A method for measuring micro displacement based on interference of vortex light and speckle field

Abstract

The present application relates to a kind of micro displacement measurement methods based on vortex light and speckle field interference, belong to optical precision measurement technical field.The method makes vortex reference light carrying certain topological phase and speckle object light carrying the displacement information of measured object interfere;Collect the interference pattern before and after displacement and calculate global wrapped phase map;Extract phase singularity coordinates directly in wrapped phase map using closed loop integration method;By matching and screening effective singularity, and calculating its global space average displacement;Finally, according to the calibration coefficient, the displacement is converted into axial displacement.The present application uses singularity translation statistics to replace complex continuous phase unwrapping operation, effectively separates local spatial disturbance and global displacement, without phase unwrapping, not only has strong anti-interference ability such as mirror defect, but also can realize sub-nanometer level ultra-high precision displacement measurement.

Description

Technical Field

[0001] This invention relates to the field of optical precision measurement technology, specifically to a precision displacement measurement method based on the interference of vortex light and speckle field. Background Technology

[0002] Precision displacement measurement technology is widely used in semiconductor mask alignment, super-resolution imaging in life sciences, and micro-strain monitoring of the Earth's crust in geophysics. These applications place extremely high demands on the measurement accuracy and resolution of the system, ranging from sub-nanometer to picometer levels. Optical measurement, with its non-contact sensing advantage, possesses excellent dynamic response characteristics while avoiding mechanical load interference. Currently, vortex beam-based interferometry provides a novel multi-degree-of-freedom approach for solving minute displacements. However, existing vortex beam interferometry, such as coaxial vortex beam interference or interference with spherical or plane waves, mainly relies on a definite, continuous wavefront phase. This continuous interference pattern is prone to local interference fringe breakage and phase abrupt changes when faced with local device physical defects, such as mirror scratches or dust obstruction. This leads to huge error crosstalk in traditional continuous phase unwrapping algorithms, resulting in measurement failure. On the other hand, speckle fields, as a speckled optical field formed by the superposition of random phase wavelet interference, can carry intensity and phase information across the entire domain. However, traditional speckle interferometric displacement measurements are mostly limited to solving displacement through the morphological changes and gray-level correlation of a single speckle field. This method is limited by the extraction of local speckle micromorphological features and fails to make full use of the topological changes of the special phase light field, thus limiting the measurement stability and sensitivity. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a precision displacement measurement method based on vortex light and speckle field interferometry. This invention aims to break away from the reliance of traditional interferometry on continuous phase and unwrapping algorithms, achieving axial displacement measurement with extremely strong defect immunity and sub-nanometer precision by separating local perturbations from global displacement.

[0004] This invention employs a precision displacement measurement method based on vortex light and speckle field interference, comprising the following steps.

[0005] Step 1: Constructing the interference light field. The light beam emitted from the light source is split into two paths. One path is modulated by a spatial light modulator (SLM) to generate a vortex beam carrying a specific topological charge as a reference beam. The other path illuminates the target reflecting surface and generates a speckle field with a random phase through a scattering medium as the object beam. The vortex beam and the speckle field are then interfered with.

[0006] Step 2: Obtain the enveloping phase. Use a detector to acquire interference intensity patterns before and after the axial displacement of the object under test, and calculate the global enveloping phase diagrams before and after the displacement using the phase-shifting method.

[0007] Step 3: Extract phase singularities. For the wrap-around phase diagrams before and after displacement, the topological load is determined using the closed-loop integration method, and the coordinates of discrete positive and negative phase singularities carrying topological load information in the whole field are extracted.

[0008] Step 4: Singularity Matching and Anomaly Screening. An anomaly screening mechanism is performed based on the singularities in the phase maps of the two frames before and after the displacement. Invalid anomalous singularities that cannot achieve bidirectional matching due to local defects or noise are eliminated, while valid singularity pairs are retained.

[0009] Step 5: Displacement Calculation. Calculate the average spatial offset of all valid singularity pairs between adjacent frames, and convert the average spatial offset into axial displacement based on pre-calibrated relation coefficients.

[0010] Compared with existing technologies, the advantages of this invention are: this method completely avoids phase unwrapping operations, and by finding discrete topological singularity coordinates, it directly extracts phase singularities from the wrapped phase map and calculates their spatial average offset, significantly reducing the dependence on the continuity of the optical field. This method also has extremely strong immunity to physical defects; by coupling the spiral phase of the vortex light with the random phase of the speckle, the local phase distortion caused by local physical defects is effectively diluted and canceled out by the global statistical averaging effect. Attached Figure Description

[0011] Figure 1 A schematic diagram of the optical path of the vortex light and speckle field interference experimental apparatus provided in this embodiment of the invention. Reference numerals: 1. Laser; 2. Polarizer; 3. First beam splitter; 4. Second beam splitter; 5. Mirror; 6. Scattering medium; 7. Quarter-wave plate; 8. Third beam splitter; 9. Quarter-wave plate; 10. Fourth beam splitter; 11. Spatial light modulator; 12. Polarizing camera.

[0012] Figure 2 The embodiments of the present invention include (a) intensity distribution diagram, (b) phase distribution diagram, and (c)(d) schematic diagrams of positive and negative phase singularity distribution of vortex light and speckle field interference.

[0013] Figure 3 The displacement measurement results and error curves of this invention under conditions without mirror defects.

[0014] Figure 4 Interference light field distribution diagrams under the condition of introducing mirror-like linear defects in the embodiments of the present invention: (a) Roof prism with a fixed hair strand; (b) Gaussian spot appearance with introduced mirror defects; (c) Intensity distribution of interference between vortex light and speckle field; (d) Phase distribution of interference between vortex light and speckle field.

