A high-throughput measurement and spatial distribution resolution system and method for transient absorption microscopy

Abstract

The application discloses a high-throughput measurement and spatial distribution analysis system and method for transient absorption microscopy. The method comprises the following steps: obtaining a measurement parameter, generating a spatial switching sequence and a time delay scanning sequence of a target region based on the measurement parameter; moving the sample to be measured to each target region in turn according to the spatial switching sequence, and collecting pump-on images and pump-off images under different time delays in each target region according to the time delay scanning sequence, and processing to obtain a set of two-dimensional differential images corresponding to each target region; extracting the radial distribution of the two-dimensional differential images to obtain a corresponding one-dimensional radial distribution curve; fitting the one-dimensional radial distribution curve according to the contour characteristics of the one-dimensional radial distribution curve by using a single Gaussian model or a negative double Gaussian model with physical constraints, and outputting the spatial distribution analysis results of each target region under different time delays. The application improves the accuracy and stability of the spatial distribution analysis results.

Description

Technical Field

[0001] This invention relates to the field of optical microscopy imaging technology, and in particular to a high-throughput measurement and spatial distribution analysis system and method for transient absorption microscopy. Background Technology

[0002] Traditional pump-probe microscopy typically employs a point-scan method to acquire spatial response information of a sample. This involves scanning the sample surface point by point with a focused beam and measuring the transient response signal at each scan location to construct a two-dimensional spatial distribution map. While this method offers high spatial resolution, it requires frequent mechanical movement and repeated data acquisition in scenarios involving multiple regions and time delays, resulting in low testing efficiency, compromised data consistency, and difficulty in meeting the demands of high-throughput automated characterization.

[0003] With the development of area array imaging devices and synchronous acquisition technology, camera-based wide-field transient absorption microscopy can directly obtain two-dimensional transient differential images of the sample region under a specific time delay, providing a technical foundation for rapid multi-region testing and two-dimensional spatial distribution analysis. However, existing camera-based transient absorption microscopy techniques still have the following shortcomings in practical applications: First, the level of automation and collaboration between different hardware modules in the existing system is not high, and the testing process still requires a lot of manual intervention, making it difficult to achieve high-throughput automatic measurement in multiple regions and with multiple time delays.

[0004] Second, under local pump excitation conditions, the transient spatial distribution of the sample is not always an ideal single-peak structure. In actual tests, complex contours such as central depression, local inversion, edge enhancement, double peaks or crater shape often appear. Traditional single Gaussian models are difficult to accurately describe the above complex contours, resulting in insufficient accuracy and stability of spatial distribution parameter extraction.

[0005] Therefore, the existing technology lacks an integrated system and method that can simultaneously achieve automated high-throughput acquisition of multiple regions, stable reconstruction of two-dimensional weak signal images, and quantitative analysis of complex spatial distributions for camera-based pump-probe microscopy measurement scenarios. Summary of the Invention

[0006] To address the technical problems existing in the background art, this invention proposes a high-throughput measurement and spatial distribution analysis system and method for transient absorption microscopy.

[0007] In a first aspect, the present invention proposes a high-throughput measurement and spatial distribution analysis method for transient absorption microscopy, comprising: Acquire measurement parameters, which include at least delayed scan parameters and a set of coordinates for multiple target regions; generate a spatial switching sequence and a temporal delayed scan sequence for the target regions based on the measurement parameters; The sample to be tested is moved to each target region in sequence according to the spatial switching sequence, and pump-on images and pump-off images under different time delays are collected in each target region in sequence according to the time delay scanning sequence. The process is then used to obtain a set of two-dimensional differential images corresponding to each target region. Radial distribution extraction is performed on the two-dimensional difference image to obtain the corresponding one-dimensional radial distribution curve; Based on the contour features of the one-dimensional radial distribution curve, a single Gaussian model or a physically constrained inverse double Gaussian model is used for fitting, and the spatial distribution analysis results of each target region under different time delays are output.

[0008] Furthermore, the processing to obtain a set of two-dimensional difference images corresponding to each target region includes: performing differential calculations on pump-on images and pump-off images continuously acquired in the same target region under the same time delay, and then accumulating and averaging the obtained multi-frame difference images to obtain a two-dimensional difference image of the target region under the corresponding time delay.

[0009] Furthermore, when the one-dimensional radial distribution curve conforms to the unimodal distribution characteristics, the single Gaussian model is used for fitting; when the one-dimensional radial distribution curve does not conform to the unimodal distribution characteristics, the physically constrained inverse double Gaussian model is used for separation fitting.

[0010] Furthermore, the inverse-sign double Gaussian model is expressed as:

[0011] in, These are the amplitude parameters for the positive and negative signal components, respectively. These are the width parameters for the positive and negative signal components, respectively. Baseline parameters, This represents the radial distance corresponding to the one-dimensional radial distribution curve.

[0012] Furthermore, after normalizing the one-dimensional radial distribution curve to its global maximum value, the following physical constraints are applied to the inverse-sign double Gaussian model: Amplitude upper limit constraint: The amplitude parameter satisfies ; Central point constraint: At this point, the value of the inverse-sign double Gaussian model is equal to the value of the one-dimensional radial distribution curve, satisfying: ; Width lower limit constraint: The width parameter satisfies and ,in, The minimum resolvable width is preset based on the spatial resolution capability of the imaging system; Regularization constraint: A regularization penalty term is introduced into the optimization objective function for solving the parameters of the inverse-sign double Gaussian model. ,in The regularization coefficient is . This is the regularization weight index.

[0013] Furthermore, it also includes an iterative background correction step: Fit the current one-dimensional radial distribution curve to a preset spatial distribution model and calculate the fitting residuals. Extract the residual values ​​corresponding to each time delay at the preset radial position, and determine the intensity scaling factor corresponding to each time delay; The residual radial distribution curve corresponding to the time delay with the largest residual amplitude is selected as the reference background template. The background update amount is constructed by combining the reference background template and the intensity scaling factor corresponding to each time delay, and the current one-dimensional radial distribution curve is updated. Repeat the above iterative background correction steps until the preset number of iterations is reached or the residual amplitude meets the stopping condition.

[0014] Furthermore, when the interfering signal is positive relative to the target signal, the maximum residual amplitude is manifested as the maximum positive residual; when the interfering signal is negative, the maximum residual amplitude is manifested as the maximum absolute value of the negative residual. By selecting the maximum residual amplitude, this application can be applied to both positive and negative interference scenarios.

[0015] Optionally, the preset spatial distribution model is a single Gaussian model.

[0016] Optionally, when the target transient response exhibits a complex profile such as a central depression, localized inverse sign, or bimodal peaks, the preset spatial distribution model is an inverse sign double Gaussian model.

[0017] Optionally, the intensity scaling factor can be directly taken as the residual value of each time delay at the preset radial position.

[0018] Optionally, the residual value at the preset radial position where the time delay with the largest residual amplitude is located is used as the reference amplitude, and the intensity scaling factor is the ratio of the residual value of each time delay at the preset radial position to the reference amplitude.

[0019] Optionally, the intensity scaling factor is obtained by normalizing the residual values ​​of each time delay at the preset radial position r0.

[0020] Furthermore, the iteration termination condition is at least one of the following: reaching a preset number of iterations; the residual amplitude is less than a preset threshold; the parameter change between two adjacent iterations is less than a preset threshold; the change in the fitting residual between two adjacent iterations is less than a preset threshold.

[0021] Further, the radial distribution extraction includes: The two-dimensional difference image is preprocessed, and the excitation response center and effective spatial analysis radius are determined based on the effective signal distribution in the preprocessed image. Using the excitation response center as the origin, the radial distance of each pixel is calculated, and within the effective spatial analysis radius, pixels in the same radial distance interval are grouped and averaged to obtain the corresponding one-dimensional radial distribution curve.

[0022] Furthermore, determining the excitation response center includes: performing a local search within its neighborhood based on a preset approximate center position, and performing integral calculation on the pixel signals within a preset integral window around each candidate position, with the candidate position having the largest absolute value of the integral result as the excitation response center.

