METHOD AND DEVICE FOR DETECTING A PARTICLE

Description

[0001] The invention relates to a method and a device for detecting one or more particles. In particular, the present invention relates to a method and a device designed to detect the occurrence of a particle based on a characteristic signature.

[0002] Methods and devices for detecting particles are known in principle. For example, a sensor arrangement for detecting and characterizing particles is known from the publication DE 10 2019 209 213 A1. This sensor arrangement uses, in particular, a characteristic field distribution of a laser beam, which exhibits a different combination of local intensity and local polarization direction at each position. The degree of polarization (DOP) is one of the measured variables.

[0003] The evaluation device according to DE 10 2019 209 213 A1 uses, in particular, the formation of a sum signal or a difference signal to determine a particle trajectory consisting of particle position, particle velocity, and particle acceleration in two spatial directions. The particle size can be determined from the amplitude value of the Euclidean sum ( x 2 + y 2 ) of the signal components.

[0004] Each particle is represented by a characteristic signature. However, the method for determining particle properties disclosed in DE 10 2019 209 213 A1 is prone to errors, particularly with regard to false-positive particle detections. Furthermore, several adjustment parameters are necessary to calibrate the detection method to properties, such as noise, of the data set.

[0005] US 2011 / 0 221 892 A1 discloses a method for calculating a drop delay in a jet using flow cytometry. US 2017 / 0 322 137 A1 discloses a method and system for characterizing particles using flow cytometry.

[0006] Systems and methods for detecting particles can be found in the documents US 2022 / 0 003 657 A1 and US 2017 / 0 191 923 A1.

[0007] It is therefore an object to provide an improved method and an improved device for detecting particles.

[0008] This object is achieved by a method according to claim 1, comprising capturing a time series of a particle detection, segmenting the time series and classifying the segments of the time series.

[0009] The segmentation of the time series comprises transforming the time series into a transformed feature space, which can also be referred to as original space or τ-space, low-pass filtering of the transformed space, in particular the transformed signal, and back-transforming the transformed space, in particular the signal, into the time domain.

[0010] Classifying the time series segments involves determining one or more peaks, in particular one or more double peaks, in the acquired (original) time series based on the low-pass filtered and inversely transformed signal from the feature space. In particular, the segmentation provides the position of one or more peaks or double peaks, which are then located and classified in the original time series as originally acquired. The original time series is used as a basis instead of the transformed or inversely transformed time series, since the signal level is distorted in the inversely transformed space due to the transformation.

[0011] Whether there are one or more single peaks or one or more double peaks depends primarily on the type of time series acquisition and whether one or more peaks are detected per particle. The following will focus on the example with one or more characteristic double peaks, although the lessons learned are also applicable to time series with characteristic single peaks.

[0012] Based on these calculations, it can then be determined whether a particle was actually detected or whether it was a false positive. In principle, the method (and also the device explained below) can output a signal indicating the detection of a particle and / or indicating how many particles were detected.

[0013] According to the invention, the occurrence of one or more particles over time is first recorded in a time series.

[0014] In this case, characteristic features that can be derived from a characterizing measured variable are depicted in the time series, for example a degree of polarization of a laser beam or an intensity distribution of electromagnetic radiation that changes due to being covered by a particle. This change can be detected by a suitable detector, such as a CCD camera, photodiode, or infrared camera, and recorded over time. Changes in digitized pulses, such as electrocardiograms or Geiger counter pulses, can also serve as a basis for the time series. The term "particle" is not limited to size. The method according to the invention can also be used to detect other objects, such as articles that occur, in particular randomly, along a time series.

[0015] The particles randomly appear at a detector and generate an amplitude dependent on the particle size. The measurement principle suggests that continuous random processes exist for the occurrence of the events, the particle size, and the particle velocity. The sensor array captures individual realizations of these properties and thus samples the corresponding distribution functions of the observed random process. The time series itself, however, can be considered discontinuous, since individual pulses occur that ideally do not overlap. Therefore, the measurement effect is nonexistent in the period between the events; only the detector noise is recorded.

[0016] All further steps, in particular segmentation and classification as well as their sub-steps described below, are carried out by a suitable processor.

[0017] The signal processing of the data segmentation is partly carried out in the frequency-transformed τ-space, which is subsequently referred to as the original domain. The original time series itself is assigned the property of image domain, so that the Fourier transformation (FT) has a unique mathematical relationship DOP ( t ) = ( after (τ)) between the two views.

[0018] The method's functionality is based on the effect that continuous and band-limited signals in the original range map to band-limited pulse spectra in the image range. In the present case, the image range is already given as a real-valued spectrum by the pulse sequence and has a phase position of zero, i.e. arg ( DOP ( t )) = 0.

[0019] The method according to the invention thus makes it possible to determine essential parameters, such as a characteristic peak width or a signal-to-noise ratio or noise behavior, from the continuous signal by the global approach after ( τ ), i.e., in frequency-transformed τ-space. An individual evaluation of these parameters for each individual peak during segmentation is thus unnecessary. A sliding window, as in some common methods, is therefore not necessary, since the probable positions of the peaks or double peaks are the result of the segmentation.

