Optoacoustic gas sensor and method

Abstract

This invention relates to a photoacoustic gas sensor, comprising a measuring cavity for containing gas, a light source, a microphone, and a light source driver. The light source driver has a control signal that modulates the intensity of emitted light according to the control signal. The control signal drives the light source to drive the light source with periodic intensity in a sequence of time windows, wherein the frequency of intensity modulation in one time window is different from the frequency of intensity modulation in the next time window, and the frequency sequence thus defined is periodic with a period of n. f ≥2.

Description

Technical Field

[0001] This invention relates to a photoacoustic gas sensor, a method for determining a measurement value using the photoacoustic gas sensor, and a corresponding computer-implemented method. Background Technology

[0002] Photoacoustic gas sensors utilize the interaction of electromagnetic radiation (light) with matter to determine the concentration of a target gas in a carrier gas. Molecules in the target gas absorb light energy when the light energy corresponds to the energy level difference of the rotational / vibrational states of the molecules. These excited molecules can then distribute the energy they have gained through collisions with neighboring molecules in the carrier gas: generating pressure fluctuations that propagate at the speed of sound and can be measured, for example, using a microphone. The more light-absorbing molecules in the gas, the greater the pressure fluctuations and therefore the stronger the microphone signal. If the light intensity is now periodically modulated, the microphone signal is also modulated accordingly, and the target gas concentration can be determined without offset using, for example, phase-locked demodulation of the microphone signal. Pressure fluctuations in the carrier gas caused by vibration or noise (which may also have the same periodicity) may interfere with this determination.

[0003] EP3550286A1 describes a small, simple photoacoustic gas sensor in which the measuring unit forms a measuring volume on a substrate, yet the gas sensor still provides accurate concentration values ​​of gas components. A microphone has a bottom port that points towards the substrate and is communicatively connected to the measuring volume.

[0004] EP3859307A1 discloses a method for operating a photoacoustic gas sensor, wherein in a first step, an acoustic reference signal is received in a measurement cavity, the reference signal is analyzed to obtain noise information, and a filter function is adapted based on the noise information; and then in a second step, the light intensity is modulated based on the filter function, and the acoustic measurement signal is analyzed based on the filter function to obtain information about the target gas in the measurement cavity.

[0005] The purpose of this invention is to provide a simple photoacoustic gas sensor and a corresponding measurement method, which are resistant to interference in the form of vibration or noise and can provide measurement data without interruption. Summary of the Invention

[0006] In this context, a photoacoustic gas sensor, a method for determining a measurement using the photoacoustic gas sensor, and a corresponding computer-implemented method are proposed herein according to independent claims 1, 6, 8, 9, and 10; a computer program according to claim 11 and a computer-readable storage medium according to claim 12 are also proposed.

[0007] The photoacoustic gas sensor includes a measurement cavity for containing gas, a light source for emitting light into the measurement cavity, a microphone for detecting sound waves in the measurement cavity and adapted to output a corresponding sound signal, and a light source driver connected to provide a control signal for the light source. The intensity of the emitted light is modulated according to the control signal. The control signal drives the light source with periodic intensity modulation at a frequency within a sequence of time windows. The frequency of intensity modulation in one time window is different from the frequency of intensity modulation in the next time window, and this frequency sequence is periodic with a period of n. f ≥2.

[0008] Vibration and / or acoustic noise (caused by motors, compressors, or other rotating or oscillating equipment in the vicinity of the photoacoustic sensor) may be periodic. This vibration and / or acoustic noise is received by a microphone and superimposed as interference signals on the effective photoacoustic signal. If one frequency component of the interference signal is close to the frequency of the effective photoacoustic signal, this can lead to a loss of accuracy (noise in the measurement) and / or a loss of precision (the measurement may be noise-free but biased). This occurs when the frequency difference Δf between the interference signal and the effective signal is small. In this context, small means: τ is the integration time (the total duration during which data is sampled and the concentration value is ultimately determined by the total duration).

[0009] We consider a frequency of f PA Amplitude is a, phase shift is photoacoustic signal y k Its frequency f s Time-based collection:

[0010] We assume: the ratio It is a natural number (i.e., the acoustic period is an integer multiple of the sampling period), and we perform a discrete Fourier transform on length N:

[0011] Where w = 0, 1, 2, ... are the indices of the Fourier window. The values ​​of the Fourier coefficients are independent of w because y in the above formula... k Both the complex exponent and the exponent have a period of N.

