A method for evaluating the particle size of deep subwavelength scatterers based on coherent axial diffraction calculations

Abstract

The present invention discloses a deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation, which belongs to the field of optical imaging and microstructure analysis technology, including: acquiring an image, pre-processing the image; quantifying the pre-processed image, acquiring the scattered light energy concentration of each axial position of the image plane scatterer, acquiring the attenuation of the scattered light energy after defocusing based on the scattered light energy concentration, and compensating for the defocus attenuation; extracting the main peak peak position and the main peak width, based on the deep sub-wavelength scatterer sample with known characteristic size, the extracted main peak peak position and width data are respectively correlated with the corresponding scatterer characteristic size for analysis, and a peak position mapping function and a peak width mapping function are constructed; and particle size assessment is performed based on the constructed function. The present invention overcomes the problems of low signal-to-noise ratio, large defocus interference and poor applicability of the traditional method, and significantly improves the accuracy and universality of particle size assessment.

Description

Technical Field

[0001] The invention belongs to the technical field of optical imaging and microstructure analysis, and in particular relates to a deep sub-wavelength scatterer particle size evaluation method based on coherent axial diffraction calculation. Background Art

[0002] Among high signal-to-noise ratio microscopy techniques, dark-field scattering technology is one of the main forces widely used in the industry due to its superior sensitivity and efficiency. However, factors such as optical aberrations in imaging, various noises in sensors, environmental vibrations, and micro-roughness of the measured surface can lead to reduced image contrast and potential masking of nano-level defect scattering signals. In addition, even samples that are polished with extremely high precision, such as wafers, can have micron-level surface changes due to warping and other reasons, causing the optical system to defocus, making the weak signal completely submerged in the background noise. In addition, as a measurement technology, the quantitative ability of dark-field scattering technology is very limited. Although some studies have evaluated the equivalent size of scatterers by establishing the correlation curve between the theoretical light intensity of Mie scattering and the collected scattering intensity, these connections still rely on the system's detection of the optical irradiance function. In other words, the deterioration of the signal-to-noise ratio will seriously affect the reliability of the evaluation of the equivalent size of the scatterer.

[0003] Therefore, the existing technology has many deficiencies in high signal-to-noise ratio microscopic imaging. First, due to the noise and weak scattered signals of the imaging system, the low signal-to-noise ratio will lead to a decrease in image contrast, making it difficult to clearly identify nanoscale defects or tiny structures. Secondly, defocusing is common in practical applications, especially when there is slight deformation or roughness on the sample surface, which leads to the attenuation of scattered light signals and affects accurate evaluation. Third, traditional quantification methods rely on the relationship between light intensity and scatterer size, but under low signal-to-noise ratio, weak signals are difficult to reflect the actual size, resulting in inaccurate evaluation. In addition, existing imaging technologies are diffraction-limited and cannot evaluate nanoscale scatterer characteristics with high precision. Finally, traditional methods have poor adaptability to materials and shapes, and can usually only measure specific materials and geometric shapes, lacking universality. The above problems greatly limit the application of existing technologies in the detection of deep subwavelength scale scatterers. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a deep sub-wavelength scatterer particle size evaluation method based on coherent axial diffraction calculation to solve the problems existing in the above prior art.

[0005] In a first aspect, to achieve the above-mentioned object, the present invention provides a method for evaluating the particle size of a deep sub-wavelength scatterer based on coherent axial diffraction calculation, comprising the following steps:

[0006] Acquire an image, and preprocess the image;

[0007] quantifying the preprocessed image, obtaining scattered light energy concentration at each axial position of the image plane scatterer, obtaining the attenuation of scattered light energy after defocusing based on the scattered light energy concentration, and compensating for the defocus attenuation;

[0008] Extract the main peak position and the main peak width, and based on the deep subwavelength scatterer samples with known characteristic sizes, perform correlation analysis on the main peak position and the corresponding deep subwavelength scatterer characteristic size, and construct a peak position mapping function; perform correlation analysis on the main peak width and the deep subwavelength scatterer characteristic size, and construct a peak width mapping function;

[0009] The particle size of the sub-wavelength scatterer is estimated based on the peak position mapping function and the peak width mapping function.

[0010] Optionally, the process of acquiring an image and preprocessing the image includes:

[0011] Set the region of interest for the image so that the maximum point is located at the center of the image.

[0012] Optionally, the preprocessed image is quantified, and in the process of obtaining the scattered light energy concentration at each axial position of the image plane scatterer, the scattered light energy concentration at each axial position of the image plane scatterer is quantified based on a scattered light energy concentration function.

[0013] Optionally, the scattered light energy concentration function is:

[0014]

[0015]

[0016] in, are the pixel resolutions of the two-dimensional irradiance image along the x and y directions, A pixel in the image The distance to the maximum point of scattered light, Indicates that each pixel of the image corresponds to The maximum value of, after preprocessing, is equal to the pixel distance from the image corner to the center, is the scaling factor applied to the transverse intensity difference, Z represents the position of the two-dimensional image along the optical axis, Represents the intensity of a 2D image.

