Time-stretch spectroscopy apparatus and time-stretch spectroscopy method

Abstract

To provide a time-stretch spectroscopy apparatus and the like capable of restoring an original spectrum without using a high-speed modulation system or receiving system, even when temporally adjacent pulses overlap after stretching.SOLUTION: A time-stretch spectroscopy apparatus 100 comprises: an optical modulator 20 that performs intensity modulation in pulse unit on a group of measurement pulse lights BP obtained by irradiating a measurement target having characteristics with respect to optical transmittance or reflectance with a group of pulse lights; a pulse stretcher 30 that time-stretches the group of measurement pulse lights BP; and a signal processing device that, under the assumption that each measurement pulse light EP is sparse as data, performs reconstruction that estimates respective pulse signal wavelength components PS corresponding to respective stretched pulse lights EP obtained by individually time-stretching the group of measurement pulse lights BP, from a superimposed signal SS synthesized so as to cause temporal overlap after time stretching.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a time stretch spectroscopy device and a time stretch spectroscopy method that uses a compressed sensing technique to resolve superimposed pulses, based on time stretch spectroscopy, which stretches measured pulsed light in time to create a correspondence between wavelength and time. [Background technology]

[0002] Time-stretch spectroscopy is a technique for measuring targets whose optical absorptance or reflectance fluctuates on a short time scale, such as microseconds. In time-stretch spectroscopy, a large second-order dispersion is imparted to the optical pulse obtained by measurement, stretching the pulse in time, and the time waveform of this stretched pulse is then detected. The time waveform of the stretched pulse has a one-to-one correspondence between time and wavelength, and wavelength (or frequency) spectra can be obtained from this time waveform. In time-stretch spectroscopy, the pulse repetition frequency corresponds to the acquisition rate, making it possible to perform spectroscopy at ultra-high acquisition rates, for example, on the order of 10 MHz. Furthermore, compared to other techniques such as Fourier transform spectroscopy, time-stretch spectroscopy offers the advantage of a superior signal-to-noise ratio.

[0003] In conventional time-stretch spectroscopy, the amount of pulse stretching and the pulse repetition frequency (the inverse of the measurement interval) are adjusted to prevent overlap between adjacent pulses after stretching. Under the condition that stretched pulses do not overlap, the effective sampling rate fR of the analog-to-digital converter in the receiving system, taking into account the electrical bandwidth of the receiving system, must be greater than N / δτ (N = Δν / δν, where Δν is the frequency bandwidth and δν is the frequency resolution), assuming the number of measurement points N and the spectrum acquisition time interval δτ are approximately 12.5 ns. For example, assuming the number of measurement points N and the spectrum acquisition time interval δτ are approximately 12.5 ns, fR must be greater than approximately 6.4 GHz. However, the high cost of analog-to-digital converters with fR of 5 GHz or higher poses a major obstacle to practical application.

[0004] As a prior art technique for mitigating the problem of the bandwidth of the analog-digital converter, there is a method in which the time-stretched pulse is intensity-modulated using a known modulation pattern, and after receiving it using a low-speed receiving system, the spectrum is restored using the modulation pattern and the measured waveform (see Non-Patent Document 1). This method has a low cost improvement effect because the modulation system requires an optical intensity modulator and a digital-to-analog converter with a bandwidth as high as that originally required for the receiving system (approximately 5 GHz).

[0005] There is also research that applies a technique called compressed sensing (CS) to time-stretch imaging to attempt to resolve overlapping time-stretch pulses (see Non-Patent Document 2). However, the method in this research relies on a fixed spatial mask designed specifically for imaging, and is therefore not suitable for time-stretch spectroscopy in other fields. [Prior art documents] [Patent documents]

[0006] [Non-Patent Document 1] R. Li, et al. ACS Photonics 2023, 10, 7, 2399-2406 [Non-patent document 2] C. Lei, et al. IEEE Photon. J. 9, 1 (2017). Summary of the Invention

[0007] The present invention has been made in view of the above-mentioned background art, and aims to provide a time stretch spectroscopy device and a time stretch spectroscopy method that can restore the original spectrum without using a high-speed modulation system or receiving system, even if adjacent pulses overlap after stretching.

[0008] In order to achieve the above object, a time stretch spectroscopy device according to the present invention includes an optical modulator that performs intensity modulation on a pulse-by-pulse basis on a group of measurement pulse light obtained by irradiating a measurement target having characteristics related to optical transmittance or reflectance with the group of pulse light; a pulse stretcher that time stretches the group of measurement pulse light; and a signal processing device that performs reconstruction to estimate pulse signal wavelength components corresponding to each stretched pulse light obtained by individually time-stretching the group of measurement pulse light from a superimposed signal that is synthesized so that temporal overlap occurs after time stretching, on the assumption that each measurement pulse light is sparse as data.

