its mechanical properties and surface characteristics. In biomedicine, using vortex light to detect tiny displacements in biological tissue can monitor blood flow and provide important physiological indicators. Furthermore, vortex light technology can be used in rehabilitation therapy and sports science research to monitor tiny movements in human joints, helping to improve medical treatments. Therefore, research on micro-displacement measurement methods based on vortex light is needed.

[0003] Currently, vortex light is generally generated through free-space structures or fiber structures. Free-space structures include: spiral phase plates: By introducing a spiral phase plate into the optical path, the light wave can acquire orbital angular momentum, thereby generating vortex light; vortex wave plates: By adjusting the phase delay of the wave plate, the phase of different parts of the light wave changes to varying degrees, ultimately forming a light wave with a spiral phase structure; spatial light modulators: By loading a specific phase modulation pattern on the spatial light modulator, the phase distribution of the light wave can be changed, thereby forming vortex light with a spiral phase structure. Fiber structures include: spiral fiber: a specially designed fiber structure that can generate vortex light during transmission within the optical fiber, usually achieved through devices such as fiber gratings; fiber gratings: introducing periodic changes in the optical fiber can achieve diffraction and interference of light, thereby generating vortex light.

[0004] However, the micro-displacement measurement in the above-mentioned prior art has poor working range, environmental adaptability and measurement accuracy. Summary of the Invention

[0005] The present application provides a micro-displacement measurement method based on conjugate vortex optical interference of a dielectric metasurface, which is used to solve the problems of poor working range, environmental adaptability and measurement accuracy of existing optical micro-displacement measurement technologies.

[0006] On the one hand, the present application provides a micro-displacement measurement method based on conjugate vortex optical interferometry of a dielectric metasurface, comprising the following steps:

[0007] Step 1: Design the dielectric metasurface through numerical simulation.

[0008] Step 2: Use the dielectric metasurface to construct a precision displacement measurement system based on conjugate vortex optical interference.

[0009] Step three: using the precision displacement measurement system to collect interference intensity distribution images before and after the object moves.

[0010] Step 4: extract the light intensity change of the interference intensity distribution image in multiple regions to invert the full rotation angle.

[0011] Step 5: Calculate the micro-displacement according to the full rotation angle.

[0012] In one possible implementation, step one includes:

[0013] The phase characteristics and transmittance characteristics of nano-cylinders of different sizes, spacings and heights are calculated by numerical simulation, and the corresponding nanostructure groups are screened out according to the phase characteristics and transmittance characteristics.

[0014] According to the topological charge phase characteristics of the required OAM vortex beam, the corresponding nanocylinders are called from the screened nanostructure group to construct the dielectric metasurface.

[0015] In a possible implementation, in step 1, plasma enhanced chemical vapor deposition, spin coating of photoresist, electron beam exposure, development, and etching are sequentially used to process the designed dielectric metasurface.

[0016] In one possible implementation, in step 2, the precision displacement measurement system includes: a tunable laser, a self-focusing lens, a first objective lens, a dielectric metasurface, a second objective lens, a first polarization beam splitter, a Dove prism, a second polarization beam splitter, a first quarter-wave plate, a first reflector, a third polarization beam splitter, a second quarter-wave plate, a second reflector, a fourth polarization beam splitter, and a CCD camera.

[0017] The Gaussian beam emitted by the tunable laser passes through the self-focusing lens, the first objective lens, the dielectric metasurface, the second objective lens, and the first polarization beam splitter in sequence.

[0018] The first polarization beam splitter splits the light beam into two paths. One path enters the measuring arm, passes through the Dove prism, the second polarization beam splitter, the first quarter-wave plate, and the first reflector in sequence, and is reflected back to the second polarization beam splitter by the first reflector. The other path enters the reference arm, passes through the third polarization beam splitter, the second quarter-wave plate, and the second reflector in sequence, and is reflected back to the third polarization beam splitter by the second reflector.

[0019] The second polarization beam splitter and the third polarization beam splitter respectively reflect the reflected light beam to the fourth polarization beam splitter to reach the CCD camera.

[0020] In a possible implementation, in step three, noise reduction processing is performed on the interference intensity distribution image.

[0021] The noise reduction process includes: filtering algorithm, morphological operation, and closing operation.

[0022] In one possible implementation, in step four, the multi-region extraction of the light intensity change of the interference intensity distribution image includes: setting a number of target rings with different radii on the petals of the interference intensity distribution image, extracting the light intensity change of the target rings, and obtaining the light intensity extreme points of the petals.

[0023] In one possible implementation, in step four, the light intensity extreme point is processed using fast Fourier transform to obtain the angle corresponding to the light intensity extreme point, and the angle array after smoothing is matched with the light intensity extreme point to average the angles of all petals to obtain the full rotation angle.

