Optical element stress measurement and defect identification method based on digital holographic photoelastic method

Abstract

The invention belongs to the technical field of digital holographic measurement, and particularly relates to an optical element stress measurement and defect identification method based on a digital holographic photoelastic method. The method is realized based on a transmission-type off-axis digital holographic light path system; light beams emitted by the laser assembly are divided into reference light and object light, the object light is reflected by the surface of a sample and carries sample information, the object light and the reference light intersect in front of the CMOS camera to generate interference, the CMOS converts an interference light intensity signal into an electric signal, and holographic image processing is performed by the computer; the hologram before and after external force loading is reconstructed to obtain surface topography distribution, and the reconstruction precision is improved through the steps of positive first-order spectrum extraction, angular spectrum reconstruction automatic focusing and the like; the phase difference before and after external force loading is calculated through reconstruction complex amplitude phase extraction, and then the direction and size distribution of the principal stress of the sample are measured and calculated based on a digital photoelastic method and a stress optical law; and the defect of the optical element is identified by measuring the stress value change under the same external force loading, so that the method has important practical significance.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital holographic measurement, and particularly relates to a method for measuring stress and identifying defects of an optical element based on digital holographic photoelasticity. Background Technique

[0002] Optical elements are widely used in high-precision optical fields such as lithography masks, laser optical elements, and astronomical telescope lenses due to their excellent optical uniformity, low thermal expansion coefficient, and high heat resistance. During their production process (such as cutting, grinding, polishing, etc.) or under the action of the external environment (such as temperature, mechanical load), optical elements are prone to surface defects or stress non-uniformity, and at the same time, subsurface defect damage may be introduced during the polishing process. Current traditional detection methods are often limited to the identification of defects in the surface topography of optical elements and are difficult to achieve synchronous high-precision characterization of surface and subsurface defects. And the subsurface defects of optical elements will affect their photoelastic coefficient when stressed. Therefore, developing a technology that can comprehensively measure the surface topography of materials and measure stress is of great significance for the comprehensive identification of material defects and the application reliability analysis of optical elements.

[0003] Digital holography is a non-contact, non-destructive, all-round real-time measurement quantitative imaging technology, which can capture and analyze the wavefront information of three-dimensional objects. Digital holography can reconstruct the wave field of an object, so it has a unique autofocus function to track and observe moving objects in real time. The autofocus characteristic simulates the diffraction process of the object wave from the holographic plane to the image plane by changing the propagation distance z, and then numerically reconstructs the object wave field. To achieve autofocus of digital holography, the image plane of the object needs to be determined numerically. The main method of autofocus is to use the method of introducing an external evaluation function to determine the position of the focusing plane. Lyu et al. [M. Lyu, C. Yuan, D. Li, G. Situ, Fast autofocusing in digital holography using the magnitude differential, Appl Opt. 56(2017)F152–F157.] proposed to use the square of the magnitude difference (DIF) between two reconstructed images as the focusing evaluation function to achieve autofocus.

[0004] The digital holographic imaging optical path takes the imaging process of the measured object as the object light optical path, introduces a reference light to interfere with it, uses a charge-coupled device (CMOS) to replace the chemical film to record the interference pattern, and then the three-dimensional image and phase information of the object to be measured can be reconstructed through numerical methods. To solve the problem of interference between the zero-order image and the conjugate image in the holographic image, generally, the positive first-order image is extracted in the frequency spectrum domain and then angular spectrum reconstruction is performed to obtain the holographic reconstruction image. To achieve the accurate extraction of the positive first-order spectrum, it is necessary to determine the optimal filtering window after determining the center of the positive first-order spectrum. Weng et al. [J. Weng, H. Li, Z. Zhang, and J. Zhong, “Design of adaptive spatial filter at uniform standard for automatic analysis of digital holographic microscopy,” Optik 125(11), 2633–2637(2014).] used histogram analysis technology for adaptive filtering, but the parameter settings still required manual intervention during the analysis process. Dang et al. [DANG Changying, LI Jiansu, ZHAO Pengfei, et al. Adaptivly locating holographic positive first-order spectrum using maximum value of spectral phase[J]. Optics and Precision Engineering, 2022, 30(11):1272-1281.] used the minimum distance between the maximum value point of the spectral phase and the centroids of the zero-order, positive and negative first-order three regions to judge the position of the positive first-order region, realizing the adaptive positioning of the spectral region. Usually, research teams will ignore the determination of the optimal reconstruction distance when studying the method for extracting the positive first-order image in digital holographic reconstruction. Adding this step of the optimal reconstruction distance in the extraction of the positive first-order image in the present invention can improve the reconstruction accuracy.