[0012] The duration of the Fourier transform is The photoacoustic signal therefore has exactly one period within the Fourier window. For this reason, the target quantity (i.e., the photoacoustic amplitude a) is contained only in the Fourier coefficients. and In this context, the two Fourier coefficients form a conjugate complex pair because the photoacoustic signal is real-valued. These two Fourier coefficients correspond to frequencies ±f. PA In existing technology, only calculations are performed. This is because it contains all the information about the photoacoustic signal. Of course, the Fourier window can also be chosen to be longer. However, a duration that is an integer multiple of N is preferred. If the duration is equal to qN (q is a natural number), then the information about the amplitude of the photoacoustic signal is located in the Fourier coefficients Y. q and Y qN-q superior.

[0013] We now consider the same photoacoustic signal as described above, but with an amplitude of b and a frequency of f. intf and phase shift as The interference signals are superimposed. Therefore, the total signal is given as follows:

[0014] Discrete Fourier transform of length N:

[0015] in, These are terms that vary only with respect to the interfering signal and may change from one Fourier window to the next. This invention provides an apparatus and a method that, on the one hand, detect the presence of the interfering signal, and on the other hand, mitigate the influence of such interfering signal on concentration measurements.

[0016] In existing technologies, the light source is modulated at a fixed frequency. = (N is a natural number); this guarantees that the amplitude of the photoacoustic signal is only within the Fourier coefficient range, as described above. and middle.

[0017] In this invention, the frequency of the photoacoustic signal changes periodically and traverses n f ≥2 distinct values, n f It is a natural number. Therefore, the measurement time is divided into time windows, referred to here as modulation windows, during which the intensity of the light source is modulated at a fixed frequency. This modulation frequency changes periodically from one modulation window to the next: the sequence of modulation windows corresponds to the sequence of modulation frequencies, and this sequence of modulation frequencies is n f For period ( Therefore, with a frequency f0 for a certain duration D0, then with another frequency f1 for duration D1, and so on until finally with a frequency f0 for duration D2. nf-1 frequency f nf-1The intensity of the light source is modulated, and then modulated again at frequency f0, and so on. All D m They can be equal. Furthermore, it is advantageous that all selected frequencies satisfy… N m It is a natural number (here and in the following text, m in the subscripts f and N should always be understood as m modulo n). f Then, regarding the frequency... The amplitude information of the photoacoustic signal is only within the length N. m The first (and last) Fourier coefficients of the Fourier transform. The modulation window advantageously has multiple Fourier window lengths, meaning the number of samples in a single modulation window is much greater than N. m (That is, the photoacoustic signal has multiple cycles within each modulation window). Advantageously, the duration D of the modulation window... m This selection ensures that an integer number of cycles of the photoacoustic signal to be measured always fit into the corresponding modulation window, i.e. q m It is a natural number. It goes without saying that the duration of the modulation window is not constant and the modulation windows do not need to be adjacent to each other, for example, to save energy.

[0018] Then, for example, for each defined as n f The measurement cycle of the set of consecutive modulation windows outputs a single measurement value. Frequency shifting ensures that at least one frequency in each measurement cycle is unaffected or significantly unaffected by interference signals. Advantageously, the timescale in which the frequency characteristics of the measurement cycle remain substantially unchanged relative to the interference is short.

[0019] In a preferred embodiment, the photoacoustic gas sensor further includes a signal processor connected to receive and process the acoustic signal and determine and output a measurement value within a measurement period, the measurement period being defined as n of the sequence. f The measurement cycle consists of several consecutive time windows. In each time window of the measurement cycle, the signal processor demodulates the acoustic signal at the frequency of the control signal in that time window to obtain an effective value, and demodulates the acoustic signal at the frequency of the control signal in the next time window to obtain an interference value. The determination of the measured value takes into account both the effective value and the interference value.