[0017] Optionally, the process of compensating for defocus attenuation includes: enhancing the weight of the scatterer area in the image by the scaling factor, so as to minimize the influence of the defocus effect on the corresponding analysis result.

[0018] Optionally, the process of correlating the main peak position with the corresponding deep sub-wavelength scatterer characteristic size and constructing a peak position mapping function includes:

[0019] The peak position of the main peak is correlated with the characteristic size of the corresponding deep subwavelength scatterer, and a peak position mapping function is constructed using a data fitting algorithm, wherein the data fitting algorithm includes a least squares method.

[0020] Optionally, the process of correlating the main peak width with the characteristic size of the deep sub-wavelength scatterer and constructing a peak width mapping function includes:

[0021] The main peak width is correlated with the characteristic size of the deep subwavelength scatterer and a peak width mapping function is constructed using a data fitting algorithm, wherein the data fitting algorithm includes a least squares method.

[0022] In a second aspect, the present invention further provides a computer terminal device, comprising:

[0023] one or more processors;

[0024] A memory, coupled to the processor, for storing one or more programs;

[0025] When the one or more programs are executed by the one or more processors, the one or more processors implement the steps of a deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation.

[0026] In a third aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of a method for evaluating the particle size of deep subwavelength scatterers based on coherent axial diffraction calculations.

[0027] Compared with the prior art, the present invention has the following advantages and technical effects:

[0028] The present invention provides a deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation. The present invention realizes high-precision assessment of deep sub-wavelength scatterer particle size through image preprocessing, scattered light energy concentration calculation, defocus compensation and digital refocusing. First, the region of interest (ROI) is set by preprocessing technology to enhance the energy weight of the scatterer area; then, the light intensity distribution change of the image plane scatterer position is quantified by the defined scattered light energy concentration function, and the defocus effect is compensated by the scaling factor to ensure signal stability. With the help of digital refocusing technology, the interference of the defocus phenomenon on the light field is corrected, and the complex amplitude distribution of the axial light field is optimized. Then, the main peak position and width of the scattered light field are extracted, and the linear and quadratic mapping functions reflecting the characteristic size of the scatterer are constructed, and the robustness of the mapping function is calibrated by known samples. Finally, the calibrated function is used to accurately evaluate the particle size information of the unknown scatterer. Based on this, the present invention overcomes the problems of low signal-to-noise ratio, large defocus interference and poor applicability of traditional methods, and significantly improves the accuracy and universality of particle size assessment. The present invention is suitable for any coherent imaging system that can obtain a good scattered light complex amplitude light field, such as nanomaterial research and biological microstructure detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0030] Figure 1 Schematic diagram of the axial diffraction structure of nanoparticles according to an embodiment of the present invention, in which Es represents the complex amplitude of the scattered light electric field, and E R represents the complex amplitude of the reference optical electric field;

[0031] Figure 2 Schematic diagram of normalized values ​​of pure dipole axial concentration dissipation curves at different axial positions according to an embodiment of the present invention;

[0032] Figure 3 Schematic diagram of normalized values ​​of axial concentration dissipation curves of pure interference electric field at different axial positions according to an embodiment of the present invention;

[0033] Figure 4 A schematic diagram illustrating the physical meaning of the peak position and width of the energy concentration function according to an embodiment of the present invention;

[0034] Figure 5 The results of fitting the peak position mapping function and the discrete characteristic schematic diagram of the main peak information of the axial concentration of the interference scattered field of particles of different characteristic sizes calculated by simulation according to the embodiment of the present invention;

[0035] Figure 6The schematic diagram of the discrete characteristics and the fitting result of the half-height width mapping function according to the main peak information of the axial concentration of the interference scattered field of particles of different characteristic sizes calculated by simulation in an embodiment of the present invention;

[0036] Figure 7 The results of fitting the peak mapping function and the discrete characteristic schematic diagram are shown in the actual experiment of the embodiment of the present invention, showing the main peak information of the axial concentration of the interference scattered field of nanoparticles of different characteristic sizes;

[0037] Figure 8 It is a schematic diagram of the fitting results and discrete characteristics of the half-width mapping function of the main peak information of the axial concentration of the interference scattered field of nanoparticles of different characteristic sizes in the actual experiment of the embodiment of the present invention. DETAILED DESCRIPTION

[0038] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0039] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0040] First, the technical terms involved in the following embodiments are explained.

[0041] High signal-to-noise ratio microscopy technology: High signal-to-noise ratio microscopy technology refers to the process of optimizing the optical system, data processing algorithm or other technical means in microscopy to enhance effective signals and suppress noise, thereby achieving clearer and more reliable image acquisition. The core of high signal-to-noise ratio is to make the signal stronger than the noise, ensuring that detailed information will not be obscured by background noise.

