Method for measuring micro-displacement of curved surface based on virtual vortex phase and moire technique

Abstract

The application discloses a curved surface micro-displacement measurement method based on virtual vortex phase and Moire technology and belongs to the technical field of optical interference detection. The method of the application relies on a simple Tymann-Green interferometer, first collects an interference graph before displacement of a measured curved surface, demodulates the phase of the interference graph to obtain an initial phase, then superimposes a virtual vortex phase to generate a virtual vortex interference graph and stores the virtual vortex interference graph; Moire operation is performed on the virtual vortex interference graph and the interference graph collected in real time after displacement to obtain a Moire pointer containing displacement information, and the rotation angle of the Moire pointer can be directly used to inverse the micro-displacement of the measured curved surface. The application can effectively inhibit the adverse effects of fringe distortion on the measurement results, significantly improve the measurement precision and stability of the curved surface micro-displacement, is suitable for high-precision curved surface micro-displacement detection scenes, and solves the problem that the precision of a traditional interferometer sharply decreases due to interference fringe distortion when measuring the displacement of a curved surface.

Description

Technical Field

[0001] This invention relates to the field of optical detection, specifically to a method for measuring the micro-displacement of curved surfaces based on virtual vortex phase and moiré techniques. Background Technology

[0002] Optical interferometry, with its inherent advantages of non-contact operation, high sensitivity, and nanometer-level resolution, has become an important tool in the field of micro-displacement measurement, finding widespread application in modern manufacturing, materials science, medical and health, and aerospace. Traditional interferometers (such as Michelson interferometers and Thyman-Green interferometers) invert the displacement of the target object by detecting the movement of interference fringes. This technology is well-developed for measuring planar targets, achieving sub-nanometer level measurement accuracy. However, when measuring curved surfaces, the complex reflections of the surface cause distorted fringes in the interferometer. The electronic subdivision algorithms relied upon by traditional interferometers are only applicable to regular straight fringes and cannot handle the irregular movement of these distorted fringes, ultimately leading to a significant decrease in the accuracy of curved surface measurements or even complete failure.

[0003] In recent years, vortex beam-based interferometry has provided a novel approach to displacement measurement. This technique utilizes the interference of two vortex beams with conjugate topological charges to generate a petal-shaped interference pattern with a periodic angular distribution. The phase change caused by the displacement being measured is converted into the rotation angle of the pattern, theoretically enabling extremely high angle measurement sensitivity and thus high-precision displacement measurement. However, similar to traditional interferometers, vortex beam-based interferometry also faces measurement failure issues when dealing with curved surfaces. Its core principle heavily relies on the rotational symmetry of the interference pattern. The petal-shaped structure formed by the interference of two conjugate vortex beams requires a perfect helical phase distribution on the reflected wavefront; however, the wavefront distortion introduced by the measured curved surface disrupts the original phase distribution, causing the interference pattern to become distorted and deformed, making the petal structure difficult to identify and the rotation angle impossible to extract accurately. Therefore, there is an urgent need for a micro-displacement measurement method capable of measuring complex-shaped optical surfaces without relying on regular interference fringes, to overcome the shortcomings of existing technologies and achieve high-precision and stable measurement of micro-displacements on curved surfaces. Summary of the Invention

[0004] To address the core shortcomings of existing surface micro-displacement measurement techniques, this invention proposes a surface micro-displacement measurement method based on virtual vortex phase and Moiré technique, aiming to solve the following technical problems:

[0005] 1. Traditional displacement measurement interferometers are only suitable for planar measurements. For curved surfaces, an auxiliary plane mirror needs to be added. However, the conditions for adding the mirror cannot be met for scenarios such as liquid surfaces, micro-optical surfaces, and stress-constrained surfaces, making the measurement impossible.

[0006] 2. Existing vortex-based interferometers rely on complex devices such as Q-wave plates and spatial light modulators (SLMs) to generate vortex beams. In addition to phase modulation devices such as Q-wave plates and SLMs, vortex-based interferometers usually require additional polarization devices for premodulation, and may even require the use of Dowell prisms for topological charge sign conversion, which increases the complexity and cost of the system.

[0007] 3. Traditional interferometry is susceptible to systematic errors and alignment errors. Furthermore, interferometers based on vortex light have strict requirements for the rotational symmetry of the interferogram. Higher-order aberrations introduced by curved surfaces can destroy the symmetry and lead to measurement failure.

