Point-diffraction interferometry method and system for measuring surface shape under environmental disturbance factors

Abstract

This invention discloses a method and system for measuring the surface shape of point diffraction interferometry under environmental disturbances, belonging to the field of optical precision measurement technology. It solves the technical problem of low accuracy and stability in point diffraction interferometry under environmental disturbances. The method includes: constructing a point diffraction interferometry system; establishing a mathematical model of environmental factors and measurement phase error based on mechanical vibration and aero-optics theories; acquiring two interferograms with a fixed phase difference using a two-step phase-shifting method; quantitatively assessing environmental interference based on the mathematical model; extracting the phase and calculating the surface shape data using a two-step phase-shifting algorithm; and completing dynamic calibration by eliminating environmental phase errors. This invention achieves quantitative modeling of multiple environmental factors, improves sampling efficiency by 50%, significantly reduces the impact of environmental disturbances through dynamic calibration, and achieves measurement results highly consistent with standard interferometers. It improves measurement accuracy and stability under non-ideal environments and is suitable for ultra-high precision surface shape detection of precision optical components and semiconductor wafers.

Description

Technical Field

[0001] This invention belongs to the technical field, specifically relating to a method and system for measuring point diffraction interferometry surface shape under environmental disturbance factors. Background Technology

[0002] Interferometry is a high-precision, non-contact optical measurement technique capable of characterizing the microscopic surface of objects with micrometer or even nanometer-level resolution. By analyzing the interference fringe pattern generated after the superposition of two coherent beams, this technique can accurately calculate the three-dimensional morphology and minute height variations of the measured surface. Due to its extremely high longitudinal resolution and non-destructive nature, interferometry plays an irreplaceable role in fields with extremely high requirements for surface profile accuracy, such as precision optical component inspection, semiconductor wafer manufacturing, and nanotechnology.

[0003] Point diffraction interferometry (PDI) is an advanced optical measurement technique for ultra-high precision surface morphology characterization and wavefront distortion detection. It is known for its high precision, large range, and non-contact operation, but it is extremely sensitive to environmental disturbances (vibration, temperature, humidity, and airflow).

[0004] Unlike traditional interferometry methods that rely on beam splitters to divide and recombine light rays, PDI uses a point diffraction source to generate interferograms. This diffraction source is typically created from a high-precision pinhole, acting as a virtual coherent light source. Light from the point source is guided onto the object or surface under study, which overcomes the precision limitations of lenses in other interferometers. Therefore, PDI excels in detecting minute surface features, high resolution, and non-contact measurements.

[0005] The schematic diagram of PDI is as follows: Figure 1 As shown in the diagram, in PDI (Precision Difference), the light emitted from the laser source passes through BS1 and BS2 to reach the beam expander and generate collimated parallel light. Subsequently, the objective lens focuses this collimated beam onto the pinhole plate, exciting the diffraction effect to form an ideal spherical reference wavefront. In this optical path structure, the optical path branched off from BS1 is used for real-time analysis of beam quality, while the optical path branched off from BS2 is used for auxiliary alignment of the diffraction units. To ensure that the focused spot accurately falls into the center of the pinhole, this system specifically introduces machine vision-based active alignment technology to effectively correct the positioning deviation between the focused spot and the diffraction pinhole, ensuring stable system operation.

[0006] However, the complex structure of PDI systems and their high sensitivity to environmental disturbances (such as vibration, temperature, humidity and airflow) have become the main bottlenecks limiting their application.

[0007] Current error calibration mainly focuses on theoretical wavefront quality, positioning error, and geometric aberration analysis, with limited research on quantitative analysis and calibration involving environmental interference. Traditional time-domain phase shifting methods (such as the four-step phase shifting method) are highly susceptible to environmental vibration and temperature drift when using PZT for phase shifting due to the long acquisition time, leading to phase extraction errors. Although transient polarization phase shifting methods can effectively resist vibration interference, their lateral resolution is usually low. While deep learning-based wavefront reconstruction methods have shown potential as an emerging technology, they are currently limited by the universality and generalization ability of the training dataset, making it difficult to meet the complex and ever-changing practical testing needs.