[0042] Key applications include:

[0043] Biomedical field:

[0044] Cell imaging: Observe the structure and dynamic processes of living cells (e.g. fluorescence microscopy).

[0045] Tissue section analysis: High resolution display of the characteristics of pathological tissue.

[0046] Molecular tracking: Tracking the movement of molecules within cells (such as single-molecule imaging).

[0047] Nanomaterials Research:

[0048] Nanoparticle Characterization: Measure the size, shape, and distribution of nanoparticles.

[0049] Surface plasmon resonance studies: used to detect molecular adsorption or reaction processes.

[0050] Semiconductor and industrial testing:

[0051] Wafer defect inspection: Detecting tiny defects during the production process.

[0052] Thin film uniformity assessment: Detect the uniformity of film thickness and optical properties.

[0053] Physics and Chemistry Research:

[0054] Optical property research: Analyze the light absorption and scattering characteristics of samples.

[0055] Characterization of optical properties of quantum dots and other nanomaterials.

[0056] Dark field scattering technology:

[0057] Dark-field scattering technology is a technique that uses a dark-field microscope for optical imaging. Its characteristic is that by blocking direct light, only the light scattered or deflected by the sample is recorded, so that the background remains dark and the scattered light emitted by the sample is highlighted.

[0058] Working principle:

[0059] Optical setup: Dark-field microscopy uses a special condenser. When the light beam passes through the sample, only the scattered light is recorded and the direct light is blocked.

[0060] Imaging characteristics: The background around the sample is dark, and the sample itself appears bright due to scattering. This high contrast effect is suitable for detecting weak signals.

[0061] Key applications include:

[0062] Biological Research:

[0063] Living cell observation: observing the subtle structures or dynamic behaviors in cells.

[0064] Microbiological testing: such as bacteria or virus particles in the blood.

[0065] Nanoparticle Analysis:

[0066] Particle size measurement: Particle size is analyzed by scattered light intensity.

[0067] Distribution and behavior of particles: study the dynamic behavior of particles in colloidal solutions.

[0068] Materials Science and Industrial Testing:

[0069] Defect Detection: Finding tiny scratches or defects on the surface of materials.

[0070] Study on properties of nanomaterials: Optical characterization of the surface structure of nanoparticles.

[0071] Environmental monitoring:

[0072] Particle detection: Monitors the quantity and nature of suspended particles in air or water.

[0073] In general, high signal-to-noise ratio microscopy technology is a broader concept that includes a variety of methods (such as fluorescence microscopy, confocal microscopy, etc.), which aims to improve signal quality and is widely used in many fields.

[0074] Dark-field scattering technology is a specific microscopic imaging method that is particularly suitable for detecting weak scattering signals, such as nanoparticles, microorganisms, etc.

[0075] Dark-field scattering technology is often regarded as an important component of high signal-to-noise ratio microscopy technology due to its high sensitivity and strong background contrast, and its application in the fields of nanomaterials and biology is particularly prominent.

[0076] Embodiment 1

[0077] This embodiment provides a deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation, and is therefore applicable to any system with good coherent imaging, that is, capable of obtaining the complex amplitude of the light field from the scattered light signal of the scatterer. After this condition is met, the particle size of deep subwavelength scatterers can be evaluated by the following steps:

[0078] Acquire an image, and preprocess the image;

[0079] quantifying the preprocessed image, obtaining scattered light energy concentration at each axial position of the image plane scatterer, obtaining the attenuation of scattered light energy after defocusing based on the scattered light energy concentration, and compensating for the defocus attenuation;

[0080] Extract the main peak position and the main peak width, and based on the deep subwavelength scatterer samples with known characteristic sizes, perform correlation analysis on the main peak position and the corresponding deep subwavelength scatterer characteristic size, and construct a peak position mapping function; perform correlation analysis on the main peak width and the deep subwavelength scatterer characteristic size, and construct a peak width mapping function;

[0081] The particle size of the sub-wavelength scatterer is estimated based on the peak position mapping function and the peak width mapping function.

[0082] Specifically, the current discussion on the propagation of scattered light in diffraction-limited systems is based on the focal plane, but in fact, defocusing often occurs in industrial inspection environments. The defocusing phenomenon in coherent diffraction systems can be conveniently described by the angular spectrum transfer function express:

[0083]

[0084] in Indicates the defocus distance, represents the imaginary unit, represents the wavelength of the incident light. Therefore, the complex amplitude of the electric field at different defocus planes can be calculated by the following formula:

[0085]

[0086] in represents the complex amplitude of the electric field in the image plane, Indicates out of focus The complex amplitude of the electric field in the plane at represents the two-dimensional Fourier transform operator. The technology of recalculating the complex amplitude distribution of the electric field at other axial positions with the help of equations (1) and (2) is also called digital refocusing technology.