[0020] According to one embodiment, the segmentation further comprises generating a single-sideband spectrum from the time series by appropriately supplementing it with zeros so that necessary mathematical properties are maintained. The transformation of the modified time series into a frequency-transformed space is performed by transforming the single-sideband spectrum of the time series.

[0021] In particular, the time series of length N is interpreted as a single-sideband spectrum. To further calculate using the discrete Fourier transform, the time series must be supplemented with N zeros, resulting in the single-sideband spectrum of an analytical signal. The analytical signal in the original range is obtained by Fourier transforming the modified time series.

[0022] According to one embodiment, the segmenting further comprises calculating the signal bandwidth in the after(τ) signal. The signal-to-noise ratio and the characteristic peak width depend on this.

[0023] This makes it particularly advantageous to enable the original area after (τ) and with a low-pass ( TP (τ) · after (τ)) → DOP *( t ). The filtered (time series) signal is created DOP *( t ) .

[0024] According to one embodiment, transforming the frequency-transformed space back into the time domain comprises discarding the imaginary part of the after (τ) signal.

[0025] This makes it particularly easy to correct the phase detuned by the filtering, arg ( DOP* ( t )) , to reconstruct.

[0026] According to one embodiment, determining a peak or double peak comprises determining the inflection points of the phase curve arg ( DOP *) and / or finding zeros.

[0027] According to the invention, determining a peak or double peak comprises determining a global maximum and one or more local maxima in the amplitude function, max | DOP *( t )| .

[0028] In addition, a local minimum can optionally be determined, which is located between the global maximum and a local maximum.

[0029] This makes it particularly safe to rule out a false-positive determination.

[0030] According to the invention, determining a peak or double peak comprises determining a normalized distance between the global maximum and the one or more local maxima.

[0031] According to one embodiment, classifying the segments of the time series further comprises normalizing the time series segments.

[0032] According to one embodiment, classifying the segments of the time series further comprises determining an error probability resulting from the signal-to-noise ratio of the feature space.

[0033] According to one embodiment, classifying the segments of the time series further comprises filtering and / or windowing the original time series.

[0034] According to one embodiment, the method further comprises determining a particle size based on the amplitude of the determined peak or double peak.

[0035] According to one embodiment, the method further comprises determining a particle velocity based on the distance of the determined peak or double peak.

[0036] According to one embodiment, classifying the segments of the time series further comprises evaluating the detected peaks with the amplitude-dependent error probability in order to exclude false-positive pulses.

[0037] The object mentioned at the outset is also achieved by a device for detecting a particle, comprising a processor and a memory in which instructions are stored which, when executed by the processor, carry out a method for detecting a particle according to one of the previously described embodiments.

[0038] In particular, the device also comprises one or more sensors configured to record the time series, or the device has access to such a sensor. Likewise, the device can also have one or more means configured to generate a characteristic field distribution of electromagnetic radiation. For example, a laser beam can have a different combination of a local intensity and a local polarization direction at each position. The device can accordingly have a laser source for generating the laser beam. Further, in particular, the device can have one or more features of the device as described in DE 10 2019 209 213 A1 or communicate with them.

[0039] The means for generating the local intensity and the local polarization direction can be designed to generate a laser beam with radially symmetric polarization directions.

[0040] In other words, embodiments of the present method and device divide a given time series into non-uniformly distributed sections, and determine the positions and amplitudes of pulse structures, and in particular double-pulse or double-peak structures, contained in these sections. Each of these structures can be assigned to a single particle and can thus be considered an object within the time series.

[0041] Embodiments of the present method and device make it possible to reliably determine the presence or occurrence of a particle. In particular, false-positive determinations are eliminated or greatly reduced by the present methods and devices.

[0042] Embodiments of the present method and apparatus make it possible to segment randomly distributed pulses without empirical calibration of the algorithm. Necessary characteristic features are determined adaptively from the data in τ-space.

[0043] Embodiments of a method and apparatus for detecting a particle will now be described in detail in conjunction with the following figures. They show: Fig. 1 shows a schematic view of a device for detecting a particle; Fig. 2 shows a schematic flow diagram of a method for detecting a particle; Fig. 3 shows an idealized double pulse; Fig. 4 shows an exemplary particle detection; Fig. 5 shows a temporal profile of a degree of polarization DOP(t); Fig. 6 shows the profile of a Fourier-transformed degree of polarization dop(τ) with an envelope; Fig. 7 shows the profile of a noise behavior of the profile from Figs. 4; Fig. 8 shows the course of a phase position for two exemplary double pulses; Fig. 9 shows a partial step of a classification of a detection of a particle; Fig. 10 shows a partial step of a classification of a detection of a particle; Fig. 11 shows an overview of the detected and discarded detections.

[0044] In the figures, the same reference symbols denote the same or similar features.