[0008] The core objective of this invention is to provide a method for measuring curved surface micro-displacement that requires no auxiliary plane mirror, no actual vortex light generation device, has a simple system structure, strong error resistance, and high-precision measurement capabilities, thereby reducing the technical threshold and cost of curved surface micro-displacement measurement. The technical solution of this invention is based on a core architecture of "simple Thyman-Green interferometer + virtual vortex phase loading + Moiré technique," using digital signal processing to replace complex optical modulation to achieve accurate measurement of curved surface micro-displacement.

[0009] The technical solution adopted in this invention is:

[0010] A surface micro-displacement measurement method based on virtual vortex phase and Moiré technique is characterized by the following steps:

[0011] Step 1: Acquire the initial interferogram of the surface under test using a Thyman-Green interferometer, demodulate the initial interferogram to obtain the initial phase, and superimpose a preset virtual vortex phase on the initial phase to generate and store the virtual vortex interferogram.

[0012] Step 2: When the measured surface undergoes a slight displacement, the real-time interferogram after the surface displacement is acquired using the Thyman-Green interferometer;

[0013] Step 3: Multiply the real-time interferogram with the pre-stored virtual vortex interferogram to generate a moiré fringe pattern, perform frequency domain processing on the moiré fringe pattern, and extract the low-frequency effective components related to the phase change;

[0014] Step 4: Based on the low-frequency effective components, obtain the moiré pointer, calculate the phase change by calculating the rotation angle of the moiré pointer, and then combine the mapping relationship between optical interference phase and displacement to solve for the micro-displacement of the measured surface.

[0015] Furthermore, the specific processing procedure for step 1 is as follows:

[0016] (1) Initial interferogram acquisition and preprocessing

[0017] The interferogram before surface displacement is acquired using a CCD in a Thyman-Green interferometer and denoted as the initial interferogram. Its expression is: ;in Background light intensity, For amplitude modulation, This is a systematic error, caused by defects in optical components, resulting in higher-order aberration modes appearing in the interferogram. The initial carrier phase is the relative wavefront tilt of the reference light and the light under test, i.e., the alignment error.

[0018] (2) Initial phase demodulation

[0019] For the initial interferogram Phase demodulation is performed using the Fourier transform method to extract the initial phase of the measured surface. ;

[0020] (3) Virtual vortex phase loading and virtual vortex interferogram generation

[0021] The initial phase obtained by demodulation Above, superimposed virtual vortex phase Generate virtual vortex interferogram Its expression is: , For virtual topological load, This is the azimuth angle.

[0022] Furthermore, the specific processing procedure for step 2 is as follows:

[0023] When the measured surface undergoes a normal micro-displacement When this happens, its phase will change accordingly, and the amount of change is... The interferogram acquired in real time using a Thyman-Green interferometer is recorded as the real-time interferogram. Its light intensity distribution expression is: .

[0024] Furthermore, the specific processing procedure for step 3 is as follows:

[0025] (1) Generation of Moiré fringe pattern

[0026] Real-time interferogram With pre-stored virtual vortex interferogram Perform dot product operation to generate moiré fringe pattern. Its expression is:

[0027]

[0028]

[0029]

[0030] Among them, including and The term represents the high-frequency interference components introduced by system errors and alignment errors, which are related to phase changes. It is a low-frequency effective component;

[0031] (2) Frequency domain filtering and extraction of low-frequency effective components

[0032] Perform Fourier transform, frequency domain low-pass filtering, and inverse Fourier transform sequentially on the moiré fringe pattern: The Fourier transform will... When transitioning from the spatial domain to the frequency domain, the high-frequency interference components and the low-frequency effective components are now distributed separately in the frequency spectrum. The larger the value, the more significant the separation effect; low-pass filtering removes high-frequency interference components far from the center of the spectrum, retaining only those with phase changes. The relevant low-frequency components; the inverse Fourier transform converts the filtered frequency domain signal back to the spatial domain to obtain the effective low-frequency components. Its expression is: ,right Take absolute value This reverses the brightness of the original negative value region, thus forming 21 bright probes distributed in a petal shape in the polar coordinate system, which are called Mohr's pointers.

[0033] Furthermore, the specific processing procedure for step 4 is as follows:

[0034] (1) Calculation of rotation angle

[0035] Calculate the radial pixel grayscale sum of the Moiré pointer along the angular direction, and then normalize the grayscale sum. With higher-order exponentiation The sharpened probe curve is obtained. The angle of the rotating probe in its initial and displacement states is determined using an image recognition algorithm. , Then the rotation angle ;

[0036] (2) Solving for small displacements of curved surfaces

[0037] Based on the principle of optical interference, phase change With surface normal micro-displacement The mapping relationship is as follows: λ is the wavelength of the laser used in the Thyman-Green interferometer; combined with The formula for solving the micro-displacement is derived as follows: This enables precise solutions for nanoscale surface micro-displacements.