[0087] According to Poynting's theorem, when a light wave field propagates in free space, the paraxial approximate time-averaged Poynting vector under the action of the three-dimensional Hamiltonian operator should be zero, that is, the change in energy along the transverse direction should be the same as the change in the longitudinal component in order to maintain energy conservation. From this perspective, the attenuation of scattered light energy after defocusing can be reflected by evaluating the change in light intensity along the transverse direction near the position of the image plane scatterer. Here, the scattered light energy concentration function near the position of the image plane scatterer is defined as:

[0088]

[0089]

[0090] in, are the pixel resolutions of the two-dimensional irradiance image along the x and y directions, A pixel in the image The distance to the maximum point of scattered light. In image preprocessing, the region of interest has been set so that the maximum point is located in the center of the image. Indicates that each pixel of the image corresponds to The maximum value of , after preprocessing, is equal to the pixel distance from the corner to the center of the image. The scaling factor applied to the lateral intensity difference It is to enhance the weight of scattered light energy in the scatterer position area. Z represents the position of the two-dimensional image along the optical axis. Represents the intensity of a 2D image.

[0091] As an implementation in this embodiment, the process of compensating for defocus attenuation includes: enhancing the weight of the scatterer area in the image by the scaling factor, so as to minimize the influence of the defocus effect on the corresponding analysis result.

[0092] Specifically, this function is used in combination with the image pixel resolution , and the distance from the pixel to the maximum point of scattered light , the energy weight of the scatterer area is enhanced by the scaling factor to evaluate the defocus attenuation of scattered light energy;

[0093] Specifically, the energy weight of the scatterer area is enhanced by a scaling factor, and the scattered light energy defocus attenuation is evaluated. A method for compensating for the defocus effect and increasing the importance of the signal in the scatterer area is described. The core of this method is to use a scaling factor to enhance the energy weight of the scatterer area during image processing, thereby improving the impact of light intensity attenuation and defocus on the evaluation results.

[0094] Defocus refers to the phenomenon that when the imaging system is not focused on the scatterer, the intensity of the scattered light will decay with the distance from the focus, especially the light intensity distribution around the scatterer will change. This will affect the accuracy of particle size assessment, especially at the nanoscale with high precision requirements.

[0095] The scaling factor is a value used to enhance or adjust the weight of certain areas in the image. Specifically, the scaling factor is used to adjust the energy weight of the area around the scatterer so that the light intensity around the scatterer plays a more important role in the calculation process.

[0096] This enhancement process is to offset the light intensity attenuation effect caused by defocus, so that the signal of the scatterer can still be accurately quantified in the defocused state. By enhancing the energy of the scatterer area, the subsequent quantitative analysis will be more accurate.

[0097] In the present invention, by applying a scaling factor to the scatterer regions in the image, the signal strength of these regions is enhanced, thereby compensating for the attenuation effect caused by defocus.

[0098] The evaluation of defocus attenuation does not rely solely on the scaling factor, but combines multiple techniques such as image preprocessing (such as ROI setting), image enhancement, digital refocusing, etc. Through these processes, the impact of defocus can be quantified by evaluating the energy concentration of scattered light.

[0099] Therefore, the evaluation of scattered light energy defocus attenuation does not completely rely on the scaling factor, but the scaling factor is an important means to enhance the energy weight of the scatterer area and compensate for the light intensity attenuation caused by defocus, so that the size of the scatterer can still be accurately evaluated in the defocused case. This is an image processing and quantification step that helps to improve the accuracy of scatterer particle size evaluation.

[0100] As an implementation manner in this embodiment, the process of acquiring an image and preprocessing the image includes:

[0101] Set the region of interest for the image so that the maximum point is located at the center of the image.

[0102] Specifically, images refer to image data obtained using microscopic imaging or other imaging techniques (such as scattering imaging). These image data are usually scattered light intensity distribution images captured by coherent imaging systems (such as microscopes or optical instruments), reflecting the optical properties of scatterers (such as nanoparticles) in the imaging area. At this stage, the image contains scatterers and background noise, and there may be effects such as defocus or light intensity attenuation.

[0103] The main function of the image is to present the light field information around the scatterer, especially the intensity distribution of the scattered light. By analyzing the intensity of the scattered light in the image, potential information about the particle size, morphology, etc. of the scatterer can be obtained. Therefore, the image is the basic data source for scatterer particle size assessment. Image preprocessing is a very important step in the data analysis process and is usually performed after imaging data acquisition. The specific preprocessing steps include the following aspects:

[0104] Image cropping (ROI setting):

[0105] The ROI (Region of Interest) setting is to select a region of the image, usually focusing on a specific area of ​​the scatterer. The purpose of this step is to remove background noise and only analyze the area related to the scatterer.