[0045] Figs. 1 shows a schematic view of a device 100 for detecting a particle. The device 100 comprises a detector 110, a processor 120, and a memory 130. Instructions are stored in the memory 130 which, when executed by the processor 120, carry out a method for detecting a particle, as described in particular in connection with the following figures.

[0046] Figs. 2shows a schematic flow diagram of a method 1000 for detecting a particle.

[0047] The method 1000 begins in a first step 1100 in which a time series of an occurrence of individual particles is recorded.

[0048] The method continues with step 1200, in which the time series is segmented.

[0049] The segmentation step 1200 can be broken down into the following substeps: First, a single-sideband spectrum of the time series is generated in step 1210. In particular, in this step 1210, N zeros are added so that the properties of a single-sideband spectrum DOP *[ i ] = 0, for i > N 2 are fulfilled.

[0050] Then, in a step 1220, the single-sideband spectrum of the time series is transformed into a transformed, in particular frequency-transformed, space.

[0051] This is followed by a step 1230 in which the transformed space is low-pass filtered. In particular, a convolution with the filter kernel is performed in this step, with the moving average being prominent. Alternatively, masking or weighting in the frequency domain can also be performed in this step 1230, which leads to an equivalent result.

[0052] In a following step 1235, the necessary cut-off frequency is derived or estimated from the bandwidth determined in the frequency domain (τ-domain).

[0053] Then, in a step 1240, the imaginary part of the low-pass filtered transformed space is discarded and only the real part is retained.

[0054] This is followed by a step 1250 in which the real part of the low-pass filtered transformed space is transformed back into the time domain. This results in the detuned phase, at whose zeros or inflection points peaks can be found.

[0055] The method continues with step 1300, in which the positions obtained from the segmentation are extracted and classified as segments of the time series, and thus one or more double peaks can be identified.

[0056] The classification step 1300 can be broken down into the following sub-steps: In an optional step 1310, the original time series is filtered. In particular, only a portion of the original time series, for example, every eighth data point, can be used, thereby achieving data reduction. In a further step 1320, the original time series is windowed according to the calculated time points.

[0057] In a subsequent step 1330, the time series segments are normalized.

[0058] In a further step 1340, a global maximum and one or more local maxima within the time series segment under consideration are determined.

[0059] In a subsequent step 1350, a normalized distance between the global maximum and the one or more local maxima in a segment of the original time series is determined.

[0060] In a further step 1360, an error probability of the significant amplitude in the original time series is determined.

[0061] Finally, in step 1370, a double peak is determined in the originally acquired time series based on the results from steps 1200 of segmentation or based on the positions of the zero points or inflection points.

[0062] Optionally, a step 1400 can follow in which the segmented and classified double peak is evaluated.

[0063] Therein, in a step 1410, a particle size can be determined based on the amplitude of the determined double peak and / or in a step 1420, a particle velocity can be determined based on the distance of the maxima of the determined double peak.

[0064] Likewise, in a step 1430, a particle shape can be determined based on the temporal course of the determined double peak.

[0065] The method 1000 thus comprises the steps of capturing 1100, segmenting 1200, classifying 1300 and evaluating 1400, which are now described in connection with the following Figures 3 to 11 be explained in detail.

[0066] Figs. 3 shows an idealized double pulse or an idealized double pulse structure. The function corresponds to a structure according to the function f x : = sin 2 x x .

[0067] The peak or maximum values, which can also be referred to as peaks, are highlighted with a dot. The ringing to the left and right of the double pulses or double peaks is a characteristic of the function. In real data, as shown in the following Figs. 4 , especially the left side, these secondary maxima are usually negligibly small, but in some cases such signal shapes can be observed in the measured time series.

[0068] Figs. 4 shows a section of an example of an actual particle detection over time, as recorded by the detector. The degree of polarization (DOP) is plotted on the vertical axis, and the time course in milliseconds is plotted on the right axis, i.e., a time series of the degree of polarization. DOP ( t). The left curve shows a particle measurement of an actual particle bed, which is repeatedly referred to in the following figures and which shows the actual double pulse or double peak, which is to be detected or correctly identified as such by the present methods and devices.

[0069] The right-hand curve is an example of a so-called standard particle disk, which contains standardized particles of known shape and size. Rotating the standard particle disk creates a recurring data or signal structure (correlated data) that no longer satisfies the assumption of a random process for the occurrence of the particles. This process is a periodic and correlated one.

[0070] A recorded time series containing double peaks is not mean-free. The more pulses the data set contains, the more the mean and the scatter of the signal shift. In addition, each pulse can be realized differently in terms of amplitude and pulse width. This property, and the fact that the desired structure consists of two local maxima, render most established methods unusable. Methods for detecting ECG signals, for example, are optimized for signals from a continuous process with a main pulse that recurs periodically. However, this does not work in this case because the nature of randomly occurring pulses is different. The respective distribution functions of the observed process for particle size and velocity are assumed to be constant and therefore do not change within the observed time window or data set.