[0015] Figure 5The displacement measurement results and error curves under mirror defect conditions in this embodiment of the invention are shown in the figure. Detailed Implementation

[0016] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0017] Example 1: A Precision Displacement Measurement System Based on Vortex Beam and Speckle Field Interference like Figure 1 As shown, this system consists of a laser 1, a polarizer 2, a first beam splitter 3, a second beam splitter 4, a reflector 5, a scattering medium 6, a quarter-wave plate 7, a third beam splitter 8, a quarter-wave plate 9, a fourth beam splitter 10, a spatial light modulator 11, and a polarization camera 12.

[0018] The beam emitted by laser 1 is split into two beams by beam splitter prism 3 after passing through polarizer 2: the first beam is modulated by spatial light modulator 11 to obtain a pure orbital angular momentum (OAM) beam, i.e., it has... A distributed vortex reference beam. The second beam passes through a beam splitter prism 4 and a reflector 5 connected to a micro-displacement platform. This reflector is used to introduce the measured axial displacement, and then passes through a scattering medium 6 to generate a vortex reference beam. Distributed speckle light. After passing through phase delay elements on their respective paths, the two beams converge at beam splitter 10 and interfere, and the interference pattern is recorded by polarization camera 12.

[0019] Example 2: Detailed Algorithm Flow for Displacement Calculation When the target being measured, i.e., reflector 5, undergoes axial displacement At that time, the globally uniform phase difference introduced by the system is Δ = k Δ z The interference optical field is formed by the coupling of deterministic vortex topological phase and random speckle phase, resulting in a ring interference pattern with speckle modulation characteristics.

[0020] The specific calculation steps are as follows: First, the enclosed phase of the interference field is calculated using the four-step phase-shifting method. Then, the enclosed phase field is scanned using the 2×2 pixel closed-loop integration method. When the local loop integration result is ±1, a positive / negative phase singularity is determined, and its initial coordinates are recorded. The introduction of axial displacement causes phase singularities to drift in space. Although speckle phase causes the local velocities of each singularity to be random, under the macroscopic statistics of the entire field of view, the random motions cancel each other out, and the global translation is retained as a valid signal. A two-way matching mechanism for inter-frame singularities is adopted. If a singularity is caused by a local mirror defect, it cannot complete a valid match between frames before and after the displacement, and the system discards it as abnormal noise. For all N validly matched singularities, the formula is used. Calculate the statistical average offset. These are the coordinates of the singularity after displacement. Based on the linear mapping relationship between axial displacement and singularity translation. The actual displacement is calculated. In this embodiment, the proportionality coefficient obtained through calibration is used. The value is 107.3983. Through the above steps, verification was performed within the 0-100 nm range in 10 nm steps: In the absence of defects, the average absolute error was 0.352 nm; even after artificially introducing mirror defects such as hair obstruction, the average absolute measurement error remained at 0.488 nm. This achieved interference-resistant sub-nanometer ultra-precision measurement.

Claims

1. A method for measuring minute displacements based on the interference of vortex light and speckle field, characterized in that, Includes the following steps: S1, using a vortex beam carrying a defined topological phase as a reference beam, and interfering with a speckle field carrying a random phase as an object beam, wherein the speckle field carries axial displacement information of the object being measured. S2, collect the interference field intensity patterns of the measured object before and after axial displacement, and calculate and obtain the global wrap-around phase diagram before and after displacement; S3, directly extract the discrete phase singularity carrying topological load information from the global wrapping phase map before and after the displacement, and obtain the spatial coordinates of the phase singularity; S4, Match and filter the phase singularities before and after the displacement to find valid singularity pairs, and calculate the average spatial offset of all valid singularity pairs in the entire domain. S5. Based on the pre-calibrated relationship coefficients, the average spatial offset is linearly converted into the axial displacement of the object being measured, thus completing the measurement of minute displacements.

2. The method according to claim 1, characterized in that, The specific method for constructing the interference light field in step S1 is as follows: the light beam emitted by the laser source is divided into two paths, one of which is modulated by a spatial light modulator to generate the vortex beam; the other path generates the speckle field through a reflecting surface with the measured displacement and a scattering medium, and then the two beams are merged and interfered.

3. The method according to claim 1, characterized in that, The specific method for obtaining the wrapping phase in step S2 is as follows: using the phase shift method, by collecting the interference field intensity under different phase shift states, the global wrapping phase map before and after the displacement of the measured object can be directly calculated without phase unwrapping.

4. The method according to claim 1, characterized in that, The specific method for extracting phase singularities in step S3 is as follows: the 2×2 pixel closed loop integration method is used to perform local gradient integration on the global wrapped phase map. When the local loop integration result is ±1, it is determined that there is a positive or negative phase singularity at that location, and the pixel coordinate position at that location is extracted.

5. The method according to claim 1, characterized in that, The process of singularity matching and offset calculation in step S4 specifically includes: relying on the singularity pair matching mechanism of the phase maps of the two frames before and after displacement to complete the anomaly screening, invalid phase singularities that are generated by local defects or noise and cannot achieve bidirectional matching between frames are removed as abnormal singularities, and singularities that have completed bidirectional matching are retained as the effective singularity pairs; for all effective singularity pairs, the average spatial offset between adjacent frames is calculated under global statistics to dilute the impact of local spatial offset on the overall mean.

6. The method according to claim 5, characterized in that, The average spatial offset The calculation formula is: In the formula, and These are the coordinates of the phase singularity before the displacement. and The coordinates of the phase singularity corresponding to the displacement are given, and N is the total number of valid phase singularity pairs in the global domain.

7. The method according to claim 1, characterized in that, The specific formula for displacement calculation in step S5 is as follows: In the formula, To calculate the axial displacement, This represents the spatial average offset. This is a pre-calibrated coefficient relating axial displacement to the average offset of phase singularities.

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