[0009] In the time stretch spectroscopy device, the signal processing device performs reconstruction to estimate each pulse signal wavelength component corresponding to each stretched pulse light obtained by individually time-stretching a group of measurement pulse lights from a superimposed signal that is combined so that temporal overlap occurs after time stretching, on the assumption that each measurement pulse light is sparse as data, so that each stretched pulse light included in the group of time-stretched measurement pulse lights can be separated as data.In other words, it is possible to restore individual spectral information included in the group of time-stretched measurement pulse lights as pulse signal wavelength components while performing time stretching that allows overlapping of each measurement pulse light without using a high-speed modulation system or receiving system.

[0010] In order to achieve the above object, a time stretch spectroscopy according to the present invention includes the steps of: intensity-modulating, on a pulse-by-pulse basis, a group of measurement pulse beams obtained by irradiating a measurement target having characteristics related to optical transmittance or reflectance with the group of pulse beams; time-stretching the group of measurement pulse beams; and, on the premise that each measurement pulse beam is sparse as data after the time stretching, performing reconstruction to estimate each pulse signal wavelength component corresponding to each stretched pulse beam obtained by individually time-stretching the group of measurement pulse beams from a superimposed signal that is synthesized so that temporal overlap occurs after the time stretching. [Brief explanation of the drawings]

[0011] [Figure 1] 1 is a conceptual block diagram illustrating a time stretch spectroscopy device according to an embodiment. [Figure 2] FIG. 10 is a conceptual block diagram illustrating a modified time stretch spectroscopy device. [Figure 3] FIG. 1 is a diagram showing a specific example of a time stretch spectroscopy device. [Figure 4] FIG. 4(a) shows a group of measurement pulse light beams that have passed through the measurement object, FIG. 4(b) shows a group of measurement pulse light beams that have been randomly intensity-modulated, FIG. 4(c) shows the superimposed signal captured by the photodetector, and FIG. 4(d) shows the pulse signal wavelength components after decomposition by reconstruction processing. [Figure 5] Figure 5(a) illustrates a numerical experiment for analyzing particulate flow, Figure 5(b) shows a simulation of the transmission spectrum of a particulate, Figure 5(c) illustrates the time-domain signal when the overlap ratio is 4, and Figure 5(d) shows the RMSE between the reconstructed bead image and the original bead image as a function of the overlap ratio. [Figure 6] This figure shows the reconstructed CH4 and OCS spectra at three different times (nt = 15, 30, 45) alongside the ground truth. [Figure 7] Figure 7(a) shows the RMSE between the reconstructed and GT spectra, Figure 7(b) shows the relative peak positions from GT, Figure 7(c) shows the deviation of the mean linewidth from GT, and Figure 7(d) shows the effect of SNR on the individual peak heights of the reconstructed spectra. DETAILED DESCRIPTION OF THE INVENTION

[0012] [Embodiment] Hereinafter, an embodiment of a time stretch spectroscopy device and a time stretch spectroscopy method according to the present invention will be described with reference to the drawings.

[0013] The time stretch spectroscopy device 100 includes an optical modulator 20, a pulse stretcher 30, and a signal processing device 60. The optical modulator 20 includes, for example, an acousto-optic element 21 or an electro-optic element 22. The optical modulator 20 is an amplitude modulator that operates under the control of the signal processing device 60 and performs intensity modulation, i.e., amplitude modulation, on a pulse-by-pulse basis on a group of measurement pulsed light BP obtained from an object under test (OB). Here, the group of measurement pulsed light BP is obtained by irradiating a group of pulsed light beams onto a measurement target, i.e., the object under test (OB), having characteristics related to optical transmittance or reflectance. The optical transmittance (indirectly including absorptance and scattering rate) and reflectance of the object under test (OB) fluctuate on a time scale approximately equal to, but not limited to, the pulse interval. The optical modulator 20 operates at a normal bandwidth, for example, approximately 10 MHz. The pulse stretcher 30 is, for example, an optical fiber 31 having chromatic dispersion and time stretches the group of measurement pulsed light BP. The pulse stretcher 30 time-stretches the group of intensity-modulated measurement pulsed light BP to generate a superposed signal SS0 that is synthesized so as to overlap in time. The superposed signal SS0 corresponds to the group of time-stretched measurement pulsed light and includes the time-stretched stretched pulsed light EP.