[0023] Furthermore, the spatial distribution analysis results include at least one of the following: two-dimensional difference image, one-dimensional radial distribution curve, fitting curve, spatial distribution width, fitting parameters, mean square error, and diffusion transport analysis results.

[0024] Secondly, the present invention also provides a high-throughput measurement and spatial distribution analysis system for transient absorption microscopy, comprising: The laser output module is used to output pump light and probe light to excite and probe the sample under test; A pump modulation module is used to periodically modulate the pump light into a pump-on state and a pump-off state; The delay adjustment module is used to adjust the relative time delay between the pump light and the probe light; The microscopic imaging module is used to focus the probe light onto the surface of the sample to be tested and to image the response signal of the sample to be tested onto the image acquisition module; The image acquisition module is used to acquire pump-on and pump-off images of the sample under test at different time delays; The sample displacement module is used to carry the sample to be tested and drive the sample to move to each target area; The control and data processing module is electrically connected to the laser output module, pump modulation module, delay adjustment module, image acquisition module and sample displacement module respectively, and is used to coordinate the control of each module to implement the method described in any one of the first aspects.

[0025] This invention generates spatial switching sequences and time-delayed scanning sequences for target areas based on measurement parameters. These sequences serve as the measurement control timing, enabling automated pump-probe microscopy measurements across multiple regions and time delay points. This reduces manual intervention, improves testing efficiency and data consistency, and solves the technical challenges of insufficient automation and low testing efficiency in existing measurements. By employing a control method that completes all time-delayed scans region by region, and acquiring a complete time series within each target area before switching to the next, it significantly reduces unnecessary back-and-forth movements, improves the stability of the measurement process and the clarity of data organization, making it suitable for high-throughput automated measurement scenarios.

[0026] Furthermore, this invention addresses the problem that the transient spatial distribution of samples under localized pumping excitation conditions often exhibits complex contours such as central depressions, localized inverse signs, edge enhancement, and bimodal peaks. It proposes a physically constrained inverse-sign double Gaussian model. This model effectively separates spatially overlapping positive and negative signal components through the algebraic superposition of positive and negative signal components, overcoming the limitation of traditional single Gaussian models in accurately describing complex contours. In particular, for solving the inverse-sign double Gaussian model, this invention introduces four physical constraints, effectively improving the fitting accuracy, parameter stability, and physical interpretability of complex contours.

[0027] This invention automates data acquisition, generates two-dimensional differential images, reconstructs spatial distributions, and outputs parameters within the same measurement process. It can be widely applied in the spatiotemporal dynamic characterization and high-throughput screening of various samples, such as two-dimensional semiconductors, perovskites, and their heterostructures, significantly improving testing efficiency and data consistency. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the device structure of a high-throughput measurement and spatial distribution analysis system for transient absorption microscopy proposed in this invention; Figure 2 This is a schematic diagram of the collaborative operation between the user interface and the control system in a high-throughput measurement and spatial distribution analysis method for transient absorption microscopy proposed in this invention. Figure 3 This invention provides fitting results for an unconstrained double Gaussian model with different amplitude parameters under the same original data. Figure 4 This invention presents the positive amplitude parameters in the form of box plots under two conditions: physical constraints and conventional fitting. Negative amplitude parameters Positive width parameter Negative width parameter A comparison of the probability distributions of the fitting error rates; Figure 5 This invention demonstrates the positive amplitude parameters under two conditions: physical constraints and conventional fitting. Negative amplitude parameters Positive width parameter Negative width parameter A comparison chart of fitting error rate percentages; Figure 6 This is a schematic diagram of two-dimensional pump-probe differential images and corresponding processing results under different delay times for a high-throughput measurement and spatial distribution analysis method of transient absorption microscopy proposed in this invention. Figure 7 This is a schematic diagram of the one-dimensional radial distribution curve and the results of single Gaussian fitting and reversed sign double Gaussian separation fitting in a high-throughput measurement and spatial distribution analysis method for transient absorption microscopy proposed in this invention. Figure 8 This is a schematic diagram showing the spatial distribution evolution of positive and negative signals and the corresponding radial curve changes under different delay times in a high-throughput measurement and spatial distribution analysis method for transient absorption microscopy proposed in this invention. Figure 9 This is a schematic diagram illustrating the variation of the amplitude, width, and diffusion parameters of the positive and negative signals with time delay in a high-throughput measurement and spatial distribution analysis method for transient absorption microscopy proposed in this invention. Detailed Implementation

[0029] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and embodiments. The embodiments are implemented based on the technical solution of the present invention, providing detailed implementation methods and specific operating procedures. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them, and the scope of protection of the present invention is not limited to the following embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0030] Example 1, such as Figure 1 As shown, a high-throughput measurement and spatial distribution analysis system for transient absorption microscopy includes a laser output module, a pump modulation module, a delay adjustment module, a microscopic imaging module, an image acquisition module, a sample displacement module, and a control and data processing module. The control and data processing module is electrically connected to the laser output module, pump modulation module, delay adjustment module, image acquisition module, and sample displacement module, respectively, and is used for coordinated control and data processing of each module.

[0031] Specifically, the laser output module is used to output pump light and probe light to excite and probe the sample under test. In this embodiment, the laser output module includes a high repetition rate femtosecond laser, a first optical parametric amplifier, and a second optical parametric amplifier.

[0032] The high-repetition-rate femtosecond laser has an output pulse width of 180 fs and a repetition frequency of 500 kHz. The laser beam output from the femtosecond laser enters a first optical parametric amplifier and a second optical parametric amplifier, respectively, to form the pump optical path and the probe optical path.

[0033] The first optical parametric amplifier is used to perform wavelength conversion on the laser beam output by the femtosecond laser output module to obtain a pump pulse beam.

[0034] The second optical parametric amplifier is used to perform wavelength conversion on the laser beam output by the femtosecond laser output module to obtain a probe pulse beam.

[0035] Specifically, the pump modulation module is disposed in the optical path of the pump light and is used to periodically modulate the pump light into a pump-on state and a pump-off state. In this embodiment, the pump modulation module is preferably an optical chopper or an equivalent light intensity modulation device, such as any one of a mechanical chopper, an electro-optic modulator, or an acousto-optic modulator. Its reference signal is synchronously connected to the image acquisition module to realize the alternating acquisition of pump-on images and pump-off images.

[0036] The pump modulation module is also connected to a frequency generator, which provides a synchronization trigger signal to the pump modulation module and the image acquisition module to ensure that the pump modulation timing is consistent with the image acquisition timing.

[0037] Specifically, the delay adjustment module is used to adjust the relative time delay between the pump light and the probe light. In this embodiment, the delay adjustment module is preferably an electrically driven delay line, used to achieve imaging measurements at different time delay positions by changing the propagation optical path of the probe pulse beam or the pump pulse beam. The delay adjustment module is communicatively connected to the control module and can automatically move to the target delay position according to the set time delay sequence.

[0038] Specifically, the microscopic imaging module is used to focus the probe light onto the surface of the sample under test and to image the response signal of the sample onto the image acquisition module. In this embodiment, the microscopic imaging module includes: The first, second, third, and fourth reflecting mirrors are used to guide the propagation of the pump pulse beam, the probe pulse beam, and the returning imaging beam. The first spatial filter and the second spatial filter are used to improve the beam spatial pattern, enhance illumination uniformity, and reduce stray light effects. The first and second beam splitters are used for combining and splitting the pump optical path, the probe optical path, and the imaging optical path. Objective lens, used to focus pump pulse beam and probe pulse beam onto the surface of the sample to be tested, and to collect the reflected light signal returned from the sample surface; The beam splitter cube is used to distribute the returned reflected light signal to the imaging channel; An imaging lens is used to image the sample return signal onto the image acquisition module. Filters are used to remove stray light signals in the non-target wavelength band from the sample return signal, thereby improving the imaging signal-to-noise ratio.