[0071] Based on this, the following objective arises, which is fulfilled or solved by the present methods and devices: In a one-dimensional time series, double peaks occur randomly, so pulses must be characterized as realizations of a random process. The distribution parameters for the magnitude and velocity distribution are unknown and are considered invariant to the random exclusion of individual data points. Undetected peaks therefore do not change the density distribution.

[0072] The embodiments of the present method and the present device have the following properties and advantages: A reliable identification of significant double peaks is enabled and, in particular, false-positive detections are excluded and double peaks that are too close together or are not correctly shaped are also excluded, which is made possible by the segmentation and classification described below.

[0073] From the detected curves or values ​​of the double peaks as well as the adaptively determined parameters, the following quantities can be derived, among others: Amplitudes determine particle size. The time interval between the left and right peaks indicates the velocity. The global signal-to-noise ratio (SNR) is a measure of particle density / number; the required minimum number of particles can be derived from this, or the signal-to-noise ratio can be used to distinguish a blank measurement. An amplitude-independent detection probability can be derived (adaptively) from the local SNR. The maximum number of particles can be derived from the bandwidth / characteristic peak width.

[0074] A particle size can be derived from the amplitude of the individual peaks and a velocity can be derived from the distance between the main maxima or double peaks.

[0075] The global SNR, the maximum value of the magnitude function in the feature space and the determined signal bandwidth allow an assessment of the data quality in such a way that the cases "too many (too high concentration)" or "too few" particles (empty measurement) can be distinguished.

[0076] Furthermore, certain tuning parameters can be derived from the detected curves. A tuning parameter has a physical or signal-theoretical standard value. The present methods and devices function under the defined boundary conditions of the randomly occurring pulses without the need to adjust this parameter. If these boundary conditions change, for example, in correlated signals, this parameter can be adjusted to achieve better results. In contrast, in common prior art methods, the necessary tuning parameters are determined empirically through an experiment or a calibration campaign. According to the invention, such tuning parameters are not required, and the tuning parameters are determined adaptively from the data.The present methods and devices also provide automatic calibration capability, which reduces the number of adjustment options compared to the state of the art. In particular, a basic parameterization or default setting can be derived from an IT perspective, eliminating the need for further adjustments.

[0077] In contrast to false-positive detections, which are particularly avoided by the present methods and devices, false-negative data can be tolerated by the present methods and devices. Furthermore, based on the present methods and devices, a generalization to multidimensional real-valued ( ℝ n ) data is possible.

[0078] These properties and advantages are achieved in particular through the following sub-steps of segmenting and classifying the acquired data or time series. In particular, the Figs. 5 to 8 Sub-steps of segmentation and the Figs. 9 to 11 the substeps of the classification of the double peaks.

[0079] The segmentation specifically aims to determine a list of the most probable positions of the particles in the time series, i.e., to identify those sections in the time series that exhibit a double peak. In this case, a so-called spectral approach is used, which uses an analytical signal associated with the Hilbert transform and the Fourier transform, which translates between an image region and an original region.

[0080] Figs. 5 shows an example recorded time series of a degree of polarization DOP(t),where again, as in Figs. 4 , the degree of polarization is plotted on the vertical axis and the time course in milliseconds is plotted on the right axis.

[0081] This time series comprises a set of consistently positive individual pulses of similar width. Depending on their probability of occurrence, they shift the first- and second-order moments of the underlying distribution function, so that with an increasing number of individual events, neither the mean nor the scatter can provide any meaningful information about the noise behavior, signal-to-noise ratio (SNR), or confidence intervals (within the time series). However, as the scatter increases with increasing pulse density, the detection probability of small-amplitude pulses decreases when simple thresholds are applied in the time domain. The time of occurrence and the amplitude distribution of the pulses are random processes whose properties can be exploited with suitable transformation, as explained here.

[0082] The DOP signal, DOP ( t ), in Figs. 5shows the temporal course of the signal amplitude DOP t = S 1 t 2 + S 2 t 2 a complete series of measurements with N = 2 16< data points. The degree of polarization is composed of the Stokes parameters S 1 ( t ) and S 2 ( t ), which are typical characteristics of polarized light, as detected by the detector here. Each pulse consists of a central minimum and two maxima positioned to the right and left of it, as shown in Figs. 4 shown.

[0083] The following basic hypotheses ultimately lead to the present spectral approach using analytical signal: 1. DOP ( t ) corresponds to the amplitude of an image area / frequency range 2. DOP t ∈ ℝ is real-valued 3. there exists an original domain after (τ) that meets all requirements, so that DOP ( t ) exists

[0084] The single sideband spectrum is then DOP *( t ) of the time series DOP ( t ) , by an adequate extension. This step corresponds to the one described above in connection with Figs. 2 described step 1210. The function DOP* ( t ) corresponds to the single-sideband spectrum of an analytical signal after (τ), so that the inverse Fourier transform dop τ = 1 2 T F − 1 DOP ∗ t is valid and serves as an aid to the original area after (τ). Conversely, the Fourier transformation ( after (τ)) again to DOP* ( t ) and thus establishes the link between both functions.