[0038] The advantages of this invention are:

[0039] This invention utilizes a simple Thyman-Green interferometer. First, it acquires the interferogram of the surface before displacement. Phase demodulation of this interferogram is then performed to obtain the initial phase. A virtual vortex phase is then superimposed to generate and store a virtual vortex interferogram. Moiré operations are performed on the virtual vortex interferogram and the real-time acquired interferogram after displacement to obtain a Moiré pointer containing displacement information. The rotation angle of the Moiré pointer allows direct inversion of the micro-displacement of the surface under test. This invention effectively suppresses the adverse effects of fringe distortion on the measurement results, significantly improving the accuracy and stability of surface micro-displacement measurement. It is suitable for high-precision surface micro-displacement detection scenarios and solves the problem of a sharp decrease in accuracy due to interference fringe distortion when measuring surface displacement using traditional interferometers. Attached Figure Description

[0040] Figure 1 Topological load number A schematic diagram of the phase clock, where (a) represents the topological charge number. Mohr pointer before surface displacement, (b) is the topological charge number. The Mohr pointer after the surface displacement, (c) is the GS curve corresponding to the Mohr pointer.

[0041] Figure 2 This is a flowchart of the experimental setup and data processing for measuring surface displacement.

[0042] Figure 3 The experimental results for measuring surface displacement are shown in (a) and (b), which are interferograms before and after displacement; (c) and (d), which are Mohr pointers before and after displacement; and (e), which is the GS curve. Detailed Implementation

[0043] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0044] Example 1.

[0045] 1. Experimental System Setup

[0046] This embodiment uses a Thyman-Green interferometry system to measure micro-displacement of curved surfaces. The experimental setup is as follows: Figure 2 As shown, the system consists of the following components:

[0047] Laser L1: A monochromatic coherent laser with a wavelength of λ=632.8nm is selected as the light source for interferometry to ensure the stability of the interference signal and provide a reliable basis for phase measurement. Its output power is stable.

[0048] Beam expander L2: Used to expand and collimate the laser beam output to obtain a parallel beam that sufficiently covers the surface under test.

[0049] Reference plane mirror L3: Select one with a surface flatness superior to The plane mirror is used to reflect the reference light, ensuring the wavefront stability of the reference light, providing a stable phase reference for measurement, and avoiding the impact of reference light phase fluctuations on measurement accuracy.

[0050] Surface to be tested L4;

[0051] Piezoelectric ceramic (PZT) L5: Used to fix the measured curved surface L4. Its displacement resolution is 0.05nm. It can accurately output the preset standard micro-displacement as the analog signal of the surface micro-displacement and the verification benchmark of the measurement results.

[0052] Beam splitter L6: A non-polarized beam splitter is used to split the laser emitted by the laser into two paths at a 1:1 ratio, which are used as reference light and measurement light respectively, to ensure that the intensity of the two beams is matched and to form a clear interference pattern on the CCD target surface.

[0053] Imaging lens L7;

[0054] The L8 CCD image acquisition device has a resolution of 1280×960 pixels and an acquisition frame rate of 35fps. It can acquire interferograms in real time and convert optical signals into digital image signals, which are then transmitted to a computer for subsequent processing to ensure the quality of the interferograms.

[0055] Computer: Data processing flow such as Figure 2 As shown, computer data processing software is used to perform functions such as phase demodulation, virtual vortex phase generation and superposition, moiré fringe generation, frequency domain processing, rotation angle calculation, and micro-displacement solution on the interferogram.

[0056] 2. Specific measurement steps

[0057] 1. Initial Interferogram Acquisition and Preprocessing

[0058] like Figure 2 As shown, in the Thyman-Green interferometer, the beam emitted by the helium-neon laser L1 is collimated by the beam expander L2 and then split into two paths by the beam splitter L6: one path serves as the reference beam, incident on the plane mirror and reflected back to the CCD L8; the other path serves as the measurement beam, incident on the surface to be measured L4 and reflected back to the CCD L8. The two beams converge after passing through the imaging lens L7 and form interference on the target surface of the CCD L8. The initial interference pattern before the surface displacement is acquired by the CCD L8. Its expression is: .in Background light intensity, For amplitude modulation, It is a systematic error (caused by defects in optical components, resulting in higher-order aberration modes in the interferogram). The initial carrier phase (the relative wavefront tilt of the reference light and the light under test, i.e., alignment error).