[0039] The objective lens is preferably a high numerical aperture microscope objective lens. The pump pulse beam is focused by the objective lens to form a local excitation spot on the sample surface, and the probe beam is shaped into a wide field and then illuminates the sample surface through the objective lens, thereby forming a wide field detection area on the sample plane.

[0040] Specifically, the sample displacement module is used to carry the sample to be tested and drive it to move to each target area. In this embodiment, the sample displacement module is preferably an electric two-dimensional displacement stage, an electric three-dimensional displacement stage, or a piezoelectric displacement stage, which can automatically move the sample to be tested according to the preset target area coordinates and output position feedback information after the movement is completed.

[0041] Specifically, the image acquisition module is used to acquire pump-on images and pump-off images of the sample under test at different time delays. In this embodiment, the image acquisition module is preferably a high-sensitivity CMOS camera. Under the control of a synchronous trigger signal, the image acquisition module acquires pump-on images in the pump-on state and pump-off images in the pump-off state, respectively.

[0042] Specifically, the control and data processing module is used to control the femtosecond laser output module, pump modulation module, delay adjustment module, sample displacement module and image acquisition module to work together, and to perform differential processing, averaging processing, contour extraction and fitting analysis on the acquired images.

[0043] Specifically, the system also includes a white light illumination module for providing visible light illumination during the initial positioning and observation phases of the sample to be tested.

[0044] Specifically, the system also includes a visual operation panel for inputting experimental parameters, controlling the measurement process, and displaying measurement results.

[0045] In this embodiment, the pump pulse beam and the probe pulse beam are incident on the objective lens after passing through the corresponding optical paths, and then irradiate the surface of the sample to be tested. The reflected light returned from the sample surface is incident on the image acquisition module after passing through the objective lens, the second beam splitter, the third reflecting mirror, the imaging lens, and the filter, so as to obtain microscopic images of the sample under different time delays.

[0046] In this embodiment, the white light beam output by the white light illumination module can also be coupled to the main optical path via a beam splitter cube, so that the white light shares part of the imaging optical path with the pump light and the probe light, thereby realizing real-time optical positioning and regional observation of the sample under test.

[0047] Example 2: A high-throughput measurement and spatial distribution analysis method for transient absorption microscopy proposed in this application includes the following steps: S1. Obtain measurement parameters, which include at least delayed scan parameters and a set of coordinates or spatial scan sequences of multiple target areas; generate spatial switching sequences and time-delayed scan sequences of the target areas based on the measurement parameters.

[0048] Specifically, the delay scan parameters include the zero-delay position, the delay scan range, and the delay step size. Measurement parameters may also include the number of repeated sampling frames, the number of samples, and the data storage path. In this embodiment, the time delay scan sequence preferably adopts a segmented variable step size sampling strategy, that is, a smaller step size is used in the time range near the zero delay, and a larger step size is used in the longer delay time range, so as to balance time resolution accuracy and measurement efficiency.

[0049] S2. Move the sample to be tested to each target area in sequence according to the spatial switching sequence, and in each target area, collect pump-on images and pump-off images under different time delays in sequence according to the time delay scanning sequence. Process to obtain a set of two-dimensional differential images corresponding to each target area.

[0050] Specifically, the control and data processing module acquires the measurement parameters set by the user, reads the current target area coordinates from the target area coordinate set, controls the sample displacement module to drive the sample to be tested to move to the current target area, and completes closed-loop positioning correction and stability confirmation. In this embodiment, the sample displacement module returns real-time position data to the control and data processing module during the movement. After determining that the sample has entered the allowable error range of the target position and the position is stable, the control and data processing module then performs subsequent measurements.

[0051] The control and data processing module controls the delay adjustment module to change the propagation optical path of the probe pulse beam or pump pulse beam according to the time delay scanning sequence, so that it moves to each time delay position in sequence. After the closed loop stabilizes at each time delay position, the image acquisition module is triggered to perform multi-frame repeated sampling to acquire the pump-on image and the pump-off image.

[0052] In this embodiment, after the delay adjustment module moves to the target delay position, the control and data processing module continues to read the position feedback and motion state feedback of the delay adjustment module. Only after the target position is reached and the motion state is stable will the image acquisition module be triggered to acquire images, so as to improve the time delay positioning accuracy and repeatability consistency.

[0053] In this embodiment, the image acquisition module continuously acquires multiple frames of images under synchronous trigger control. The acquired images include pump-on image signals corresponding to the pump-on state and pump-off image signals corresponding to the pump-off state.

[0054] Specifically, the process of obtaining a set of two-dimensional difference images corresponding to each target region includes: performing differential calculations on pump-on images and pump-off images continuously acquired under the same time delay for the same target region, and then accumulating and averaging the obtained multi-frame difference images to obtain a two-dimensional difference image of the target region under the corresponding time delay.

[0055] Specifically, for pump-on and pump-off images continuously acquired at the same time delay for the same target area, a two-dimensional difference image is obtained by differential calculation according to the following formula:

[0056] in, Let x and y represent the x and y coordinates of a pixel in the two-dimensional difference image, respectively, and t be the time delay. Indicates the coordinates in the pump-on image. Pixel value at that location, Represents the coordinates in the pump-off image. Pixel value at that location, Represents coordinates in a two-dimensional difference image The pixel value at that location.

[0057] In this embodiment, the control and data processing module preferably uses streaming averaging to perform frame-by-frame cumulative averaging of the difference results. This can effectively suppress background fluctuations and random noise, improve the extraction capability of weak transient signals, the signal-to-noise ratio and stability of the two-dimensional difference image, and reduce the storage burden of large amounts of original image data.

[0058] After completing image acquisition and differential image generation at all time-delay positions in the current target area, the control and data processing module sequentially determines whether there are any unmeasured areas according to the preset target area coordinate set. If the current target area has been completed and there are still unmeasured target areas, the control sample displacement module switches to the next target area to continue the measurement. If all target areas have been completed, the subsequent spatial contour extraction and fitting analysis steps are entered.

[0059] In one optional implementation, while acquiring pump-on images and pump-off images at different time delays according to the time delay scanning sequence, the pump-detection signal output by the avalanche photodetector can also be acquired simultaneously, and the detection signal intensity corresponding to each time delay position can be recorded to obtain the pump-detection signal dynamic curve.

[0060] Specifically, after the control delay adjustment module sequentially switches to each time delay position and completes stability confirmation, the control and data processing module synchronously triggers the avalanche photodetector to read the signal and establishes the correspondence between the time delay and the detection signal response. The obtained pump-detector signal dynamics curve can be used to characterize the temporal evolution characteristics of the transient response of the sample under test, and can be correlated with the spatial distribution analysis results of each target region in subsequent processing to construct a spatiotemporal evolution distribution map of the sample under test.

[0061] S3. Extract the radial distribution from the two-dimensional difference images in the set to obtain the corresponding one-dimensional radial distribution curve.

[0062] Specifically, radial distribution extraction includes: The two-dimensional difference image is preprocessed, and the excitation response center and effective spatial analysis radius are determined based on the effective signal distribution in the preprocessed image. Using the excitation response center as the origin, the radial distance of each pixel is calculated, and within the effective spatial analysis radius, pixels in the same radial distance interval are grouped and averaged to obtain the corresponding one-dimensional radial distribution curve.

[0063] The preprocessing includes median baseline removal, zero-point normalization, and optional background subtraction to reduce the effects of background bias, system drift, and random noise.

[0064] The control and data processing module determines the coordinates of the excitation response center based on the grayscale distribution of the two-dimensional difference image. Specifically, it first performs a local search within the neighborhood of a preset approximate center location, and then integrates the pixel signals within a preset integration window around each candidate location. The candidate location with the largest absolute value of the integration result is taken as the excitation response center (x). c , y c Using this method to determine the center position can reduce the impact of local noise, individual abnormal pixels, and weak background inhomogeneity on the center recognition results, thereby improving the accuracy and stability of response center localization.