[0085] Accordingly, a double peak (DP) in the image area corresponds to a continuous band-limited signal f (τ) in the original area, DOP t DP ↔ F dop τ t DP , with the phase position arg ( dopDP (τ)) =0. The sum of all double peaks leads to a large mixture of constructive and destructive overlay in the original range.

[0086] The single sideband spectrum is band-limited, so that in the upper half, but at least for t > T, all values ​​disappear, DOP *( t )| t > T → 0 must.

[0087] This requirement means that DOP ∗ t = DOP t 0 0 0 ≤ t < T T ≤ t < 2 ⋅ T t < 0 , where DOP *( t )an extended function up to t = 2 · T It contains the measurement series DOP(t) and will be until 2 · T This creates a band-limited spectrum and leads to a one-to-one mapping when the Discrete Fourier Transform (DFT) is applied. This is sufficient because the DFT is symmetric with respect to N / 2 and has no negative indices.

[0088] Furthermore, this guarantees that ∫ − ∞ ∞ dop τ d τ = 0 becomes absolutely integrable.

[0089] Bandlimitation and absolute integrability are essential properties that signals generally need to possess for orthogonal mode decompositions, such as FT or DFT, to function properly. Engineering these properties, as in the present case, eliminates the need for typical correction techniques such as windowing.

[0090] From the property DOP t ∈ ℝ + follows for the phase arg ( DOP ( t )) = 0 and thus also arg ( DOP *( t )) = 0 is a sufficient statement. It means that by filtering or manipulating DOP ( t ) the phase may deviate locally.

[0091] The average phase position 1 T ∫ 0 T arg DOP t d t = 0 but must necessarily be zero. For DOP *( t ) the same applies accordingly.

[0092] If the signal is detuned by low-pass filtering in the original range, local deviations occur at the peak locations, arg ( DOP ( tn )) ≠ 0, with an inflection point (necessary) or a zero crossing (sufficient). These local properties can be easily detected via sign changes, from which the positions of the particles follow.

[0093] The original domain represents an analytical and complex-valued function in the mathematical sense, dop τ ∈ ℂ . This results in the imaginary part up Him = In the( after (τ)) from the Hilbert transform, as follows dop τ = dop ℜ τ + j H dop ℜ τ .

[0094] The envelope ev τ = dop ℜ τ 2 + dop ℑ τ 2 , which can be used to estimate the signal bandwidth, is obtained directly from the analytical signal.

[0095] It can be seen that the scaling of the FT at this point is 2 N This is due to the expansion with '0', also called zero padding. The chosen scaling ensures that the FT remains energy-conserving, so that Parsevall's theorem ∫ | x ( t )| 2< d t = ∫ | X ( ω )| 2< d ω remains valid.

[0096] Figs. 6 shows the course of a Fourier-transformed degree of polarization after (τ) with an envelope. The vertical axis represents the degree of polarization after (τ) and on the right-hand axis a running number or the index. For the signal after (τ) is the original range of the extended DOP signal DOP *( t ) , as explained previously.

[0097] As in Figs. 6 The envelope curve becomes visible house (τ) = | after (τ)| 2< at the beginning of the data set up to an index of n≤ 1500 is displayed, with the complete data set being N = 2 16< support points.

[0098] It can be seen that the amplitude drops to almost zero in a short range. The white line only visually indicates that the signal energy (envelope) is similar to an exponential density distribution 0.025 e - x 2 / (2 bw 2)< decreases. Here, bw the bandwidth, which can be read from the diagram.

[0099] This special behavior arises from the requirement arg ( DOP* ( t )) = 0 in the image area and by the (band) width and pulse shape. The latter corresponds roughly to a bell curve ~ e - x 2< , which, according to the FT scaling theorem, translates back into a bell curve with scaled width and amplitude in the original range, F g ax → 1 a G 1 a ω . As explained below, the bandwidth can be related to the mean peak width.

[0100] In the original range, all signal components (per double peak) start with the same phase position and initially overlap constructively. This leads to a ~ e - x 2< -like progression, as in Figs. 6 The mean amplitude decreases monotonically with increasing index, since the signals become out of phase with increasing index and thus overlap more destructively.

[0101] Figs. 7 shows the course of a noise behavior of the course from Figs. 6 The amplitude is plotted logarithmically on the vertical axis and the index on the right axis. This makes noise processes clear.

[0102] The dashed lines show that there are at least two stochastic processes: (left line) house (τ) ~ e -x / 3000< and (right line) v (τ) ~ e - x / 10000< . These two processes could be related to a typical 1 / f noise. The noise may be typical of electronics, and a change in the noise behavior can provide information about the system's condition, such as aging.

[0103] In Figs. 6 The vertical line shows the index at which approximately 70% of the signal energy is reached. This point is referred to here as the (signal) bandwidth bw : = ∫ 0 bw ev τ 2 d τ ∫ 0 ∞ ev τ 2 d t = 1 2 and is calculated from the ratio of the moving sum (integral) of the energy E , based on the total energy The Σ . For the data example above, we get bw = 397.

