Angle-resolved dual photoelectron extraction method based on time-of-flight background calibration

Abstract

The application discloses an angle-resolved dual-photoelectron extraction method based on a time-of-flight background calibration, and belongs to the technical field of photoelectron spectroscopy. The angle-resolved dual-photoelectron extraction method comprises a calibration stage and a subsequent measurement stage. In the calibration stage, the time-of-arrival distribution of each channel is collected under a pulsed light source, and the time-of-flight background parameters of each channel are determined. In the subsequent measurement stage, photoelectron events are collected separately, and the time-of-flight background parameters are corrected and deducted to obtain corrected times. Based on the corrected times, photoelectron events from different spatial channels are paired two by two in the same cycle to generate candidate pairs. It is judged whether the candidate pairs meet a preset correlation condition, and the event pairs meeting the condition are output as dual-photoelectron events. The application realizes decoupling of the time-of-flight bias and the emission time difference, reduces the accidental coincidence probability, improves the dual-photoelectron extraction accuracy, and is suitable for continuous or pulsed light sources.

Description

Technical Field

[0001] This invention relates to the field of photoelectron spectroscopy, specifically to an angle-resolved dual photoelectron extraction method based on time-of-flight background calibration. Background Technology

[0002] Angle-resolved photoelectron spectroscopy (ARPS) is an important experimental technique for studying the electronic structure of materials. It obtains the electronic band distribution by measuring the energy and momentum of photoelectrons. In recent years, with the deepening research on electron correlation effects, two-photoelectron and multi-photoelectron processes have gradually attracted attention. By performing correlation analysis on multiple photoelectrons emitted in the same excitation process, electron correlation information that is difficult to reveal by single-electron measurements can be obtained.

[0003] In angle-resolved dual-photoelectron measurements, it is often necessary to distinguish which electrons originate from the same photon excitation process among multiple electron events. To this end, existing techniques mostly employ coincidence selection methods based on time windows, i.e., correlating multiple detected electron events within a given time window. However, in actual experiments, the flight time of electrons from the sample surface to the detector is not only related to the initial energy of the electrons but is also affected by various factors such as detector geometry and differences in the detection area.

[0004] Especially under event-driven detection conditions, there are often systematic differences in flight time between different spatial channels or detection areas. This difference is particularly evident under continuous light source conditions: since electron emission time itself is random, if absolute arrival time or simple time difference is directly used as the criteria for matching, the flight time difference can easily be mistaken for the emission time difference, thus introducing mismatch or accidental matching and reducing the accuracy of dual photoelectron extraction.

[0005] To mitigate the aforementioned effects, some techniques attempt to analyze electron arrival times by using the emission time of light pulses as a time reference under pulsed light source conditions. However, existing methods typically only focus on the overall time distribution and fail to establish corresponding time-of-flight background models for different spatial channels. When these methods are directly applied to continuous light source measurements, it remains difficult to effectively distinguish between time-of-flight differences and emission time differences.

[0006] Therefore, in angle-resolved dual photoelectron measurements, there is still a lack of a method that can accurately distinguish between flight time differences and emission time differences, reduce the probability of accidental coincidence, and improve the reliability of dual photoelectron extraction by calibrating the flight time background of different spatial channels and subtracting it in subsequent measurements under event-type detection conditions. Summary of the Invention

