Method and apparatus for time-domain spectroscopy with reduced support point acquisition

Abstract

The invention relates to a method and a device for time-domain spectroscopy with a reduced number of sampling points compared to the WKS sampling theorem. The aim is to enable the approximation of a time signal using a limited number of periodic and / or periodically attenuated fundamental signals. In particular, the invention relates to the selection of suitable sampling points for measuring a time signal and the measurement itself, in order to approximate the time signal using the limited number of fundamental signals. The sampling points are determined according to a deterministic method.

Description

[0001] The invention relates to a method and a device for approximating a time signal using a limited number of periodic and / or periodically attenuated fundamental signals. In particular, the invention relates to the selection of suitable support points for measuring a time signal and the measurement itself, in order to approximate the time signal using the limited number of fundamental signals.

[0002] Time-domain spectroscopy is a spectroscopic method based on measuring the temporal change or evolution of a signal. A frequency, wavelength, or energy spectrum can be obtained from this time-domain signal by performing a suitable Fourier transform on the sampled signal. The development and availability of short-pulse lasers have made it possible to determine optical material properties or electric light fields with resonances or natural frequencies in the terahertz spectral range using time-domain measurements and so-called optical gating. For this purpose, a signal is sampled after a trigger laser pulse using a second probe laser pulse. In this established method, a laser pulse duration and a sampling interval determine a usable spectral range, while the length of the sampled time interval determines the achievable spectral resolution.To measure a given spectral range with a specific resolution, the time domain is measured in typically equidistant, discrete steps, resulting in a minimum required number of measurement points or support locations. This number of required measurement points or support locations is determined by the WKS sampling theorem (for Whittaker, Kotelnikov, and Shannon), also known as the Nyquist-Shannon sampling theorem.

[0003] The current state of the art requires a significant number of equidistant measurement points to accurately determine any spectral function from time-domain measurements (WKS sampling theorem), which leads to the following disadvantages: (i) long measurement times, (ii) complex experimental setups, (iii) large sizes for spectrometers and measuring instruments and (iv) high volumes of data to be processed.

[0004] Integrating the functionality of time domain sampling into a chip is technologically complex and therefore expensive due to the large number of required measurement points.

[0005] In “Compressed Sensing of Field-resolved Molecular Fingerprints Beyond the Nyquist Frequency”, arXiv:2307.11692v2 [physics.optics], April 4, 2024, K. Scheffter et al. describe ultrafast spectroscopy and field-resolved spectroscopy of molecular fingerprints, which are considered gold standards for detecting sample constituents and internal dynamics. However, these techniques are hampered by the Nyquist criterion, resulting in long data acquisition and processing times and large datasets. Scheffter et al. present experimental results of applying compressed sensing to field-resolved molecular fingerprinting via random scanning. Primary absorption peaks of atmospheric water vapor in response to terahertz light transients were determined while scanning beyond the Nyquist limit.By drastically undersampling the electric field of the molecular response at a Nyquist frequency of 0.8 THz, water absorption peaks up to 2.5 THz could be detected with a mean squared error of 12×10. -4 be identified.

[0006] The compressed sensing method described by Scheffter et al. does not solve this problem, as it does achieve a reduction in the required measurement points, but requires a random sequence of measurement points and therefore a highly complex, variable sampling, which is also very disadvantageous for chip integration.

[0007] Furthermore, random sampling does not always lead to a correct measurement.

[0008] An introductory and overview article, “an introduction to compressive sampling,” by Emmanuel J. Candés and Michael B. Wakin, was published in IEEE signal processing magazine, Vol. 25, 2008 No. 2, pages 21–30 – ISSN 1053-5888.

[0009] For many signals from physical systems that need to be measured, the signal to be measured can be represented as a linear combination of a finite number of periodic and / or damped periodic basic signals.

[0010] The sampling process itself can then be mathematically described using the following equation. y=Ax+e where y is the M-dimensional vector of samples, x is the N-dimensional vector of possible frequencies (according to the WKS theorem), and the M-dimensional vector e contains an additive disturbance (for example, noise). The MxN-dimensional matrix A is obtained by explicitly choosing the M sampling points and assuming N possible fundamental signals (for example, via the WKS theorem). For subsequent signal measurement, this means that A is known, y is measured, and x and e are unknown and are determined during signal reconstruction, whereby an estimate for the disturbance e is necessarily required when determining the vector x of interest.