[0065] After determining the excitation response center, the distance from each pixel in the two-dimensional difference image to the response center is calculated, and the distance satisfies:

[0066] in, To respond to the center coordinates, pixels within the same radius are grouped together, and the signal values ​​of pixels in the same group are averaged to obtain one-dimensional radial distribution data at the corresponding radius position. By repeating the above process for all radius intervals, a complete one-dimensional radial distribution curve is finally obtained.

[0067] Determining the excitation response center and effective spatial analysis radius based on the effective signal distribution in the preprocessed image can reduce the influence of image edge background regions on subsequent analysis. The planar coordinates of each pixel can be converted to polar coordinates with the excitation response center as the origin through methods such as polar coordinate mapping, thereby obtaining the radial distance of each pixel. By averaging the pixels according to their radial distances, the influence of random noise on the profile results of a single line can be reduced. While preserving the physical meaning of the spatial distribution, local noise is suppressed, thus improving the stability of the extracted one-dimensional radial distribution curve.

[0068] S4. Based on the contour characteristics of the one-dimensional radial distribution curve, a single Gaussian model or a physically constrained inverse double Gaussian model is used for fitting, and the spatial distribution analysis results of each target region under different time delays are output.

[0069] Specifically, when the one-dimensional radial distribution curve exhibits a near-unimodal distribution, a single Gaussian model is used for fitting; when the one-dimensional radial distribution curve does not conform to the unimodal distribution characteristics, a double Gaussian model with physical constraints is used for separation and fitting.

[0070] Specifically, the single Gaussian model is represented as:

[0071] Where A is the amplitude parameter, For width parameter, For background items.

[0072] Specifically, under local pump excitation conditions, the transient spatial distribution of the sample is not always an ideal Gaussian unimodal structure. When nonlinear processes such as exciton-exciton annihilation and Auger recombination are present, the carrier distribution often exhibits complex contours such as central depression, local inversion, edge enhancement, or crater-like shape. The corresponding one-dimensional radial distribution curves show characteristics that do not conform to a unimodal distribution, such as central depression, local inversion, edge enhancement, bimodal or single Gaussian fitting residuals exceeding a preset threshold.

[0073] For quantitative analysis of such complex spatial contours, existing techniques typically still employ single Gaussian models for fitting. However, a single Gaussian model has only one peak position and one width parameter, essentially only describing symmetrical broadening behavior at a single spatial scale, and cannot characterize non-monotonic features such as central depressions or localized inversions. When forcibly applied to complex contours, the fitting residuals exhibit systematic bias in the central region, causing the extracted spatial distribution parameters (such as width and amplitude) to deviate significantly from the true values, or even exhibit completely erroneous evolutionary trends.

[0074] Another common approach is to use a double positive Gaussian superposition model (i.e., the linear superposition of two positive Gaussian components). This model can describe bimodal or multi-scale broadening features, but it still cannot handle the case where the central signal is reversed.

[0075] In fact, under local pump excitation conditions, the transient spatial distribution of the sample exhibits the characteristics of superposition of positive and negative Gaussian signals. Therefore, this invention uses an inverse-sign double Gaussian model, which is a linear combination of a positive Gaussian component and a negative Gaussian component, for separation and fitting. The inverse-sign double Gaussian model is expressed as follows:

[0076] in, These represent the amplitude parameters of the positive and negative signal components, respectively. These represent the width parameters of the positive and negative signal components, respectively. Baseline parameters, This represents the radial distance corresponding to the one-dimensional radial distribution curve. Positive signal component. This represents the positive transient absorption response generated by pump excitation, with a Gaussian spatial distribution; negative signal components... This represents the negative transient absorption response generated by the high-density excitation region at the center. Both the positive and negative components have the same excitation response center as their origin and completely overlap in space; the observed signal is an algebraic superposition of the two.

[0077] However, the superposition of positive and negative Gaussian components is mathematically highly complex. Due to the strong local cancellation effect between components of opposite signs, the overall signal shape is extremely sensitive to changes in individual parameters, but exhibits high insensitivity to joint changes in specific parameter combinations. Mathematically, this means that the solution space (error surface) of the fitted model contains numerous gentle "valleys" or multiple local extrema, representing a typical ill-conditioned inverse problem. Conventional fitting methods, such as traditional unconstrained least squares numerical optimization, are prone to falling into the trap of "compensatory substitution" when dealing with such signals. This involves forcibly approximating the experimental curve by abnormally amplifying the amplitude of the main peak while simultaneously assigning extremely strong negative compensation to the negative peak, or by irrationally replacing the width. While this algorithm may converge mathematically and produce minimal residuals, it is physically absurdly spurious, leading to drastic jumps or discontinuities in the conventional evolution curve, completely obscuring the true physical evolution.

[0078] To illustrate the above issues more clearly, Figure 3 A typical example is given. Figure 3The four subplots used identical original noisy data, and the final double Gaussian total fitting curves all perfectly passed through the data points, mathematically achieving minimal residuals. However, when the amplitudes of the positive Gaussian components were artificially fixed to different values ​​(A=0.7, A=1, A=2, A=3), the model could still fit the data. This is because, as the positive amplitude expanded, the negative Gaussian components (dotted lines) achieved perfect local cancellation by irrationally deepening synchronously (drastically increasing the negative absolute amplitude and self-adjusting its width). This result indicates that, in the absence of underlying physical constraints, the solution space of the positive and negative Gaussian superposition model suffers from severe degradation and overlap. For the same set of visually defined experimental data, there are countless combinations of positive and negative Gaussian parameters that are mathematically equivalent but physically distinct.

[0079] Faced with such highly coupled nonlinear multi-solution problems, the conventional approach is to set empirical upper and lower bounds for the parameters of the algorithm. However, this static and isolated parameter truncation method is ineffective in the case of superposition of positive and negative Gaussians. This is because the parameter distortion caused by the superposition of opposite signs does not originate from the out-of-bounds behavior of a single parameter, but rather from the dynamic coupling compensation between parameters (such as between positive and negative peak amplitudes, and between amplitude and width). Isolating and restricting a single parameter not only fails to break the error compensation chain, but also leads to erroneous physical evolution processes.

[0080] To address the aforementioned issues, this application employs physical constraints to limit the divergence direction of the parameters, selecting results with genuine physical meaning from numerous mathematically feasible solutions. After normalizing the one-dimensional radial distribution curve to its global maximum value, the physical constraints include upper limit of amplitude constraints, center point constraints, lower limit of width constraints, and regularization constraints.

[0081] Specifically, the upper limit constraint on amplitude is expressed as: the amplitude parameter satisfies Since the signal value at any radial position after normalization does not exceed 1, the sum of the positive and negative component amplitudes exceeding 1 means that there is an additional contribution in the central region that cannot be canceled out. This constraint is mainly used to avoid amplitude combinations that deviate from the actual signal.

[0082] This invention addresses the physical characteristics of transient absorption measurement signals by imposing corresponding restrictions on the mathematically feasible region. Specifically, the transient absorption measurement signal originates from transient pulse excitation. Under these physical conditions, the system gradually transforms from a single initial signal into two signal components: positive and negative. Furthermore, due to the single pulse excitation, there is no other continuous external energy or signal input during the evolution process. Therefore, the evolution of the total signal intensity necessarily follows a monotonically decreasing dissipative physical law and will not exhibit spontaneous growth.

[0083] It should be noted that the physical law of monotonically decreasing signal after pulse excitation without external energy input is common knowledge in the field of spectroscopy. However, in existing technologies, this physical law is usually only used as a qualitative interpretation framework for experimental results or to determine whether measurement data is affected by external interference, and has not been further transformed into quantitative constraints in the fitting and optimization process.

[0084] This invention transforms the aforementioned physical laws into operable quantitative mathematical constraints. After normalizing the signal, the sum of the amplitudes of the positive and negative Gaussian bimodal peaks is constrained to be always less than or equal to 1. Under this constraint, when the optimization algorithm explores the solution space, the parameters cannot compensate for each other by simultaneously amplifying the positive and negative amplitudes to reduce the residual. Any search path that attempts to approximate the experimental curve by irrationally amplifying the positive and negative amplitudes simultaneously (resulting in an amplitude sum much greater than 1) will be directly rejected because it violates the physical premise of "monotonically decreasing and passive evolution".