[0008] Therefore, there is an urgent need for a new PDI measurement and calibration strategy that can quantitatively analyze the impact of environmental factors and efficiently and quickly extract the phase to avoid environmental interference. Summary of the Invention

[0009] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a point diffraction interferometry surface shape measurement method and system under environmental disturbances. Under the interference of various environmental factors such as vibration and temperature changes, a point diffraction interferometer is used to perform high-precision surface morphology measurement and error calibration. This solves the technical problem that existing point diffraction interferometry measurement technology is extremely sensitive to environmental disturbances, lacks effective quantitative analysis and real-time calibration methods, and thus suffers from a serious decrease in measurement accuracy and poor stability in non-ideal laboratory environments.

[0010] The present invention adopts the following technical solution: A method for measuring point diffraction interferometry surface shape under environmental disturbances includes the following steps: S1. Construct a point diffraction interferometry measurement system and establish a mathematical model between environmental factors and measurement phase error based on mechanical vibration and aero-optics theory; S2. The test piece is measured using the point diffraction interferometry system. Two interferograms with a fixed phase difference are acquired using the two-step phase shifting method of light intensity. S3. Based on the mathematical model established in step S1, analyze the changes in refractive index and optical path difference (OPD) caused by environmental factors, and quantitatively assess environmental interference. S4. Using the light intensity information of the interferogram collected in step S2, combined with the background light intensity distribution, the phase information of the measured surface is extracted through a two-step phase-shifting algorithm, and the surface shape data of the measured mirror is calculated. S5. Combining the environmental error assessment results from step S3 with the phase information extracted from step S4, complete the dynamic calibration of environmental interference and obtain high-precision surface morphology measurement results.

[0011] Preferably, in step S1, the environmental factors include vibration, temperature, humidity, and airflow. When establishing the mathematical model, the atmospheric refractive index is calculated based on the Gladstone-Dale formula and the Rüeger modified formula, and the environmental vibration is modeled in combination with mechanical vibration theory.

[0012] Preferably, the mathematical model includes an optical path difference variation model, wherein the optical path difference variation model is as follows: The corresponding phase change model is ;in, This represents the change in the refractive index of air. To measure the geometric distance difference between the test light and the reference light, The wavelength of the laser. This represents the phase change value caused by environmental factors.

[0013] Preferably, the mathematical model includes a vibration phase change model and a vibration interference light intensity model, wherein the vibration phase change model is as follows: The vibration interference light intensity model is as follows: ;in, For vibration amplitude, The vibration frequency, The initial phase of the vibration, For time, Background light intensity, For striped tones, This is for testing the phase.

[0014] Preferably, in step S2, the fixed phase difference is π / 2, and the two interference patterns are interference patterns with a phase difference of π / 2. and interferogram Background light intensity during phase shifting The background light intensity is approximately constant. Obtained through pre-calibration or light intensity statistics.

[0015] Preferably, the background light intensity B(x,y) is calculated as follows:

[0016] in, Let be the intensity of the interference light with phase π. The intensity of the interference light with a phase of 3π / 2.

[0017] Preferably, in step S4, the formula for extracting the phase information of the measured surface using a two-step phase-shifting algorithm is as follows:

[0018] in, The background light intensity during phase shifting. and The phase difference is Two interference diagrams.

[0019] Preferably, in step S, when calculating the surface shape data of the mirror under test, the surface shape is characterized by the distance from the center of the diffraction aperture to the mirror under test, and the distance is calculated as follows:

[0020] in, The distance from the center of the diffraction aperture to the surface of the mirror being measured is denoted as . λ is the output wavelength of the laser source in the point diffraction interferometry system.

[0021] Preferably, in step S5, the specific method for completing the dynamic calibration of environmental interference is as follows: The phase error value caused by environmental factors obtained from the quantitative assessment in step S3 is removed from the phase information of the measured surface extracted in step S4. The surface shape data of the measured mirror is recalculated based on the phase information after removing the error, and the calibrated surface morphology measurement result is obtained.

[0022] Secondly, embodiments of the present invention provide a point diffraction interferometry surface shape measurement system oriented towards environmental disturbance factors, comprising: The modeling module is used to establish a mathematical model between environmental factors and measurement phase error based on mechanical vibration and aero-optics theory. The acquisition module is used to control the point diffraction interferometry measurement system to measure the device under test, and to acquire two interferograms with a fixed phase difference using the two-step phase shifting method of light intensity. The analysis module is used to analyze the changes in refractive index and optical path difference (OPD) caused by environmental factors based on the mathematical model, and to quantitatively assess environmental interference. The phase module is used to extract the phase information of the measured surface by using the light intensity information of the acquired interferogram and combining it with the background light intensity distribution, and to calculate the surface shape data of the measured mirror through a two-step phase shifting algorithm. The calibration module is used to combine the environmental error assessment results with the extracted phase information to perform dynamic calibration of environmental interference and obtain high-precision surface morphology measurement results.

