Computer-implemented method for generating event-averaged time-resolved spectra

Abstract

A computer-implemented method for generating an event-averaged time-resolved spectrum from a plurality of time-resolved spectra of charged particles emitted from a surface (3) of a sample (2) on which events periodically repeat, is disclosed, the method comprising the steps of: receiving (101) a plurality of time-resolved spectra covering a plurality of events from a charged particle analyzer (1); obtaining (102) a selected portion of at least one of the plurality of time-resolved spectra; determining (103) a time point of another event among the plurality of events by matching the at least one selected portion with other portions of the plurality of time-resolved spectra to find similar portions; and generating (104) an event-averaged time-resolved spectrum of the event based on the plurality of time-resolved charged particle energy spectra and the determined time point.

Description

[Technical Field]

[0001] The present invention relates to charged particle spectroscopy, and in particular to generating an event-averaged time-resolved spectrum from a plurality of time-resolved spectra of charged particles emitted from the surface of a sample in a periodic event, the time-resolved spectrum being obtained using a charged particle analyzer. [Background technology]

[0002] Understanding surface structure under reaction conditions and correlating it with catalytic reactivity has been a rapidly growing research field for decades, and many new in situ surface-sensing methods have been developed for catalytic reaction studies. One such technique, ambient pressure X-ray photoelectron spectroscopy (APXPS), allows simultaneous probing of surface atoms, adatoms, molecules on the surface, and the gas phase near the surface at mbar pressures while the chemical reaction of interest occurs on the surface. APXPS, which uses a charged particle analyzer to detect photoelectrons from the element of interest, is a relatively slow technique, typically requiring acquisition times of several minutes to achieve a sufficient signal-to-noise ratio, even with powerful fourth-generation synchrotron sources. The long acquisition time is not due to the slow response time of the charged particle analyzer, which easily reaches millisecond or even microsecond time resolution, but rather to the weak photoelectron probe signal. Because the signal is measured on top of a large background signal of inelastically scattered electrons, it simply takes time to detect the weak signal of elastically scattered core electrons from a given element before peak fitting can be performed reliably. Therefore, in situ catalytic reaction studies performed using charged particle analyzers have so far been limited to studying steady-state surfaces at specific fixed temperature, gas composition, and pressure conditions, and are unable to track surface dynamics in situ, and in particular how quickly the catalytic surface responds to changing temperature, gas composition, and pressure.

[0003] The above problems also exist when using other techniques such as SXRD (surface X-ray diffraction), PM-IRRAS (polarized light-modulated infrared reflectance spectroscopy), and PES (photoelectron spectroscopy), and also when the charged particles being analyzed are not electrons but, for example, positively or negatively charged ions or various elementary particles.

[0004] Therefore, there is a need to improve the signal quality (eg, signal-to-noise ratio, etc.) using techniques such as those described above, so that fast reactions can be tracked. Summary of the Invention [Problem to be solved by the invention]

[0005] It is an object of the present invention to provide a method for improving signal quality measures (eg, signal-to-noise ratio) of charged particle spectra using a charged particle analyzer.

[0006] This object is achieved by a computer-implemented method according to independent claim 1.

[0007] Another object of the present invention is to provide a computer program for generating an event-averaged and time-resolved spectrum, the computer program comprising instructions that, when executed by at least one processor of a computer, cause the at least one computer to perform a method for improving signal quality measures (e.g., signal-to-noise ratio, etc.) of charged particle spectra using a charged particle analyzer.

[0008] This object is achieved by a computer program according to claim 14.

[0009] Further advantages are obtained by the features of the dependent claims. [Means for solving the problem]

[0010] According to a first aspect of the present invention, there is provided a computer-implemented method for generating an event-averaged time-resolved spectrum from a plurality of time-resolved spectra of charged particles emitted from a surface of a sample, the events repeating periodically at the surface and the plurality of time-resolved spectra being obtained using a charged particle analyzer. The method comprises receiving a plurality of time-resolved spectra covering a plurality of events from the charged particle analyzer, the period being defined by the time between adjacent events in time, and each time-resolved spectrum comprising information on the distribution of charged particles as a function of a physical property for an interval of magnitude of the physical property. The method further comprises obtaining at least one selected portion of the series of the plurality of time-resolved spectra, the at least one selected portion comprising a spectrum from a portion of the period in which the event occurs and at least a portion of the intensity interval of the physical property. The method also comprises determining time points for other events among the plurality of events by matching the at least one selected portion with other portions of the series of the plurality of time-resolved spectra to find similar portions, and generating an event-averaged time-resolved spectrum for the event based on the series of the plurality of time-resolved charged particle energy spectra and the determined time points.