[0007] This invention provides an angle-resolved dual photoelectron extraction method based on time-of-flight background calibration, aiming to solve the technical problem in existing angle-resolved dual photoelectron measurements that, due to the systematic time-of-flight bias in different spatial channels, it is impossible to accurately distinguish between time-of-flight differences and electron emission time differences under event-type detection conditions. As a result, in dual photoelectron correlation judgment, the time-of-flight bias is easily misjudged as emission time difference, introducing a large number of random coincidence events, making it difficult to achieve high-reliability dual photoelectron extraction.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides an angle-resolved dual-photoelectron extraction method based on time-of-flight background calibration, comprising: a calibration stage and a subsequent measurement stage; The calibration phase includes the following steps: Time-of-flight background calibration steps: Under the condition of irradiating the sample with a pulsed light source, the arrival time distribution of photoelectron events in different spatial channels is collected using the light pulse emission time as a time reference, and the time-of-flight background parameters of the corresponding spatial channels are determined based on the arrival time distribution. The subsequent measurement phase includes the following steps: Event time correction step: After completing the flight time background calibration step, photoelectron events are collected separately, and the arrival time of the collected photoelectron events is corrected to obtain the corrected time after deducting the flight time background parameters; Dual photoelectron candidate event screening steps: Within the same measurement period or time window, photoelectron events from different spatial channels are paired up based on the correction time to generate candidate event pairs; Dual photoelectron event output steps: Determine whether the candidate event pair meets the preset association conditions, and output the candidate event pair that meets the conditions as a dual photoelectron event.

[0009] Furthermore, the flight time background parameters include distribution center values, characteristic times, or statistics, which are used to characterize the systematic flight time bias of the corresponding spatial channel.

[0010] Furthermore, in the flight time background calibration step, the center position of the arrival time distribution is determined by Gaussian fitting or centroid method, and used as the flight time background parameter.

[0011] Furthermore, the time-of-flight background calibration step further includes: summarizing the time-of-flight background parameters of different space channels to form a time-of-flight background baseline mapping table. The baseline mapping table is a two-dimensional or three-dimensional lookup table, which is used to quickly query the time-of-flight background parameters of the corresponding space channel in the event time correction step.

[0012] In the event time correction step, the correction time t corrThe original arrival time t is obtained by subtracting the corresponding space channel's flight time background parameter t0, i.e., t corr =t t0.

[0013] Furthermore, the event time correction step is performed during real-time data acquisition or during offline data processing.

[0014] Furthermore, in the dual-photoelectronic event output step, the preset correlation condition includes calculating the time difference Δt between event pairs based on the correction time. corr And determine the time difference Δt corr Is it less than a preset time window threshold τ? Does it satisfy the time difference Δt? corr Candidate event pairs that are less than the preset time window threshold τ are output as two-photoelectron events for subsequent angle-resolved two-photoelectron analysis; those that do not meet the time difference Δt are output as two-photoelectron events. corr Candidate event pairs that are less than a preset time window threshold τ are discarded.

[0015] Furthermore, the preset association conditions also include energy conservation and / or momentum conservation constraints to further suppress accidental coincidence events.

[0016] Furthermore, the photoelectronic events on which the subsequent measurement stage is based are collected under conditions where the sample is irradiated by a continuous light source or a pulsed light source.

[0017] Furthermore, the photoelectronic events are collected by an event-type detector, which includes a time delay line detector, a CMOS sensor, or a time digitization readout module.

[0018] Compared with the prior art, the present invention has the following beneficial effects: This invention employs a time-of-flight background calibration step to pre-acquire time-of-flight background parameters for different spatial channels under pulsed light source conditions. Then, an event time correction step subtracts the arrival times of subsequent measurement events, ensuring that the corrected time primarily reflects the relative emission times of electrons. This directly solves the problem in existing technologies where time-of-flight bias is misinterpreted as emission time difference, thus improving the reliability of the physical meaning of two-photoelectron correlation.

[0019] This invention employs a dual-photoelectron candidate event screening step, pairing events together based on correction time to generate candidate event pairs; then, a dual-photoelectron event output step applies preset correlation conditions to the candidate event pairs for selection. Since the correction time eliminates systematic time-of-flight bias, selection based on the time difference of the correction time can more accurately reflect the temporal correlation of electron emission, thereby effectively suppressing accidental coincidence events caused by time-of-flight differences and improving the purity and accuracy of dual-photoelectron extraction.