[0106] Region of Interest (ROI) refers to a specific part or area in a specific image, data set or other research object that the researcher, observer or system pays attention to and needs to focus on analysis and processing. The following is a detailed explanation of the meaning of the region of interest:

[0107] Specificity: The region of interest is determined based on specific research objectives, application scenarios or task requirements. It is not a randomly selected area, but is closely related to the research purpose. For example, in medical imaging, the region of interest is determined based on the patient's specific lesion site; in industrial testing, the region of interest is determined based on the key quality inspection site of the product.

[0108] Variability: Different research objects, different research stages or different researchers may have different regions of interest. Even for the same research object, the region of interest may change under different research tasks. For example, for the same image, the region of interest for object detection may be completely different from the region of interest for image enhancement.

[0109] Limitedness: The region of interest is usually a relatively small part of the research object, and it has a clear boundary range. This limitedness allows researchers to focus limited resources and attention on the most valuable areas, improving research efficiency and analysis accuracy.

[0110] For example, when studying the microstructure of a material, a representative microscopic area is used as the region of interest. For example, in a scanning electron microscope (SEM) image, a specific grain area on the surface of a material is used as the region of interest, and the performance and quality of the material are evaluated by analyzing its morphology, size, distribution and other characteristics. In this application, the region with obvious high-energy point features and its surrounding areas in the captured dark field image is used as the region of interest.

[0111] In the present invention, the maximum point (i.e., the position of the maximum intensity of the scattered light) is usually set to the center of the image in order to more accurately analyze the characteristics of the scatterer. This is done to ensure that the analysis is focused on the central area of ​​the scatterer and to avoid interference from other irrelevant areas in the analysis.

[0112] Image Enhancement:

[0113] By enhancing the energy weight of the area around the scatterer, the signal of the scatterer is made more prominent and the influence of background noise is reduced. This helps to improve the accuracy of subsequent analysis.

[0114] Out-of-focus light attenuation correction:

[0115] By correcting the distribution of scattered light in the image and quantifying the change in light intensity due to defocus, the imaging analysis results are ensured not to be affected by changes in focal length.

[0116] In summary, images are scattered light images captured during microscopy, and preprocessing is the processing of these images in order to more accurately analyze the characteristics of the scatterer, especially by setting the region of interest and enhancing the energy weight of the scatterer area to ensure the signal accuracy during the analysis process.

[0117] As an implementation method of this embodiment, the preprocessed image is quantified, and in the process of obtaining the scattered light energy concentration of each axial position of the image plane scatterer, the scattered light energy concentration of each axial position of the image plane scatterer is quantified based on the scattered light energy concentration function.

[0118] Specifically, the preprocessed image is quantified based on the energy concentration of the scattered light. The purpose of quantification is to evaluate the scattered light intensity distribution near the position of the image plane scatterer. By analyzing the change in the energy concentration of the scattered light, the size, shape and distribution of the scatterer can be reflected.

[0119] Specifically, the scattered light energy concentration is used to evaluate the change in light intensity near the image plane scatterer position along the lateral direction.

[0120] The scattered light energy concentration function is defined to quantify the energy distribution of scattered light near the image plane scatterer. This function is mainly used to describe the change in the intensity of scattered light in the lateral direction. Specifically, by analyzing the scattered light energy near the image plane scatterer, the attenuation degree of scattered light in the defocused state can be reflected, thereby revealing the influence of the defocus phenomenon on the scattered light distribution.

[0121] This method calculates the energy concentration of scattered light around the image plane, combines the image pixel resolution and the distance from the pixel to the maximum point of scattered light, and quantifies the change of light intensity along the lateral direction, thus providing a basis for evaluating the size, morphology and other characteristics of the scatterer. This is of great significance for high-precision scatterer particle size assessment, especially when the signal-to-noise ratio is low or the defocus phenomenon is severe.

[0122] As an implementation method of this embodiment, by analyzing the scattered light intensity distribution near the position of the image plane scatterer, the attenuation of the scattered light energy after defocusing is inferred.

[0123] Specifically, in scattered imaging, the intensity distribution of scattered light is affected by the focal length, defocus, and properties of the scatterer (such as size, shape, etc.). When the imaging system is defocused, the propagation of scattered light changes, which is manifested in the following aspects:

[0124] Defocus effect:

[0125] When the scatterer is not on the focal plane, the imaging system will be defocused. This means that the position where the scattered light is focused on the image plane will shift, and the distribution of light intensity near the scatterer will change, resulting in attenuation. This change in light intensity caused by defocus is manifested as a gradual weakening of the light intensity in the area around the scatterer, especially the greater the defocus distance, the more significant the attenuation.

[0126] The defocus falloff is evaluated by the intensity distribution at the image plane scatterer position:

[0127] The scattered light intensity distribution near the image plane scatterer can be used to analyze the effect of defocus on light intensity. By calculating the change in scattered light intensity, it is possible to infer how the light energy decays with the degree of defocus.

[0128] Specifically, the change in the scattered light intensity distribution in the image can be quantified by calculating the change in light intensity along the lateral direction (x, y direction), which reflects the attenuation of scattered light energy due to defocus.