[0020] During each modulation window, the microphone signal can be demodulated first at the current photoacoustic frequency and then at the photoacoustic frequency of the next modulation window, for example, by explicitly calculating the above sum of selected Fourier coefficients or all Fourier coefficients using a commonly used FFT algorithm. The first demodulation yields the amplitude (RMS value, as in the prior art) of the photoacoustic signal, and the second demodulation (interference value) yields the interference power at the next photoacoustic frequency (high interference power means that an interference signal exists at this frequency and will interfere with the photoacoustic measurement in the next modulation window). If the interference power is high, the photoacoustic amplitude measured in the next modulation window is ignored because the amplitude is expected to contain noise and / or bias. Therefore, 2n is generated in each measurement cycle. f There are n intermediate values. f One effective value α m (m=0, ...,n) f -1) and n f Predicted interference value β m (m=0,…,n) f -1). 2n f Several intermediate values ​​are aggregated into a single measurement value, for example:

[0021] In this method, the effective value α of each modulation window is weighted using a weighting function of the interference value β from the previous modulation window. The weighting function is a monotonically decreasing function, such as a step function, which vanishes above a certain threshold. This simple measurement scheme has the particular advantage of outputting a continuous series of gas concentrations because it eliminates the need to wait for acoustic reference measurements and analysis of the noise, during which no effective signal is generated.

[0022] In the modulation window m, when the frequency f m When modulating the photoacoustic signal, we calculate the first Fourier coefficient:

[0023] The first Fourier coefficient provides a measure of the photoacoustic amplitude 'a', but also includes potential interference terms. The contribution of . The superscripts m and w in Y1 denote the modulation window and the Fourier window in the modulation window. The first parameter in square brackets is the modulation frequency in the modulation window and therefore belongs to y. k [f m ]:

[0024] The second parameter in square brackets represents the demodulation frequency, that is, the frequency of this Fourier coefficient that belongs to the complex exponential term (Note: N). m =f s / f m),

[0025] This calculation is existing technology. However, we also additionally calculate the value corresponding to frequency f. m+1 The Fourier coefficients of (the modulation frequency of the light source in the next modulation window), where the modulation frequency is always f. m :

[0026] in, It is in f m The photoacoustic signal at f m+1 The contribution of the measured spectral amplitude (spectral leakage effect). This complex quantity should be approximated to zero by the modulation window average (provided that f...). m and f m+1 (Sufficiently different). Alternatively, the duration of the modulation window can be chosen such that Q is precisely averaged. This is, for example, when the duration of the modulation window is simultaneously N. m and N m+1 The situation described occurs when the value is a multiple of [a certain value]. Interference item. The contribution may also be averaged (e.g., when f intf with f m (sufficiently different at the same time), but because f intf It is usually unknown, so it cannot be derived. Therefore, it applies to:

[0027] in, This means averaging all Fourier windows w=0, ..., M-1 in the modulation window.

[0028] In the next modulation window m+1, the photoacoustic signal has f m+1 The frequency, and the measurement is:

[0029] If we assume that the interference in modulation window m+1 also exists in the previous modulation window m, then we can estimate the interference term:

[0030] If this value is large relative to the power of a pure photoacoustic signal, then we can assume that the current measurement... Significant deviations exist and should be ignored. The above equation is generally not applicable when there are no absolute values. Otherwise, the measurement can be easily corrected by subtraction: .

[0031] Therefore, when the interference value (that is, in the modulation window m at frequency f) m+1Demodulation, where the photoacoustic frequency is f m When the threshold is exceeded, the effective value of photoacoustic sound is ignored. (That is, in the modulation window m+1 at frequency f) m+1 Demodulation, where the photoacoustic frequency is f m+1 (or a smaller weighted value is included in the measurement value of the measurement period).

[0032] In one embodiment of the invention, the reception of raw data (i.e., microphone signals) and the determination of effective values, interference values, and thus measured values ​​can be performed asynchronously: the raw data can be locally cached in a storage medium, such as a memory chip that is part of a signal processor, and / or sent to the cloud for further data processing. The determination of the measured values ​​and the final gas concentration values ​​can then be completed in the cloud, where calibration computational capabilities and / or computation time are provided. The advantage of this embodiment is that the simpler and, in particular, the cheaper the signal processor can be selected, the lower the requirements for its computational and storage performance.