[0020] The event time correction step of this invention does not depend on the pulse characteristics of the light source, and the corrected time can be directly used for correlation selection. Therefore, this method is applicable to both pulsed light source conditions and continuous light source conditions, overcoming the limitation of existing methods in effectively extracting pulsed light under continuous light source conditions, and significantly expanding the applicability of angle-resolved pulsed light measurement.

[0021] The method of this invention does not depend on specific detector internal structures or dedicated hardware; it only requires the addition of background calibration, time correction, and correlation selection modules to the data acquisition and processing flow. Therefore, this method is easy to integrate and implement in existing angle-resolved photoelectron spectroscopy systems, and has good versatility and application value. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of flight time background calibration according to an embodiment of the present invention; Figure 2 This is a schematic diagram of event time correction based on time-of-flight background according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the dual-photoelectronic correlation selection process based on the correction time according to an embodiment of the present invention; Figure 4 This is a schematic diagram showing the comparison of the intensity (normalized) of the matching events before and after time-of-flight background subtraction under the same testing and screening conditions in an embodiment of the present invention. Figure 5 This is a schematic diagram comparing the joint distribution of energy and angle of event pairs before and after time-of-flight background subtraction under the same test and screening conditions in an embodiment of the present invention. Time window filtering). Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0024] This invention provides an angle-resolved dual-photoelectron extraction method based on time-of-flight background calibration, comprising: a calibration stage and a subsequent measurement stage; The calibration phase includes the following steps: S1. Flight time background calibration steps; The subsequent measurement phase includes the following steps: S2. Event time correction steps; S3. Steps for screening candidate events for two-photoelectron events; S4. Two-photoelectronic event output steps.

[0025] The calibration phase steps are as follows: The specific implementation steps for time-of-flight background calibration are as follows: like Figure 1As shown, under the condition of irradiating the sample with a pulsed light source, the arrival time distribution of photoelectron events in different spatial channels is collected using the emission time of the light pulse as a time reference.

[0026] For each spatial channel (corresponding to specific detection coordinates (x,y) or physical coordinates (E,k)), the arrival times of a large number of photoelectron events are collected to form an arrival time distribution curve. Figure 1 (a) Red curve in the image). The center location of this distribution is determined using a Gaussian fitting method. Figure 1 (a) Blue dashed line in the figure), the center position value is defined as the time-of-flight background parameter t0 of the channel, where time broadening is used to characterize the time response characteristics of the channel.

[0027] The flight time background parameters t0 corresponding to different space channels are summarized to form a flight time background baseline mapping table. This mapping table is a two-dimensional or three-dimensional lookup table, which is used to quickly look up the flight time background parameters of the corresponding space channel in subsequent steps. Figure 1 (b) shows the distribution of t0 as a function of energy / momentum (or probe coordinates) on a three-dimensional surface, used to characterize the systematic time-of-arrival offset caused by flight path differences, analyzer dispersion geometry, and electronic link delays. The blue markers indicate a selected channel location, with t0 corresponding to a given value. Figure 1 The result was obtained by fitting from (a) in the dataset.

[0028] Through the calibration steps described above, the systematic time-of-flight bias of each spatial channel caused by factors such as differences in electron flight paths, analyzer dispersion geometry, and electronic link delays can be accurately quantified. After establishing a time-of-flight background baseline mapping, a background subtraction basis that accurately corresponds to the spatial location of each photoelectron event in subsequent measurements can be provided. This is the foundation for effectively decoupling time-of-flight bias from emission time differences.

[0029] After completing the above calibration steps, the obtained time-of-flight background parameters will be saved for time correction of photoelectron events in subsequent measurements.

[0030] The subsequent measurement phase steps are as follows: In this invention, "subsequent measurement" refers to the photoelectron event acquisition process performed after the time-of-flight background calibration step to obtain actual experimental data for dual photoelectron analysis. In the subsequent measurement, the sample can be illuminated with a continuous or pulsed light source, and the acquired photoelectron events will be time-corrected and correlated based on the time-of-flight background parameters obtained during the calibration phase.