[0085] Furthermore, this invention applies this upper limit constraint on amplitude to transient radial distribution signals processed by maximum value normalization, demonstrating a unique advantage. Generally, while normalization unifies the relative scale of signals at different times, it erases the baseline information of absolute intensity. In conventional bimodal fitting, this typically increases the coupling between amplitude and width parameters, leading to increased parameter degrees of freedom and a greater risk of fitting divergence. However, the upper limit constraint on amplitude set by this invention ensures that normalization not only does not result in the loss of constraint force but also provides a unified scale benchmark for physical constraints. Specifically, the normalized signal amplitude is confined to the [0,1] interval, giving a clear and strict criterion for the constraint condition that "the sum of the positive and negative component amplitudes does not exceed 1." This upper limit constraint on amplitude, working synergistically with the normalization scale, utilizes the natural decay characteristics of physical evolution to effectively limit the irrational expansion of the amplitude parameter, providing a stable physical boundary for the multi-parameter optimization process.

[0086] Specifically, the center point constraint is expressed as: in At this point, the value of the inverse-sign double Gaussian model is equal to the value of the one-dimensional radial distribution curve, satisfying... Once baseline subtraction has been completed, the formula can be further expressed as: .

[0087] In localized pumping mode, the pump light is focused onto a micrometer-scale region on the sample surface. The excitation response center r=0 corresponds to the center of the pump spot, where the signal has the highest signal-to-noise ratio and determinism among all radial positions. This invention utilizes this experimental characteristic, locking the fitted free value at the center position to the experimental observation value through a center-point constraint. This fixes the difference between positive and negative amplitudes, eliminating the compensatory path of the optimization algorithm that maintains the fitting residual unchanged by synchronously shifting positive and negative amplitudes at the excitation center, thus enhancing the ability to describe localized inverse or concave structures.

[0088] Specifically, the width lower limit constraint is expressed as: the width parameter satisfies... and, ,in, This is the minimum resolvable width preset based on the spatial resolution capability of the imaging system.

[0089] In optical microscopy imaging systems, due to diffraction effects, there exists a minimum resolvable width determined by the objective lens numerical aperture and the probe wavelength. Any spatial distribution feature width obtained through fitting that is less than this physical limit is optically indistinguishable and represents a spurious narrow peak result driven by noise. The lower limit constraint on width is used to exclude physically meaningless fitting results from the perspective of instrument physics, ensuring that the extracted spatial distribution width parameter always remains within the resolvable range of the imaging system.

[0090] The regularization constraint is expressed as follows: In the optimization objective function of solving the parameters of the inverse-sign double Gaussian model, a regularization penalty term is introduced to apply to the optimization objective function. Constraints are applied to reduce the impact of multi-parameter nonlinear coupling on the stability of the fitting results.

[0091] Specifically, based on minimizing the sum of squared residuals between the experimental data and the inverse-sign double Gaussian model, the objective function is optimized as follows:

[0092] in, The regularization coefficient is . The regularization weight exponent, This represents the radial distance corresponding to the i-th data point on the one-dimensional radial distribution curve. This represents the measured signal value corresponding to the i-th data point on the one-dimensional radial distribution curve.

[0093] In the above optimization objective function, the regularization penalty term This design addresses the issue of positive and negative signal components increasing synchronously and canceling each other out; it can control the amplitude of the positive signal component. With the amplitude of the negative signal component The synchronous increase of Gaussian components is penalized to prevent the optimization algorithm from reducing the residual by simultaneously increasing two Gaussian components with opposite signs and causing them to cancel each other out. This suppresses problems such as overfitting noise, parameter divergence, and non-unique solutions. This regularization constraint ensures that while minimizing the residual, it prioritizes obtaining parameter combinations with limited amplitude, more stable structure, and better physical meaning.

[0094] Furthermore, the regularization coefficient Used to adjust the weights between the fitted residual term and the regularization penalty term. When it increases, for With enhanced constraints, the parameter solutions tend to be more stable, effectively reducing parameter fluctuations under weak signal or low signal-to-noise ratio conditions; when When the value is reduced, the inverse-sign double Gaussian model exhibits enhanced ability to follow the details of experimental data, preserving the true local structural changes in the one-dimensional radial distribution curve. Regularization weight exponent It is used to adjust the growth form of the regularization penalty term as the amplitude combination changes, and it can be set according to the signal-to-noise ratio of the experimental data, the level of the fitting residual, the signal strength, or a preset empirical value.

[0095] In one alternative implementation, the regularization coefficient and regularization weight exponent The regularization coefficient is determined by user input or by the system adaptively based on noise level, residual variation, or signal strength. For time points with low signal-to-noise ratios or weak signal amplitudes, the regularization coefficient is increased. To enhance the suppression of non-physical understanding; for time points with high signal-to-noise ratios, reduce the regularization coefficient. This is to improve the model's response to actual signal structures.

[0096] To verify the feasibility of the method, this invention simulated 10,000 sets of biGaussian distribution data and performed conventional fitting and physically constrained fitting respectively to compare the differences in parameter inversion error and stability between the two fitting methods. The parameter range of the simulated data was set with reference to the distribution characteristics of the actual experimental data after maximum value normalization. After maximum value normalization, the signal amplitude was limited to the aforementioned unified range; therefore, the amplitude parameter in the simulation... The range of values ​​and The constraints can reflect the relative intensity relationship between positive and negative components after normalization; the width parameter The value range of corresponds to the variation range of peak broadening in the actual experimental data. Meanwhile, 5% Gaussian noise is added to the simulation to characterize the level of background disturbance commonly found in the normalized experimental signal. The simulated data constructed in this way is consistent with the experimental data after normalization of the maximum value in terms of amplitude scale, parameter variation range, and noise level. It can be used to characterize the difficulty of parameter inversion during actual signal fitting and the error distribution characteristics of different fitting strategies.

[0097] Figure 4 The positive amplitude parameter is presented in the form of a box plot for both physically constrained fitting and conventional fitting. Negative amplitude parameters Positive width parameter Negative width parameter The probability distribution of the fitting error rate is compared. For box plots, the upper and lower boundaries of the box represent the distribution range of the middle 50% of the data, the horizontal line inside the box represents the median, and the upper and lower limits represent the upper and lower extension range of the error distribution. Therefore, the higher the box and the larger the span of the upper and lower limits, the stronger the error dispersion; the higher the median, the greater the typical error level of the parameter.

[0098] Based on the conventional fitting results, and The error distributions are relatively dispersed, with a generally high box height, a large range between the upper and lower limits, and a relatively high median. This indicates that under conventional fitting, a large number of fitting results are not concentrated in the low-error region, but are distributed over a wider error range, with a typical error level that is relatively high. This discrete distribution suggests that conventional optimization algorithms, lacking physical laws, are prone to deviating from the true evolution trajectory of physical parameters when faced with the cancellation of opposite-sign components and background noise disturbances. Conventional fitting, simply pursuing residual minimization, approximates the target curve by simultaneously amplifying positive and negative amplitudes or by cross-substituting between width parameters. The resulting compensatory substitutions lead to a large number of mathematically equivalent but physically unreasonable pseudo-solutions in the solution space. In contrast, the error rate distribution of physically constrained fitting results shows a significantly lower box height across all four parameters, a more concentrated distribution range, a significantly smaller range between the upper and lower limits, and a generally lower median that is closer to the zero-error region. This indicates that the constraints limit the disordered drift of parameters, concentrating most fitting results within a smaller error range and reducing the occurrence of high-error results. For amplitude parameters... and In other words, the constraint suppresses unreasonable amplitude compensation between peaks of different signs; for the width parameter and In other words, the constraints reduce the width substitution phenomenon between different components, making the parameter search process closer to the actual physical range of change.