[0005] The stress of optical components comes from operations involving material deformation, different types of welding, heat treatment, and machining during manufacturing. Uneven stress distribution can cause deformation or cracking of optical components during long-term use. Traditional mechanical stress detection methods (such as the drilling method) are destructive and have low efficiency. Currently, non-destructive testing methods for measuring material stress usually include X-ray diffraction, neutron diffraction, ultrasonic testing, etc. Huang et al. [Huang H, Zhang K, Wu M, Li H, Wang M J, Zhang S M, et al. Comparison between axial residual stresses measured by Raman spectroscopy and X-ray diffraction in SiC fiber reinforced titanium matrix composite. Acta Physica Sinica 2018; 67(19): 267 - 76.] measured the residual stress of SICf / C / Ti17 composite materials using Raman spectroscopy and XRD. This method is limited in its application fields because of the high requirements for instruments and experimental conditions and high costs. Quartz glass is an isotropic material without external stress applied, but when quartz glass is subjected to external stress, it will produce anisotropy similar to that of crystalline materials, resulting in the birefringence phenomenon, that is, a beam of light passing through materials such as glass will be decomposed into two plane-polarized lights with different propagation speeds. The two beams of light 1 and σ 2 coincide with the principal stress directions. During the propagation of the two beams of light, an optical path difference will be generated in the two principal stress directions. The refractive index difference between the two directions of light is proportional to the principal stress difference. When calculating the optical path difference, it is first necessary to determine the phase difference after the propagation of the two beams of light. Therefore, by combining the photoelastic method and the digital holographic interferometry optical path, the numerical distribution of the principal stress can be calculated by extracting the phase difference before and after the external force is applied. By measuring the stress value, surface defects during the manufacturing process and subsurface defect damage generated by femtosecond laser processing can also be identified.

[0006] The digital holographic reconstruction process can only characterize the surface topography of materials. Combining with the characterization of material physical properties can further evaluate the subsurface state of materials, and then identify surface and subsurface defects. The present invention proposes a complete optical component characterization method. This method can not only accurately reconstruct the surface topography of optical components, but also realize the comprehensive analysis of subsurface defects through the measurement of the principal stress under the compressed state. This characterization ability has important theoretical and application values for deeply understanding the stress distribution characteristics in the processing and application of optical components and improving the reliability of optical devices. Summary of the Invention

[0007] Aiming at the problem that digital holographic measurement in the prior art is limited to surface topography, the purpose of the present invention is to provide a method for stress measurement and defect identification of optical elements based on digital holographic photoelasticity, which can more completely characterize the surface and subsurface defect states of materials through the physical property measurement of photoelastic materials.

[0008] The purpose of the present invention is to provide a method for stress measurement and defect identification of optical elements based on digital holographic photoelasticity, which is realized based on a transmissive off-axis digital holographic optical path system; the beam emitted by the laser assembly is divided into a reference light and an object light, the object light is reflected by the sample surface to carry the sample information and interferes with the reference light in front of the CMOS camera, and the CMOS converts the interference light intensity signal into an electrical signal, which is processed by a computer for holographic image processing; then the holograms before and after external force loading are reconstructed to obtain the surface topography distribution, and the reconstruction accuracy is improved through positive first-order spectrum extraction and angular spectrum reconstruction autofocus; the phase difference before and after external force loading is calculated by extracting and calculating the complex amplitude phase before and after external force loading, and then the principal stress direction and magnitude distribution of the sample are calculated based on digital photoelasticity and the stress-optical law; the defects of the optical element are identified by measuring the change in stress value under the same external force loading; the specific steps are as follows:

[0009] S1. Build a transmissive off-axis digital holographic optical path system based on a Mach-Zehnder interference system, and adjust the off-axis angle. The optical path system includes a digital holographic imaging optical path with a He-Ne laser as the light source;

[0010] S2. Respectively collect holographic patterns of the glass sample before and after external force loading through the above optical path system. During the process, the polarization direction of the reference light is changed by rotating the polarization plate of the reference optical path, and four groups of holograms of the sample before and after external force loading at different rotation angles (such as 0°, 10°, 20°, 30°) are collected;

[0011] S3. Perform Fourier transform on the hologram, and perform spatial filtering in the frequency domain by setting different sizes of filtering windows to extract the positive first-order term and determine the optimal filtering window size to eliminate the influence of the zero-order term on the quality of the reconstructed image;

[0012] S4. Take the diffraction distance as a variable and set its change range and spacing according to preliminary measurement, and perform diffraction reconstruction on the above collected holograms respectively. During this process, the square of the amplitude difference (DIF) between two reconstructed images is used as the focus evaluation function to determine the optimal reconstruction distance, and angular spectrum reconstruction is performed under the determined optimal reconstruction distance and optimal filtering window size;

[0013] S5. Respectively obtain the reconstructed complex amplitudes before and after external force loading through the above steps, extract the phase from the complex amplitude and calculate the phase difference before and after external force loading;

[0014] S6. Through the intensity equation The first-order light intensity containing only interference information is extracted from the reconstructed complex amplitudes before and after the external force loading at four different reference light polarization angles, and the phase difference of the object light wave vector in the two principal stress directions caused by the external force loading is obtained through numerical calculation; where W 1k+ represents the first-order light intensity of the hologram when there is no external force loading, W 2k+ A represents the first-order light intensity of the hologram after external force loading, o and A r Respectively represent the amplitudes of the object light and the reference light, k = 1, 2, 3, 4 correspond to the reference light path polarizer rotated at different angles of 0°, 10°, 20°, 30°;

[0015] S7. Using the principle of birefringence of optical elements of photoelastic materials under stress, the four light intensity equations obtained in S6 are combined to calculate the phase difference caused by external force loading in the two principal stress directions, and then the distribution of the first and second principal stress values ​​is deduced according to the law of stress optics. At the same time, the defects of optical elements can be identified by measuring the abnormal area of ​​stress value distribution under the same external force load. Experiments have shown that this method can identify surface cracks, internal hole defects and sub-surface defect damage caused by femtosecond laser processing in the glass manufacturing process.