[0031] The specific implementation of the event time correction procedure is as follows: In subsequent measurements, after completing the time-of-flight background calibration step, photoelectron events are collected separately (in this embodiment, the sample is illuminated by a continuous light source). For each collected photoelectron event, the time-of-flight background baseline mapping is queried according to its spatial channel to obtain the corresponding time-of-flight background parameter t0. Then, according to t corr =t Correction is performed at t0, where t is the original arrival time. corr This is for time correction.

[0032] like Figure 2 As shown, before correction, electrons with different energies and momentum have different time-of-flight biases. Figure 2 (a), (b), and (c) in the text). Figure 2 (a) illustrates the dependence of the time-of-flight background baseline on photoelectron kinetic energy: time of flight varies with photoelectron kinetic energy. The change can be approximated as a monotonic relationship (e.g., approximately linear within a certain range), corresponding to The calibration curve. Figure 2 (b) illustrates the dependence of the time-of-flight background baseline on photoelectron momentum: time of flight varies with photoelectron momentum. The change can exhibit a symmetrical parabolic shape (reflecting the difference in effective flight path caused by different launch angles), corresponding to... or The cross-sectional relationship. Figure 2 (c) in the diagram illustrates the three-dimensional curved surface and the time-of-flight background baseline. Distribution in space This surface can be obtained by fitting / interpolating calibration data, and can be used to quickly look up the background baseline of any event in measurement mode.

[0033] After correction, the time of all electrons is unified to the same reference, forming an approximately constant plane. Figure 2 (d) Cyan plane (or a unified reference value) to achieve a unified time base across channels / energy and momentum.

[0034] In this embodiment, the calibration step is performed during real-time data acquisition, but it can also be performed during the offline data processing stage as needed. Real-time calibration is suitable for experimental scenarios with online monitoring and real-time feedback, while offline calibration facilitates flexible adjustment of calibration parameters and backtracking.

[0035] The event time correction step directly eliminates the systematic time offset between different channels by subtracting the time-of-flight background parameter of the space channel to which each event belongs. The corrected time t corrIt no longer includes fixed delays introduced by detector geometry and electronic links, but primarily reflects the relative emission times of electrons. This processing allows subsequent time-based correlation selection to be truly based on the temporal relationship of electron emission, rather than the artificial bias introduced by the detector.

[0036] The specific implementation of the two-photoelectron candidate event screening process is as follows: Within the same measurement period, photoelectron events from different spatial channels are paired up based on the calibration time to generate candidate event pairs. For example... Figure 3 As shown, the input event stream contains event number, probe coordinates, and correction time. Adjacent events are paired up, and the correction time difference Δt between candidate event pairs is calculated. corr .

[0037] Pairing events based on their corrected time ensures that the event pairs entering the candidate pool have been free from the interference of systematic time-of-flight bias. Since the corrected time is unified to the same benchmark, events from different spatial channels can be directly compared in time without having to consider time offsets between channels, greatly simplifying the complexity of correlation selection and improving the physical correlation of candidate event pairs.

[0038] The specific implementation of the two-photoelectron event output steps is as follows: Determine whether the candidate event pair meets the preset association conditions. In this embodiment, the preset association conditions include: such as Figure 3 As shown, the time difference condition is: |Δt corr |<τ, where the time window threshold τ=2 ns. This threshold is set according to the system's time resolution, usually 2 to 3 times the time resolution, to balance the detection rate and the false positive rate.

[0039] Event pairs that meet the above conditions are output as two-photoelectron events for subsequent angle-resolved two-photoelectron analysis. Event pairs that do not meet the above conditions are discarded.

[0040] Furthermore, the preset correlation conditions also include energy conservation and / or momentum conservation constraints to further suppress accidental coincidence events.

[0041] Energy conservation constraint: The sum of the energies of the two electrons should be close to the energy of the incident photon, with an allowable error range of ±0.1 eV. This constraint is based on the physical laws of the two-photon emission process: when one photon excites two electrons, the sum of their energies should be equal to the photon energy minus the sum of the binding energies of the two electrons.