[0099] Figure 5The positive amplitude parameters are shown in both physically constrained fitting and conventional fitting cases. Negative amplitude parameters Positive width parameter Negative width parameter The histogram of the fitting error rate percentage. Figure 5 This indicates that, for these four parameters, the error rate distribution of conventional fitting exhibits a highly significant characteristic of "low concentration and broad spread." Specifically, the proportion of conventional fitting error rates in the near-zero error range (i.e., high-fidelity fitting) is extremely low (for example, the extremely low error rate for amplitude parameters accounts for only about 0.2%, and for width parameters, only about 0.3%), while the vast majority of fitting results diffuse into the high error range of 0.5 to 2.0. This discrete distribution pattern intuitively shows that conventional fitting of positive and negative Gaussian signals easily deviates from the true evolution trajectory of physical parameters, generating a large number of local extrema and spurious solutions with no physical meaning. Conversely, the error rate of fitting with physical constraints in the figure converges highly towards zero, with the proportion of the main peak and negative peak amplitudes in the extremely low error range jumping to about 0.45, and the extremely low error rate for the width parameter strongly exceeding 0.6. More importantly, the severely distorted solutions that are widely present under conventional fitting (such as long trailing regions with medium to high errors greater than 0.5) are significantly reduced or even completely blocked by this method, indicating that after introducing physical boundary constraints based on central measured features, this invention has excellent parameter locking capability and anti-distortion performance.

[0100] Therefore, the physical constraint fitting adopted in this invention, whether in the harsh region where components are severely canceled out or in the complex situation where signal normalization leads to the loss of absolute scale and abnormally high parameter degrees of freedom, on the one hand, restricts and eliminates mathematically feasible but physically unreasonable parameter combinations, and on the other hand, suppresses the interference of noise on parameter solution, thus achieving a balance between tolerating measurement noise and resisting mathematically distorted solutions.

[0101] This physical constraint, which combines the physical mechanism of pulse excitation with the underlying mathematical optimization logic, changes the previous fitting dilemma of "residual theory only". It enables the inverse double Gaussian model to effectively describe complex spatial contours such as central depression, local inverse sign, edge enhancement or double peak, while greatly improving the stability, repeatability and physical interpretability of parameter solution under weak signal conditions.

[0102] In one optional implementation, when the one-dimensional radial distribution curve exhibits obvious diffraction ring residue, positive edge enhancement, or other positive interference signals not belonging to the target transient response, an iterative background correction step for the one-dimensional radial distribution curve is further included. The following explanation assumes the target transient response satisfies a single Gaussian spatial distribution.

[0103] When the spatial distribution shape of the positive interference signal is approximately the same under different time delays, and its spatial distribution difference with time can be approximately ignored and mainly manifested as intensity change, the observed one-dimensional radial distribution curve can be expressed as:

[0104] in, This represents the observed signal at radial position r with a time delay of t. The amplitude parameters of the target single Gaussian signal, The width parameter of the target single Gaussian signal. A reference spatial distribution template representing a positive interference signal. This represents the intensity scaling factor of the positive interference signal over a time delay t. This represents the random noise term.

[0105] In the nth iteration, the current corrected one-dimensional radial distribution curve Perform single Gaussian fitting to obtain the fitted curve. And calculate the residual between the two:

[0106] Subsequently, at the preset radial position The positive residual amplitude corresponding to each time delay is extracted, and the intensity scaling factor under each time delay is determined based on the positive residual amplitude. The residual radial distribution curve corresponding to the time delay with the largest positive residual is selected as the reference background template. Then, based on the reference background template and the intensity scaling factor at each time delay, the background update amount is constructed. Update the current correction curve:

[0107] Repeat the above process of single Gaussian fitting, residual extraction, background template construction, and background subtraction until the preset number of iterations is reached, or the positive residual magnitude meets the stopping condition. Finally, the iteratively obtained... The radial distribution curve after removing positive interference is used as the basis for re-fitting with a single Gaussian to obtain the corrected amplitude parameter, width parameter and spatial distribution analytical results.

[0108] Through the aforementioned iterative background correction, without prior precise knowledge of the specific form of the positive interference signal, a one-dimensional radial distribution curve closer to the target transient response can be obtained by successively estimating and subtracting non-target response components such as diffraction ring residues and edge positive enhancements using single Gaussian fitting residuals. After correction, the radial distribution curves at various time delays can be further used for spatial distribution model fitting, parameter extraction, and optimization analysis among different candidate models to improve the accuracy and stability of subsequent spatial distribution analysis results.

[0109] It should be noted that the above description takes the target transient response satisfying a single Gaussian spatial distribution as an example, only to facilitate understanding of the basic principle of the present invention; when the target transient response satisfies other spatial distribution forms (such as a double Gaussian distribution with inverse sign), the iterative background correction method is also applicable, only the single Gaussian fitting is replaced with the corresponding spatial distribution model.

[0110] Specifically, the output of spatial distribution analysis results for each target region under different time delays includes: optimizing and evaluating the fitting results of different candidate models, comparing goodness of fit, residual distribution, parameter stability, and physical rationality, and automatically selecting the optimal model based on the goodness of fit index, residual statistics, and parameter boundary satisfaction of each candidate model, thereby outputting the spatial distribution analysis results for each target region under different time delays. The spatial distribution analysis results include at least one of the following: two-dimensional difference image, one-dimensional radial distribution curve, fitting curve, spatial distribution width, fitting parameters, mean square error, and diffusion transport analysis results. By summarizing and analyzing the fitting results for different target regions and different time delay locations, the spatial distribution evolution law and complex non-equilibrium dynamic characteristics of the tested sample can be further obtained.

[0111] Furthermore, based on the spatial location and spatial distribution analysis results of each target region, the carrier diffusion performance distribution image of the sample under test can be reconstructed.

[0112] Specifically, the control and data processing module reads the spatial position of each target region in the coordinate set and extracts the spatial distribution parameters of each target region obtained by fitting under different time delays. The spatial distribution parameters include at least the amplitude parameter, the width parameter, and the diffusion-related parameter characterized by the relationship between the width parameter and the time delay.

[0113] Specifically, for each target region, a parameter sequence characterizing the evolution of spatial broadening over time can be established based on the fitting results of the one-dimensional radial distribution curves obtained under different time delays, and the carrier diffusion performance parameters of the corresponding target region can be calculated accordingly. The carrier diffusion performance parameters can be the diffusion width change rate, the effective diffusion coefficient, or other parameters that can characterize the spatial transport capacity of carriers.

[0114] In one implementation, when the spatial distribution satisfies the Gaussian broadening evolution relationship, the width parameter of each target region satisfies the relationship that changes with time delay:

[0115] in, The width parameter is given by the time delay t. Here, is the initial width parameter, and D is the carrier diffusion coefficient. The control and data processing module can be based on different time delays. By fitting the relationship between t and diffusion coefficient D, the diffusion coefficient D corresponding to each target region is obtained.

[0116] Furthermore, the control and data processing module maps the carrier diffusion performance parameters of each target region to the spatial coordinates of that region, backfilling the data according to the arrangement order of the target regions on the sample or the actual spatial coordinate relationship, thereby generating a carrier diffusion performance distribution image of the sample. The distribution image can be output in the form of a two-dimensional matrix, pseudo-color image, contour map, or grayscale image to characterize the spatial differences in carrier diffusion capability at different locations on the sample.

[0117] Specifically, when the target region coordinate set corresponds to a regular grid scan, the control and data processing module directly maps the diffusion performance parameters corresponding to each target region to two-dimensional image pixel values ​​according to the row and column positions; when the target region coordinate set corresponds to irregular spatial sampling, the control and data processing module can generate a continuous carrier diffusion performance distribution image based on the actual coordinates of each target region through interpolation, weighted averaging, or neighborhood reconstruction.