[0023] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described point diffraction interferometry surface shape measurement method under environmental disturbance factors.

[0024] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described point diffraction interferometry surface shape measurement method under environmental disturbance factors.

[0025] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the above-described point diffraction interferometry surface shape measurement method under environmental disturbance factors.

[0026] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-described point diffraction interferometry surface shape measurement method under environmental disturbance factors.

[0027] Compared with the prior art, the present invention has at least the following beneficial effects: A point diffraction interferometry (PDI) surface shape measurement method under environmental disturbances is proposed. This method establishes a quantitative mathematical model of environmental interference and phase error; acquires two interferograms using a two-step phase-shifting method; quantitatively assesses environmental interference based on the model; extracts the phase and calculates the surface shape data; and performs dynamic calibration based on the assessment results to obtain the final result. First, through the established mathematical model, environmental disturbances such as vibration, temperature, and humidity are systematically quantified into calculable phase errors in PDI measurements for the first time, providing a precise theoretical basis for subsequent calibration. Second, the proposed two-step phase-shifting method reduces the image acquisition steps by half compared to the traditional four-step method, significantly shortening the data acquisition time window and fundamentally reducing the impact of accumulated environmental disturbances caused by excessively long acquisition cycles on the measurement results. The method also automates the assessment-extraction-calibration process. Overall, this invention significantly improves the robustness, measurement efficiency, and final accuracy of point diffraction interferometry in non-ideal environments, solving the bottleneck problem of PDI technology's dependence on harsh laboratory environments.

[0028] Furthermore, environmental factors are precisely defined as vibration, temperature, humidity, and airflow, avoiding model distortion caused by omitting key interfering factors. During modeling, atmospheric refractive index is calculated based on the Gladstone-Dale formula and the Rüeger modified formula, combined with mechanical vibration theory for vibration modeling. This accurately characterizes atmospheric physical properties and the actual impact of vibration, achieving systematic and quantitative modeling of multiple environmental factors.

[0029] Furthermore, a direct quantitative correlation was established between changes in air refractive index, geometric distance difference, and phase error, transforming the abstract influence of environmental factors into calculable physical parameters. This formula, derived from the fundamental principles of light interference, can accurately calculate the optical path difference and phase change values ​​caused by factors such as temperature, humidity, and pressure. This transforms the assessment of non-vibration-related environmental disturbances from qualitative analysis to quantitative calculation, providing a concrete and operable calculation basis for subsequent environmental disturbance assessments. The corresponding phase error can be directly calculated from the changes in environmental parameters, improving the accuracy of environmental disturbance assessments and providing a clear quantitative standard for subsequent phase error elimination.

[0030] Furthermore, environmental vibration is decomposed into a superposition of cosine vibrations, closely reflecting the dynamic changes of vibration in real-world environments. This overcomes the shortcomings of traditional models that neglect the temporal characteristics of vibration and only perform static analysis. This model can accurately characterize the dynamic influence of vibration amplitude, frequency, and other parameters on the interference light intensity and test phase, clearly reflecting the time-varying pattern of vibration-induced light intensity. This makes the analysis of vibration interference more closely aligned with actual measurement scenarios, accurately calculating phase deviations under different vibration parameters, and achieving precise quantitative assessment of vibration interference.

[0031] Furthermore, by setting the fixed phase difference to π / 2, which is the optimal difference for interferometric phase extraction, the accuracy of phase extraction is guaranteed. Simultaneously, combined with the technical characteristics of PDI phase shifting, the background light intensity is approximated as a constant, significantly simplifying the phase extraction calculation process. In addition, the background light intensity can be obtained through pre-calibration or light intensity statistics, balancing measurement accuracy and efficiency without requiring additional acquisition steps. Compared to the traditional four-step phase shifting method, acquiring only two interferograms reduces the sampling steps by 50%, effectively reducing the cumulative error of environmental interference during time-domain phase shifting, significantly improving the efficiency of interferogram acquisition and subsequent phase calculation, while ensuring the validity of the acquired data.

[0032] Furthermore, the background light intensity is obtained by averaging the four interferometric light intensity data from the traditional four-step phase-shifting method, eliminating the need for additional interferogram acquisition to obtain the background light intensity, thus saving measurement time and hardware resources. Since the four-step phase-shifting light intensity data covers the entire phase range of 0, π / 2, π, and 3π / 2, averaging effectively compensates for light intensity fluctuations caused by different phases, making the background light intensity value more closely match the actual measurement scenario and avoiding errors caused by manual settings or single data values.