[0042] Momentum conservation constraint: The momentum vectors of the two electrons must satisfy a symmetry relationship. In crystalline samples, the emission of two photoelectrons must also satisfy momentum conservation, which is usually manifested as the symmetry of the distribution of the two electrons in momentum space.

[0043] By employing a combined selection process based on multiple pre-defined correlation conditions, the accuracy of dual-photoelectronic identification is significantly improved. The time difference condition, based on the correction time, directly utilizes the time unification advantage derived from step 2; the energy conservation and momentum conservation constraints further filter from a physical law perspective, effectively suppressing accidental coincidence events. Figure 4 and Figure 5 As shown, the experimental results indicate that, after adopting this method, the events exhibit a clear peak in the time difference distribution and clear physical laws in the energy and momentum distribution, proving that this method can effectively extract real two-photoelectron events from a uniform background.

[0044] Figure 4 The comparison results of coincidence event intensity before and after time-of-flight background subtraction are shown under the same test and screening conditions. Without time-of-flight background subtraction (blue curve), the Δt distribution of coincidence events is approximately uniform, mainly corresponding to accidental coincidence background; therefore, the normalized coincidence intensity does not differ significantly between points. After time-of-flight background subtraction (red curve), the Δt distribution shows a significant peak near Δt=0. The broadening of the peak originates from the system's temporal resolution, indicating that true coincidence events are effectively extracted. Therefore, time-of-flight background subtraction can effectively suppress accidental coincidence events, allowing the coincidence results to highlight true coincidence event signals from a uniform background, improving the physical reliability of coincidence selection and the purity of subsequent two-photoelectron correlation analysis.

[0045] Figure 5 This demonstrates a comparison of the joint distribution of energy and angle (momentum) of event pairs before and after time-of-flight background subtraction under the same test conditions and screening conditions. Without time-of-flight background subtraction ( Figure 5 In (a) and (c) of the data, the event pairs exhibit an approximately uniform scatter distribution in the energy and angular dimensions, lacking physical structure, indicating that they mainly originate from a random coincidence background; after deducting the time-of-flight background ( Figure 5 In (b) and (d) of the data, the event pairs exhibit clear physical laws: the energy distribution tends to be evenly distributed, and the angular distribution shows a symmetrical relationship, which conforms to the constraints of energy conservation and momentum conservation. Therefore, time-of-flight background subtraction can effectively suppress random coincidence backgrounds, allowing real physical event pairs to stand out from the uniform background, thereby improving the purity and reliability of the coincidence screening results.

[0046] The embodiments of the present invention are not limited to the above-described examples. Various modifications can be made without departing from the technical concept of the present invention. Methods for determining time-of-flight background parameters: In addition to the distribution center value, characteristic time or other statistical measures can also be used; in addition to Gaussian fitting, centroid method, peak localization method or other statistical methods can also be used. Multiple parameter determination methods can be flexibly selected according to specific experimental conditions and data characteristics, improving the adaptability and robustness of the method.

[0047] The representation of time-of-flight background baseline mapping: In addition to the lookup table method, a function fitting method can also be used to subtract background by fitting the mathematical expression of t0(E,k). The function fitting method can perform smooth interpolation when the calibration points are sparse, reducing the workload of calibration experiments, and facilitating theoretical analysis and model extrapolation.

[0048] The time window threshold for association selection can be dynamically adjusted according to the system's temporal resolution or experimental requirements. For example, a narrower time window can be used in systems with higher resolution to reduce accidental coincidences. Dynamically adjusting the time window can optimize the balance between detection rate and false positive rate under different experimental conditions, improving the flexibility of the method.

[0049] Energy and momentum conservation constraints: These can be flexibly set according to specific sample characteristics and experimental conditions. For example, the allowable error range can be adjusted appropriately for different material systems. This flexible physical constraint setting makes this method applicable to a variety of material systems and experimental needs, thus expanding its application scope.