[0033] In one embodiment, the photoacoustic gas sensor includes a measurement cavity for containing gas, a light source for emitting light into the measurement cavity, a microphone for detecting sound waves in the measurement cavity and adapted to output a corresponding acoustic signal, a light source driver connected to provide a control signal for the light source (modulating the intensity of the emitted light according to the control signal), and a signal processor connected to receive and process the acoustic signal and determine and output the measured value. The control signal drives the light source with periodic intensity modulation at a frequency in one time window of a sequence, and the signal processor demodulates the acoustic signal at the frequency of the control signal in the first time window to obtain an effective value and demodulates the acoustic signal at a second frequency not equal to the first frequency to obtain an interference value in the subsequent second time window. The intensity modulation frequency in the subsequent second time window is based on the interference value, and the determination of the measured value in the first time window takes the effective value into account.

[0034] Especially in the modulation window m+1 at frequency f m+1 Interference measurement is performed before the optical acoustic measurement (i.e., at frequency f in the modulation window m). m+1 (Time demodulation) and (if the interference exceeds a certain threshold) at frequency f m+1 After ignoring the effective value, the measurement can also be completely omitted. In one embodiment, the effective photoacoustic signal can be calculated in the modulation window m. and all other frequencies interference value (not only f) m+1 Then, the modulation frequency in the next modulation window m+1 is changed to the frequency with the minimum interference value. Attached Figure Description

[0035] Figure 1 The effect of periodic interference on the effective signal is shown based on the interference frequency.

[0036] Figure 2 The mean and variance of the first averaged Fourier coefficients are derived from the difference between the excitation frequency and the interference frequency.

[0037] Figure 3 The figure shows a series of measurement data from a photoacoustic gas sensor operating sequentially at three different frequencies.

[0038] Figure 4 The invention provides a comparison between the determination of measured values ​​and the moving average method.

[0039] Figure 5 A photoacoustic gas sensor is shown.

[0040] Figure 6 The time curve of the control signal of the light source is shown schematically. Detailed Implementation

[0041] The measurement results of the specific embodiment are as follows: Figure 3 and Figure 4 As shown in the figure. The photoacoustic CO2 gas sensor 1 with measuring cavity 2 (in...) Figure 5 (Illustrated schematically) It operates in indoor air with approximately 400 ppm CO2. The microprocessor 5 is configured to periodically drive the light source 3 alternately for 1 second at frequencies f0 = 41.7 Hz, f1 = 55.6 Hz, and f2 = 62.5 Hz. The light source 3 is a heater (i.e., a blackbody radiator) plus a frequency filter at 4.3 μm (where the CO2 absorption peak exists, which is also the absorption valley for H2O). This frequency filter can achieve temperatures up to 500°C by means of pulse density modulation (100 kHz) of the 5 V operating voltage. The control signal is a square wave with a duty cycle of 50% and a frequency of f0 = 41.7 Hz, f1 = 55.6 Hz, and f2 = 62.5 Hz. m (m=0, 1, 2), between two values ​​representing room temperature and a target temperature of approximately 500°C. The time curve of the control signal is... Figure 6 As shown in the diagram. The measurement period 7 is divided into three modulation windows 8, 9, and 10. Within each modulation window, the control signal has corresponding modulation periods 11, 12, and 13. Due to the non-zero thermal mass of the heater, the time curve of the actual temperature of the heater is naturally only approximately a square wave. From time t = 90 seconds to t = 230 seconds, the gas sensor is now subjected to vibration with a peak acceleration of 1g at a frequency of 55Hz. Figure 3 The above figure shows the 1-second average of the real part of the measured amplitude. As a function of time (seconds), the signals correspond to three frequencies. We take the real part because the Fourier transform has been rotated so that the effective signal has only the real part. The measurement at 55.6 Hz is severely affected by interference and fluctuates around the correct value (normalized to 1).

[0042] exist Figure 1 This illustrates a calculation example of the effect of periodic interference signals on the Fourier coefficients. In the graph above, the vertical axis represents the absolute value of the 1-second average of the first Fourier coefficient. ,in, Furthermore, Np represents the number of Fourier windows adapted to a length N within 1 second, and in the graph below, the vertical axis represents the argument, and the horizontal axis represents time (seconds). The parameters are a=b=1. f PA =40Hz, f s =1kHz, N=25, and the interference frequency f intf The five different values ​​are given. When the interference frequency approaches the photoacoustic frequency, the absolute value begins to oscillate, with an increased amplitude and decreased frequency. This is because the two signals transition between constructive and destructive interference through different 1-second windows. When the interference frequency equals the photoacoustic frequency, the signals are completely constructive and the absolute value is constant but has a deviation of 2.