[0011] The invention is based on the objective of providing a method and a device for time-domain spectroscopy with reduced sample point acquisition, as well as a method for manufacturing such a device. In particular, one objective is to select the sample points so that, based on the measured values ​​at the sample points, a plurality K not exceeding S and their weightings can be determined from a population N of fundamental signals, the weighted linear combination of which approximates the sampled measurement signal. Basic idea of ​​the invention

[0012] While it is fundamentally possible, for an arbitrary selection of sample points M from a population N of temporally equidistant sample points necessary for complete information acquisition of an arbitrary signal according to the WKS sampling theorem, where M <= N, leading to a measurement matrix A of dimension MxN, it is numerically very expensive, but formally possible, to determine whether this matrix allows for successful reconstruction of the measured signal as a linear combination of up to S possible fundamental signals. One possibility is to assign a value to a so-called "Restricted Isometry Property" constant δ. 2S , (RIP constant) of order 2S. The "Restricted Isometry Property" constant δ 2S , (RIP-constant) of order 2S is defined as the minimum of the smallest non-zero singular values ​​of all Mx2S submatrices of A. If δ2S<12, then the reconstruction is successful.

[0013] To avoid this effort, it is proposed to use a deterministic method for selecting the support points, which ensures from the outset that the selection of support points leads to a matrix describing the measurement process, so that the signal can be reliably reconstructed as a linear combination from a maximum of S basic signals. This approach is referred to here as dCSTD – deterministic Compressed Sensing in the Time-Domain.

[0014] The object of the invention is to determine resonances / natural frequencies based on signals originating in physical systems. For this purpose, an established and accurate physical model for describing the resonance spectrum in materials is employed. Each resonance can be traced back to a harmonic oscillator model with a specific natural frequency, which means that the signal of a resonance in the time domain (e.g., measured as the temporal change in transmission or reflection) can be described by a potentially damped sine or cosine function. The invention is based on the physically grounded assumption that a time-domain spectrum of at most K resonances results from a linear combination of the cosine or sine function with corresponding at most K natural frequencies or periodic, optionally damped, fundamental signals.

[0015] Knowing the exact number of possible natural frequencies in the actual signal is not necessary. Knowing the upper limit S for the number K is helpful. The natural frequencies themselves do not need to be known, nor does the noise characteristic of the detector. However, the set of possible signals (cosine or sine signals and any possible attenuations), i.e., the possible natural frequencies or resonances that could be linearly combined, is assumed to be known and is referred to below as the "fundamental signals."

[0016] The reduced-spot time-domain spectroscopy method comprises the following steps: a) Capturing a number N of possible basic signals, from which a time signal to be measured is to be reconstructed as a linear combination; b) Capturing a maximum number of components S max, which specifies a maximum number of basic signals that can be combined for reconstruction in the linear combination; c1) Developing a deterministic support point determination model, based on which a number of support points can be deterministically determined from a basic set of support points whose cardinality is preferably greater than or equal to N, and c2) Identifying a determination criterion by which it can be determined whether a sampling with a number of support points determined according to the deterministic support point determination model results in a successful reconstruction of any sampled measurement signal linearly combined from the basic signals with a maximum number S max guaranteed by basic signals or not; d) Selecting or estimating the required number of support points M, e) Determining M support points using the deterministic support point determination model, f) Setting up an MxN measurement matrix A, by means of which the sampling process is described as a linear process according to the following equation: y=Ax+e, where y is an M-dimensional vector of the sampled values ​​measured at the M determined support points, x is an N-dimensional vector of the coefficients that specify the contributions of the possible fundamental signals in the linear combination for the reconstruction of the measurement signal, and e is an M-dimensional vector representing an additive disturbance; g) Evaluate the determination criterion and determine whether, when sampling with the determined M support points, the measurement signal, which consists of any linear combination of a maximum of S max The N possible basic signals can be formed and reconstructed, but not all measurement signals can be reconstructed that result from a linear combination of at least S max +1 of the N possible basic signals are formed, and g1) If this is not the case, change the estimated required number of support points M and repeat the procedure steps e) to g) g2) and if this is the case, h) Performing measurements to determine the M sample values ​​at the M support points, and i) Evaluating the linear equation describing the sampling process; j) Outputting information indicating the basic signals and coefficients of the linear combination required for reconstruction, as determined during the evaluation.