[0024] In a possible implementation, in step five, based on a functional relationship between the micro-displacement and the full-range rotation angle, the micro-displacement is calculated according to the full-range rotation angle.

[0025] The micro-displacement measurement method based on conjugate vortex optical interferometry of dielectric metasurfaces in this application has the following advantages:

[0026] By numerically simulating and designing dielectric metasurfaces, stable vortex light with different topological charges can be generated. The light intensity changes of the interference intensity distribution image extracted in multiple regions can be combined to invert the full rotation angle, thereby improving the working range, environmental adaptability and measurement accuracy of micro-displacement measurement.

[0027] By adopting dielectric metasurfaces to construct a precision displacement measurement system based on conjugate vortex optical interference, the interference intensity distribution image is obtained by utilizing the interference generated by two conjugate vortex light beams. During the process of displacement change of the object to be measured, the interference intensity distribution image will rotate accordingly, and the full rotation angle can be inverted to obtain the micro-displacement, and the micro-displacement can be calculated based on the functional relationship between the micro-displacement and the full rotation angle.

[0028] By sequentially using plasma-enhanced chemical vapor deposition, spin-coating photoresist, electron beam exposure, development, and etching, the designed dielectric metasurface is processed to ensure that the spectral performance is stable and does not degrade over time. At the same time, it has the characteristics of compact structure, good compatibility, low loss, high conversion efficiency, and adaptability to harsh environments.

[0029] By placing several target rings of varying radii on the petals of the interference intensity distribution image, the intensity variations of the target rings are extracted to determine the extreme intensity points of the petals. This multi-region extraction method overcomes the bottleneck problem of large-displacement measurement, where the periodic rotation of the interference image makes it impossible to determine the displacement. This further improves the operating range and applicability of the measurement system, providing new technical support for the design of picometer-level displacement measurement methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0031] Figure 1 A schematic flow chart of a micro-displacement measurement method based on conjugate vortex optical interferometry of a dielectric metasurface provided in an embodiment of the present application;

[0032] Figure 2 A schematic diagram of a group of nanostructures screened out according to an embodiment of the present application;

[0033] Figure 3 Phase characteristics and transmittance characteristics data diagram provided by the embodiment of the present application;

[0034] Figure 4 Output light intensity distribution diagram of a dielectric metasurface with a designed topological charge of 4 provided in an embodiment of the present application;

[0035] Figure 5 Output light phase distribution diagram of a dielectric metasurface with a designed topological charge of 4 provided in an embodiment of the present application;

[0036] Figure 6 Schematic diagram of the equiphase surface distribution of the vortex beam under different topological charges provided in the embodiment of the present application;

[0037] Figure 7 A cross-sectional phase distribution diagram perpendicular to the propagation direction provided in an embodiment of the present application;

[0038] Figure 8 This is a diagram showing the electric field intensity distribution of the vortex light provided in an embodiment of the present application;

[0039] Figure 9 The electric field intensity distribution diagram of the interference between the vortex beam and the plane wave provided in the embodiment of the present application;

[0040] Figure 10 This is an electron microscope scan of the dielectric metasurface provided in the embodiment of the present application;

[0041] Figure 11 A schematic structural diagram of a precision displacement measurement system provided in an embodiment of the present application;

[0042] Figure 12 Interference intensity distribution image of the displacement from 0 to 500 nm provided in the embodiment of the present application;

[0043] Figure 13 Provided in the embodiments of this application Figure 12 Corresponding micro-displacement measurement results.

[0044] Description of reference numerals:

[0045] 1-tunable laser, 2-self-focusing lens, 3-first objective lens, 4-dielectric metasurface, 5-second objective lens, 6-first polarization beam splitter, 7-Dove prism, 8-second polarization beam splitter, 9-first quarter-wave plate, 10-first reflector, 11-third polarization beam splitter, 12-second quarter-wave plate, 13-second reflector, 14-fourth polarization beam splitter, 15-CCD camera. DETAILED DESCRIPTION

[0046] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0047] like Figure 1 As shown, the embodiment of the present application provides a micro-displacement measurement method based on conjugate vortex optical interferometry of a dielectric metasurface, comprising the following steps:

[0048] Step 1: Design the dielectric metasurface 4 through numerical simulation.

[0049] Step 2: Use the dielectric metasurface 4 to construct a precision displacement measurement system based on conjugate vortex optical interference.

[0050] Step three: using the precision displacement measurement system to collect interference intensity distribution images before and after the object moves.

[0051] Step 4: extract the light intensity change of the interference intensity distribution image in multiple regions to invert the full rotation angle.

[0052] Step 5: Calculate the micro-displacement according to the full rotation angle.