[0011] The distribution information can be intensity, which reflects the number of charged particles as a function of a physical property.

[0012] By obtaining at least one selected portion and matching it with other portions of a series of time-resolved spectra to find similar portions, the time point of a subsequent event in the series can be accurately determined. Therefore, the method is not susceptible to variations in the period between two subsequent events. This allows for the generation of an event-averaged time-resolved spectrum with good signal quality (e.g., good signal-to-noise ratio) from a periodically acquired spectrum with poor signal quality. The periodic repetition of events can be achieved in a variety of ways. The periodic repetition of events can be achieved by oscillating the surface conditions. Examples of such oscillating conditions include oscillating pressure at the surface, oscillating temperature at the surface, oscillating gas composition at the surface, oscillating electromagnetic fields at the surface, oscillating optical fields incident on the surface, and oscillating gas temperature at the surface.

[0013] The present invention uses pattern recognition of the raw data to determine each event and generate an event average signal rather than an externally triggered signal from a vibration condition.

[0014] The at least one selected portion may be obtained based on data entered by a user. Alternatively, the at least one selected portion may be obtained automatically using a computer program.

[0015] At least one selected portion may be obtained during reception of a series of the plurality of time-resolved spectra, matching may be initiated during reception of the series of the plurality of time-resolved spectra, and the event-averaged time-resolved spectrum may be generated during reception of the series of the plurality of time-resolved spectra. By starting the process of generating the event-averaged time-resolved spectrum while reception of the series of the plurality of time-resolved spectra is in progress, acquisition of the spectra may be terminated when sufficiently good results are obtained.

[0016] The generation of the event-averaged time-resolved spectrum may be terminated when a termination condition is met, which may be one of receiving a termination input signal or a signal quality measure of the event-averaged time-resolved spectrum being better than a predetermined value. The termination condition allows the acquisition of the spectrum to be terminated as soon as possible. This can save time, for example, saving the time required to use an X-ray source to generate charged particles on the surface of the sample. When a synchrotron is used to generate X-rays, the X-ray source is typically a very limited resource.

[0017] The termination condition may be that the signal-to-noise ratio exceeds a predetermined threshold, which is an objective measure of signal quality.

[0018] The signal quality measure may alternatively be one of the contrast and peak-to-value ratio of the event-averaged image formed by the multiple spectra.

[0019] The computer-implemented method may also comprise sending a control signal to control the cycle of events, which may be advantageous, for example, if the method is also configured to perform other steps automatically.

[0020] The control signals may control at least one of the gas mixture at the surface, the gas pressure at the surface, the temperature of the surface, the electromagnetic field at the surface, the optical field incident on the surface, and the gas temperature at the surface. Once the computer-implemented method determines that the event-averaged spectrum is good enough, it may automatically change the physical conditions of the experiment and begin generating other spectra.

[0021] The multiple time-resolved spectra may comprise multiple data points, and matching is performed by subtracting the data of each data point in the selected portion from the data of the corresponding data point in the other portions of the series of multiple time-resolved spectra, summing the differences to obtain a result as a function of time for the other portions of the series, and finding the minimum of the result to determine the time point for the other events. The data of each data point may be intensity, reflecting the number of charged particles as a function of a physical property. That is, for each successive other portion, the difference between the data of each data point in the selected portion and the data of the corresponding data point in the other portions is integrated. This results in an integrated difference as a function of time. The integrated difference as a function of time describes how well the selected portion matches the successive other portions as the selected portion is moved along the time axis of the series of multiple time-resolved spectra. The minimum integrated difference reflects a matching event.