[0104] By the FT scaling theorem, F g ax → 1 a G 1 a ω , can be determined from the range bw the width of a double peak in the image area with ΔP ≈ 1 / ( bw). In the implementation, the number of samples must be multiplied, since the DFT does not have normalized frequencies (0 < ω < 2 π ), but rather by indices. This approach also assumes that all double peaks are approximately the same width. This should be the case, since the measured particles all have similar velocities in the measurement time window ( T = (100 ms)). The estimated peak width for the working example is dP = 165.08 and is used for segmentation and classification.

[0105] The next step consists of a low-pass filtering and a reconstruction into the image domain to obtain the mean phase of the DOP *( t ) signal, which is related to the following Figs. 8 This corresponds to steps 1220 and 1230 described above. The bandwidth bw serves here as the cutoff frequency for a filter function filt τ = dop τ ⋅ BP τ bw , τ < bw ≈ 0 , sonst . which acts as a low-pass filter. BP (τ , bw ) a general bandpass function, so that BP (τ)| τ> b w = 0. For a Gaussian-type low-pass filter, bw ≈ 3σ. In the present case, which has proven to be useful, BP f f c bw = e − 2.3025 f − f c 2 BW 2 defined, where fc = 0 can be selected as the center frequency and is therefore omitted.

[0106] For the inversely transformed function peaks t ∈ ℂ peaks t = F ℜ dop τ The real part is decisive, since the imaginary part of the analytic signal "only" represents a supplement to create a single-sideband spectrum. Therefore, the imaginary part is discarded and only the relevant real part is processed further. This reconstructs the phase. This corresponds to steps 1240 and 1250 described above.

[0107] This is related to Figs. 8, which shows the phase relationship of two exemplary double pulses. The degree of polarization (DOP) or phase relationship is plotted on the vertical axis, and the index is plotted on the right axis. dP denotes half the peak width.

[0108] As in Figs. 8 As can be seen, both conditions are met for the large double peak on the right. The small double peak on the left of the image has only one inflection point.

[0109] The amplitude curve | peaks ( t )| corresponds to the low-pass filtered version of the DOP *( t ) signal. It therefore has a maximum in the range that will be used as a criterion for classification. The calculated bandwidth thus serves as the cutoff frequency and for calculating the peak width.

[0110] From the information about the local maxima of the amplitude curve and the phase inflection points, the centers of the double peaks can now be determined. Phase zeros are also inflection points.

[0111] Projected into the area of Figs. 8 In this case, the right peak has an index of 123 and the left peak has an index of 711.

[0112] The previously calculated band limit bw not only estimates the maximum width of a particle pulse ΔP , but also the typical required distance between double peaks. If these are too close together, there is no inflection point / zero crossing or the maximum of the filtered peaks ( t ) function disappears or shifts. Due to this behavior, possible double peaks are ignored in dense clusters, leading to false negatives. However, false positive counts are minimized.

[0113] Based on the previously described segmentation, which provides the basic positions for possible peaks, the data sections must now be separated and individually checked for plausibility. The result is sections DOP(t) with t 1 < t < t 2 , which has a width of at least t 2 - t 1 > ΔP which is now related to the Figs. 9 to 11 is described by the partial aspects of the classification according to the invention.

[0114] First, the following local metrics are calculated for each section: 1. Variance σ 2< of the original range 2. Power spectral density (SLD) 3. False alarm probability (FAP) p

[0115] The local variance Var ∗ y x = σ ∗ 2 = 1 N ∗ ∑ n = n 1 n 2 y ¯ − y x n 2 corresponds to the squared scatter in a data segment in which a particle or double peak is suspected. The data range is given here in discrete form as n 1 ... n 2 ↔ t 1 ... t 2 and corresponds to the time points of the continuous signal. The number of data points is N * = n 2 - n 1 given.

[0116] The local variance of the original area is determined by a transformation of the image area DOP *( t ) derived.

[0117] Again, the assumption is that this is an analytical signal, according to the definitions above.

[0118] It follows that Var ∗ dop τ = Var ∗ 1 4 ℜ F DOP ∗ t → ? Var ∗ N 2 DOP t = σ dop 2 initially arises from the FT of the DOP*(t) data.

[0119] In the image area, which is equivalent to an amplitude spectrum, the standardized power density (SLD) results from SLD t = N σ dop 2 N − 1 DOP t and scaled for sine signals between 0 < SLD ( t ) ≤ 1. The SLD represents a standardized version of the amplitude spectrum. Standardized SLDs allow comparison of different spectra with different noise behavior. This is the case when the same process is observed at different times and extrinsic influences change the measurement quality, but not the actual process.

[0120] The standardized SLD results in a false alarm probability (FAP) for each data point. This evaluation acts as a dynamic resolution limit, since the local noise (local SNR) of the original range is decisive.