[0053] Exemplarily, step one includes:

[0054] The phase characteristics and transmittance characteristics of nano-cylinders of different sizes, spacings and heights are calculated by numerical simulation, and the corresponding nanostructure groups are screened out according to the phase characteristics and transmittance characteristics.

[0055] According to the topological charge phase characteristics of the required OAM vortex beam, the corresponding nanocylinders are called from the screened nanostructure group to construct the dielectric metasurface 4.

[0056] Specifically, in this embodiment, the orbital angular momentum mode conversion equation and the phase matching of the metasurface are used for simulation calculation, and the phase characteristics and transmittance characteristics of nano-cylinders of different sizes, spacings, and heights are calculated using numerical simulation (FDTD, CWA) in the simulation program, such as Figure 2 Shown is a schematic diagram of the screened nanostructure group, such as Figure 3 Shown are the phase characteristics and transmittance characteristics data graphs. Figure 2 Where U represents the side length of the nanostructure group, R represents the radius of the nanocylinder, and H represents the height of the nanocylinder. The wavelength was set at 1550 nm, and nanostructure groups with high transmittance and a phase coverage of 0 to 2π were selected.

[0057] Specifically, in this embodiment, according to the topological charge phase characteristics of the desired OAM vortex beam, the corresponding nanocylinders are called from the screened nanostructure group to construct the dielectric metasurface 4, and the FDTD method is used to simulate the space of interest. The boundary conditions are all set as perfect absorption layers, and the intensity and phase distribution of the transmitted light field are studied. Figure 4 and Figure 5 Shown are the output light intensity and phase distributions of dielectric metasurface 4, respectively, with a designed topological charge of 4. The intensity distribution is a hollow ring, while the phase distribution is four spiral lobes, meeting the design requirements. Furthermore, the modulation mode conversion efficiency of dielectric metasurface 4 approaches 100%, successfully achieving the research goal of broadband and high conversion efficiency.

[0058] Specifically, for a general OAM vortex beam, only the spiral phase distribution of the light needs to be considered. However, tight focusing must also be considered, so the overall phase distribution is as follows:

[0059]

[0060] When the incident light is left-handed circularly polarized, the phase shift caused by the rotation of the nanorods is 2α. Therefore, the rotation angles of the nanorods at different positions are expressed as follows:

[0061]

[0062] Among them, λ is the wavelength of the incident light, R is the radius of the metasurface, l is the phase topological charge, θ and r are the azimuth angle and radius of the nanopillar in the cylindrical coordinate system, respectively. In addition, the transmitted light will also obtain a focusing / diverging phase with a numerical aperture of NA. The divergence or focusing characteristics are still determined by the polarization state of the incident light.

[0063] A vortex beam is a special type of beam with a spiral phase factor, in which the angular momentum topological charge determines the size of the photons in the beam. The topological charge of a vortex beam can take any positive integer, so the photons can have infinite values. The central phase of the vortex beam is uncertain. During the transmission process, the central intensity is 0 due to the mutual interference of the electric field, so its intensity distribution has a ring structure. In addition, as the absolute value of the topological charge increases, the diffraction of the beam becomes stronger during propagation, so its ring radius becomes larger. The intrinsic vortex beam is also a solution to the wave equation in the paraxial approximation. For convenience, it is assumed that the beam is linearly polarized light, then the amplitude of the field should satisfy the Helmholtz equation, as shown below:

[0064]

[0065] Where k = ω / c is the light wave vector. Substituting the formal solution f into the above equation, the above equation becomes:

[0066]

[0067] Considering the paraxial approximation, the amplitude u changes little in the propagation direction z, so the second-order partial derivative in the z direction is discarded, and we can get:

[0068]

[0069] Common OAM beams such as Laguerre-Gaussian beams and Bessel-Gaussian beams are all solutions to this paraxial wave equation. For simplicity, the expression of the OAM beam can be written as:

[0070] E=E0(ρ,z)e ilθ e -ikzi

[0071] Where E0 is the amplitude distribution of the beam, ρ is the transverse radius of the beam, and e ilθ and e -ikzi Represent the vortex phase factor and propagation phase factor of the beam respectively, and z is the propagation direction. Therefore, it is concluded that the vortex beam is only related to the phase topological charge. Figure 6The following is a schematic diagram of the isophase surface distribution of a vortex beam under different topological charges. It can be seen that the isophase surface undergoes different degrees of distortion depending on the topological charge. As the topological charge increases, the degree of distortion of the isophase surface increases, and the direction of distortion is determined by the sign of the topological charge. When the topological charge is 0, the isophase surface is not distorted and is identical to the wavefront of a plane wave. Furthermore, it can be observed that the number of distorted isophase surfaces is equal to the absolute value of the topological charge. Figure 7 This is the phase distribution diagram of a cross section perpendicular to the propagation direction. When the topological charge is not zero, the phase varies with the azimuth angle, and the period and handedness are determined by the magnitude and sign of the topological charge. However, when the topological charge is zero, the phase no longer varies with the azimuth angle, and the values of the entire phase surface are exactly the same. Figure 8 The electric field intensity distribution of the vortex light is shown in Figure 2. It can be concluded that the larger the absolute value of the topological charge, the larger the radius R of the light ring. When the topological charge is 0, the hollow dark spot in the light field disappears and becomes a solid light spot. At this point, the light beam no longer carries orbital angular momentum. Figure 9 The electric field intensity distribution of the interference between a vortex beam and a plane wave is shown in Figure 2. It can be seen that the number of interference lobes is equal to the absolute value of the vortex beam's topological charge, and the handedness of the interference lobe is related to the sign of the topological charge. This unique interference property is used to detect the topological charge of a vortex beam.

[0072] Vortex beams are generated using metasurface optical structures. First, in the design of the metasurface, the vortex characteristics of the beam can be precisely controlled by adopting different structures such as circular nanopillars or elliptical cylinders and adjusting their geometric parameters (such as size, shape, and phase delay). The metasurface is composed of periodic microstructures, and their electromagnetic properties can be adjusted by changing their size, arrangement, or spacing. Secondly, phase modulation is achieved. Through the design of the metasurface structure, the phase of the incident light can be precisely controlled. The light emitted by the laser is coupled to the collimator via a single-mode optical fiber and then collimated for output. Subsequently, the light beam is converted into a circularly polarized state through the action of a linear polarizer and a quarter-wave plate. Next, the circularly polarized light passes through a metasurface containing a specific phase structure, which can change the phase distribution of the incident light, thereby giving the light orbital angular momentum. In order to measure and analyze the vortex beam, the light beam will be magnified and imaged by a microscope and lens, and finally captured by a CCD detector. By adjusting the polarization state of the light and using specific optical elements, the vortex beam carried by the light beam can be verified.

[0073] For example, in step 1, plasma enhanced chemical vapor deposition, spin coating of photoresist, electron beam exposure, development, and etching are sequentially used to process the designed dielectric metasurface 4.

[0074] Specifically, the PB phase-type metasurface controls the local PB phase by changing the rotation angle of the nanopillar, which can realize arbitrary regulation of the spin photon phase and has the characteristics of small size and compact structure. By using the PB phase-type metasurface to simultaneously load the spiral phase and the tightly focused phase, a tightly focused OAM beam can be directly generated. The metasurface is composed of rectangular nanopillars of the same size and different rotation angles. After passing through the metasurface, the incident circularly polarized light obtains the corresponding OAM and is then focused near the focal point. In this process, the polarization state will be reversed due to the birefringence effect of the nanopillar. When polarized light passes through anisotropic nanopillars (if loss is not considered), its light field transmission can be described in the following matrix form:

[0075]

[0076] in and are the x and y components of the incident electric field, and are the x and y components of the output electric field. α is the rotation angle of the nanorod. R is a 2×2 rotation matrix. φ x and φ y They represent the phase delay of the nanorod to the x-polarized and y-polarized incident light, respectively. x -φ y When |=π, the response of the nanorod to circularly polarized light can be described as:

[0077]

[0078] If the rotation angle α satisfies:

[0079]

[0080] Where λ is the wavelength of the incident light, R is the radius of the metasurface, θ and r are the azimuth angle and radius of the nanopillar in the cylindrical coordinate system, respectively. Substituting them into the equation, we can see that the incident light wavefront will be distorted and carry orbital angular momentum. The sign of the polarization state of the incident light is determined by the positive or negative sign. Furthermore, the transmitted light also acquires a focusing / diverging phase with a numerical aperture (NA). The divergence or focusing characteristics are still determined by the polarization state of the incident light. When designing a metasurface, it is important to carefully select the polarization state of the incident light to avoid divergence of the OAM beam.

[0081] Specifically, in this embodiment, a 700 nm thick amorphous silicon is deposited on quartz glass using plasma enhanced chemical vapor deposition, followed by spin coating of photoresist, electron beam exposure, development, and etching to produce the designed dielectric metasurface 4. The processed area of the dielectric metasurface 4 is a circular area with a diameter of 100 μm. Figure 10The figure shows a scanning electron microscope image of the dielectric metasurface 4. As can be seen, the size and lattice constant of the Si nanopillars are very close to the designed values.

[0082] For example, Figure 11 As shown, in step 2, the precision displacement measurement system includes: a tunable laser 1, a self-focusing lens 2, a first objective lens 3, a dielectric metasurface 4, a second objective lens 5, a first polarization beam splitter 6, a Dove prism 7, a second polarization beam splitter 8, a first quarter-wave plate 9, a first reflector 10, a third polarization beam splitter 11, a second quarter-wave plate 12, a second reflector 13, a fourth polarization beam splitter 14, and a CCD camera 15.