[0016] Furthermore, in step S1, the transmission-type off-axis digital holographic multifunctional optical path system includes a laser component, a sample platform, a beam splitting component, a polarization component, a CMOS image sensor and a computer; wherein the He-Ne laser in the laser component is used as a holographic imaging light source; the sample platform is used to carry the stress measurement sample and apply external stress to it; the beam splitting component constitutes a digital holographic imaging system based on Mach-Zehnder interference, and the digital holographic imaging system is used to record a hologram formed by the interference of object light and reference light before and after the sample is loaded with external force; the polarization component is used to change the polarization direction of the reference light; the CMOS image sensor is used to record the interference information generated by the digital holographic microscopy imaging system and form an interference image; and the computer is used to store and analyze the interference image.

[0017] Furthermore, the transmission-type off-axis digital holographic optical path system also includes a beam expansion component for filtering, expanding and collimating the He-Ne laser.

[0018] In some preferred embodiments, in step S4, the diffraction reconstruction calculation process is implemented by an accurate transfer function method based on angular spectrum theory.

[0019] The beneficial effects of the present invention are:

[0020] Based on the principle of digital holographic microscopy measurement, the present invention reconstructs the holograms collected by the system to obtain the surface topography distribution of the optical element, and improves the reconstruction accuracy through positive first-order spectrum extraction, angular spectrum reconstruction, etc.; calculates the phase difference before and after the external force loading by extracting and reconstructing the complex amplitude phase, and then realizes the measurement of the principal stress direction and magnitude distribution of the sample based on the digital photoelastic method and the stress-optics law. While ensuring the surface topography characterization of the glass material, the present invention realizes the defect identification of the main component material quartz glass of the optical element by locating the abnormal region of the principal stress value. Experiments prove that the present invention can identify surface cracks, internal hole defects and subsurface defect damages generated by femtosecond laser processing during the glass manufacturing process. This method provides a reference idea for the complete characterization of surface and subsurface defects of optical elements and has important practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of the method for stress measurement and defect identification of an optical element based on digital holographic photoelasticity of the present invention.

[0022] Figure 2 It is a schematic structural diagram and an actual built diagram of a transmissive off-axis digital holographic optical path system in the present invention.

[0023] Figure 3 They are holograms before and after external force loading with different reference light polarization directions collected for defect-free glass in an embodiment of the present invention.

[0024] Among them, (a-d) are holograms without external force loading, (e-h) are holograms obtained after fixed load is applied, (a, e) are the initial states of the polarizing plates, (b, f) are when the reference light polarizing plate is rotated by 10°, (c, g) are when the polarizing plate is rotated by 20°, and (d, h) are holograms collected when the polarizing plate is rotated by 30°.

[0025] Figure 4 They are holograms before and after external force loading and phase difference distribution diagrams for defect-free and hole-defect samples in an embodiment of the present invention. Among them, (a) is the hologram of the defect-free sample without loading, (b) is the hologram of the defect-free sample with external force loading, (c) is the phase difference before and after loading of the defect-free sample, (d) is the hologram of the defective sample without loading, (e) is the hologram of the defective sample with external force loading, and (f) is the phase difference before and after loading of the defect-free sample.

[0026] Figure 5 They are intensity diagrams of the intensity ratio function of the defect-free sample rotating different reference light polarization angles in an embodiment of the present invention. Among them, (a) is when the reference light polarization rotates by 0°, (b) is when the reference light polarization rotates by 10°, (c) is when the reference light polarization rotates by 20°, and (d) is when the reference light polarization rotates by 30°.

[0027] Figure 6The distributions of the first and second principal stresses after external stress loading on the defect-free sample in the embodiment of the present invention. Among them, (a) is the distribution of the first principal stress, and (b) is the distribution of the second principal stress.

[0028] Figure 7 The function graphs of the ratio of the positive first-order light intensities when the polarization direction of the reference light rotates at different angles for the samples with cracks and internal holes in the embodiment of the present invention. Among them, (a-d) are the function graphs of the ratio of the positive first-order light intensities when the polarization direction of the reference light rotates at different angles for the sample with cracks, and the rotation angles of the reference light are 0°, 10°, 20°, and 30° respectively; (e-h) are the function graphs of the ratio of the positive first-order light intensities when the polarization direction of the reference light rotates at different angles for the sample with internal holes, and the rotation angles are 0°, 10°, 20°, and 30° respectively.

[0029] Figure 8 The numerical distribution graphs of the first and second principal stresses for the samples with cracks and internal holes in the embodiment of the present invention. Among them, (a) is the distribution of the first principal stress of the sample with cracks, (b) is the distribution of the second principal stress of the sample with cracks, (c) is the distribution of the first principal stress of the sample with cracks, and (d) is the distribution of the second principal stress of the sample with cracks.

[0030] Figure 9 The stress distribution of the glass after femtosecond laser processing and the selection of ROI in the embodiment of the present invention. Among them, (a) is the image of the damaged glass, (b) is the damaged area within the microscope positioning field of view, (c) is the distribution graph of the first principal stress, and (d) is the distribution graph of the second principal stress.