[0014] The signal processing device 60 includes a signal input device 40 and a data processing device 50. The signal input device 40 has a photodetector 41 that photoelectrically converts the superimposed signal SS0, and an A / D conversion circuit 42 that A / D converts the signal from the photodetector 41, and outputs a digital superimposed signal SS as digital data from the superimposed signal SS0.

[0015] The data processing device 50 includes an arithmetic processing circuit 51, an interface circuit 52, a storage device 53, and a user interface device 54. The arithmetic processing circuit 51 operates based on a program or the like stored in the storage device 53 and uses a compressive sensing (CS) technique to reconstruct each pulse signal wavelength component PS corresponding to the stretched pulse light EP included in the superimposed signal SS0, which is a group of time-stretched measurement pulse light. That is, on the assumption that each measurement pulse light EP is sparse data, the arithmetic processing circuit 51 estimates and reconstructs each pulse signal wavelength component PS corresponding to each stretched pulse light EP obtained by individually time-stretching the group of measurement pulse light BP from the digital superimposed signal SS obtained by digitizing the superimposed signal SS0. These pulse signal wavelength components PS correspond to a virtual group of stretched pulse light EP0 obtained when the components of the group of measurement pulse light BP are individually time-stretched without intensity modulation. The pulse signal wavelength component PS is a time waveform having a one-to-one correspondence between time and wavelength, and can be converted into a wavenumber spectrum or frequency spectrum of a group of measurement pulse light BP by adjusting the scale in consideration of the characteristics of the optical fiber 31.

[0016] The reconstruction process or spectrum recovery process for estimating the pulse signal wavelength component PS performed by the data processing device 50 is an application of a compressed sensing algorithm. As the compressed sensing algorithm, TwIST (Two-step iterative shrinkage / thresholding) or a machine learning model can be used.

[0017] The compressed sensing algorithm specifically executed by the data processing device 50 is based on a reconstruction algorithm that reduces the difference between the actual and estimated values, and recovers the vector x of the pulse signal wavelength component PS so as to minimize a predetermined loss function Φ(x). The loss function Φ(x) is, for example, Φ(x)=λ||D ν x||1+λ2||D t x||1, where || ||1 is the L1 norm, Dν is the frequency derivative, D t is a differential in the time direction, and the values ​​λ1 and λ2 are parameters that are determined in advance. By using such a loss function Φ(x), it is possible to obtain better reconstruction results when the fluctuations in the time direction and the fluctuations in the frequency direction differ. Furthermore, the loss function Φ(x) may include a term proportional to ||x||1. In this case, the reconstruction accuracy can be improved when the pulse signal wavelength component PS, which is the reconstructed spectrum, is sparse (the proportion of non-zero components to the whole is small). Note that instead of directly reconstructing the vector x, the spectrum x in the case where a sample, i.e., an object under test (OB) does not exist in advance is calculated. B Measure the difference xx from B In this case, the reconstruction becomes sparser, which can improve the reconstruction accuracy.

[0018] Assuming that the overlap ratio R=6.4 of the superimposed signal SS0 to be processed by the time stretch spectroscopy device 100 is acceptable, under the following conditions: TIFF2025128532000002.tif38168Measurements can be made using a detector with a sampling rate of 1 GHz. Note that if R=1 (conventional configuration), a sampling rate of 6.4 GHz is required.

[0019] In the above, the pulse stretcher 30 time-stretches the group of intensity-modulated measurement pulsed light BP to obtain the superposed signal SS0, but the present invention is not limited to this processing. That is, the time stretch spectroscopy device 100 may be configured such that the pulse stretcher 30 time-stretches the group of measurement pulsed light BP to obtain a group of stretched pulsed light EP0, and then the optical modulator 20 intensity-modulates the group of stretched pulsed light EP0 and combines these groups of stretched pulsed light EP0 to obtain the superposed signal SS0.

[0020] FIG. 2 is a conceptual block diagram illustrating a modified time-stretch spectroscopy device 100. In this case, a wavelength converter 80 is disposed between an object under test (OB) and an optical modulator 20. The pulsed light source 10 generates a group of illumination pulsed light IP set in a first wavelength range, and the wavelength converter 80 wavelength-converts a group of measurement pulsed light BP01 obtained from the object under test OB into a group of measurement pulsed light BP02 in a second wavelength range suitable for processing by the optical modulator 20 or the like. Specifically, the first wavelength range is, for example, a mid-infrared range (e.g., 3 μm), and the second wavelength range is, for example, a near-infrared range (1 to 2 μm band). This is referred to as up-conversion time-stretch spectroscopy. Note that the first wavelength range may be shorter than the second wavelength range; in this case, it is referred to as down-conversion time-stretch spectroscopy (see International Publication WO 2023 / 112909 for details).