[0118] Furthermore, the carrier diffusion performance distribution image can be registered and overlaid with sample surface morphology images, reflection images, transmission images, or other characterization images to achieve a correlation between sample microstructure information and carrier diffusion performance information. This facilitates the identification of the influence of grain boundaries, defects, stress regions, compositional inhomogeneities, or other local structural factors on carrier diffusion behavior, improving the analytical capabilities for sample spatial inhomogeneity, local anomalous regions, and performance distribution patterns. Furthermore, by combining the pump-probe dynamics results acquired by the avalanche photodetector with the spatial distribution analysis results of each target region under different time delays, a spatiotemporal evolution distribution map of the sample under test can be constructed. This enables a joint characterization of transient carrier transport behavior in both time and space dimensions, obtaining a spatiotemporal dynamic parameter distribution map of the sample.

[0119] The above method was used to measure two-dimensional semiconductor samples, such as... Figure 2 As shown, the operation steps are as follows: Step 1: The user sets the measurement parameters through the user interface. First, basic parameters are set, including zero-delay position, camera frame rate, sample size, and data storage path. Then, measurement and scanning settings are completed, including delayed scan range, delay step size, and coordinate set of each target area. The program is then started, the system initializes, and completes device self-test and communication connection confirmation. The control and data processing module generates the spatial switching sequence and time-delayed scan sequence for the target area based on the user settings.

[0120] Step 2: The control and data processing module reads the current target area coordinates from the target area coordinate set and controls the sample displacement module to drive the sample to be tested to move to the target area. During the movement, the sample displacement module feeds back real-time position data, and the control and data processing module monitors the progress in real time. The control and data processing module determines whether the sample has entered the allowable error range of the target area and whether its position is stable. If the target area is not reached or the position is not stable, continue to drive the sample displacement module for adjustment; If the target area has been reached and the position is stable, the positioning is confirmed to be complete, and the electric delay line is adjusted to the specified delay time.

[0121] Step 3: Under the control of the synchronous trigger signal, the image acquisition module continuously acquires multiple frames of pump-on and pump-off images at the current time delay position, and transmits the acquired image data to the control and data processing module. The control and data processing module processes the received pump-on and pump-off images to obtain a two-dimensional differential image of the current target area at the current time delay, and saves the two-dimensional differential image at the current time delay and the original image data to the storage medium, recording the current measurement progress.

[0122] Step 4: The control and data processing module determines whether the scanning of all time-delay positions in the current target area has been completed. If there are still unmeasured time delay positions in the time delay scan sequence, return to step S3 and control the motorized delay line to adjust to the next time delay position; if all time delay positions in the current target area have been measured, proceed to step S5.

[0123] Step 5: The control and data processing module determines whether all target areas have been measured. If there are still unmeasured target areas in the target area coordinate set, repeat steps 2 to 4 to control the sample displacement module to switch to the next target area for measurement; if all target areas have been measured, proceed to step S6.

[0124] Step 6: The control and data processing module summarizes and processes the two-dimensional difference images of each target region under different time delays, including image preprocessing, radial distribution extraction, spatial distribution model fitting and spatial distribution parameter extraction, and outputs the spatial distribution analysis results of each target region under different time delays.

[0125] The pump light, after modulation, is focused onto the surface of a two-dimensional semiconductor sample to form local excitation. A 160 fs 500 kHz femtosecond laser is used as a seed source, modulated by a first optical parametric amplifier into a 3.06 eV pump pulse beam, and then modulated by a second optical parametric amplifier into a 1.48 eV probe pulse beam. The probe pulse beam forms a wide-field illumination on the sample surface. The image acquisition module simultaneously acquires pump-on and pump-off images at various time delays (pump light modulated at 400 Hz, camera acquisition frequency modulated at 800 Hz), and obtains a two-dimensional difference image through difference calculation and streaming averaging. Radial distribution is extracted from the obtained two-dimensional difference image to obtain a one-dimensional radial distribution curve at the corresponding time delay. Model fitting is performed on this curve: when the curve has a near-unimodal distribution, a single Gaussian model is used for fitting; when the curve has a central depression, local inverse sign, or multi-component characteristics, a double Gaussian model with physical boundary constraints is used for separation fitting. By analyzing the fitting results under different time delays, the evolution relationship of characteristic parameters such as the width and amplitude of each component over time is obtained, thereby realizing the quantitative characterization of complex ultrafast dynamic processes in two-dimensional materials.

[0126] Figure 6 The transient absorption spatial distribution of two-dimensional semiconductor samples under different time delays is shown, where Figure 6 Figure 'a' shows the original transient microscopic images of a two-dimensional semiconductor sample obtained at different time delays. Figure 6 b in the figure shows the pair. Figure 6 The image shown in Figure 'a' is a one-dimensional radial distribution curve obtained after radial distribution extraction. Specifically, Figure 6 In step a, the two-dimensional difference image is obtained by differential and flow cytometry averaging of the pump on / off state images, which intuitively characterizes the transient spatial response distribution of the sample under test at different time delays. Since local noise may still remain in the two-dimensional difference image, this embodiment extracts the response center and averages it according to the radial distance to convert it into... Figure 6 The one-dimensional radial distribution curve shown in b is shown in the figure. Figure 6 The correspondence between a and b in the figure shows that the present invention effectively suppresses random noise while fully preserving the main features related to spatial broadening, making the signal profile smoother and clearer, and providing stable data input for the subsequent extraction of dynamic parameters.

[0127] Figure 7The one-dimensional radial distribution curve obtained by radial averaging and the fitting analysis results are shown. Figure 7 In the figure, 'a' represents the radial distribution fitting result obtained by radial averaging. The experimental data at different delay times (0ps to 565ps) are distinguished by the shape of the scatter points (circles, triangles, etc.). The continuous solid line represents the curve obtained by fitting the experimental data based on the above model. The figure shows that the experimental data points and the fitting results are in good agreement overall. The model used can accurately characterize the spatial distribution and broadening evolution of the signal under different delay times. Figure 7 In the figure, 'b' represents the decoupling result of the central concave signal. The experimental data are distinguished by the shape of the scatter plots. Solid lines of different colors represent the overall fitting effect at different delay times (105ps~365ps), while dashed lines represent the positive and negative signal components obtained after decoupling the superimposed signals according to the above-mentioned physically constrained separation fitting method. Furthermore, to visually demonstrate the separation effect, normalization was performed based on the maximum value of the positive component. This figure illustrates that this method not only has good fitting accuracy but also effectively separates the main positive signal component from the central negative signal component, thereby achieving accurate analysis of complex spatial distribution characteristics.

[0128] By selecting a reasonable model and using a physically constrained separation fitting method, this invention can effectively separate the superimposed main positive signal components from the central local abnormal negative components in the experimental data, thereby accurately obtaining the amplitude, width, and baseline parameters of each component, avoiding parameter distortion or non-convergence problems caused by forcibly fitting complex contours with a single model.

[0129] Reference Figure 8 , Figure 8 In the diagrams, a and b represent the spatiotemporal evolution of the positive and negative signal components obtained by using a physically constrained double Gaussian model with inverse signs, respectively. Figure 8 In the figure, c and d are the radial distribution curves of the positive and negative signal components under different delay times, respectively.

[0130] Specifically, Figure 8 In parameter 'a', the positive signal component forms near the excitation response center and maintains a continuous spatial distribution throughout the entire measurement delay. As the delay time increases, the high-intensity region of the positive signal component gradually expands to a larger radial distance. Correspondingly, Figure 8 In the c-value, the radial curves of the positive signal at different delay times, such as 0 ps, ​​5 ps, 15 ps, 30 ps, ​​105 ps, 205 ps and 565 ps, are all symmetrical about the excitation center. However, the peaks of the curves gradually widen and the tails on both sides increase, indicating that the positive signal component has undergone significant lateral spatial broadening.

[0131] Figure 8The value of 'b' indicates that the negative signal component does not dominate throughout the entire delay time, but rather mainly appears in a localized region near the excitation center. This negative signal component exhibits relatively independent evolutionary characteristics in the temporal dimension and maintains a narrow spatial distribution range. Figure 8 As can be seen from d, at delay times of 5 ps, 15 ps, 30 ps, ​​105 ps, 205 ps, and 565 ps, the negative signal components are mainly concentrated near the center, and their radial curve width is significantly smaller than that of the positive signal components, with a weaker broadening with delay time. This indicates that the transient process corresponding to the negative signal components has stronger spatial locality.