[0031] Reference numerals in the figure: 1 - laser light source assembly, 632.8 nm wavelength He-Ne laser; 2 - beam expander and filter collimation assembly, 21 - plano-convex lens, 22 - pinhole diaphragm, 23 - doublet lens; 3 - sample platform (stage, for placing the sample to be measured); 4 - polarization adjustment assembly, 41, 42 - polarizers; 5 - beam splitting and reflecting filter assembly, 51, 52 - beam splitters, 53, 54, 55 - reflectors; 6 - CMOS image sensor; 7 - computer. Detailed implementation manners

[0032] The following further describes the detailed implementation manners of the present invention with reference to the accompanying drawings. It should be noted here that the description of these implementation manners is for helping to understand the present invention, but does not constitute a limitation to the present invention. In addition, the technical features involved in the various implementation manners of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0033] Embodiment, an optical element stress measurement and defect recognition method based on digital holographic photoelasticity, as Figure 1 shown, this method includes a total of seven steps S1 - S7.

[0034] S1. Build a transmissive off-axis digital holographic optical path system based on a Mach-Zehnder interference system, and adjust the off-axis angle. The optical path system includes a digital holographic imaging optical path with a He-Ne laser as the light source;

[0035] The transmissive off-axis digital holographic optical path system based on the Mach-Zehnder interference system is as Figure 2 shown, and includes a laser light source assembly 1, a beam expander assembly 2, a sample platform 3, two polarizers 41, 42, a beam splitting and reflecting filter assembly 5, a CMOS image sensor 6, and a computer 7; among them:

[0036] The laser light source assembly 1 is a He-Ne laser, used as the light source for the holographic imaging optical path;

[0037] The beam expander and light intensity adjustment assembly 2 is used to expand, collimate, and adjust the light intensity of the He-Ne laser beam; the beam expander assembly 2 includes a plano-convex lens 21, a pinhole aperture 22, and a doublet lens 23; the plano-convex lens 21, the pinhole aperture 22, and the doublet lens 23 together form a Keplerian beam expander system, used to perform beam expansion, filtering, and collimation operations on the incident beam;

[0038] The sample platform 3 is used to carry the optical element sample to be measured and can perform translation and focusing operations;

[0039] The polarizers 41, 42 are used to adjust the polarization direction of the reference light;

[0040] The beam splitting assembly 5 includes 2 beam splitting prisms 51, 52, and 3 mirrors 53, 54, 55; the beam splitting prisms 51, 52 are used to split the beam to form a Mach-Zehnder system, and the mirrors 53, 54, 55 are used to perform total reflection on the beam;

[0041] The CMOS image sensor 6 is used to record the interference information generated by the interference imaging system and form an interference image; the CMOS image sensor 6 has a 2048×2048 rectangular pixel array, has a high quantum efficiency and a 16-bit depth, the CMOS image sensor 6 is connected to the computer 7, and its exposure time parameter is controlled by the computer 7, and the collected interference image is transmitted to the computer 7 for processing;

[0042] The computer 7 is used to store and analyze the interference image.

[0043] The working process of this optical path is as follows:

[0044] First, the laser is reflected by the mirror 55 and then enters the beam expander assembly 2, where it is filtered, expanded, and collimated. The stray light is filtered out, and the incident parallel beam is divided into an object wave and a reference wave by the beam splitter prism 51: The object wave passes through the sample to be measured 3, is reflected by the mirror 5, and then enters the beam splitter prism 52; The reference wave is reflected by the mirror 53 and also enters the beam splitter prism 53; The object wave and the reference wave are converged by the beam splitter prism 53 to generate interference and are recorded on the computer 7 by the CMOS image sensor 6; The polarization components 41 and 42 in the optical path are used to ensure that the polarization directions are the same at the beginning of the optical path, and then 42 is rotated to change the polarization direction of the reference light.

[0045] S2. The holographic patterns of the glass sample before and after the external force is applied are collected through the above optical path system. During the process, the polarization direction of the reference light is changed by rotating the polarization sheet in the reference optical path, and the holograms of the sample before and after the external force is applied are collected at four different rotation angles (0°, 10°, 20°, 30°).

[0046] In the experiment, a fixed load external stress is applied to the optical element sample by a torque wrench holder. Due to the birefringence effect of the glass under the external force, the unknowns in the stress solution process include the angle between the polarization direction of the object light and the first principal stress, the phase change of the object wave passing through the object when no external force is applied, and the phase changes of the object wave passing through the object in the directions of the two principal stress unit vectors when the external force is applied. Therefore, four holograms with different polarization directions of the reference light need to be collected to solve these four unknowns. A polarization sheet is placed in each of the reference optical path and the object optical path of the experimental device to change the polarization direction of the reference light. Digital holograms of the defect-free intact glass before and after the external force is applied are taken at four different polarization directions of the reference light (by rotating the polarization sheet 0°, 10°, 20°, 30° respectively), a total of eight holograms are taken to obtain holograms with different polarization angles of the reference light, as Figure 3 shown.