[0043] exist Figure 3 The figure in the middle shows the standard deviation of the real part of the measured amplitude. It is worth noting that the 55.6 Hz frequency, which is most affected by vibration, has the smallest standard deviation. This is because, during a 1-second period, the photoacoustic signal and the interference signal caused by vibration are coherent. Therefore, the measured amplitude is approximately constant but subject to bias.

[0044] exist Figure 2 China with the help of Figure 1 The calculation example explains this situation in more detail. Figure 2 The above diagram shows calculations for 10 seconds. The average value is calculated, and the standard deviation is shown in the figure below as a function of the frequency difference between the photoacoustic frequency and the interference frequency. Within a frequency difference of approximately 1 Hz, the average value is approximately correct (1 in this calculation example). For frequency differences below 1 Hz, an integration time of 1 second is insufficient to provide spectral resolution to distinguish the contributions of the photoacoustic signal from those of the interference signal. Measurement The standard deviation comprises non-zero contributions from both signals. As the frequency difference approaches zero, the standard deviation generally increases. However, as described above, there exist specific frequency differences where the standard deviation is zero (the mean is constant but has a bias).

[0045] exist Figure 3The following figure shows the interference power. During the period when the gas sensor was subjected to vibration, the interference power at 55.6 Hz was several orders of magnitude greater than at other frequencies, indicating the presence of strong interference signals near 55.6 Hz. When determining the measured value within a 3-second measurement period, the effective value at the photoacoustic frequency of 55.6 Hz can be ignored or the weighting weakened. The results of different weightings are... Figure 4 As shown in the diagram. The dashed curve represents the 1-second average of the run, as shown in... Figure 3 As shown in the diagram above. The dashed line represents the weighted average of the run over 3 seconds, with the same weight of 1 / 3 for all three frequencies. Clearly, if there is interfering vibration, this measurement will oscillate strongly around the correct value of 1. The solid line represents the weighted average of the run over 3 seconds, where the weight for the frequency 55.6 Hz is set to zero if the interference power exceeds a threshold of, for example, 25000. The effect of interference on this vibration is almost imperceptible.

[0046] List of reference numerals

[0047] 1. Photoacoustic gas sensor

[0048] 2 measuring chamber

[0049] 3 light sources

[0050] 4 microphones

[0051] 5 Light Source Drivers

[0052] 6 signal processors

[0053] 7 measurement cycles

[0054] 8 to 9 modulation windows

[0055] 10 to 12 modulation cycles

Claims

1. A photoacoustic gas sensor (1), the photoacoustic gas sensor comprising: Measuring chamber (2) for containing gas. A light source (3) is provided for emitting light into the measurement cavity. A microphone (4) is provided for detecting sound waves in the measurement cavity (2) and adapted to output the corresponding sound signal. A light source driver (5) is connected to provide control signals for the light source (3), and the intensity of the emitted light is modulated according to the control signals. The control signal drives the light source with periodic intensity modulation at a frequency within a time window of the sequence (8, 9, 10). The frequency of intensity modulation in one time window (8, 9, 10) is different from the frequency of intensity modulation in the next time window, and The frequency sequence defined in this way is periodic, with a period of n. f n f It is a natural number greater than or equal to two.

2. The photoacoustic gas sensor according to claim 1, further comprising: A signal processor (6) is connected to receive and process the acoustic signal and determine and output the measurement value within a period (7), the measurement period being defined as n of the sequence. f A series of consecutive time windows (8, 9, 10). The signal processor (6) demodulates the acoustic signal with the frequency of the control signal in each time window (8, 9, 10) of the measurement cycle (7) to obtain an effective value, and demodulates the acoustic signal with the frequency of the control signal in the next time window to obtain an interference value. Furthermore, the determination of the measured value takes into account both the effective value and the interference value.

3. The photoacoustic gas sensor according to claim 2, wherein, The measured value is a function of the effective value and the interference value.

4. The photoacoustic gas sensor according to claim 3, wherein, The measured value is a linear combination of the effective values, and the weighting of the linear combination includes a monotonically decreasing function of the interference values.

5. The device according to claim 2, 3 or 4, wherein, The difference between two consecutive frequencies in the frequency sequence is greater than the reciprocal of the duration of the time window (8, 9, 10) for demodulating the acoustic signal at the two frequencies.