[0022] Matching may comprise fitting a polynomial to the result of an integration of the difference between the selected portion and other portions of the series to obtain the timing of the event. By fitting a polynomial to the integration result, the time of the event can be determined with better accuracy.

[0023] An event may be used in generating an event-averaged time-resolved spectrum only if its minimum is below a predetermined threshold. By using only a portion of the minimum, the quality of the event-averaged spectrum is improved.

[0024] Matching can be performed by convolving the selected portion with other portions of a series of multiple time-resolved spectra, obtaining the result as a function of the time point of the other portions of the series, and determining the time point of the other event by finding the maximum of the result. Convolution is an alternative to integrating the difference between data points as described above.

[0025] The matching may comprise fitting a polynomial to a result of a convolution of the selected portion with another portion of the series of multiple time-resolved spectra to obtain a result. By fitting a polynomial to the result of the convolution, the time point of the event can be determined with greater precision.

[0026] The physical property is one of the following: a starting angle of the charged particle, an energy of the charged particle, and a starting position of the charged particle.

[0027] According to a second aspect of the present invention there is provided a computer program for generating an event-averaged time-resolved spectrum, the computer program comprising instructions which, when executed by at least one processor of a computer, which may be a remote computer, cause the computer to perform the method according to the first aspect of the present invention.

[0028] Preferred embodiments of the present invention will now be described with reference to the drawings. [Brief explanation of the drawings]

[0029] [Figure 1] 1 shows an apparatus in which a charged particle analyzer is used to measure the spectrum of a reaction in a sample. [Figure 2] 1 is a three-dimensional (3D) waterfall plot obtained using the setup of FIG. 1 of multiple spectra obtained over three oscillations of the gas composition that induced the event on the surface. [Figure 3] The corresponding image plots are shown in Figure 2, along with enlarged images of selected areas. [Figure 4] 1 is a flow diagram of a method according to one embodiment of the present invention. [Figure 5] The integral of the absolute difference in intensity between each data point in the selected section and the corresponding data point in the comparison section is shown as a function of data point displacement. [Figure 6] A single CO adsorption-desorption event on the surface is shown, cut out from the image plot of FIG. [Figure 7] A single spectrum from the image in Figure 6 is shown. [Figure 8] The corresponding event average image for 48 events is shown in FIG. [Figure 9] A single spectrum from the event-averaged image of FIG. 8 is shown. DETAILED DESCRIPTION OF THE INVENTION

[0030] The present invention will be described by the following detailed description of illustrative, non-limiting example embodiments, with reference to the accompanying drawings, in which like features in different drawings are designated by the same reference numerals, and in which the drawings are not drawn to scale.

[0031] FIG. 1 illustrates an apparatus in which a charged particle analyzer 1 with a detector 11 is used to measure the spectrum of a reaction at a sample 2, more specifically at a surface 3 of the sample 2. Electromagnetic radiation 4 is directed to illuminate the surface of the sample 2 to induce the emission of charged particles from the surface 3 of the sample 2. The apparatus includes a gas cell 5 in which the sample is placed. The gas cell 5 has a volume small enough to rapidly oscillate the gas composition in the gas cell. The apparatus also includes a heater 14 for rapidly heating the sample. Thus, the temperature, pressure, and gas composition at the surface 3 of the sample 2 can be altered when investigating reactions at the surface 3 of the sample. A computer 8 with a processor 21 is connected to the charged particle analyzer 1 and receives data from the detector 11 of the charged particle analyzer 1. The apparatus of FIG. 1 also includes a gas supply unit 16 that provides a precise mixture and pressure of gases to the gas cell 5. As indicated by the dashed line between the gas supply unit 16 and the computer 8, the computer 8 can also be configured to control the heater 14 and / or the gas oscillations with respect to the mixture and / or pressure. The computer 8 can be a remote computer.