[0047] S3. Perform a Fourier transform on the hologram, and perform spatial filtering in the frequency domain by setting different sizes of filtering windows to extract the positive first-order term and determine the optimal filtering window size to eliminate the influence of the zero-order term on the quality of the reconstructed image;

[0048] First, the light intensity ratio multiplexing method is used to eliminate the zero-order term interference. By changing the light intensity ratio of the object wave and the reference wave, multiple holograms are recorded, and the zero-order term is removed by subtracting the holograms. The hologram after removing the zero-order term interference is subjected to a two-dimensional fast Fourier transform to obtain the frequency spectrum distribution. In order to improve the reconstruction effect, wavelet denoising is also performed on the frequency spectrum to remove noise interference. By detecting two global maximum points of the frequency spectrum amplitude diagram, the central coordinates of the positive first-order spectrum are determined according to the horizontal coordinate position. A two-dimensional circular filter with different radii is set with the spectrum central coordinates as the midpoint to extract the positive first-order spectrum. The radius of the circular filter is changed to try to completely extract the positive first-order spectrum. The peak signal-to-noise ratio is used as an evaluation index in the process, and the optimal filtering window radius is selected so that the positive first-order term of the spectrum can be completely extracted.

[0049] S4. Using the diffraction distance as a variable and setting its change range and interval according to the preliminary measurement, the above-collected holograms are respectively subjected to diffraction reconstruction. In this process, the square of the amplitude difference (DIF) between two reconstructed images is used as a focusing evaluation function to determine the optimal reconstruction distance, and angular spectrum reconstruction is performed at the optimal reconstruction distance and the optimal filtering window size determined above;

[0050] The spectrum term group containing only the positive first-order spectrum term after being extracted by the filter is C(f x , f y ). Performing diffraction reconstruction on it can obtain the complex amplitude distribution U(x, y). The transfer process of obtaining the reconstructed complex amplitude of the object using the angular spectrum reconstruction algorithm can be expressed as:

[0051]

[0052] Among them, G(f x , f y , z) is the transfer function in the frequency domain corresponding to the propagation distance z, represents the inverse Fourier transform.

[0053] In the angular spectrum reconstruction process, the determination of the propagation distance z is very important. In the present invention, first, the reconstructed distance z measured preliminarily is set as the midpoint, and the search area [z1, z2] is roughly determined. A step size Δ is set within this area to traverse and find the optimal reconstruction distance. The square of the amplitude difference between two reconstructed images is used as a focusing evaluation function: The optimal reconstruction distance is determined within the search area according to the evaluation function. Among them, |U(x, y; z| and |U(x, y; z + Δ)| respectively represent the reconstructed intensities at positions z and z + Δ, and Δ is the set wavelength.

[0054] S5. Respectively obtain the reconstructed complex amplitudes before and after the external force is applied through the above steps, and extract the phase from the complex amplitude to calculate the phase difference before and after the external force is applied;

[0055] The reconstructed complex amplitude is obtained by calculating the object light field distribution through the filtered spectrum at the optimal reconstruction distance. Since a phase difference will be generated along the principal stress direction after the external force is applied, the phase difference of the object wave before and after the external force is applied can be expressed as:

[0056]

[0057] where ψ(x, y) is the wrapped phase difference before and after the external stress is applied, U 1 (x, y) and U 2 (x, y) are the complex object waves before and after excitation, and Im[·] and Re[·] represent the calculations of the imaginary part and the real part respectively.

[0058] Holograms before and after the external force is applied are collected for a glass sheet with a flat surface, a diameter of 30 mm, a thickness of 5 mm, no machining defects, and a glass sheet of the same specification with hole defects on the surface as shown in Figure 4 (a, b) and 4(d, e). The phase difference diagrams of the defect-free sample and the defective sample before and after the external stress is applied are shown in Figure 4 (c), 4(f) respectively.

[0059] S6. Through the light intensity equation The first-order light intensity containing only interference information is extracted from the reconstructed complex amplitudes before and after the external force is applied at four different reference light polarization angles. The phase difference of the object light wave vector in the two principal stress directions caused by the external force is obtained through numerical operations. Among them, W 1k+ represents the first-order light intensity of the hologram without external force, and W 2k+ represents the first-order light intensity of the hologram after the external force is applied. A o and A r represent the amplitudes of the object light and the reference light respectively. k = 1, 2, 3, 4 correspond to different angles of 0°, 10°, 20°, 30° of the rotation of the polarization plate in the reference light path respectively;

[0060] A total of eight digital holograms before and after the external force is applied are taken in four different polarization directions of the reference light (different polarization rotation directions are set to 0°, 10°, 20°, 30°). The light intensities of the holograms before and after the external force is applied are respectively:

[0061]

[0062] Among them, A o and A r are the amplitudes of the object light and the reference light respectively, and are the initial phases of the reference light and the object light respectively. α is the angle between the polarization direction of the object light and the first principal stress. The unit vectors of the first and second principal stress directions are respectively and φ 1is the phase change of the principal stress direction after the object light wave passes through the glass object without external force loading, φ 2 and φ 3 They are the phase changes of the first and second principal stress directions after the object light wave passes through the glass with external force, and the direction of rotating the reference light polarizer is θ k (k=1,2,3,4), corresponding to 0°, 10°, 20°, and 30° respectively.

[0063] From formulas (3) and (4), it can be seen that the amplitude product of the object light and the reference light contained in the positive first-order term is an irrelevant interference factor. Therefore, the ratio function y of the positive first-order term intensity and the amplitude product of the object light and the reference light can be constructed in each reference light polarization direction: k , the function expression is shown in equation (5). In order to enhance the interference information and eliminate the influence of the imaginary part, the first-order light intensity before and after the external stress is added in the numerator of the ratio function and then conjugate multiplied. The intensity ratio function only contains the interference light intensity changes under different polarization angles, so constructing the ratio function can simplify the calculation process of phase change.