[0050] Detector Types: The method of this invention is applicable to various event-type detectors, including but not limited to time-delay line detectors, CMOS sensors, and time digitization readout modules. Good detector compatibility allows this method to be directly implemented on various existing experimental setups without replacing core equipment, reducing the cost and barriers to widespread application.

[0051] Light source conditions: The method of this invention is applicable to both continuous and pulsed light source conditions for dual photoelectron measurements. This broad applicability to various light source conditions allows the method to meet diverse experimental needs, and it is particularly valuable for applications in continuous light source synchrotron radiation devices.

[0052] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the technical scope of the present invention. Therefore, any minor modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. An angle-resolved dual-photoelectron extraction method based on time-of-flight background calibration, characterized in that, include: Calibration phase and subsequent measurement phase; The calibration phase includes the following steps: Time-of-flight background calibration steps: Under the condition of irradiating the sample with a pulsed light source, the arrival time distribution of photoelectron events in different spatial channels is collected using the light pulse emission time as a time reference, and the time-of-flight background parameters of the corresponding spatial channels are determined based on the arrival time distribution. The subsequent measurement phase includes the following steps: Event time correction step: After completing the flight time background calibration step, photoelectron events are collected separately, and the arrival time of the collected photoelectron events is corrected to obtain the corrected time after deducting the flight time background parameters; Dual photoelectron candidate event screening steps: Within the same measurement period or time window, photoelectron events from different spatial channels are paired up based on the correction time to generate candidate event pairs; Two-photoelectron event output steps: Determine whether the candidate event pair meets the preset association conditions, and output the candidate event pair that meets the conditions as a two-photoelectron event; the preset association conditions include calculating the time difference Δtcorr of the event pair based on the correction time, and determining whether the time difference Δtcorr is less than the preset time window threshold τ; the candidate event pair that meets the condition that the time difference Δtcorr is less than the preset time window threshold τ is output as a two-photoelectron event for subsequent angle-resolved two-photoelectron analysis; the candidate event pair that does not meet the condition that the time difference Δtcorr is less than the preset time window threshold τ is discarded.

2. The angle-resolved dual-photoelectron extraction method according to claim 1, characterized in that, The flight time background parameters include distribution center values, characteristic times, or statistics, which are used to characterize the systematic flight time bias of the corresponding spatial channel.

3. The angle-resolved dual-photoelectron extraction method according to claim 1, characterized in that, In the flight time background calibration step, the center position of the arrival time distribution is determined by Gaussian fitting or centroid method, and used as the flight time background parameter.

4. The angle-resolved dual-photoelectron extraction method according to claim 1, characterized in that, The time-of-flight background calibration step further includes: summarizing the time-of-flight background parameters of different space channels to form a time-of-flight background baseline mapping table. The baseline mapping table is a two-dimensional or three-dimensional lookup table, which is used to quickly query the time-of-flight background parameters of the corresponding space channel in the event time correction step.

5. The angle-resolved dual-photoelectron extraction method according to claim 1, characterized in that, In the event time correction step, the correction time t corr The original arrival time t is obtained by subtracting the corresponding space channel's flight time background parameter t0, i.e., t corr =t t0.

6. The angle-resolved two-photoelectron extraction method according to claim 1, characterized in that, The event time correction step is performed during real-time data acquisition or during offline data processing.

7. The angle-resolved dual-photoelectron extraction method according to claim 1, characterized in that, The preset association conditions also include energy conservation and / or momentum conservation constraints to further suppress accidental coincidence events.

8. The angle-resolved dual-photoelectron extraction method according to claim 1, characterized in that, The photoelectronic events on which the subsequent measurement stage is based are collected under conditions where the sample is irradiated by a continuous light source or a pulsed light source.

9. The angle-resolved dual-photoelectron extraction method according to claim 1, characterized in that, The photoelectronic events are collected by an event-type detector, which includes a time delay line detector, a CMOS sensor, or a time digitization readout module.

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