[0083] The Gaussian light beam emitted by the tunable laser 1 passes through the self-focusing lens 2, the first objective lens 3, the dielectric metasurface 4, the second objective lens 5, and the first polarization beam splitter 6 in sequence.

[0084] The first polarization beam splitter 6 splits the light beam into two paths. One path enters the measuring arm, passes through the Dove prism 7, the second polarization beam splitter 8, the first quarter-wave plate 9, and the first reflector 10 in sequence, and is reflected back to the second polarization beam splitter 8 by the first reflector 10. The other path enters the reference arm, passes through the third polarization beam splitter 11, the second quarter-wave plate 12, and the second reflector 13 in sequence, and is reflected back to the third polarization beam splitter 11 by the second reflector 13.

[0085] The second polarization beam splitter 8 and the third polarization beam splitter 11 respectively reflect the reflected light beams to the fourth polarization beam splitter 14 and reach the CCD camera 15 .

[0086] Specifically, in this embodiment, the dielectric metasurface 4 is mounted on a plastic plate with a small central aperture and can be precisely adjusted in the X, Y, and Z directions using a three-dimensional translation stage. The wavelength of the tunable laser 1 is 1550 nm. The Gaussian beam emitted by the tunable laser 1 passes through a self-focusing lens 2 and then through a 5× first objective lens 3 to be focused onto the dielectric metasurface 4. This Gaussian beam is modulated into a stable vortex beam with a preset topological charge (+l). The vortex beam then passes through a 20× second objective lens 5, forming a microscope device that amplifies the generated vortex beam (+l). After collimation, the vortex beam is split into two paths by the 5:5 first polarization beam splitter 6. One path enters the measurement arm and passes through the dove prism 7, which converts the vortex beam (+l) into its conjugate beam (-l). The conjugate beam passes through the second polarization beam splitter 8, the first quarter-wave plate 9, and the first reflector 10 in sequence, and is reflected back to the second polarization beam splitter 8 by the first reflector 10. The other path enters the reference arm, passes through the third polarization beam splitter 11, the second quarter-wave plate 12, and the second reflector 13 in sequence, and is reflected back to the third polarization beam splitter 11 by the second reflector 13. The second polarization beam splitter 8 and the third polarization beam splitter 11 respectively reflect the reflected conjugate beam (-l) and vortex beam (+l) to the fourth polarization beam splitter 14, and then reach the CCD camera 15, where they interfere and produce a petal-shaped interference pattern, i.e., an interference intensity distribution image. In this setup, the addition of a Dove prism 7 to a conventional Mach-Zehnder interferometer introduces a lateral position-dependent phase shift whose magnitude is significantly greater than the inherent helical phase of the beam. To mitigate this effect, this embodiment replaces the reflective elements in the conventional interference optical path with a second polarization beam splitter 8, a first quarter-wave plate 9, a first reflector 10, and a third polarization beam splitter 11, a second quarter-wave plate 12, and a second reflector 13. This modification effectively eliminates the effects of the Dove prism 7 while maintaining the high quality of the conjugate vortex beam, thereby achieving a stable and robust interference pattern.

[0087] Specifically, the vortex beam generated by modulation can be expressed as:

[0088] E=A exp(iIθ)

[0089] Where θ represents the azimuth angle (the angle variable in polar coordinates), A represents the amplitude of the vortex, and the vortex beam is split into a reference beam E1 and a measurement beam E2 by the first polarization beam splitter 6, which can be described as:

[0090] E1=A1exp(-iIθ)

[0091] E2=A2exp(iIθ)

[0092] Where E1 represents the complex amplitude of the reference beam, and E2 represents the complex amplitude of the measurement beam.

[0093] The measurement beam passes through Dove prism 7, converting +1 to -1. When the object undergoes microdisplacement, the measurement beam is reflected by the object, converting -1 to +1. Finally, after the measurement beam is reflected back to the second polarization beam splitter 8, its light field becomes E2, which interferes with the reference beam E1. The light field containing the object's microdisplacement information can be described as:

[0094] E'2=A'2exp(ilθ+ik2z)

[0095] Where E'2 represents the complex amplitude of the measurement beam after reflection from the object, containing micro-displacement information; A'2 represents the amplitude of the measurement beam after reflection (which may vary due to object reflectivity or scattering); and kz represents the longitudinal component of the wave vector. z is the distance changed by the movement of the object to the second polarization beam splitter 8. The CCD camera 15 can record the interference pattern between the reference beam and the reflected light, resulting in:

[0096]

[0097] Where I is the intensity distribution of the interference pattern recorded by the CCD camera. To accurately measure the rotation angle of the petals, the maximum intensity (Imax) is selected as the characteristic point of each petal (the brightest position). The functional relationship between the micro-displacement and the full rotation angle can be obtained from the above formula as shown below:

[0098]

[0099] Wherein, λ represents the wavelength of light, z(0) represents the initial distance between the object and the second polarization beam splitter 8, and the collected data is processed using data processing software to obtain the full rotation angle. The precise displacement data is then obtained through the functional relationship between the micro-displacement and the full rotation angle.