[0032] The following describes the study of the carbon monoxide (CO) adsorption process on a surface and the reverse process of CO desorption. The gas composition in the gas cell 5 is repeatedly switched by alternating pulses of a CO-rich gas mixture (2.7:1 CO:O for a 45-second period) and an O2-rich gas mixture (1:2.7 CO:O for a 100-second period). While the gas composition alternates between the CO2-rich and O2-rich gas mixtures, electromagnetic radiation in the form of X-rays illuminates the surface 3 of the sample 2, inducing the emission of photoelectrons from the surface 3 of the sample 2. A portion of the photoelectrons emitted from the surface 3 are incident on the charged particle analyzer 1, where their kinetic energy is analyzed to obtain a spectrum. The spectra are continuously collected at a fast frame rate or acquisition rate of approximately 1-50 Hz. The detector can be a camera detector, a delay-line detector, or a pulse-count detector. These various detectors are well known to those skilled in the art and will not be described in detail here.

[0033] Figure 2 shows a waterfall plot of multiple spectra obtained over three gas composition oscillations using the apparatus of Figure 1. The waterfall plot shows binding energy, electron counts or intensity, and time. The CO gas-phase signal is visible as peak 12, and its apparent binding energy shift, signaling the work function shift at the sample surface caused by CO adsorption, is shown as peak 13. CO in the gas is also visible as peak 6 in Figure 2, while CO adsorbed on surface 3 of sample 2 is shown as peak 7 in Figure 2. The increase in CO gas concentration in the gas cell is visible as the onset of CO gas peak 6, and the increase in O gas concentration is visible as the end of CO gas peak 6. CO adsorption and desorption from surface 3 constitute two events that are periodically repeated by oscillating the gas composition as described above.

[0034] Figure 3 is an image plot corresponding to Figure 2, covering multiple time-resolved spectra. The gas composition changes from O2-rich to CO2-rich at 105, 250, and 395 seconds in Figure 3. The gas composition changes from CO2-rich to O2-rich at 150, 295, and 440 seconds in Figure 3. Each gas composition change represents an event. As can be seen in Figure 3, the multiple time-resolved spectra in Figure 3 cover multiple events, and the time between adjacent events on the time axis defines a period T. Each time-resolved spectrum contains information about the distribution of charged particles as a function of the physical properties of CO and O2, respectively, within two different composition periods. The multiple spectra are a data matrix, where the number of pixels / data points 15 along the time axis is equal to the number of spectra registered per second multiplied by the registration time, while the number of pixels / data points 15 along the energy axis is equal to the detector's energy resolution multiplied by the energy interval. The data at each data point is an intensity that reflects the number of charged particles at that data point. In Figure 3, darker colors correspond to higher intensities.

[0035] As mentioned above, the physical property may alternatively be the temperature or gas pressure of the sample, which may be varied within the interval, preferably between two different values.

[0036] Shown at the bottom of Figure 3 is the time-averaged spectrum of the image plot.

[0037] The method according to the present invention will now be described with reference also to Figure 4, which shows a flow chart of a method according to one embodiment of the present invention. In a first step 101, the computer 8 receives from the charged particle analyzer 3 a number of time-resolved spectra covering a number of events. The time between adjacent events in time defines a period T, as shown in Figure 3. Each time-resolved spectrum contains information on the distribution of charged particles as a function of a physical property for an intensity interval of the physical property. In the example of Figures 2 and 3, the physical property is the binding energy, which lies in the interval from 283 to 293 eV.

[0038] Instead of the binding energy, the physical property may be, for example, one of the following: the starting angle of the charged particles, the energy of the charged particles, and the starting position of the charged particles.

[0039] The series of multiple time-resolved spectra shown in Figures 2 and 3 constitute an acquisition matrix in which the number of pixels / data points 15 along the energy axis depends on the number of pixels / data points 15 on the detector 11 of the charged particle analyzer 1, and the number of pixels / data points 15 along the time axis depends on the frame rate / acquisition rate and acquisition time per second.