[0017] With a reasonable amount of effort, the required support points can be reliably determined and the physically important information can be derived from a measurement.

[0018] In some embodiments, steps d) and e) may coincide because support point distributions exist only for certain combinations of N and M, or the design of the support points implicitly provides the number M.

[0019] A sampling point is always correlated with a time at which a measured value is sampled relative to a fixed signal point in the measurement signal being measured, for example, relative to the start of the signal. Determining the sampling points is therefore equivalent to determining the measurement or sampling times for a sampling.

[0020] Preferably, the sampling points are determined as a subset M of N possible sampling points that divide the temporal signal to be sampled into equidistant intervals according to the WCS sampling theorem, thus lying on an equally spaced temporal grid. This allows for a simple determination.

[0021] In one embodiment, the evaluation of the linear equation of the sampling process with the determined sample values ​​is carried out according to a method called Square-root-LASSO, which is described, for example, by HB Petersen and P. Jung in “Robust instance-optimal recovery of sparse signals at unknown noise levels”, in Information and Inference: A Journal of the IMA, Volume 11, Issue 3, September 2022, pages 845-887, https: / / doi.org / 10.1093 / imaiai / iaab015.

[0022] In a preferred embodiment, scanning is performed using optical gating, in which the support points each define a time interval between an optical excitation pulse and an optical scanning pulse. This method enables the precise measurement of fast and / or high-frequency physical processes in the terahertz range.

[0023] To eliminate systematic errors during measurement that depend on a temporal correlation between the excitation pulse and one or more sampling pulses, a second set of support points is determined in one embodiment by cyclically permuting the M determined support points from N possible support points, preferably by one possible support point, more preferably by a number of support points corresponding to one-tenth of the difference NM between the number of possible support points N and the determined support points M. This exploits the fact that every set of support points that is a cyclic permutation of the originally determined support points and fulfills the determination criterion for a reconstruction also fulfills the determination criterion.A cyclic permutation is defined as a permutation in which the points selected from a set of equally distributed possible points in time are "shifted" by a certain number of points. Points that are "pushed out" of the set of possible points in this process are "pushed in" again at the other end of the set. If the possible points are numbered from 0 to N-1 and the determined points are indicated by their indices, then a cyclic permutation is mathematically equivalent to addition or subtraction modulo N of a natural number.

[0024] According to a further aspect of the invention, a method for manufacturing a spectrometer is provided that samples the measurement signal at the identified support points. Instead of carrying out the measurement and evaluation according to process steps h) to j) of the measurement method described above, a sampling device, an evaluation device, and an output device are provided such that the sampling device performs sampling and acquisition of measurement signals at the identified M support points, the evaluation device is configured to solve the linear equation that describes the sampling, and the output device is designed to output information indicating the basic signals and coefficients of the linear combination required for reconstruction, as determined during the evaluation.

[0025] Furthermore, a spectrometer is created that includes a scanning device and a recording device, which controls the scanning of the measurement signal and the recording of measured values ​​at the M support points, and includes the evaluation device for evaluating the linear equation describing the scanning, as well as an output device for outputting information that specifies the basic signals and coefficients of the linear combination required for reconstruction during the evaluation.

[0026] The spectrometer can be configured to select a specific set of M sample points from a population of N possible sample points. In this case, the time delays required for an optical gating measurement method can be implemented, for example, on an integrated semiconductor circuit using alternatively switchable delay lines.

[0027] In another embodiment, the spectrometer includes a support point determination unit configured to also perform process steps a) to f). The advantage lies in the fact that the total number of possible support points or the number of basic signals can be flexibly adapted to the measurement signal to be measured. Furthermore, the maximum permissible number S of possible basic signals that can be combined for reconstruction can be independently adjusted.

[0028] Such a spectrometer is therefore very versatile.

[0029] The spectrometer can generate the laser pulses necessary for a measurement itself, or it can generate and output only control pulses for timing the laser pulses. Likewise, the spectrometer can have a detector for signal acquisition or a signal input that acquires the detector signal, which represents the measurement signal strength at a given sampling point.