[0033] Furthermore, based on the fundamental principles of interference light intensity and adapted to a technical setting where the background light intensity is approximately constant, the test phase can be directly calculated from the light intensities of two interferograms and the background light intensity. This eliminates the need to eliminate background light intensity and fringe modulation as required by the traditional four-step phase-shifting method, significantly simplifying the calculation process and reducing the accumulation of errors. The formula utilizes only two interferograms with a phase difference of π / 2, avoiding the accumulation of environmental interference caused by multiple image acquisitions. Simultaneously, the calculation logic is direct, enabling rapid extraction of phase information from the measured surface. This improves phase extraction efficiency while ensuring the accuracy of the extracted results, meeting the phase extraction requirements of ultra-high precision measurements.

[0034] Furthermore, by characterizing the surface shape through the distance from the center of the diffraction aperture to the measured mirror, a direct quantitative correlation between the test phase and the actual physical distance was established, transforming abstract phase information into physical data that can intuitively reflect the microscopic morphology of the measured mirror. Based on the fundamental relationship between the interference phase and optical path of light, the derivation is theoretically rigorous and the calculation process is concise, accurately converting phase information into nanometer-level surface shape and distance data, meeting the technical requirements of ultra-high precision point diffraction interferometry measurement.

[0035] Furthermore, a calibration logic of eliminating phase errors and recalculating surface shape is adopted. This directly targets and eliminates the core error source caused by environmental factors, namely phase errors, instead of simply correcting the surface shape data as in traditional methods. This avoids the problem of error superposition during the correction process. Aligned with the entire measurement workflow, the preliminary steps have already achieved a quantitative assessment of environmental phase errors, allowing these errors to be directly removed from the extracted phase information. Then, the surface shape data is recalculated based on the corrected phase. The calibration process is precise and operable, adaptable to different levels and types of environmental interference, significantly improving the accuracy and stability of point diffraction interferometry under non-ideal environments, and making the measurement results more closely match the actual surface shape of the measured object.

[0036] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0037] In summary, this invention establishes a quantitative physical model of environmental disturbances and phase errors, and combines it with a fast and robust two-step phase-shifting algorithm to construct a complete technical system from theoretical analysis to real-time calibration. This significantly improves anti-interference capabilities, effectively suppresses the effects of vibration and temperature changes, greatly increases measurement efficiency, and enables faster sampling and calculation. It also achieves high-precision dynamic calibration, with output results consistent with the reference height. Overall, it solves the bottleneck problems of poor stability and low accuracy of PDI technology in complex environments.

[0038] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0039] Figure 1 This is a schematic diagram of the point diffraction interferometry principle. Figure 2 This represents the change in background light intensity after phase shift; Figure 3 The light intensity distribution diagram is shown, where (a) is... (b) is the light intensity distribution; Light intensity distribution; Figure 4 The change in OPD caused by environmental disturbances, where (a) is right The impact, (b) is right The effect, (c) is right The effect, (d) is With the trend of phase change; Figure 5 The images show surface topography measured by different methods, where (a) is the surface topography measured using a 4-step phase-shifting algorithm, (b) is the surface topography measured using a 2-step phase-shifting algorithm plus a calibration algorithm, and (c) is the surface topography measured using a Zygo interferometer. Figure 6 A schematic diagram of a computer device provided in an embodiment of the present invention; Figure 7 This is a block diagram of a chip according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the method steps of the present invention.

[0040] Among them, 60. Computer equipment; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access memory unit; 6202. Cache memory unit; 6203. Read-only memory unit; 6204. Program / utility; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0043] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0044] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0045] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0046] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0047] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0048] This invention provides a point diffraction interferometry (PDI) surface shape measurement method under environmental disturbances. First, based on mechanical vibration and aero-optics theory, a quantitative model is established between environmental factors and the test phase error. To address environmental sensitivity, a two-step phase-shifting method based on interference light intensity is proposed for efficient and robust extraction of the surface phase. Experimental verification shows that this method not only reveals the significant impact of vibration and temperature on measurement accuracy but also effectively calibrates these errors through the model. The new two-step phase-shifting method is 50% more efficient than the traditional four-step algorithm, overcomes the environmental sensitivity of time-domain phase shifting, and significantly improves the measurement accuracy and efficiency of PDI in complex environments.