[0100] Exemplarily, in step three, noise reduction processing is performed on the interference intensity distribution image.

[0101] The noise reduction process includes: filtering algorithm, morphological operation, and closing operation.

[0102] Specifically, in this embodiment, the median-Gaussian filtering algorithm and morphological operations are used to reduce the noise of the interference intensity distribution image after imaging to reduce the error, and the circular structural element is further used to perform a closing operation to repair the segmentation defects and smooth the edges to eliminate small noise and high eccentricity artifacts.

[0103] Exemplarily, in step four, the multi-region extraction of light intensity changes of the interference intensity distribution image includes: setting a number of target rings with different radii on the petals of the interference intensity distribution image, extracting the light intensity changes of the target rings, and obtaining the light intensity extreme points of the petals.

[0104] Specifically, in this embodiment, adaptive threshold segmentation and sensitivity adjustment are used to obtain the Euclidean distance measured by the geometric center and sort it in ascending order, retaining all valid fringe centers, and through circular constraint correction and feature point completion, a number of target rings with different radii are set on the petals of the collected conjugate vortex light interference image (i.e., the petals of the interference intensity distribution image), the data information on the target ring is demodulated, the angle step is subdivided to traverse the points on the ring, the brightness value of each coordinate on the target ring is identified, and the light intensity extreme point of the petals is obtained. Projection correction is used to ensure the spatial consistency of the fringe center point, thereby reducing the influence of outlier error on angle measurement.

[0105] Exemplarily, in step four, the light intensity extreme point is processed using fast Fourier transform to obtain the angle corresponding to the light intensity extreme point, and the angle array after smoothing is matched with the light intensity extreme point to average the angles of all petals to obtain the full rotation angle.

[0106] Specifically, in this embodiment, the fast Fourier transform (FFT) is used to process the extreme points of light intensity. The main frequency components are intercepted and then reconstructed using the inverse transform to obtain a smooth signal and further suppress high-frequency noise. The angle corresponding to the extreme point of light intensity is obtained when the wavelength is 1550nm. The angle array after smoothing is matched with the extreme point of light intensity, and the angles of all petals are averaged to obtain the full rotation angle Δθ. When the object to be measured is displaced, the output of the tunable laser 1 is adjusted, and the angle difference before and after the rotation is calculated based on the fitting result. The angle after rotation is the angle difference between it and the reference image. The full rotation angle is inverted by extracting the light intensity change of the interference pattern in multiple regions, which effectively solves the problem of the inability to determine the displacement caused by the periodic rotation of the interference image during large displacement measurement, thereby improving the range of the measurement system. The interference pattern before and after the displacement rotates. By determining the number of rotations n of the interference image, the full rotation angle Δθ of the interference intensity distribution image is calculated as shown in the following formula:

[0107] Δθ=2πn+Δθ2

[0108] Exemplarily, in step five, based on the functional relationship between the micro-displacement and the full-range rotation angle, the micro-displacement is calculated according to the full-range rotation angle.

[0109] Specifically, in this embodiment, the interference intensity distribution image (eg, Figure 12 As shown, Figure 12 The eight interference intensity distribution images from the upper left to the lower right correspond to 0, 10, 50, 100, 200, 300, 400, and 500 nm, respectively, and the demodulation operation is performed to obtain the micro-displacement measurement results as shown in FIG. Figure 13 It can be seen that the micro-displacement measurement results are basically consistent with the actual displacement, with high measurement accuracy.

[0110] The basic principles of this application are as follows:

[0111] Since the vortex light has an azimuthal phase structure, the electric field intensity of the reference light can be expressed by the formula in polar coordinates:

[0112] E1(r,θ)=Aexp[i(Iθ+kz1)]

[0113] Where A is the amplitude, I is the topological charge number, θ is the azimuth angle, k = 2π / λ is the wave number, λ is the wavelength, and z1 is the initial arm length of the reference arm.