[0030] In one embodiment, the deterministic support point selection model is a selection of exponentially increasing time intervals, such as those provided, for example, by a geometric progression within the indices 1, ..., N. In one embodiment, the temporally ordered support points t k (k = 1 ... M) chosen such that they satisfy the property: aAk≤tk+1−tk≤bBk where a, b, A, B are real constants.

[0031] A specific educational regulation might read: 1) Define an equidistant grid of time interval Δt and reference the M support points t k = Δt · i k about position i k ∈ {0 ... N - 1} for k = 1... M on the grid.

[0032] This involves ik=int(bk−1c) set where b and c are positive real numbers such that b k-1 ≤ N - 1, and i kis set to the next largest integer not already selected, if i k specifies a previously selected support point. For b=2, such a selection is based on a sequence known as a geometric progression.

[0033] A coherence of less than 1 is required as a criterion for determining coherence. Coherence is determined by considering all possible column pairs of the mapping matrix A, normalizing each column vector individually, and then calculating the magnitudes of the scalar products for the normalized column vector pairs. From this set of magnitude values, a maximum value is designated as the coherence of the matrix. If the coherence µ is less than the reciprocal of twice the maximum permissible fundamental signal S increased by one, i.e., μ≤12Smax+1, The determined set of M support points is thus suitable for reconstruction. As long as the coherence is less than a predefined threshold, any measurement signal that can be formed from a maximum of S basic signals as a linear combination can be reconstructed.

[0034] According to another embodiment, the deterministic sample point selection model provides that the distribution of time intervals from each sampling point to every other sampling point approximates a uniform distribution. For example, if the M sampling points are chosen as a subset of N possible sample points arranged on a fixed, equidistant time grid, each sampling point or each possible sample point can be referenced by its index 0...N-1. The distribution of the differences of the indices of two different sampling points in an arithmetic modulo N is divided into a histogram H with N-1 bins H[I] where I=1..N-1. There are a maximum of M(M-1) / 2 "modulo-N" differences (arithmetic modulo N) that are entered into the histogram.Then, empty histogram positions are eliminated and the histogram H is normalized by dividing the value of each of the remaining L histogram positions by the sum of all histogram position values. H1[l]=H[l]∑k=1LH[k]. The normalized histogram is called H1. A mean value is calculated for the normalized histogram H1. ∑H1[I]L and at least one associated measure of deviation is determined, and a threshold is specified for this measure. The statistical measures that can be evaluated are a standard deviation of the mean, a maximum deviation from the mean, and a mean deviation from the mean.

[0035] However, it is possible that with the given number of support points M, not only measurement signals that manifest as linear combinations of a maximum of S are obtained. maxThe N basic signals can be represented, measured, and reconstructed. Furthermore, it is possible to reliably reconstruct measurement signals that include a linear combination with more than S. max The basic signals are based on S max +J basic signals are formed, where J is a positive natural number. Some embodiments, in particular one embodiment of the method for manufacturing a spectrometer, provide that an additional quality criterion is evaluated, namely whether the M support points, for which the determination criterion for S is met, are sufficient. max If the condition is met, then a J greater than or equal to zero also exists, such that arbitrary measurement signals based on linear combinations of S can also be used. min The basic signals are based on the J signals and can be reliably reconstructed. A quality criterion is to be evaluated for this purpose.

[0036] One embodiment of a quality criterion is the determination of the Restricted Isometry Property constant δ.2S , (RIP-constant), where this criterion for S= S max +J is evaluated. J is preferably iteratively increased until the threshold is exceeded. δ2S<12 no longer fulfilled. The largest J, together with S, gives max In total S = S max +J specifies how many natural frequencies a signal may have in order to be reliably reconstructed.

[0037] Some embodiments therefore provide for an additional quality criterion to be evaluated in order to check whether, with the determined number M of support points, measurement signals can also be reliably reconstructed that are derived from an extended number of S erw =Smax+J, with a positive natural number J, of which N basic signals can be formed as a linear combination.

[0038] In some embodiments, it is provided that the maximum extended number S erw max is determined by calculating the maximum expanded number S erwis determined for which the quality criterion is still met.

[0039] The invention will be explained in more detail below with reference to a drawing, which will show: Fig. 1 a schematic representation of a flowchart to explain the execution of a time domain spectroscopy; Fig. 2 a signal of a coherent phonon spectroscopy, in which the signal measured according to the WKS sampling theorem, an apodization of the measured 330 support points and a reconstructed signal together with the 85 support points according to the procedure described here are represented; Fig. 3 the Fourier transforms of the signal sampled according to the WKS sampling theorem, transformed after truncation of the first 400 fs and apodization, and the Fourier spectrum of the signal reconstructed according to the method proposed here; and Fig. 4 A schematic representation of a spectrometer.