[0049] Please see Figure 8 The present invention provides a method for measuring point diffraction interferometry surface shape under environmental disturbance factors, comprising the following steps: S1. Construct a point diffraction interferometry measurement system and establish a mathematical model between environmental factors (vibration, temperature, humidity, airflow) and measurement phase error based on mechanical vibration and aero-optics theory. Environmental factors such as air disturbances have a significant impact on all high-precision interferometry. According to aerodynamic optics theory (Luneburg RK, 1966), changes in the density distribution of the gas flow field directly affect the optical refractive index of the gas, as expressed by the Gladstone-Dale formula (…). (KGD is a constant). As factors such as pressure, temperature, humidity, and velocity change in the flow field, the density distribution at its spatial location also changes, causing a change in the refractive index distribution of the gas flow field. In interferometry, this manifests as a certain degree of random variation in the OPD between the two beams, resulting in irregular variations in the interference fringes.

[0050] Air disturbances have a significant impact on high-precision interferometric measurements. According to aero-optics theory, changes in airflow density distribution directly affect the gas refractive index, which in turn leads to random variations in the optical path difference (OPD) between two beams.

[0051] If the geometric distance difference between the test light and the reference light is L, the refractive index change is... Then the optical path difference changes The corresponding phase change:

[0052] To analyze the effects of temperature, humidity, and pressure on the refractive index of air, this invention uses the Rüeger modified formula to calculate the atmospheric refractive index in the visible and near-infrared bands.

[0053] When the specified standard atmospheric environment is temperature T=273.15K, atmospheric pressure p=1013.25hpa, CO2 content x=0.0375%, and water vapor pressure e=0hpa, the atmospheric phase refractive index The calculation formula is:

[0054]

[0055] When setting wavelength At that time, the actual atmospheric refractive index The formula for absolute error propagation is as follows:

[0056] Differential analysis shows that changes in temperature and pressure have a significant impact on the refractive index and the final phase measurement.

[0057] Due to pressure changes Temperature changes and water vapor pressure changes Caused refractive index change The formula for absolute error propagation is:

[0058] Regarding the effects of vibration, excessive ambient vibration amplitude or prolonged CCD exposure time can lead to interference fringe jitter or uneven phase shifting. Vibration can be decomposed into a superposition of cosine vibrations, and the model defining the influence of vibration on interferometry is as follows: Phase changes caused by vibration Represented as:

[0059] At this time, the actual interference light intensity Represented as:

[0060] Where A is the amplitude. For frequency, The initial phase of the vibration. Background light intensity, For striped tones, This is for testing the phase.

[0061] Time-related vibration signals This will cause light intensity As time changes, the longer the phase shift period, the more significant the impact of vibration on measurement accuracy.

[0062] S2. The test piece is measured using a point diffraction interferometry system. Two interferograms with a fixed phase difference are acquired using the two-step phase shifting method of light intensity. To improve the efficiency and robustness of the phase-shifting method, this invention proposes a two-step phase-shifting algorithm. The interference of coherent light is represented as:

[0063] in, , Let be the light intensities of the two coherent beams. To test the phase, This is the phase shift step size. Let the background light intensity... striped tone system = .

[0064] like Figure 2 As shown, in the PDI simulation, it was found that when the tested mirror shifts phase... At that time, the grayscale change of the background light intensity is minimal (in (within the range), therefore during the phase shift process It can be approximated as a constant.

[0065] The traditional four-step phase-shifting method requires the acquisition of four interferograms (0, ...). , , The background light intensity B and modulation degree C are eliminated to calculate the phase. The equation for the four-step phase shift method is expressed as:

[0066]

[0067]

[0068]

[0069] Four interferograms were captured, and the phase representation was obtained based on the above equation:

[0070] The method of this invention only requires acquiring two images with a phase difference of 1. Interference diagram and Based on known or estimated background light intensity The phase is extracted using the following formula:

[0071] in, It is considered a constant or obtained through pre-calibration. Compared to the traditional four-step phase shifting method, the method of this invention reduces the sampling steps, thereby reducing the error introduced by environmental vibrations during the time-domain phase shifting process.

[0072] In the method of this invention, the background light intensity The calculation is crucial. In the PDI experiment, the test wavefront experiences significant attenuation as it reaches the tested mirror and is reflected back to the pinhole, while the reference wavefront interferes directly at the pinhole plate. The interference is recorded using a CCD detector, and the results are compared. and The grayscale distribution and energy, and the light intensity distribution of both are as follows: Figure 3 As shown. The formula is:

[0073] Experiments have shown that the light intensity of the test wavefront is much smaller than that of the reference wavefront. This difference can be specifically handled or ignored in precision metrology, or the background light intensity can be obtained through pre-calibration.