[0059] 2. Initial phase demodulation

[0060] For the initial interferogram Phase demodulation is performed using the Fourier transform method to extract the initial phase of the measured surface. .

[0061] 3. Virtual vortex phase loading and virtual vortex interferogram generation

[0062] The initial phase obtained by demodulation Above, a computer-generated virtual vortex phase is superimposed. ( For virtual topological load, (Assuming the azimuth angle), generating a virtual vortex interferogram. Its expression is: The virtual vortex interferogram is shown below. Figure 3 As shown in (c). Preferred virtual topology load number. This parameter design allows the subsequently constructed phase clock to naturally form a structure of "1 fixed probe + 1 rotating probe", providing a basis for solving periodic ambiguity.

[0063] 4. Real-time interferogram acquisition

[0064] When the measured surface undergoes a normal micro-displacement When this happens, its phase will change accordingly (the change is...). A standard micro-displacement of 19 nm was applied to the surface L4 under test using a PZT L5. After stabilization, the interference patterns of the surface L4 before and after the displacement were acquired in real time using a Thyman-Green interferometer (denoted as the real-time interferogram). Its light intensity distribution expression is: The initial interferogram before displacement is shown below. Figure 3 (a) and Figure 3 As shown in (b).

[0065] 5. Generation of Moiré fringe patterns

[0066] Real-time interferogram With pre-stored virtual vortex interferogram Perform dot product operation to generate moiré fringe pattern. Its expression is:

[0067]

[0068]

[0069]

[0070] Among them, including and The term represents the high-frequency interference components introduced by system errors and alignment errors, which are related to phase changes. It is a low-frequency effective component.

[0071] 6. Frequency Domain Filtering and Low-Frequency Effective Component Extraction

[0072] Perform Fourier transform (FT), frequency domain low-pass filtering, and inverse Fourier transform (IFT) sequentially on the moiré fringe pattern: The Fourier transform will... When transitioning from the spatial domain to the frequency domain, the high-frequency interference components and the low-frequency effective components are now separately distributed in the frequency spectrum. The larger the value, the more significant the separation effect; low-pass filtering removes high-frequency interference components far from the center of the spectrum, retaining only those with phase changes. The relevant low-frequency components; the inverse Fourier transform converts the filtered frequency domain signal back to the spatial domain to obtain the effective low-frequency components. Its expression is: ,right Take absolute value This reverses the brightness of the original negative region, resulting in 21 petal-shaped bright probes in polar coordinates, which are the moiré pointers. The moiré pointers before and after displacement are shown below. Figure 3 (d) and Figure 3 As shown in (e).

[0073] When virtual topology load At that time, the constructed Mohr's pointer exhibited the characteristics of "1 fixed probe + 1 rotating probe", such as Figure 1 As shown. A fixed probe position does not move with phase changes and serves as the reference for period counting, used to resolve period ambiguity issues in phase measurements. A rotating probe position changes with phase. Synchronous rotation, its rotation angle and The relationship is linear.

[0074] 7. Rotation Angle Calculation

[0075] Calculate the radial pixel grayscale sum of the Moiré pointer along the angular direction, and then normalize the grayscale sum. With higher-order exponentiation The sharpened probe curve is obtained. (Higher-order exponentiation can enhance the contrast between the probe and the background, improving angle recognition accuracy); the angle of the rotating probe in its initial and displacement states is determined using image recognition algorithms. , Then the rotation angle .

[0076] 8. Solving for small displacements of curved surfaces

[0077] Based on the principle of optical interference, phase change With surface normal micro-displacement The mapping relationship is as follows: (λ is the wavelength of the laser used in the Twyman-Green interferometer); combined with The formula for solving the micro-displacement is derived as follows: This enables precise calculation of nanoscale surface micro-displacements. Due to the rotation angle of the pointer... and Inversely proportional, therefore The smaller the value, the higher the sensitivity.

[0078] 9. Analyze the experimental data

[0079] The GS curves before and after displacement are as follows: Figure 3 (f) The pointer rotates by 21.68°. According to the displacement calculation formula... ,in , The calculated micro-displacement value of the measured surface was 19.05 nm. Comparing the measurement result with the 19 nm standard displacement applied by PZT L5, the two showed a measurement deviation of only 0.05 nm, with a relative error of 0.26%. The experimental results verify the high accuracy and reliability of this method in measuring micro-displacement of curved surfaces.