[0040] In Fig. Figure 1 schematically depicts the flowchart of a time-domain spectroscopy method 100. In a first step 110, a number N of possible fundamental signals are acquired, based on which a signal to be measured is to be approximated.

[0041] Subsequently, a number of the maximum number of components S 120 is recorded, which defines a maximum number of basic signals that can be combined for a reconstruction in a linear combination.

[0042] A deterministic support point determination model is then recorded 130, based on which a number of support points can be deterministically determined from a basic set of support points (whose cardinality is greater than or equal to N).

[0043] In addition, a determination criterion 140 is recorded, which can be used to determine whether a sampling with a number of support points determined according to the deterministic support point determination model ensures a successful reconstruction of a sampled measurement signal or not.

[0044] Then, an initial estimate of the required number M of support points for sampling is performed or recorded. This estimated value is preferably chosen to be low and corresponds, for example, to about one fifth to one quarter of the number of possible basic signals N.

[0045] A set of M support points is then determined according to the captured deterministic support point determination model 160. For example, the support points are determined according to a geometric progression.

[0046] The measurement matrix corresponding to the support points is then generated 170.

[0047] It is checked whether the measurement matrix meets the determination criterion for a reconstruction.

[0048] In one case, the columns of the matrix are treated as vectors and each is normalized. For the normalized column vectors, the magnitudes of the pairwise scalar products are determined, and the maximum magnitude of this set is calculated. This indicates the so-called coherence. If this is significantly less than 1, for example, less than 1 / 10, then sampling with the determined support points will reliably enable a reconstruction of the signal.

[0049] If the determination criterion is not met, the steps from selecting or estimating the required number M of support points 150 are repeated, varying the number M.

[0050] If the determination criterion is met, the actual measurements are then carried out and the measurement signal is sampled at the M sampling times 190.

[0051] The linear system of equations y = Ax + e^200 is solved using the vector y obtained from M samples. An example of a possible reconstruction of the spectrum in the frequency domain (the N-dimensional vector x) is given for this case. For example, the spectrum can be determined using the following convex program (also known as "square-root LASSO"), which is described by Hendrik Bernd Petersen and Peter Jung in "Robust instance-optimal recovery of sparse signals at unknown noise levels", Information and Inference: A Journal of the IMA, Volume 11, Issue 3, September 2022, pages 845-887, https: / / doi.org / 10.1093 / imaiai / iaab015: minx‖Ax−y‖2+λ‖x‖1d, where the M-dimensional vector y contains the measured samples in the time domain. Here, ||x||1 denotes the sum of the absolute values ​​of the components of the vector x, and ||Ax - y||2 is the Euclidean norm of the residual Ax-y. The regularization parameter λ can be chosen in this case depending on the dimensions M and N. This approach is also possible with other quasi-norms.

[0052] The MxN-dimensional matrix A can contain N possible sampled resonances in the N columns. The above reconstruction approach then selects as its solution a sparse (or compressible) linear combination of the available possible sampled resonances (i.e., only a few columns contribute significantly to approximating y). This information is then output.

[0053] In further training, a quality criterion can be evaluated, possibly iteratively, to determine an expanded number of basic signals from which measurement signals may be formed as linear combinations, so that they can be reliably reconstructed using this expanded number of basic signals. The determination of the so-called "Restricted Isometry Property" constant δ 2S , (RIP-constant) represents such a criterion.

[0054] The following will be discussed in connection with Fig. 2 and Fig. 3. A specific application example is described. The application example is coherent phonon spectroscopy (CPS) for determining the Raman-active natural frequencies of solids. Fig. Figure 2 shows the time-domain measurement of the transmission change of a near-infrared probe laser pulse at a time interval from a near-infrared control laser pulse (pulse duration 20 fs each, probe laser pulse energy: 500 pJ, control laser pulse energy: 1.5 nJ). The range between 0 and ~0.4 ps is excluded from the analysis to avoid the region of the so-called coherent artifact.