[0129] Poynting's theorem and conservation of energy:

[0130] According to Poynting's theorem, the energy of scattered light should be conserved when propagating along the optical axis. The defocus phenomenon can be reflected by the change in the lateral light intensity distribution. When defocused, the change in the scattered light energy along the lateral direction is associated with the change in the longitudinal component.

[0131] Therefore, analyzing the scattered light energy concentration (including light intensity distribution, main peak position, peak width and other characteristics) near the image plane scatterer position can reveal the light intensity attenuation caused by defocus.

[0132] Practical Application:

[0133] In the technology of the present invention, the scattered light energy concentration function is defined, combined with the light intensity distribution of the image plane scatterer, to evaluate the attenuation of the scattered light under defocus conditions. By using digital refocusing technology and analyzing the energy concentration in the image, the attenuation of the scattered light and the effect of defocus on the evaluation of the scatterer particle size can be more accurately inferred.

[0134] By analyzing the scattered light intensity distribution near the image plane scatterer position, especially the change of scattered light energy along the lateral direction, the attenuation of scattered light energy under defocus conditions can be effectively inferred. This analysis method helps to solve the influence of defocus effect on the accuracy of scatterer particle size assessment, thereby providing more accurate nanoparticle size assessment.

[0135] In fact, the position of the subwavelength scatterer in the direction of the optical axis has a strong dependence on the distribution of the scattered light along the axial direction. Therefore, under the Rayleigh scattering model approximation, the difference caused by subwavelength scatterers of different spatial characteristic scales in the axial propagation model can be explained by applying an axial offset to the dipole center. To replace. Figure 1 As shown, the substrate surface is , the characteristic scale of the scatterer is , Figure 1 In the equation, Es represents the complex amplitude of the scattered light electric field, and E R represents the complex amplitude of the reference optical electric field. According to equation (3), the deep subwavelength scatterer is located in the Cartesian coordinate system on the relay plane. The complex amplitude on can be expressed as:

[0136]

[0137] Where j represents the imaginary unit and k represents the wave vector. With the help of digital refocusing technology, other longitudinal positions can be calculated based on the complex amplitude field of any transverse plane in the diffraction space. The plane complex amplitude field.

[0138] That is, under the Rayleigh scattering model approximation, the axial propagation difference of subwavelength scatterers with different spatial characteristic scales is equivalent to applying an axial offset to the center of the dipole. , and according to the substrate and relay plane settings, the light field distribution of the scatterer in a specific plane is described by a complex amplitude function, and the axial light field resolution range is expanded by means of the digital refocusing technology corresponding to equations (1) and (2);

[0139] As an implementation method in this embodiment, the process of correlating the main peak position with the corresponding deep sub-wavelength scatterer characteristic size and constructing the peak position mapping function includes:

[0140] The peak position of the main peak is correlated with the corresponding characteristic size of the deep subwavelength scatterer, and a peak position mapping function is constructed using a data fitting algorithm, wherein the data fitting algorithm includes a least squares method, a trust region algorithm, and a LM algorithm.

[0141] As an implementation method in this embodiment, the main peak width is correlated with the characteristic size of the deep sub-wavelength scatterer and the process of constructing the peak width mapping function includes:

[0142] The main peak width is correlated with the characteristic size of the deep subwavelength scatterer, and a peak width mapping function is constructed using a data fitting algorithm, wherein the data fitting algorithm includes a least squares method, a trust region algorithm, and a LM algorithm.

[0143] Specifically, in the data processing step, a customized image processing algorithm is used to strictly calculate the energy concentration and extract the axial electric field distribution parameters in sequence. The peak position and peak width mapping function are accurately fitted and calibrated based on a series of scatterer sample data of known scales, and a reusable calibration model is constructed to ensure the accuracy of scatterer scale inversion.

[0144] Specifically, Figure 2 and Figure 3 The values ​​of the dipole electric field and the interference electric field in the diffraction space cross section after passing through a diffraction limited system with a numerical aperture of are shown respectively. In the numerical simulation, along the axial direction, the critical size of the scatterer is in the range of to nanometers. There is a certain offset and broadening of the main peak of the axial electric field distribution curve of scatterers of different sizes, but these differences are quite small. Compared with the diffraction of the pure dipole electric field, the modulation effect of different scatterers can be more clearly observed with the interference electric field as the source plane.

[0145] Figure 4 The meaning of peak position and width is shown in Figure 2. By calculating the peak position and half-maximum width (FWHM) of the main peak of each scale scatterer, as shown in Figure 2. Figure 5 and Figure 6As shown, the triangles represent the calculated values ​​corresponding to each discrete scale, and the lines represent the fitting curves. Under the dipole model, the peak position of the main peak of the axial energy concentration is approximately linearly related to the critical size of the scatterer, and is approximately quadratically related to the half-width of the main peak, which are referred to here as the peak position mapping function and the half-width mapping function, respectively. It should be noted that only a dipole model assumption is made for the scatterer here, so within the scope of the elastic scattering model, the peak position mapping function and the half-width mapping function should be applicable to any type of material. This means that nanoparticles of known size can be used to calibrate the mapping function of the system, and then the critical size of the scatterer can be evaluated by the peak position and half-width of the main peak of the diffraction light field.