[0114] The test light is conjugated with the reference light, and its electric field intensity can be expressed as:

[0115] E before (r,θ)=Aexp[-i(Iθ-kz2)]

[0116] Where z2 is the initial arm length of the test arm. Therefore, the vortex light conjugate interference intensity distribution before displacement can be expressed as:

[0117] I before =|E1+E2| 2 =2A 2 +2A 2 cos[2Iθ+k(z1-z2)]

[0118] The object to be tested is placed in the test arm. A retroreflector installed on the test arm introduces displacement changes into the optical path. When the object to be tested produces a displacement d, the optical path of the test arm in the interference light path changes by 2d. At this time, the electric field intensity of the test light changes accordingly, which can be expressed as:

[0119] E after (r,θ)=Aexp[-i(Iθ-kz2)]·exp(ik·2d)

[0120] Where d is the displacement of the object to be measured. At this time, the intensity distribution of the vortex light conjugate interference can be expressed as:

[0121] I after =|E1+E after | 2 =2A 2 +2A 2 cos[2Iθ+k(z1-z2)-2kd]

[0122] Where k(z1-z2) represents the phase introduced by the initial optical path difference between the two arms, and d represents the displacement of the object to be measured.

[0123] From the above formula, we can know that when the object to be measured produces displacement changes, the interference pattern formed will rotate accordingly, such as Figure 12As shown in the figure, the interference pattern before and after the displacement rotates. After accurately extracting the rotation angle Δθ of the interference pattern through the algorithm, the micro-displacement of the object to be measured can be obtained.

[0124] The principle of vortex light generation is as follows: A vortex beam is a new type of structured light field with orbital angular momentum and a spiral wave surface. Its phase change is directly related to the displacement of the object, thus enabling high-sensitivity measurements in precision displacement measurements. Compared to free-space structures that can generate high-order orbital angular momentum vortex light, the types of vortex light generated by metasurfaces are very limited; however, metasurfaces have some unparalleled advantages, including flexible design, low loss, and easy integration. In particular, in high-resolution measurements, it can achieve both the generation of high-power density nanofocused light sources and the elimination of background noise from far-field excitation. Fiber-structured vortex light is of great significance to the development of centralized, intelligent, low-cost, and miniaturized optical micro-measurement systems.

[0125] The principle of conjugate vortex light is as follows: Conjugate vortex light refers to a rotating phase structure formed between two mutually perpendicular polarized light waves during light wave propagation, in which there is a specific relationship between the phase of one light wave and the polarization state of the other light wave. Specifically, the formation process of conjugate vortex light can be achieved through optical elements such as optical phase modulators (such as liquid crystal spatial light modulators, spiral phase plates, vortex wave plates, and fiber-type vortex light modulators). In this case, by controlling the phase difference and polarization state of different regions, a complex interaction between the two mutually perpendicular polarized light waves can be achieved, thereby forming conjugate vortex light.

[0126] Conjugate vortex light has important applications in optics, such as in optical information processing, light field manipulation, and optical transmission. By manipulating the parameters of conjugate vortex light, complex modulation and control of light fields can be achieved, opening up new possibilities in precision measurement, optical communications, imaging, laser processing, and other fields.

[0127] Interferometric micro-displacement measurement works as follows: Optical interferometry is a commonly used method for measuring micro-displacement of an object. This method uses the analysis of the pattern information generated by the interference phenomenon to measure micro-displacement. The principle of optical interferometry is based on the relationship between the rotation angle of the interference pattern and the object's micro-displacement. The change in the pattern's rotation angle before and after the interference is used to determine the object's micro-displacement.

[0128] In optical interference measurement, interference instruments such as interferometers and interferometers are generally used. Typical interference instruments include interferometers, Michelson interferometers, thin-film interferometers, etc. These instruments use the principle of light interference to achieve measurement by comparing the phase difference between two beams of light. Specifically, the process of measuring the micro-displacement of an object by optical interference is as follows: a beam of monochromatic light is emitted to illuminate the surface of the object to be measured, the light will be reflected or transmitted, and interfere with the original light; the interference instrument will receive the interference light and generate interference fringes; when the object undergoes a small displacement, the reflected or transmitted light path will change, causing the position of the interference fringes to move; by measuring the movement of the interference fringes, the small displacement of the object can be calculated.

[0129] The embodiment of the present application designs a dielectric metasurface 4 through numerical simulation, which can generate stable vortex light with different topological charges. The light intensity change of the interference intensity distribution image extracted in multiple regions is combined to invert the full rotation angle, thereby improving the working range, environmental adaptability and measurement accuracy of micro-displacement measurement.

[0130] By adopting dielectric metasurfaces to construct a precision displacement measurement system based on conjugate vortex optical interference, the interference intensity distribution image is obtained by utilizing the interference generated by two conjugate vortex light beams. During the process of displacement change of the object to be measured, the interference intensity distribution image will rotate accordingly, and the full rotation angle can be inverted to obtain the micro-displacement, and the micro-displacement can be calculated based on the functional relationship between the micro-displacement and the full rotation angle.