[0064]

[0065] It can be seen that the above ratio function contains α, φ 1 ,φ 2 ,φ 3 The four unknown quantities are formed into a system of equations by combining the intensity equations of the four different reference light polarization angles. The four unknown quantities can be solved by the least square method. The intensity of the eight intact glass external force loading holograms recorded above is calculated according to the definition of the intensity ratio function, and the intensity ratio function diagrams of the four different reference light polarization directions are obtained as follows Figure 5 shown.

[0066] S7. Using the principle of birefringence of optical elements of photoelastic materials under stress, the four light intensity equations obtained in S6 are combined to calculate the phase difference caused by external force loading in the two principal stress directions, and then the distribution of the first and second principal stress values ​​is deduced according to the law of stress optics. At the same time, the defects of optical elements can be identified by measuring the abnormal area of ​​stress value distribution under the same external force load. Experiments have shown that this method can identify surface cracks, internal hole defects and sub-surface defect damage caused by femtosecond laser processing in the glass manufacturing process.

[0067] Since the above ratio intensity function includes the phase change before and after stress loading, and since the principal stress value is proportional to the phase change in the corresponding direction, the numerical distribution of the first and second principal stresses of intact defect-free glass after external stress loading can be calculated according to the following empirical formula: Figure 6 shown.

[0068]

[0069] Among them, d is the sample thickness, A and B are stress-optical constants, and λ is the laser wavelength.

[0070] The defects of fused silica mainly include surface cracks and internal bubble or hole defects. First, the present invention imitates the size of an optical lens element to fabricate surface cracks and internal hole defects on a fused silica with a diameter of 30 mm and a thickness of 5 mm, and observes the influence of the defects on the stress distribution of the glass under external force loading through stress numerical measurement. Before the experiment, ensure that the polarization directions of the reference light and the object light are the same. Then, rotate the polarization plate of the reference optical path by 0°, 10°, 20°, and 30° respectively to collect four interference holograms of the samples with surface cracks and internal hole defects. Then, apply a fixed load external force to the two samples through a clamping device to collect interference holograms with the same reference light polarization angle Figure Four sheets, and calculate the positive first-order light intensity map using formula (5) as follows Figure 7 as shown.

[0071] Based on the positive first-order ratio function light intensity map, calculate the principal stresses. The numerical distribution maps of the first and second principal stresses are obtained by calculating the isochromatic line distribution of the phase difference as follows Figure 8 as shown. It can be seen that for the glass with either cracks or internal hole defects, local abnormal regions appear in the stress value distribution in the defect regions. At the same time, the stress values in the surrounding regions of the defects increase because the local defects cause local stress concentration regions to appear in the glass sample under external stress loading.

[0072] The present invention continues to identify the defects of the glass damaged by femtosecond laser processing. The experimental measurement samples are 3 fused silicas of the same specification batch with a diameter of 30 mm and a thickness of 5 mm. First, rotate the polarization direction of the reference light by 0°, 10°, 20°, and 30° for the 3 glasses not processed by femtosecond laser to collect four groups of holograms and calculate the stress distribution in the field of view as a control group. Then, use femtosecond laser technology to process square surface damages with side lengths of 600 μm, 800 μm, and 1000 μm on the subsurface of the three glasses at the same processing depth. After processing, use a microscope to locate the subsurface damage position so that the damage is within the field of view of the digital holographic camera, and calculate the local stress mean value and the principal stress values at the four vertices of the square by framing the area where the damage is located as follows Figure 9 as shown. In the figure, groups 1-3 correspond to the surface damages with side lengths of 1000 μm, 800 μm, and 600 μm respectively.

[0073] It can be seen from the above principal stress distribution diagram that the stress value abnormal area is difficult to directly identify. Therefore, the influence of femtosecond laser processing damage intervention on the stress value is analyzed by comparing the same area. Calculate the local average first and second principal stress values for the selected areas of the above three groups of glasses, and compare them with the average principal stress values selected at the same positions in the field of view of the glass before processing. It is found that the stress values increase with the addition of damage, and the stress values also increase with the increase of the damage area, as shown in Table 1 below.

[0074] Table 1

[0075]

[0076] In summary, the optical element stress measurement method provided by the present invention based on digital holographic photoelasticity can reconstruct the surface topography distribution of the optical element by reconstructing the hologram collected by the system based on the digital holographic measurement principle. At the same time, the reconstruction accuracy is improved through multiple steps such as positive first-order spectrum extraction, evaluation function autofocus, and angular spectrum reconstruction. The phase difference before and after external force loading is extracted and calculated by reconstructing the complex amplitude phase, and then the principal stress value of the sample is measured. While ensuring the accurate characterization of the surface topography of the optical element material, the present invention extracts and calculates the phase difference before and after external force loading by reconstructing the complex amplitude phase, and then realizes the measurement of the principal stress direction and magnitude distribution of the sample based on the digital photoelasticity method and the stress-optical law. While ensuring the characterization of the surface topography of the glass material, the present invention realizes the defect identification of the main component material quartz glass of the optical element by locating the abnormal area of the principal stress value, and can identify the surface defects generated during manufacturing and the subsurface defect damage generated by femtosecond laser processing, providing a reference idea for the complete characterization of the surface and subsurface defects of the optical element, which has important practical significance.