[0121] The FAP indicates the probability that the observed point is not a significant peak. In other words, the observed data point has a probability 1 - p an amplitude of SLD > SLD0 . SLD Here, 0 is the reference or noise threshold for the data section under consideration, resulting from the transformed data in the original range. The FAP corresponds to a kind of p-value, known from statistics. p = 1 − 1 − P SLD > SLD 0 M , which is used to assess the significance of a result. The probability P SLD > SLD 0 ≈ 1 − SLD N − 3 / 2 that a selected data point of the SLD differs significantly from the noise is calculated from the spectral power density and the number of support points N. The parameter M = -6.362 + 1.193 · N + 0.00098 · N 2< describes the number of degrees of freedom that can be determined with non-uniform sampling.

[0122] In doing so, M a measure of the number of independent frequencies. Alternatively, M = N / 2 should be set.

[0123] Since the SLDand the p-value are calculated separately for each data section, this is a dynamic (adaptive) adjustment of the noise threshold.

[0124] In the following, the detection or finding of a double peak in connection with the Figs. 9 and 10 explained in detail.

[0125] Figs. 9 and 10 show substeps of a classification process. The vertical axis represents the degree of polarization (DOP), and the right axis represents time in milliseconds.

[0126] The detection of the double peaks requires the following conditions, which are described in Figs. 10 shown are: There is exactly one global maximum in the data section, which is labeled A1; the nearest (large) local maximum, which is labeled A2, is the other peak of the double peak; in between lies the minimum, which is labeled A3; the function under consideration is sufficiently smooth, there is almost no noise on the curve; and both ordinates are normalized to allow a general formulation.

[0127] The classification steps are now based on the Figs. 9 explained in detail: First, post-processing is carried out, which may include a low-pass filter and / or windowing of the original time series, as described above in steps 1310 and 1320, as well as normalizing the ordinates of the time series segments and calculating all local maxima, as described above in step 1330.

[0128] Then, the global maximum at the point { t̂ max, DOP ( t̂max )}, see A1 in Figs. 10 , which serves as a starting point, cf. (1) in Figs. 9 , which corresponds to step 1340 described above.

[0129] Then the global maximum is "run down" to the left and right, ie the progression to a value Δt followed, whereby t l = t max - Δt and t r = t max + Δt, as indicated by the arrows to the left and right of (1).

[0130] It is taken into account that all local maxima t̂ lie below the line (2a), ∀ t̂ l : DOP ( t min ) < DOP ( t̂ ) < DOP ( t̂ ) and a local maximum on the left, (3) the projection line (2b), ∃ t̂ : DOP ( t̂ ) > DOP ( t l ) meets.

[0131] Then the local maximum (3) is evaluated with the result from the other side by selecting the three time points t̂ max, t̂ l , t̂ rand calculating the normalized distance between the global maximum and the second peak d ^ = t ^ max 2 − t ^ l , r The point with the greatest distance d̂ max is discarded, leaving only two points, (1) and (3), which corresponds to step 1350 described above.

[0132] The standardized distance already provides a preselection, in the sense that in the case of a double peak both maxima DOP ( t̂ ) ≈ DOP ( t̂ r,l ) should be approximately the same size. Normalization ensures that an amplitude difference is weighted similarly to the time difference.

[0133] In addition to the steps described above, the signal can, for example, be masked and / or curve smoothed, which prevents incorrect assignments in the case of high noise or overlaps with neighboring pulses.

[0134] The result of the peak finding is in Figs. 10 visible.

[0135] The local minimum A3 DOP min = min DOP t ^ 1 < t < t ^ 2 between the peaks as an evaluation parameter. The point DPK : t ^ ¯ A ¯ describes the middle position between the two maxima.

[0136] In the example shown, the average DOP amplitude depends on the particle coverage of the laser beam, which results in a proportional change in intensity and thus in a DOP dependence. The particle size can be calculated from the DOP value using a calibration function.

[0137] For the Figs. 10 The example shown results in the following exemplary values: DOP t / ms FAP A1 0,01727 10,85 0,00000 A2 0,01331 10,76 0,00582 A3 0,00065 10,81 1,00000 DPK 0,01529 10,81 0,00000

[0138] The result of the data classification are essentially the three points that indicate the double peak (A1 and A2) and the minimum (A3) of the desired pulse shape.

[0139] Finally, the classified points are evaluated. The goal is to verify the classification estimate and thus exclude points that do not adhere to the desired pulse shape.

[0140] Examples of valid, invalid and ignored data points are shown in Abbildung 11 summarized.

[0141] In particular, the previously described error probability, the momentum ratio and the presence of a central minimum are considered, which is explained below.

[0142] The FAP (false alarm probability) indicates the probability that a point in the image area ( DOP ( t )) from signal noise (variance).

[0143] For the purposes of these proceedings, P A > A 0 : = p > 0.2 that the probability p> 20% for at least one of the two peaks to be considered a valid double peak. This corresponds to step 1360 described above.

[0144] A double peak consists of two pulses. These must be in a certain ratio (peak ratio, pR = 0.75) pR > min A 1 , A 2 max A 1 , A 2 to obtain a pulse shape that can be easily classified. The relative difference between the two points is therefore less than 1 - pR = 25%.