[0055] Gray line 410 (gray) represents the transmission change of quartz in the time domain after excitation with a near-infrared short-pulse laser and a pump laser pulse from the same laser. The time domain is sampled by measuring a total of 356 data points. The number of data points is determined by the desired spectral range (30 THz) and the desired resolution (200 GHz) according to the WKS sampling theorem. To determine the natural frequencies according to the state of the art, the first 400 fs of the signal are truncated. The measurement is then subjected to Hamming apodization to minimize artifacts caused by discontinuities in the Fourier transform. 330 of the original 356 data points are used as reference points for further analysis. The apodized signal is shown as black line 420, and the reference points as black triangles 440.

[0056] The 85 support points determined according to the method described here are represented by gray spheres 450. These 85 support points correspond to the reduced number of necessary support points. This results in a reconstructed time transient, shown as a dashed gray line 430, which agrees very well with the original measurement.

[0057] The Fourier transform then yields the spectra of the eigenfrequencies, which are in Fig. Figure 3 shows the natural frequency spectrum 510 corresponding to the apodized signal sampled according to the WKS theorem. The signal corresponding to the support points determined according to the method described here is shown as a gray dashed line 520. A very good agreement can be observed. The natural frequencies and waveforms are correctly reproduced according to the method described here.

[0058] The dCSTD method performs a reconstruction using only 85 "determined," i.e., pre-defined, support points. The good agreement between the time transient reconstructed with this significantly smaller number of support points and the original measurement demonstrates the high performance of the proposed method. This is confirmed by the very good agreement of the spectral function in the frequency domain.

[0059] In Fig.Figure 4 schematically depicts a spectrometer 500. This includes a scanning device 600, which controls or performs the scanning of a measurement signal at deterministically determined reference points. For this purpose, the scanning device includes, in addition to a control unit 602, for example a short-pulse laser 604 to perform optical gating. In order to detect the different reference points irregularly distributed over the measured time transients, in one embodiment M delay lines 610-1 - 610-M, for example in an integrated semiconductor circuit 620, are designed as delay lines that delay an optical or electronic control signal according to the time durations that correlate with the scanning times.

[0060] An evaluation circuit 700 is designed to solve the linear equation that describes the measurement procedure.

[0061] An output device 800, which may include a display or be configured as an interface, is configured to output information indicating the basic signals and their coefficients, from which the sampled signal can be reconstructed as a linear combination of a few periodic, possibly damped, basic signals.

[0062] In one embodiment, the spectrometer additionally comprises a support point determination unit 900, which is configured to determine the required support points for a scan according to the method described above.