6. A photoacoustic gas sensor, wherein the photoacoustic gas sensor comprises: Measuring chamber (2) for containing gas. A light source (3) is provided for emitting light into the measurement cavity. A microphone (4) is provided for detecting sound waves in the measurement cavity and adapted to output the corresponding sound signal. A light source driver (5) is connected to provide control signals for the light source, and the intensity of the emitted light is modulated according to the control signals. A signal processor (6) is connected to receive and process the acoustic signal and determine and output the measured value. The control signal drives the light source with periodic intensity modulation at a frequency in the first time window (8, 9, 10) of the sequence. The signal processor (6) demodulates the acoustic signal at the frequency of the control signal in the first time window to obtain an effective value, and demodulates the acoustic signal at a second frequency that is not equal to the first frequency to obtain an interference value. The frequency of intensity modulation in the subsequent second time window is based on the interference value. Furthermore, the determination of the measured value within the first time window takes into account the valid value.

7. The device according to claim 5, wherein, The difference between the first frequency and the second frequency is greater than the reciprocal of the duration of the first time window (8, 9, 10).

8. A method for determining a measured value using a photoacoustic gas sensor (1), the method comprising: A measuring cavity (2) for containing gas is provided, a light source (3) for emitting light into the measuring cavity (2) is provided, and a microphone (4) for detecting sound waves in the measuring cavity (2) and adapted to output corresponding signals is provided. A light source driver (5) provides a control signal for the light source (3) and modulates the intensity of the emitted light according to the control signal. A signal processor (6) is provided for receiving and processing the acoustic signals and determining and outputting the measured values. The light intensity is modulated with a periodic function of a frequency within a sequence of time windows (8, 9, 10), the frequency in one time window (8, 9, 10) being different from the frequency in the next time window, and the frequency sequence thus defined is periodic with a period of n. f n f It is a natural number greater than or equal to two. In one modulation window, the acoustic signal is demodulated at the frequency of the control signal in the modulation window to obtain an effective value, and in the next modulation window, the acoustic signal is demodulated at the frequency of the control signal to obtain an interference value. In a modulation window, n is defined as the sequence. f The measurement value is determined by taking into account the effective value and the interference value during the measurement period of each continuous modulation window (7). Output the measured value.

9. A method for determining a measured value using a photoacoustic gas sensor (1), the method comprising: A measuring cavity (2) for containing gas is provided, a light source (3) for emitting light into the measuring cavity (2) is provided, and a microphone (4) for detecting sound waves in the measuring cavity (2) and adapted to output corresponding sound signals is provided. A light source driver (5) provides a control signal for the light source (3) and modulates the intensity of the emitted light according to the control signal. A signal processor (6) is provided for receiving and processing the acoustic signals and determining and outputting the measured values. The light intensity is modulated as a periodic function of a frequency within a sequence of time windows. Within a time window, the acoustic signal is demodulated at the frequency of the control signal within that time window to obtain an effective value, and the acoustic signal is demodulated at a second frequency not equal to the first frequency to obtain an interference value. In the next time window, the frequency of the control signal is set based on the interference value. The measured value is determined within a time window, taking into account the effective value. Output the measured value.

10. A computer-implemented method, the method comprising the following steps: The acoustic signal is received, which represents the sound wave in the measurement cavity (2) of the photoacoustic gas sensor (1), where the gas is subjected to light with light intensity modulation, which is periodic in frequency within a sequence of time windows, the frequency in one time window (8, 9, 10) being different from the frequency in the next time window, and the frequency sequence thus defined is periodic with a period of n. f n f It is a natural number greater than two. Receive a configured frequency, wherein the configured frequency corresponds to the frequency of the frequency sequence. The acoustic signal is segmented into signal segments corresponding to the time window. A signal segment is demodulated at the configured frequency within the corresponding time window to obtain an effective value, and the acoustic signal is demodulated at the configured frequency corresponding to the next time window to obtain an interference value. For each n defined as the sequence f The measurement period (7) of the signal segment of each continuous time window is determined with regard to the effective value and the interference value.

11. A computer program comprising instructions that, when executed by a computer, cause the computer to perform the method according to claim 9.

12. A computer-readable storage medium comprising instructions that, when executed by a computer, cause the computer to perform the method according to claim 9.

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