[0146] That is, by experimentally collecting and analyzing the diffraction light field images of scatterers of different scales, it is determined that when imaging through a diffraction limited system under a dipole model, the linear function relationship between the axial main peak position of the scattered light field and the characteristic size of the scatterer is the peak position mapping function, and the quadratic function relationship between the main peak width and the characteristic size of the scatterer is the peak width mapping function. This function is calibrated using known nanoparticles and is used to evaluate the characteristic scale of unknown scatterers.

[0147] In addition, two groups of samples were prepared in this study. One group of samples was used to calibrate the energy concentration characteristic mapping function, and the other group was used to evaluate the correlation between the function and the critical size of the actual sample. Among them, the critical sizes of the calibration group samples were 5 nanometers, 20 nanometers and 50 nanometers, and the nanoparticles were all made of spherical gold materials. In order to verify that the proposed method is not significantly affected by the material and shape of the nanoparticles, the verification group prepared cubic perovskite particle samples with a size of 7 nanometers and spherical gold particle samples with a size of nanometers, and measured them. Figure 7 and Figure 8 The calibration results of the peak position and half-width mapping functions and the distribution of the raw data are shown respectively. Obviously, the 7-nm perovskite particles and the 10-nm gold particles can be clearly distinguished and are in good agreement with the half-width mapping function. Of course, it should also be pointed out that compared with the ideal situation in the simulation, the peak position mapping function does not show a significant correlation with the actual critical size of the particles. This result may be caused by a variety of factors, such as the inconsistency of the system focal length when measuring different samples, or the influence of platform vibration. Nevertheless, the half-width mapping function shows a relatively good quadratic function relationship with the critical size of the particles. This good relationship can be reasonably attributed to the insensitivity of the half-width to defocus conditions. This inherent property of the half-width makes it less susceptible to interference caused by the defocus effect, thereby supporting the robustness and consistency of this quadratic correlation, which is particularly important for accurately characterizing the particle system under study. It should be emphasized that in addition to the differences in material properties, perovskite particles and gold particles also differ in shape and critical size. These characteristics further verify the universality of the proposed method for various materials of different geometric shapes.

[0148] Based on this, an embodiment of the present invention provides a deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation. By analyzing image preprocessing, scattered light energy concentration calculation, defocus attenuation compensation and digital refocusing and other technical means, the present invention realizes high-precision assessment of scatterer particle size at a deep sub-wavelength scale. First, the image preprocessing technology is used to set the region of interest (ROI) for the scattered light image and enhance the energy weight of the scatterer area, laying the foundation for subsequent analysis. Then, through the defined scattered light energy concentration function, combined with the light intensity distribution near the image plane scatterer position, the attenuation characteristics of the scattered light after defocusing are quantified, and the defocus effect is compensated by the scaling factor to ensure the stability of the signal. Subsequently, the axial light field complex amplitude distribution is recalculated with the help of digital refocusing technology to correct the interference of the defocus phenomenon on the light field, further optimizing the accuracy of the data.

[0149] Based on the above data processing, the two key parameters of the main peak position and main peak width of the scattered light field were extracted, and the peak mapping function and peak width mapping function reflecting the characteristic size of the scatterer were constructed. The mapping function was calibrated through known nanoparticle samples, so that the function has good robustness and versatility. Finally, through the calibrated mapping function, the light field characteristic parameters of the unknown scatterer are converted into particle size information, achieving efficient and accurate particle size assessment. Based on this, the present invention overcomes the problems of low signal-to-noise ratio, significant defocus and limited scope of application of traditional methods, significantly improves the accuracy and universality of scatterer characteristic size assessment, and expands its application prospects in the fields of nanomaterial research and biological microstructure detection.

[0150] Embodiment 2

[0151] This embodiment mainly describes a deep sub-wavelength scatterer particle size assessment method based on a coherent system, and is therefore applicable to any system with good coherent imaging, that is, a system that can well obtain the complex amplitude of the light field from the scattered light signal of the scatterer. After this condition is met, the particle size of deep subwavelength scatterers can be evaluated by the following steps:

[0152] (1) The angular spectrum diffraction theory is used to calculate the complex amplitude of the light field in the entire axis, where the angular spectrum transfer function is expressed as:

[0153] ;

[0154] The complex amplitude of the light field at different axial positions is calculated by the following formula:

[0155] ;

[0156] (2) According to the complex amplitude distribution of the axial light field, calculate the scattered light energy concentration at each axial position:

[0157]

[0158] ;

[0159] in, are the pixel resolutions of the two-dimensional irradiance image along the x and y directions, A pixel in the image The distance to the maximum point of scattered light.