[0074] S3. Based on the mathematical model established in step S1, analyze the changes in refractive index and optical path difference (OPD) caused by environmental factors, and quantitatively assess environmental interference. S4. Using the light intensity information of the interferogram collected in step S2, combined with the background light intensity distribution, the phase information of the measured surface is extracted through a two-step phase-shifting algorithm, and the surface shape data of the measured mirror is calculated. S5. Combining the environmental error assessment results from step S3 with the phase information extracted from step S4, complete the dynamic calibration of environmental interference and obtain high-precision surface morphology measurement results.

[0075] Phase directly derived from interferogram The distance from the center of the diffraction aperture to the surface of the mirror being measured The relationship is:

[0076] in, is the laser wavelength.

[0077] In another embodiment of the present invention, a point diffraction interferometric surface shape measurement system oriented to environmental disturbance factors is provided. This system can be used to implement the above-mentioned point diffraction interferometric surface shape measurement method oriented to environmental disturbance factors. Specifically, the point diffraction interferometric surface shape measurement system oriented to environmental disturbance factors includes a modeling module, an acquisition module, an analysis module, a phase module, and a calibration module.

[0078] Among them, the modeling module is used to establish a mathematical model between environmental factors and measurement phase error based on mechanical vibration and aero-optics theory; The acquisition module is used to control the point diffraction interferometry measurement system to measure the device under test, and to acquire two interferograms with a fixed phase difference using the two-step phase shifting method of light intensity. The analysis module is used to analyze the changes in refractive index and optical path difference (OPD) caused by environmental factors based on the mathematical model, and to quantitatively assess environmental interference. The phase module is used to extract the phase information of the measured surface by using the light intensity information of the acquired interferogram and combining it with the background light intensity distribution, and to calculate the surface shape data of the measured mirror through a two-step phase shifting algorithm. The calibration module is used to combine the environmental error assessment results with the extracted phase information to perform dynamic calibration of environmental interference and obtain high-precision surface morphology measurement results.

[0079] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for the operation of a point diffraction interferometry surface shape measurement method under environmental disturbance factors, including: A point diffraction interferometry system was constructed, and a mathematical model was established based on mechanical vibration and aero-optics theories to determine the relationship between environmental factors and measurement phase error. The system was used to measure the workpiece under test, employing a two-step phase-shifting method to acquire two interferograms with a fixed phase difference. Based on the established mathematical model, the changes in refractive index and optical path difference (OPD) caused by environmental factors were analyzed to quantitatively assess environmental interference. Using the light intensity information from the acquired interferograms, combined with the background light intensity distribution, the phase information of the measured surface was extracted using a two-step phase-shifting algorithm, and the surface shape data of the measured mirror was calculated. Combining the environmental error assessment results with the extracted phase information, dynamic calibration against environmental interference was performed, resulting in high-precision surface topography measurement results.

[0080] Please see Figure 6 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the point diffraction interferometric surface shape measurement method under environmental disturbance factors as described in this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the point diffraction interferometric surface shape measurement system under environmental disturbance factors as described in this embodiment. To avoid repetition, these details are not elaborated here.

[0081] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 6 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0082] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0083] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0084] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0085] Please see Figure 7 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0086] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 8 The steps are shown in the figure.

[0087] Storage unit 620 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include a read-only memory (ROM) 6203.

[0088] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0089] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0090] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem). This communication can be performed via input / output interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network, wide area network, and / or public network, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0091] Example 4 This invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). More specific examples of the computer-readable storage medium include: an electrical connection with one or more wires, a portable disk, a hard disk, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable compact disk read-only memory, optical storage device, magnetic storage device, or any suitable combination thereof.

[0092] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, radio frequency, etc., or any suitable combination thereof.

[0093] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0094] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the point diffraction interferometry surface shape measurement method under environmental disturbance factors in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps: A point diffraction interferometry system was constructed, and a mathematical model was established based on mechanical vibration and aero-optics theories to determine the relationship between environmental factors and measurement phase error. The system was used to measure the workpiece under test, employing a two-step phase-shifting method to acquire two interferograms with a fixed phase difference. Based on the established mathematical model, the changes in refractive index and optical path difference (OPD) caused by environmental factors were analyzed to quantitatively assess environmental interference. Using the light intensity information from the acquired interferograms, combined with the background light intensity distribution, the phase information of the measured surface was extracted using a two-step phase-shifting algorithm, and the surface shape data of the measured mirror was calculated. Combining the environmental error assessment results with the extracted phase information, dynamic calibration against environmental interference was performed, resulting in high-precision surface topography measurement results.