[0131] By sequentially using plasma-enhanced chemical vapor deposition, spin-coating photoresist, electron beam exposure, development, and etching, the designed dielectric metasurface is processed to ensure that the spectral performance is stable and does not degrade over time. At the same time, it has the characteristics of compact structure, good compatibility, low loss, high conversion efficiency, and adaptability to harsh environments.

[0132] By placing several target rings of varying radii on the petals of the interference intensity distribution image, the intensity variations of the target rings are extracted to determine the extreme intensity points of the petals. This multi-region extraction method overcomes the bottleneck problem of large-displacement measurement, where the periodic rotation of the interference image makes it impossible to determine the displacement. This further improves the operating range and applicability of the measurement system, providing new technical support for the design of picometer-level displacement measurement methods.

[0133] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0134] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A micro-displacement measurement method based on conjugate vortex optical interferometry on a dielectric metasurface, characterized in that: The following steps are involved: Step 1: Design the dielectric metasurface through numerical simulation; Step 2: Using the dielectric metasurface to construct a precision displacement measurement system based on conjugate vortex optical interferometry; Step 3, using the precision displacement measurement system to collect interference intensity distribution images before and after the object moves; Step 4: extracting the light intensity change of the interference intensity distribution image in multiple regions and inverting the full rotation angle; Step 5: Calculate the micro-displacement according to the full rotation angle.

2. The micro-displacement measurement method based on dielectric metasurface conjugate vortex optical interferometry according to claim 1 is characterized in that: Step one includes: The phase characteristics and transmittance characteristics of nano-cylinders of different sizes, spacings, and heights are calculated by numerical simulation, and the corresponding nanostructure groups are screened according to the phase characteristics and transmittance characteristics; According to the topological charge phase characteristics of the required OAM vortex beam, the corresponding nanocylinders are called from the screened nanostructure group to construct the dielectric metasurface.

3. The micro-displacement measurement method based on dielectric metasurface conjugate vortex optical interferometry according to claim 1 is characterized in that: In step 1, plasma enhanced chemical vapor deposition, spin coating of photoresist, electron beam exposure, development, and etching are sequentially used to process the designed dielectric metasurface.

4. The micro-displacement measurement method based on dielectric metasurface conjugate vortex optical interferometry according to claim 1 is characterized in that: In step 2, the precision displacement measurement system includes: a tunable laser, a self-focusing lens, a first objective lens, a dielectric metasurface, a second objective lens, a first polarization beam splitter, a Dove prism, a second polarization beam splitter, a first quarter-wave plate, a first reflector, a third polarization beam splitter, a second quarter-wave plate, a second reflector, a fourth polarization beam splitter, and a CCD camera; The Gaussian beam emitted by the tunable laser passes through the self-focusing lens, the first objective lens, the dielectric metasurface, the second objective lens, and the first polarization beam splitter in sequence; The first polarization beam splitter splits the light beam into two paths. One path enters the measuring arm, passes through the Dove prism, the second polarization beam splitter, the first quarter-wave plate, and the first reflector in sequence, and is reflected back to the second polarization beam splitter by the first reflector. The other path enters the reference arm, passes through the third polarization beam splitter, the second quarter-wave plate, and the second reflector in sequence, and is reflected back to the third polarization beam splitter by the second reflector. The second polarization beam splitter and the third polarization beam splitter respectively reflect the reflected light beam to the fourth polarization beam splitter to reach the CCD camera.

5. The micro-displacement measurement method based on dielectric metasurface conjugate vortex optical interferometry according to claim 1 is characterized in that: In step three, performing noise reduction processing on the interference intensity distribution image; The noise reduction process includes: filtering algorithm, morphological operation, and closing operation.

6. The micro-displacement measurement method based on dielectric metasurface conjugate vortex optical interferometry according to claim 1 is characterized in that: In step 4, the multi-region extraction of light intensity changes of the interference intensity distribution image includes: setting a number of target rings with different radii on the petals of the interference intensity distribution image, extracting the light intensity changes of the target rings, and obtaining the light intensity extreme points of the petals.

7. The micro-displacement measurement method based on dielectric metasurface conjugate vortex optical interferometry according to claim 6, characterized in that: In step 4, the light intensity extreme point is processed using fast Fourier transform to obtain the angle corresponding to the light intensity extreme point, and the angle array after smoothing is matched with the light intensity extreme point to average the angles of all petals to obtain the full rotation angle.

8. The micro-displacement measurement method based on dielectric metasurface conjugate vortex optical interferometry according to claim 1 is characterized in that: In step five, based on the functional relationship between the micro-displacement and the full rotation angle, the micro-displacement is calculated according to the full rotation angle.

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