[0132] Figure 8 The differences in formation time, spatial range, and broadening rate between the positive and negative signal components indicate that the observed total transient response is not a simple decay or diffusion of a single component, but rather contains at least positive and negative response processes with different dynamic behaviors. If a single Gaussian fit is directly applied to the total signal, the central negative signal will cancel out the overall profile, easily causing the extracted amplitude and width parameters to deviate from the true evolutionary pattern. This invention, through separate fitting, can obtain the spatial distribution parameters of the two types of components separately, providing a reliable basis for subsequent diffusion coefficient and component dynamics analysis.

[0133] Further reference Figure 9 In the equation 'a', based on the width parameter obtained from the inverse-sign double Gaussian fitting under different time delays, a correspondence between the mean square displacement and the delay time can be established. Data at each delay time are fitted independently, and the resulting mean square displacement still shows continuous evolution, indicating that this fitting method has good accuracy and stability for actual experimental data. For signal components that satisfy the Gaussian broadening relationship, their width parameter can be expressed as:

[0134] in, The width parameter is given by the time delay t. This is the initial width parameter. The effective diffusion coefficient.

[0135] Figure 9 The value of 'a' indicates that the positive signal component exhibits a phased diffusion characteristic: within a relatively short delay time, its effective diffusion coefficient is approximately 123.05 cm⁻¹. 2 ·s -1 During the subsequent delay time, its effective diffusion coefficient decreases to approximately 6.60 cm⁻¹. 2 ·s -1 The effective diffusion coefficient of the negative signal component is approximately 2.50 cm⁻¹. 2 ·s -1 The value is lower than that of the positive signal component, indicating that the transient process corresponding to the negative signal component has stronger localization characteristics.

[0136] Figure 9 Figure b illustrates the normalized amplitude evolution of the positive and negative signal components. The positive signal component forms rapidly near zero delay and decays significantly in the early delay time, followed by a slower decay process; the negative signal component gradually appears and strengthens after a short delay and maintains a certain response over a longer delay time range. This result indicates that the positive and negative signal components have different formation, decay, and spatial transport mechanisms.

[0137] Therefore, the present invention can separate the amplitude, width and diffusion-related parameters of different components from the total transient signal with central depression or local inversion, avoiding misjudging local negative signals as overall signal attenuation or abnormal width changes, and improving the analytical accuracy of complex ultrafast spatiotemporal dynamic processes.

[0138] Finally, the system structure and method parameters of this invention can be flexibly adjusted according to actual measurement needs. For example, the delay step size can be set in segments according to the time resolution requirements of different time intervals; the number of target regions can be set according to the sample size and region of interest; the number of repeated frames for image acquisition can be dynamically adjusted according to the signal-to-noise ratio requirements; and the fitting model can also be flexibly selected according to the observed spatial contour shape. All of the above adjustments do not affect the basic principles and implementation of this invention, nor do they depart from the scope of protection of this invention.

[0139] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A high-throughput measurement and spatial distribution analysis method for transient absorption microscopy, characterized in that, include: Acquire measurement parameters, which include at least delayed scan parameters and a set of coordinates for multiple target regions; Based on the measurement parameters, a spatial switching sequence and a time-delayed scan sequence for the target area are generated; The sample to be tested is moved to each target region in sequence according to the spatial switching sequence, and pump-on images and pump-off images under different time delays are collected in each target region in sequence according to the time delay scanning sequence. The process is then used to obtain a set of two-dimensional differential images corresponding to each target region. Radial distribution extraction is performed on the two-dimensional difference image to obtain the corresponding one-dimensional radial distribution curve; Based on the contour features of the one-dimensional radial distribution curve, a single Gaussian model or a physically constrained inverse double Gaussian model is used for fitting, and the spatial distribution analysis results of each target region under different time delays are output.

2. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 1, characterized in that, The process of obtaining a set of two-dimensional differential images corresponding to each target region includes: performing differential calculations on pump-on images and pump-off images continuously acquired in the same target region under the same time delay, and then accumulating and averaging the obtained multi-frame differential images to obtain a two-dimensional differential image of the target region under the corresponding time delay.

3. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 1, characterized in that, When the one-dimensional radial distribution curve conforms to the unimodal distribution characteristics, the single Gaussian model is used for fitting; when the one-dimensional radial distribution curve does not conform to the unimodal distribution characteristics, the reversed-sign double Gaussian model with physical constraints is used for separation fitting.

4. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 3, characterized in that, The inverse-sign double Gaussian model is represented as follows: in, These are the amplitude parameters for the positive and negative signal components, respectively. These are the width parameters for the positive and negative signal components, respectively. Baseline parameters, This represents the radial distance corresponding to the one-dimensional radial distribution curve.

5. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 4, characterized in that, After normalizing the one-dimensional radial distribution curve to its global maximum value, the following physical constraints are applied to the inverse-sign double Gaussian model: Upper limit constraint on amplitude: The amplitude parameter satisfies ; Central point constraint: At this point, the value of the inverse-sign double Gaussian model is equal to the value of the one-dimensional radial distribution curve, satisfying: ; Width lower limit constraint: The width parameter satisfies and ,in, The minimum resolvable width is preset based on the spatial resolution capability of the imaging system; Regularization constraint: A regularization penalty term is introduced into the optimization objective function for solving the parameters of the inverse-sign double Gaussian model. ,in The regularization coefficient is . This is the regularization weight index.

6. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 1, characterized in that, It also includes an iterative background correction step: Fit the current one-dimensional radial distribution curve to a preset spatial distribution model and calculate the fitting residuals. Extract the residual values ​​corresponding to each time delay at the preset radial position, and determine the intensity scaling factor corresponding to each time delay; The residual radial distribution curve corresponding to the time delay with the largest residual amplitude is selected as the reference background template. The background update amount is constructed by combining the reference background template and the intensity scaling factor corresponding to each time delay, and the current one-dimensional radial distribution curve is updated. Repeat the above iterative background correction steps until the preset number of iterations is reached or the residual amplitude meets the stopping condition.

7. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 1, characterized in that, The radial distribution extraction includes: The two-dimensional difference image is preprocessed, and the excitation response center and effective spatial analysis radius are determined based on the effective signal distribution in the preprocessed image. Using the excitation response center as the origin, the radial distance of each pixel is calculated, and within the effective spatial analysis radius, pixels in the same radial distance interval are grouped and averaged to obtain the corresponding one-dimensional radial distribution curve.

8. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 7, characterized in that, The determination of the excitation response center includes: performing a local search within its neighborhood based on a preset approximate center position, and performing integral calculation on the pixel signals within a preset integral window around each candidate position, and taking the candidate position with the largest absolute value of the integral result as the excitation response center.

9. The high-throughput measurement and spatial distribution analysis method of transient absorption microscopy according to claim 1, characterized in that, The spatial distribution analysis results include at least one of the following: two-dimensional difference image, one-dimensional radial distribution curve, fitting curve, spatial distribution width, fitting parameters, mean square error, and diffusion transport analysis results.

10. A high-throughput measurement and spatial distribution analysis system for transient absorption microscopy, characterized in that, include: The laser output module is used to output pump light and probe light to excite and probe the sample under test; A pump modulation module is used to periodically modulate the pump light into a pump-on state and a pump-off state; The delay adjustment module is used to adjust the relative time delay between the pump light and the probe light; The microscopic imaging module is used to focus the probe light onto the surface of the sample to be tested and to image the response signal of the sample to be tested onto the image acquisition module; The image acquisition module is used to acquire pump-on and pump-off images of the sample under test at different time delays; The sample displacement module is used to carry the sample to be tested and drive the sample to move to each target area; The control and data processing module is electrically connected to the laser output module, pump modulation module, delay adjustment module, image acquisition module and sample displacement module respectively, and is used to coordinate the control of each module to implement the method described in any one of claims 1-9.

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