[0160] (3) Extract the main peak position and width information from the above-mentioned axial scattered light energy concentration distribution data, which can be accurately extracted by peak detection algorithm, curve fitting algorithm, etc. For each scatterer sample with known characteristic scale in the calibration experiment, the extracted main peak position and width data are respectively correlated with the corresponding scatterer characteristic size for analysis, and a peak position mapping function (reflecting the linear function relationship between the peak position and the scatterer characteristic size) and a peak width mapping function (reflecting the quadratic function relationship between the main peak width and the scatterer characteristic size) are constructed by using a data fitting algorithm (such as the least squares method).

[0161] Using these known nanoparticle samples as calibration basis, the constructed mapping function is calibrated and optimized to ensure that the function can accurately reflect the quantitative relationship between the scatterer scale and the axial characteristics of the diffraction light field, thereby forming an effective quantitative model that can be used to evaluate the characteristic scale of unknown scatterers.

[0162] Embodiment 3

[0163] In this embodiment, a computer terminal device is provided, including:

[0164] one or more processors;

[0165] A memory, coupled to the processor, for storing one or more programs;

[0166] When the one or more programs are executed by the one or more processors, the one or more processors implement the methods in the above embodiment 1 and embodiment 2.

[0167] In this embodiment, a computer-readable storage medium is further provided, on which a computer program is stored. When the computer program is executed by a processor, the methods in the above embodiments 1 and 2 are implemented.

[0168] In this embodiment, an electronic device is further provided, including a memory and a processor, wherein a computer program is stored in the memory, and the processor is configured to run the computer program to execute the methods in the above first and second embodiments.

[0169] The above program can be run in the processor, or it can be stored in the memory (or computer-readable medium), which includes permanent and non-permanent, removable and non-removable media. Information storage can be achieved by any method or technology. Information can be computer-readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, tape disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0170] These computer programs can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps of the functions specified in one or more blocks can be implemented by different modules corresponding to different steps.

[0171] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation, characterized in that: The following steps are involved: Acquire an image, and preprocess the image; quantifying the preprocessed image, obtaining scattered light energy concentration at each axial position of the image plane scatterer, obtaining the attenuation of scattered light energy after defocusing based on the scattered light energy concentration, and compensating for the defocus attenuation; Extract the main peak position and the main peak width, and based on the deep subwavelength scatterer samples with known characteristic sizes, perform correlation analysis on the main peak position and the corresponding deep subwavelength scatterer characteristic size, and construct a peak position mapping function; perform correlation analysis on the main peak width and the deep subwavelength scatterer characteristic size, and construct a peak width mapping function; Performing particle size evaluation on the sub-wavelength scatterer based on the peak position mapping function and the peak width mapping function; quantifying the preprocessed image, and in the process of obtaining the scattered light energy concentration at each axial position of the image plane scatterer, quantifying the scattered light energy concentration at each axial position of the image plane scatterer based on the scattered light energy concentration function; The scattered light energy concentration function is: in, are the pixel resolutions of the two-dimensional irradiance image along the x and y directions, A pixel in the image The distance to the maximum point of scattered light, Indicates that each pixel of the image corresponds to The maximum value of, after preprocessing, is equal to the pixel distance from the image corner to the center, is the scaling factor applied to the transverse intensity difference, Z represents the position of the two-dimensional image along the optical axis, Represents the intensity of a 2D image.

2. The method according to claim 1, characterized in that Acquire an image, and the process of preprocessing the image includes: Set the region of interest for the image so that the maximum point is located at the center of the image.

3. The method according to claim 1, characterized in that The process of compensating for defocus attenuation includes: enhancing the weight of the scatterer area in the image by the scaling factor, so as to minimize the influence of the defocus effect on the corresponding analysis result.

4. The method according to claim 1, characterized in that The process of correlating the main peak position with the corresponding deep sub-wavelength scatterer characteristic size and constructing a peak position mapping function includes: The peak position of the main peak is correlated with the characteristic size of the corresponding deep subwavelength scatterer, and a peak position mapping function is constructed using a data fitting algorithm, wherein the data fitting algorithm includes a least squares method.

5. The method according to claim 1, characterized in that The process of correlating the main peak width with the characteristic size of the deep sub-wavelength scatterer and constructing a peak width mapping function includes: The main peak width is correlated with the characteristic size of the deep subwavelength scatterer and a peak width mapping function is constructed using a data fitting algorithm, wherein the data fitting algorithm includes a least squares method.

6. A computer terminal device, characterized in that: include: one or more processors; A memory, coupled to the processor, for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the various steps of the deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation as described in any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, each step of the deep sub-wavelength scatterer particle size assessment method based on coherent axial diffraction calculation as described in any one of claims 1 to 5 is implemented.

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