Claims

1. A method for measuring stress and identifying defects of optical components based on digital holographic photoelasticity, characterized in that: It is realized based on the transmission off-axis digital holographic optical path system; the light beam emitted by the laser component is divided into reference light and object light. The object light reflects from the sample surface and carries the sample information and intersects with the reference light in front of the CMOS camera to interfere. The CMOS converts the interference light intensity signal into an electrical signal, and the computer performs holographic image processing; the hologram before and after the external force is applied is reconstructed to obtain the surface morphology distribution. The reconstruction accuracy is improved by positive first-order spectrum extraction and angular spectrum reconstruction autofocus; the phase difference before and after the external force is applied is calculated by reconstructing the complex amplitude phase extraction, and then the direction and size distribution of the principal stress of the sample are measured based on the digital photoelastic method and the law of stress optics, and the defects of the optical element are identified by measuring the stress value change under the same external force loading; the specific steps are as follows: S1. Build a transmission off-axis digital holographic optical path system based on the Mach-Zehnder interferometer system and adjust the off-axis angle. The optical path system includes a digital holographic imaging optical path using He-Ne laser as the light source; S2. The holograms of the glass samples before and after the external force is applied are collected by the above optical system. During the process, the polarization direction of the reference light is changed by rotating the polarizer of the reference optical path, and four groups of holograms of the samples before and after the external force is applied are collected at different rotation angles, i.e., 0°, 10°, 20°, and 30°; S3. Perform Fourier transform on the hologram, extract the positive first-order term by setting filter windows of different sizes to perform spatial filtering in the spectrum domain and determine the optimal filter window size to eliminate the influence of the zero-order term on the quality of the reconstructed image; S4. Taking the diffraction distance as a variable and setting its variation range and spacing according to preliminary measurements, the above-collected holograms are respectively subjected to diffraction reconstruction. In this process, the square of the amplitude difference (DIF) between the two reconstructed images is used as a focusing evaluation function to determine the optimal reconstruction distance, and angular spectrum reconstruction is performed under the above-determined optimal reconstruction distance and optimal filter window size; S5. Obtain the reconstructed complex amplitude before and after the external force is applied through the above steps, extract the phase from the complex amplitude to calculate the phase difference before and after the external force is applied; S6. Through the light intensity equation The first-order light intensity containing only interference information is extracted from the reconstructed complex amplitudes before and after the external force loading at four different reference light polarization angles, and the phase difference of the object light wave vector in the two principal stress directions caused by the external force loading is obtained through numerical calculation; where W 1k+ represents the first-order light intensity of the hologram when there is no external force loading, W 2k+ A represents the first-order light intensity of the hologram after external force loading, o and A r Respectively represent the amplitudes of the object light and the reference light, k = 1, 2, 3, 4 correspond to the reference light path polarizer rotated at different angles of 0°, 10°, 20°, 30°; S7. Using the principle of birefringence of optical elements made of photoelastic materials under stress, the four light intensity equations obtained in S6 are combined to calculate the phase difference caused by external force loading in the two principal stress directions, and then the numerical distribution of the first and second principal stresses is deduced according to the law of stress optics. At the same time, the defects of the optical element can be identified by measuring the abnormal area of ​​stress numerical distribution under the same external force load. Experiments have shown that this method can identify surface cracks, internal hole defects in the glass manufacturing process, and sub-surface defect damage caused by femtosecond laser processing.

2. The method according to claim 1, characterized in that: In step S1, the transmission-type off-axis digital holographic optical path system based on the Mach-Zehnder interference system comprises a laser light source component (1), a beam expansion component (2), a sample platform (3), two polarizers (41, 42), a beam splitting and reflecting component (5), a CMOS image sensor (6) and a computer (7); wherein: The laser light source assembly (1) is a He-Ne laser, used as a light source for the holographic imaging optical path; The beam expansion component (2) is used to perform beam expansion, filtering and collimation operations on a He-Ne laser beam; the beam expansion component (2) comprises a plano-convex lens (21), a pinhole aperture (22) and a doublet lens (23); the plano-convex lens (21), the pinhole aperture (22) and the doublet lens (23) constitute a Keplerian beam expansion system, which is used to perform beam expansion, filtering and collimation operations on an incident beam; The sample platform (3) is used to carry the optical element sample to be tested and can perform translation and focusing actions; The two filters (41, 42) are used to adjust the polarization direction of the reference light; The beam splitting and reflecting assembly (5) comprises two beam splitting prisms (51, 52) and three reflectors (53, 54, 55); the two beam splitting prisms (51, 52) are used to split the light beam to form a Mach-Zehnder system, and the three reflectors (53, 54, 55) are used to perform total reflection on the light beam; The CMOS image sensor (6) is used to record the interference information generated by the interference imaging system and form an interference image; the CMOS image sensor (6) has a 2048×2048 rectangular pixel array, high quantum efficiency and 16-bit bit depth; the CMOS image sensor (6) is connected to a computer (7), and its exposure time parameter is controlled by the computer (7), and the collected interference image is transmitted to the computer (7) for processing; The computer (7) is used to store and analyze the interference image; The workflow of this optical path is: First, the laser is reflected by a reflector (55) and then enters a beam expansion component (2) to be filtered, expanded and collimated. The incident parallel light beam is filtered to remove stray light and is divided into an object light wave and a reference light wave by a beam splitter prism (51): the object light wave is transmitted by a sample to be measured (3) and then reflected by a reflector (5) and enters a beam splitter prism (52); the reference light wave is reflected by a reflector (53) and then enters a beam splitter prism (53); the object light wave and the reference light wave are converged by the beam splitter prism (53) to interfere and are recorded on a computer (7) via a CMOS image sensor (6); the polarizer components (41, 42) in the optical path are used to ensure that the polarization directions are the same at the beginning of the optical path, and then the polarizer (42) is rotated to change the polarization direction of the reference light.