Claims

[1] Method (100) for time-domain spectroscopy with reduced support point acquisition comprising the following steps: a) Capturing a number N of possible basic signals (110) from which a time signal to be measured is to be reconstructed as a linear combination; b) Capturing a maximum number of components S max (120), which specifies a maximum number of basic signals that can be combined for reconstruction in the linear combination; c1) Identifying a deterministic support point identification model (130) which allows a number of support points to be deterministically determined from a basic set of support points whose cardinality is preferably greater than or equal to N, and c2) a determination criterion (140) by means of which it can be determined whether a sampling with a number of support points determined according to the deterministic support point determination model results in a successful reconstruction of a sampled measurement signal with a maximum number S max guaranteed by basic signals or not; d) Selecting or estimating a required number of support points M (150); e) Determining M support points using the deterministic support point determination model (160); f) Setting up an MxN measurement matrix A (170) by means of which the sampling process is described as a linear process according to the following linear equation: y=Ax+e, where y is an M-dimensional vector of the sampled values ​​measured at the M determined support points, x is an N-dimensional vector of the coefficients that specify the contributions of the possible fundamental signals in the linear combination for the reconstruction of the measurement signal, and e is an M-dimensional vector representing an additive disturbance; (g) Evaluate the determination criterion and determine (180) whether, when sampling with the determined M support points, the measurement signal, which consists of any linear combination of a maximum of S max The N possible basic signals can be formed and reconstructed, but not all measurement signals can be reconstructed that result from a linear combination of at least S. max +1 of the N possible basic signals are formed, and g1) If this is not the case, change the number of estimated required support points M and repeat procedure steps e) to g) g2) and if this is the case, h) Performing measurements to determine the M sample values ​​at the M support points (190), and i) Evaluate the linear equation (200) describing the sampling process; j) Output of information (210) indicating the basic signals and coefficients of the linear combination required for reconstruction as determined during the evaluation. [2] Method according to claim 1, characterized by , that the support points are determined as a subset M of N possible support points that divide the temporal signal to be sampled into equidistant intervals according to the WKS sampling theorem. [3] Method according to claim 1 or 2, characterized by , that the evaluation of the linear equation of the sampling process with the determined sample values ​​is carried out according to a method called Square-root-LASSO. [4] Method according to any of the preceding claims, characterized by, that sampling is carried out using optical gating, in which the support points each define a time interval between an optical excitation pulse and an optical sampling pulse. [5] Method according to any one of claims 2 to 4, characterized by , that a second set of support points is determined by cyclically permuting the M determined support points of N possible support points, preferably by 1 possible support point, more preferably by one tenth of the difference NM of the number of possible support points N and the determined support points M, and that steps h) to j) are additionally carried out for the second set of support points. [6] Method for fabricating a spectrometer for time domain spectroscopy with reduced support point acquisition comprising the following steps: a) Capturing a number N of possible basic signals, from which a time signal to be measured is to be reconstructed as a linear combination; b) Identifying an upper estimate of a maximum number of components S, which defines a maximum number of basic signals that can be combined for a reconstruction in the linear combination; c1) Developing a deterministic support point determination model, based on which a number of support points can be deterministically determined from a basic set of support points whose cardinality is preferably greater than or equal to N, and c2) Identifying a determination criterion by which it can be determined whether a sampling with a number of support points determined according to the deterministic support point determination model results in a successful reconstruction of a sampled measurement signal with a maximum number S max is guaranteed by basic signals or not; d) Estimating the required number of support points M, e) Determining M support points using the deterministic support point determination model, f) Setting up an MxN measurement matrix A, by means of which the sampling process is described as a linear process according to the following linear equation: y=Ax+e, where y is an M-dimensional vector of the sampled values ​​measured at the M determined support points, x is an N-dimensional vector of the coefficients that specify the contributions of the possible fundamental signals in the linear combination for the reconstruction of the measurement signal, and e is an M-dimensional vector representing an additive disturbance; g) Evaluate the determination criterion and determine whether, when scanning with the determined M support points, the measurement signal, which consists of any linear combination of a maximum of S max The N possible basic signals can be formed and reconstructed, but not all measurement signals can be reconstructed that result from a linear combination of at least S max +1 of the N possible basic signals are formed, and g1) If this is not the case, change the number of estimated required support points M and repeat procedure steps e) to g) g2) and if this is the case, k) Training a scanning device which is designed to control a measurement signal acquisition to the determined M support points, I) Training an evaluation device which is trained to solve a linear equation y =Ax+e describing the measurement signal sampling on the basis of a vector y formed from the measurement results sampled for the determined M support points; m) Designing an output device to output information specifying the basic signals and coefficients of the linear combination required for reconstruction as determined during the evaluation. [7] Spectrometer (500) for time domain spectroscopy with reduced support point detection manufactured according to a method according to claim 6, comprising the scanning device (600) and a detection device (602) for controlling a sampling of measurement signals at the determined M support points and the evaluation device (700) for evaluating the linear equation describing the sampling as well as the output device (800) for outputting information that specifies the basic signals and coefficients of the linear combination required for reconstruction determined during the evaluation. [8] Spectrometer according to claim 7, characterized by , that a support point determination unit (900) is linked to the scanning device (600), which is configured to perform the process steps a) to f) according to claim 6. [9] Spectrometer according to one of claims 7 or 8, characterized by, that delay lines (610-1 to 610-M) are formed in the scanning device M, the different resulting time delays of which correlate with the measurement times associated with the determined support points. [10] Spectrometer according to any one of claims 7 to 9, characterized by , that the scanning device includes at least one laser (604) for generating the light pulses for optical gating. [11] Method or spectrometer according to any of the preceding claims characterized by , that an additional quality criterion is evaluated to check whether measurement signals can be reliably reconstructed with the determined number M of support points, which are derived from an extended number of S erw =S max +J, with a positive natural number J, of which N basic signals can be formed as a linear combination. [12] Method or spectrometer according to claim 11, characterized by , that the maximum extended number S erw maxis determined by calculating the maximum expanded number S erw is determined for which the quality criterion is still met.

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