[0040] In a second step 102, at least one selected portion 9 of a series of time-resolved spectra is obtained. The selected portion can be obtained based on user input, but alternatively, it can be obtained automatically. In FIG. 3, a first selected portion 9 and a second selected portion 10 are obtained. A close-up of the first selected portion 9 is also shown in FIG. 3, revealing individual data points, such as marked data point 15. The selected portion includes spectra from at least a portion of the time period during which the event occurs and the intensity interval of the physical property. Thus, the first selected portion 9 covers the time period for the CO adsorption event and the energy interval covering the binding energy shift indicative of the work function shift of the sample surface caused by CO adsorption on the surface. The second selected portion 10 covers the reverse event of CO desorption. The obtained first selected portion 9 and second selected portion 10 may alternatively be referred to as stamp signals. The first selected portion 9 and second selected portion 10 constitute portions of the series of time-resolved spectra equivalent to the acquisition matrix.

[0041] In a third step 103, the first selected portion 9 and the second selected portion 10 are matched with other portions of the series of time-resolved spectra to find similar portions and thereby determine the time points of other events in the plurality of events. Each of the first selected portion 9 and the second selected portion 10 comprises a plurality of pixels / data points 15.

[0042] To match the first and second selected portions 9 and 10 with similar portions of the acquisition matrix, each of the first and second selected portions 9 and 10 is displaced forward in the time axis of the acquisition matrix by individual pixel steps, i.e., displacing one spectrum in the time axis towards a new comparison portion of the acquisition matrix. For each pixel displacement, the integral of the absolute difference between the intensity of each data point in the selected portion and the intensity of the corresponding pixel in the comparison portion is determined.

[0043] When the first selected portion 9 is placed over the same spectral fingerprint of the transition occurring on the surface, the integral is minimized, i.e., a match is found. A match is found for the first selected portion 9 when it is compared with the first matching portion 9' and the second matching portion 9". A match is found for the second selected portion 10 when it is compared with the third matching portion 10' and the fourth matching portion 10". The integral as a function of pixel offset is shown in Figure 5. In Figure 3, the first and second selected portions cover only a portion of the energy interval measured using the detector of the charged particle analyzer. The energy interval used in Figure 3 is chosen to cover clear changes in the spectrum during the event. Of course, the size of the energy interval may be chosen differently.

[0044] An appropriate function is fitted to each minimum to locate the minimum as accurately as possible. This procedure yields a table of timing signals that define the transition to a CO-covered surface.

[0045] The result is a table of precise times for forward switching events onto the CO2-covered surface and for reverse switching events as the CO2 desorbs. Based on the precise times, spectra from different events can be accurately event-averaged. After determining the precise times for the forward and reverse switching events, the forward integration portions 19, 19', 19" and the reverse integration portions 20, 20', 20" are extracted from the acquisition matrix and event-averaged. Accurate event averaging is achieved even when there is jitter in the event timing.

[0046] Figure 6 shows an image of the spectrum containing the process of CO adsorption onto the surface of the sample in Figure 1 and the reverse process. Figure 7 shows a single spectrum from the image in Figure 5.

[0047] Based on the determined timing of the events, forward integrated portions 19, 19', 19" and backward integrated portions 20, 20', 20" are extracted from the acquisition matrix and event-averaged to generate the image of FIG. 8, which shows an event-averaged image of the multiple integrated spectra shown in FIG. 6, in a fourth step 104. Due to possible variations in the period between the first and second events, the averaging between events is not perfectly accurate. Therefore, the event-averaged image of FIG. 8 is not perfectly accurate around the 260 s time point. However, since no notable changes occur in the spectrum between events, any errors in the event-averaged image are irrelevant. The entire energy range of the detector is used in the event-averaged image. From the event-averaged image of FIG. 8, an event-averaged time-resolved spectrum of the event can be extracted, as shown in FIG. 9. As can be clearly seen from a comparison of FIGS. 7 and 9, the signal-to-noise ratio of the spectrum is significantly improved using the method of the present invention. Of course, other quality measures than signal-to-noise ratio can also be used (e.g., the contrast or peak-to-peak ratio of the event-averaged image formed by multiple spectra).

[0048] To optimize the quality of the event-averaged image of the multiple integrated spectra, it is not necessary to use all events in the averaging. A threshold Th can be applied to the curve in Figure 5. Then, only events belonging to the minimum value below the threshold Th are used in the event averaging. All events belonging to the minimum value above the threshold can also be used in the individual event averaging.