3. The method according to claim 1, characterized in that: In step S3, a two-dimensional circular filter is generated with different radii set with the center coordinate of the spectrum as the midpoint to extract the positive first-order spectrum. The radius of the circular filter is changed to try to completely extract the positive first-order spectrum. The peak signal-to-noise ratio is used as an evaluation index in the process, and the optimal filter window radius is selected so that the positive first-order item of the spectrum can be completely extracted.

4. The method according to claim 1, characterized in that In step S4, the spectrum items containing only positive first-order spectrum items are extracted through the filter to form C(f x ,f y ), and the complex amplitude distribution U(x,y) can be obtained by diffraction reconstruction. The transmission process of the reconstructed complex amplitude of the object obtained by the angular spectrum reconstruction algorithm can be expressed as: Among them, G(f x ,f y ,z) is the transfer function in the frequency domain corresponding to the propagation distance z, represents inverse Fourier transform; The angular spectrum reconstruction process first sets the reconstruction distance z as the midpoint according to the preliminary measurement, roughly determines the search area [z1,z2], sets the step size Δ in this area to traverse and find the optimal reconstruction distance; uses the square of the amplitude difference between the two reconstructed images as the focusing evaluation function: The optimal reconstruction distance is determined in the search area according to the evaluation function; wherein |U(x, y; z| and |U(x, y; z+Δ)| represent the reconstruction intensities at positions z and z+Δ, respectively, and Δ is the set wavelength.

5. The method according to claim 1, characterized in that In step S5, the object light field distribution is calculated by filtering the spectrum at the optimal reconstruction distance to obtain the reconstructed complex amplitude; since a phase difference value will be generated along the principal stress direction after the external force is applied, the object wave phase difference before and after the external force is applied is expressed as: Among them, ψ(x, y) is the wrapping phase difference before and after the external stress loading, U1(x, y) and U2(x, y) are the complex object waves before and after the excitation, and Im[·] and Re[·] represent the calculation of the imaginary part and the real part, respectively.

6. The method according to claim 1, characterized in that In step S6, the light intensity equation The first-order light intensity containing only interference information is extracted from the reconstructed complex amplitudes before and after the external force loading at four different reference light polarization angles, and the phase difference of the object light wave vector in the two principal stress directions caused by the external force loading is obtained through numerical calculation; where W 1k+ represents the first-order light intensity of the hologram when there is no external force loading, W 2k+ A represents the first-order light intensity of the hologram after external force loading, o and A r Respectively represent the amplitudes of the object light and the reference light, k = 1, 2, 3, 4 correspond to the reference light path polarizer rotated at different angles of 0°, 10°, 20°, 30°; A total of eight digital holograms were taken in four different polarization directions of the reference light before and after the external force was applied. The light intensities of the holograms before and after the external force was applied were: Among them, A o and A r are the amplitudes of the object light and the reference light, respectively, and are the initial phases of the reference light and the object light, respectively; α is the angle between the polarization direction of the object light and the first principal stress, and the unit vectors of the first and second principal stress directions are and φ1 is the phase change in the principal stress direction of the object light wave after passing through the glass object without external force loading, φ2 and φ3 are the phase changes in the first and second principal stress directions after the object light wave passes through the glass with external force loading, and the direction of rotating the reference light polarizer is θ k (k=1,2,3,4), corresponding to 0°, 10°, 20°, 30° respectively; From the above light intensity formula, it can be seen that the amplitude product of the object light and the reference light contained in the positive first-order term is an irrelevant interference factor. Therefore, the ratio function y of the positive first-order term intensity and the amplitude product of the object light and the reference light is constructed in each reference light polarization direction. k , the function expression is as follows: The above ratio function contains four unknown quantities α, φ1, φ2, and φ3. The light intensity equations of four different reference light polarization angles are combined into an equation group, and the four unknown quantities can be solved by the least squares method.

7. The method according to claim 1, characterized in that In step S7, the phase difference caused by the external force loading in the two principal stress directions is calculated by combining the four light intensity equations obtained in step S6 using the birefringence principle of the optical element of the photoelastic material under stress state, and then the distribution of the first and second principal stress values ​​is deduced according to the law of stress optics; at the same time, the defects of the optical element are identified by measuring the abnormal area of ​​stress value distribution under the same external force load; Since the above ratio intensity function contains the phase change before and after stress loading, and since the principal stress value is proportional to the phase change in the corresponding direction, the principal stress value distribution is calculated according to the following empirical formula: Where d is the sample thickness, A and B are stress optical constants, and λ is the laser wavelength.

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