[0080] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for measuring micro-displacement of a curved surface based on virtual vortex phase and moire technology, characterized in that, Includes the following steps: Step 1: Acquire the initial interferogram of the surface under test using a Thyman-Green interferometer, demodulate the initial interferogram to obtain the initial phase, and superimpose a preset virtual vortex phase on the initial phase to generate and store the virtual vortex interferogram. Step 2: When the measured surface undergoes a slight displacement, the real-time interferogram after the surface displacement is acquired using the Thyman-Green interferometer; Step 3: Multiply the real-time interferogram with the pre-stored virtual vortex interferogram to generate a moiré fringe pattern, perform frequency domain processing on the moiré fringe pattern, and extract the low-frequency effective components related to the phase change; Step 4: Based on the low-frequency effective components, obtain the moiré pointer, calculate the phase change by calculating the rotation angle of the moiré pointer, and then combine the mapping relationship between optical interference phase and displacement to solve for the micro-displacement of the measured surface.

2. The surface micro-displacement measurement method based on virtual vortex phase and Moiré technique according to claim 1, characterized in that, The specific processing steps for step 1 are as follows: (1) Initial interferogram acquisition and preprocessing The interferogram before surface displacement is acquired using a CCD in a Thyman-Green interferometer and denoted as the initial interferogram. Its expression is: ;in Background light intensity, For amplitude modulation, This is a systematic error, caused by defects in optical components, resulting in higher-order aberration modes appearing in the interferogram. The initial carrier phase is the relative wavefront tilt of the reference light and the light under test, i.e., the alignment error. (2) Initial phase demodulation For the initial interferogram Phase demodulation is performed using the Fourier transform method to extract the initial phase of the measured surface. ; (3) Virtual vortex phase loading and virtual vortex interferogram generation The initial phase obtained by demodulation Above, superimposed virtual vortex phase Generate virtual vortex interferogram Its expression is: , For virtual topological load, This is the azimuth angle.

3. The surface micro-displacement measurement method based on virtual vortex phase and Moiré technique according to claim 2, characterized in that, The specific processing steps for step 2 are as follows: When the measured surface undergoes a normal micro-displacement When this happens, its phase will change accordingly, and the amount of change is... The interferogram acquired in real time using a Thyman-Green interferometer is recorded as the real-time interferogram. Its light intensity distribution expression is: .

4. The surface micro-displacement measurement method based on virtual vortex phase and Moiré technique according to claim 3, characterized in that, The specific processing steps for step 3 are as follows: (1) Generation of Moiré fringe pattern Real-time interferogram With pre-stored virtual vortex interferogram Perform dot product operation to generate moiré fringe pattern. ; Its expression is: Among them, including and The terms are alignment error, high-frequency interference components introduced by system error, and phase change-related components, respectively. It is a low-frequency effective component; (2) Frequency domain filtering and extraction of low-frequency effective components Perform Fourier transform, frequency domain low-pass filtering, and inverse Fourier transform sequentially on the moiré fringe pattern: The Fourier transform will... When transitioning from the spatial domain to the frequency domain, the high-frequency interference components and the low-frequency effective components are now distributed separately in the frequency spectrum. The larger the value, the more significant the separation effect; low-pass filtering removes high-frequency interference components far from the center of the spectrum, retaining only those with phase changes. Related low-frequency components; The inverse Fourier transform converts the filtered frequency domain signal back to the spatial domain, yielding the low-frequency effective components. Its expression is: ,right Take absolute value This reverses the brightness of the original negative value region, thus forming 21 bright probes distributed in a petal shape in the polar coordinate system, which are called Mohr's pointers.

5. The surface micro-displacement measurement method based on virtual vortex phase and Moiré technique according to claim 4, characterized in that, The specific processing steps for step 4 are as follows: (1) Calculation of rotation angle Calculate the radial pixel sum of the Moiré pointer (GS) along the angular direction, and then normalize the sum of the gray levels. With higher-order exponentiation The sharpened probe curve is obtained. The angle of the rotating probe in its initial and displacement states is determined using an image recognition algorithm. , Then the rotation angle ; (2) Solving for small displacements of curved surfaces Based on the principle of optical interference, phase change With surface normal micro-displacement The mapping relationship is as follows: , The wavelength of the laser used in the Thyman-Green interferometer; combined with The formula for solving the micro-displacement is derived as follows: This enables precise solutions for nanoscale surface micro-displacements.

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