[0049] At least one selected portion can be obtained during reception of a series of multiple time-resolved spectra. By configuring the computer-implemented method in this manner, matching can be initiated during reception of a series of multiple time-resolved spectra, and an event-averaged time-resolved spectrum can be generated during reception of the series of time-resolved spectra. This allows for real-time study of the generation of the event-averaged image of multiple integrated spectra shown in FIG. 8 and the event-averaged time-resolved spectrum shown in FIG. 9. This allows averaging to be terminated when the results shown in FIGS. 8 and 9 are sufficiently good. The generation of the event-averaged time-resolved spectrum can be terminated when a termination condition is met. The termination condition can be one of receiving a termination input signal or a signal quality measure of the event-averaged time-resolved spectrum being better than a predetermined value.

[0050] The above-described embodiments may be modified in many ways without departing from the scope of the invention, which is defined solely by the appended claims and their limitations.

Claims

1. 1. A computer-implemented method for generating an event-averaged time-resolved spectrum from a plurality of time-resolved spectra of charged particles emitted from a surface (3) of a sample (2), wherein events are periodically repeated at the surface (3), and the plurality of time-resolved spectra are obtained using a charged particle analyzer (1); receiving (101) a plurality of time-resolved spectra covering a plurality of events from the charged particle analyzer (1), the time between adjacent events in time defining a period (T), each time-resolved spectrum containing information on the distribution of charged particles as a function of a physical property for an intensity interval of said physical property; obtaining (102) at least one selected portion (9, 10) of the plurality of time-resolved spectra, the at least one selected portion (9, 10) comprising a spectrum from a portion of a cycle in which an event occurs and at least a portion of an intensity interval of the physical property; determining (103) time points of other events of the plurality of events by matching the at least one selected portion (9, 10) with other portions of the plurality of time-resolved spectra to find similar portions; generating (104) an event-averaged time-resolved spectrum of the event based on the plurality of time-resolved spectra and the determined time point.

2. 2. The computer-implemented method of claim 1, wherein the at least one selected portion (9, 10) is obtained based on data entered by a user.

3. 3. The computer-implemented method of claim 1, wherein the at least one selected portion (9, 10) is obtained during reception of the plurality of time-resolved spectra, the matching is initiated during reception of the plurality of time-resolved spectra, and the event-averaged time-resolved spectrum is generated during reception of the plurality of time-resolved spectra.

4. 4. The computer-implemented method of claim 1, wherein generating the event-averaged time-resolved spectrum is terminated when a termination condition is met, the termination condition being one of receiving a termination input signal and a signal quality measure of the event-averaged time-resolved spectrum being better than a predetermined value.

5. The computer-implemented method of claim 4 , wherein the signal quality measure of the event-averaged time-resolved spectrum being better than a predetermined value is a signal-to-noise ratio above a predetermined threshold.

6. The computer-implemented method of claim 1 , further comprising sending a control signal to control the cycle of events.

7. 7. The computer-implemented method of claim 6, wherein the control signals control at least one of a gas mixture at the surface, a gas pressure at the surface, a temperature at the surface, an electromagnetic field at the surface, an optical field incident on the surface, and a gas temperature at the surface.

8. 8. The computer-implemented method of claim 1, wherein the plurality of time-resolved spectra comprises a plurality of data points, and the matching is performed by subtracting data for each data point in the selected portion from data for a corresponding data point in another portion of the plurality of time-resolved spectra, summing the differences, obtaining a result as a function of time point in the other portion of the plurality of time-resolved spectra, and finding a minimum of the obtained result to determine the time point of the other event.

9. 9. The computer-implemented method of claim 8, wherein the matching comprises fitting a polynomial to a sum of differences between the selected portion and other portions of the plurality of time-resolved spectra to determine a time point of the event.

10. 10. The computer-implemented method of claim 8 or 9, wherein an event is used in generating the event-averaged time-resolved spectrum only if its minimum value is below a predetermined threshold.

11. 11. A computer program for generating an event-averaged time-resolved spectrum, the computer program comprising instructions that, when executed by at least one processor (21) of a computer (8), cause the computer (8) to perform the computer-implemented method of any one of claims 1 to 10.

Images