[0095] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchain. The processors involved in the embodiments provided in this application may be, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc.

[0096] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0097] To verify the effectiveness of the measurement method of the present invention, a specific experimental platform was constructed for verification, and comparative tests were conducted for temperature disturbance and vibration interference, respectively.

[0098] In this embodiment, the initial standard test environment conditions are first set as follows: Thermodynamic temperature Atmospheric pressure Water vapor pressure Measuring the length of the optical path .

[0099] Then assess the impact of vibration and set the initial test conditions: amplitude ,frequency Initial phase .

[0100] Based on the aforementioned error model, the change in optical path difference (OPD) caused by environmental disturbances is calculated, such as... Figure 4 As shown in the trend, vibration and temperature cause significant changes in OPD and test phase.

[0101] Experimental environment and hardware configuration To verify the effectiveness of the error model and phase extraction algorithm in the method of this invention, the aperture will be compared. radius of curvature The spherical mirror was tested under vibration and temperature disturbances. The experiment was conducted in a professional optical laboratory (dark room), with an air compressor and air conditioner serving as the sources of vibration and temperature disturbances. The experimental objects and instruments are shown in Table 1.

[0102] Table 1 Experimental subjects, environment and instruments

[0103] Measurement verification under temperature disturbance First, a temperature disturbance experiment was conducted. The indoor air conditioner was turned on to create a temperature disturbance in the test environment. The continuous temperature change was observed. Measurements of the spherical mirror under test were performed using both the traditional four-step phase-shifting algorithm and the two-step phase-shifting error calibration method proposed in this invention (the method of this application), with the measurement results of the Zygo interferometer under the same conditions used as the true reference. The test results are shown in Table 2. The corresponding surface morphology is as follows: Figure 5 As shown.

[0104] Table 2 Test Results

[0105] Experimental data show that the traditional four-step phase-shifting method, due to its numerous sampling steps and long processing time, is severely affected by temperature changes, resulting in a peak-to-valley (PV) value as high as 0.869. The deviation from the true value is huge. However, using the method of this invention, the PV value is 0.382. The RMS value is 0.0531. The result is consistent with the standard result of the Zygo interferometer (PV=0.379). RMS=0.055 Highly consistent.

[0106] Experiments show that the present invention significantly reduces the impact of temperature drift on measurement and greatly improves measurement accuracy through error model calibration and rapid two-step phase shift.

[0107] Measurement verification under vibration interference A vibration interference experiment was then conducted. Periodic vibrations were generated using an air compressor pump, and the vibration parameters at the tested mirror and adjustment frame were measured using an NSK Laird BT900 multi-point measuring instrument. The amplitude was as follows: ,frequency .

[0108] Table 3 shows the measurement results of the two methods under strong vibration conditions.

[0109] Table 3 Test results of the two methods under vibration interference

[0110] The above results were compared with the Zygo measurement results under undisturbed conditions (PV approximately 0.379). As can be seen from the comparison, the PV value error of the traditional method exceeds 100%, which cannot meet the requirements of precision measurement. However, the PV value measured by the method of this invention is 0.391. The values ​​are very close to the reference values. This indicates that the two-step phase-shifting algorithm proposed in this invention only requires the acquisition of two images, improving the sampling efficiency by 50% compared to the four-step method. It effectively avoids the vibration accumulation error during the time-domain phase-shifting process and demonstrates excellent vibration resistance and robustness.

[0111] In summary, this invention presents a method and system for measuring the surface shape of point diffraction interferometry under environmental disturbances. Based on the Gladstone-Dale formula and mechanical vibration theory, a physical model of the influence of environmental disturbances on the measured wavefront is constructed. Combining background light intensity characteristics, a two-step phase-shifting strategy is innovatively adopted to replace the traditional four-step phase-shifting method. Comparative experiments verify that this invention not only improves measurement efficiency by 50%, but also maintains high consistency with the peak-to-valley (PV) and root-mean-square (RMS) values ​​of the measurement results under vibration and temperature disturbance environments. This invention effectively solves the problems of decreased accuracy and poor stability of point diffraction interferometry under non-ideal environments, providing a reliable technical approach for the dynamic and online detection of high-precision optical components.