[0145] Between the two maxima lies a minimum, which should be as deep as possible to be a significant peak. Calculating the central minimum A 3 − min DOP t min A 1 , A 2 − min DOP t < 0.7 shows that the amplitude of the minimum relative to the smallest maximum must be less than 70%. The shift min ( DOP ( t )) corrects the offset of the time series.

[0146] To evaluate the reconstruction, as in Figs. 8 shown, which in the image area DOP( t ) shows the original data as well as the reconstructed (low-pass filtered) function, the following must apply at the points where a probable peak is found: exactly a maximum of the peaks ( t ) function is located in the area t 0 − dP < t < t 0 + dP ; and there is no local minimum in this area, d d t peaks t ≠ 0 for ∀ t This excludes segments / areas where there are multiple peaks, which are too close together, or which are too broad / smeared.

[0147] In summary, by means of embodiments of the method and the device according to the invention, the time domain is firstly understood as a real-valued single-sideband spectrum of an analytical signal, wherein the phase is exactly zero.

[0148] The transformed feature space, also called τ-space, is obtained by the Fourier transformation of the original data when taken as a spectrum.

[0149] The time series is a random process in which particles are recorded at random times. The temporal interval between the particles is also a random process.

[0150] A narrow peak in the time domain is always mapped into a broad peak in the feature space, which is based on the scaling theorem of the Fourier transform. The Fourier transform is invariant to shift, whereby the narrow peaks of the time domain in the feature space all slide symmetrically to τ = 0 and constructively overlap, which occurs when transitioning from Figure 5 to Figure 6.

[0151] A 3 dB limit is then calculated in the feature space, as in Figure 6 shown, ( E / E max = 1 / 2 ), which contributes to the signal bandwidth bwwhich is related to the mean or characteristic width of the peak dP is linked.

[0152] The maximum amplitude in Figure 5 is a measure of the number of particles. If this elevation can be clearly distinguished from the noise, the concentration is sufficient for successful detection.

[0153] Low-pass filtering and inverse transformation yield a filtered time series in the time domain, which no longer represents a real-valued spectrum. Rather, the phase position is detuned.

[0154] A peak can be found at every inflection point, but at least at every zero. This results in a list of points with inflection point or zero characteristics.

[0155] In addition, it is checked whether there is also a local maximum of the filtered amplitude in the time series. Visit Lists

[0156] 100Device 110Detector 120Processor 130Memory 1000Process 1100Process step 1200Process step 1210Process step 1220Process step 1230Process step 1235Process step 1240Process step 1250Process step 1310Process step 1320Process step 1330Process step 1340Process step 1350Process step 1360Process step 1370Process step 1400Process step 1410Process step 1420Process step

Claims

1. A method for detecting particles, comprising: - detecting (1100) a time series of a particle detection; - segmenting (1200) the time series, comprising: - transforming (1220) the time series into a transformed space; - low-pass filtering (1230) the transformed space; and - back-transforming (1250) the transformed space into the time domain; and - classifying (1300) the segments of the time series, comprising: - determining (1370) a peak in the time series based on the low-pass filtered back-transformed time domain, characterized in that the determination (1370) of a peak takes place by determining (1340) a global maximum and a first and a second local maximum; wherein the determination (1370) of a peak takes place by determining (1350) a normalized distance between the global maximum and the first and second local maximum; and wherein the determination (1350) of a normalized distance takes place by determining a distance by d ^ = t ^ max 2 − t ^ l , r , where d̂ is the distance, t̂max is the global maximum and t̂l,r is the first and second local maximum; and by discarding that local maximum at which the distance is greater.

2. A method (1000) according to claim 1, wherein the step of segmenting (1200) further comprises the step - generating (1210) a single sideband spectrum of the time series; and wherein the step of transforming (1220) the time series into a transformed space comprises transforming the single sideband spectrum of the time series into a transformed space.

3. A method (1000) according to claim 1 or 2, wherein the step of back-transforming (1250) the transformed space into the time domain comprises discarding (1240) the imaginary part.

4. A method (1000) according to any one of the preceding claims, wherein the classifying (1300) of the segments of the time series further comprises normalizing (1330) the time series.

5. A method (1000) according to any one of the preceding claims, wherein the classifying (1300) of the segments of the time series further comprises determining (1360) an error probability of the time series.

6. A method (1000) according to any one of the preceding claims, wherein the classifying of the segments of the time series further comprises filtering (1310) and / or windowing (1320) the time series.

7. A method (1000) according to any one of the preceding claims, wherein the method further comprises determining (1410) a particle size based on the amplitude of the determined peak.

8. A method according to any one of the preceding claims, wherein the method further comprises determining (1420) a particle velocity based on the distance of the determined peak.

9. An apparatus (100) for detecting a particle, comprising: - a processor (120); and - a memory (130) in which instructions are stored that, when executed by the processor (120), perform a method for detecting a particle according to any one of the preceding claims 1 to 8.