[0112] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0113] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0114] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0115] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0116] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0117] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0118] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random-access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0119] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0120] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0121] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0122] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for measuring point diffraction interferometry surface shape under environmental disturbance factors, characterized in that, Includes the following steps: S1. Construct a point diffraction interferometry measurement system and establish a mathematical model between environmental factors and measurement phase error based on mechanical vibration and aero-optics theory; S2. The test piece is measured using the point diffraction interferometry system. Two interferograms with a fixed phase difference are acquired using the two-step phase shifting method of light intensity. S3. Based on the mathematical model established in step S1, analyze the changes in refractive index and optical path difference (OPD) caused by environmental factors, and quantitatively assess environmental interference. S4. Using the light intensity information of the interferogram collected in step S2, combined with the background light intensity distribution, the phase information of the measured surface is extracted through a two-step phase-shifting algorithm, and the surface shape data of the measured mirror is calculated. S5. Combining the environmental error assessment results from step S3 with the phase information extracted from step S4, complete the dynamic calibration of environmental interference and obtain high-precision surface morphology measurement results.

2. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 1, characterized in that, In step S1, the environmental factors include vibration, temperature, humidity, and airflow. When establishing the mathematical model, the atmospheric refractive index is calculated based on the Gladstone-Dale formula and the Rüeger modified formula, and the environmental vibration is modeled in combination with mechanical vibration theory.

3. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 2, characterized in that, The mathematical model includes an optical path difference variation model, which is as follows: The corresponding phase change model is ;in, This represents the change in the refractive index of air. To measure the geometric distance difference between the test light and the reference light, The wavelength of the laser. This represents the phase change value caused by environmental factors.

4. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 2, characterized in that, The mathematical model established includes a vibration phase change model and a vibration interference light intensity model, wherein the vibration phase change model is as follows: The vibration interference light intensity model is as follows: ;in, For vibration amplitude, The vibration frequency, The initial phase of the vibration, For time, Background light intensity, For striped tones, This is for testing the phase.

5. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 1, characterized in that, In step S2, the fixed phase difference is π / 2, and the two interference patterns are interference patterns with a phase difference of π / 2. and interferogram Background light intensity during phase shifting The background light intensity is approximately constant. Obtained through pre-calibration or light intensity statistics.

6. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 5, characterized in that, The background light intensity B(x,y) is calculated as follows: in, Let be the intensity of the interference light with phase π. The intensity of the interference light with a phase of 3π / 2.

7. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 1, characterized in that, In step S4, the formula for extracting the phase information of the measured surface using the two-step phase-shifting algorithm is as follows: in, The background light intensity during phase shifting. and The phase difference is Two interference diagrams.

8. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 1, characterized in that, In step S, when calculating the surface shape data of the mirror under test, the surface shape is characterized by the distance from the center of the diffraction aperture to the mirror under test. The distance is calculated as follows: in, The distance from the center of the diffraction aperture to the surface of the mirror being measured is denoted as . λ is the output wavelength of the laser source in the point diffraction interferometry system.

9. The point diffraction interferometry surface shape measurement method under environmental disturbance factors according to claim 1, characterized in that, In step S5, the specific method for completing the dynamic calibration of environmental interference is as follows: The phase error value caused by environmental factors obtained from the quantitative assessment in step S3 is removed from the phase information of the measured surface extracted in step S4. The surface shape data of the measured mirror is recalculated based on the phase information after removing the error, and the calibrated surface morphology measurement result is obtained.

10. A point diffraction interferometric surface shape measurement system oriented to environmental disturbance factors, characterized in that, include: The modeling module is used to establish a mathematical model between environmental factors and measurement phase error based on mechanical vibration and aero-optics theory. The acquisition module is used to control the point diffraction interferometry measurement system to measure the device under test, and to acquire two interferograms with a fixed phase difference using the two-step phase shifting method of light intensity. The analysis module is used to analyze the changes in refractive index and optical path difference (OPD) caused by environmental factors based on the mathematical model, and to quantitatively assess environmental interference. The phase module is used to extract the phase information of the measured surface by using the light intensity information of the acquired interferogram and combining it with the background light intensity distribution, and to calculate the surface shape data of the measured mirror through a two-step phase shifting algorithm. The calibration module is used to combine the environmental error assessment results with the extracted phase information to perform dynamic calibration of environmental interference and obtain high-precision surface morphology measurement results.

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