[0021] Examples of applications of the time stretch spectroscopy device 100 shown in FIGS. 1 and 2 include liquid biopsy, flow cytometry, optical coherence tomography (OCT), environmental gas analysis, and LIDAR.

[0022] The time stretch spectroscopy device 100 of the embodiment includes an optical modulator 20 that performs intensity modulation on a pulse-by-pulse basis on a group of measurement pulsed light BP obtained by irradiating a group of pulsed light onto a measurement object, a pulse stretcher 30 that time-stretches the group of measurement pulsed light BP, and a signal processing device 60 that performs reconstruction to estimate each pulse signal wavelength component PS corresponding to each stretched pulsed light EP obtained by individually time-stretching the group of measurement pulsed light BP from a superimposed signal SS0 that is synthesized so that temporal overlap occurs after time stretching, on the assumption that each measurement pulsed light EP is sparse as data.

[0023] The time stretch spectroscopy device 100 can separate, as data, each stretched pulse light EP included in the superimposed signal SS0, which is a group of measurement pulse light after time stretching. That is, it is possible to perform time stretching that allows superimposition on each measurement pulse light EP without using a high-speed modulation system or receiving system, and restore individual spectral information included in the superimposed signal SS0, which is a group of measurement pulse light after time stretching, as a pulse signal wavelength component PS.

[0024] [Specific Examples] 3 is a diagram showing a specific example of a time stretch spectroscopy apparatus 100. The time stretch spectroscopy apparatus 100 includes a pulse light source 10 which is a pulse laser, an optical modulator 20 which is an acousto-optical element 21 or the like, a pulse stretcher 30 which is an optical fiber 31, a photodetector 41, an A / D conversion circuit 42 which is an oscilloscope 142, and a computer 150 which is a data processing device 50.

[0025] The pulsed light source 10 emits a group of pulsed light IP over a predetermined wavelength range as illumination light to be irradiated onto the object under test OB. This causes the object under test OB to generate a group of measurement pulsed light BP (see FIG. 4(a)). Each element pulse E constituting the group of measurement pulsed light BP has a spectral distribution affected by the object under test OB. The individual element pulses E constituting the group of measurement pulsed light BP emitted from the object under test OB are randomly intensity-modulated by an optical modulator 20 using a bias for each element pulse E' (see FIG. 4(b)). This randomization improves the accuracy of spectral reconstruction using a compressed sensing algorithm (see reference [2]). The group of measurement pulsed light BP that has passed through the optical modulator 20 is broadly stretched along the time axis by a pulse stretcher 30, and multiple adjacent stretched pulsed light EP are overlapped and combined. This combined signal is captured by a photodetector 41 as a superimposed signal SS0 (see FIG. 4(c)). The superimposed signal SS0 is digitized and converted into a digital superimposed signal SS, which is a time-intensity waveform, by the oscilloscope 142. The computer 150 performs a spectral reconstruction process on the digitized time-intensity waveform using a compressed sensing algorithm, and acquires pulse signal wavelength components PS corresponding to a group of stretched pulsed light EP or stretched pulsed light EP0 (see FIG. 4(d)).

[0026] In the above description, the group of pulsed light IP is applied to the object under test OB before the modulation process by the optical modulator 20, but the group of pulsed light IP may also be applied to the object under test OB after the modulation process by the optical modulator 20.

[0027] The analytical formulation of the spectrum reconstruction process will be explained below. The number of pulses and the spectral element are represented by N and M, respectively. The spectra of the pulse (i.e., the measurement pulse light BP) before and after the interaction with the object under test OB are respectively expressed as x B (n ν ) and x0(n ν ,n t ), where n ν =1,2,…,M or n t=1,2,…N are wavenumber and time indices. These are It is represented as a vector, such as TIFF2025128532000003.tif13163, where T denotes the transpose of the vector. The linear measurement process is described by the following equation: TIFF2025128532000004.tif7163 where y is an L-dimensional vector representing the measured temporal intensity and K is an L×NM matrix operator representing the measurement process. The dimension L depends on the measurement parameters, such as the sampling frequency of the A / D conversion circuit 42 and the variance of the pulse stretcher 30. In the reconstruction process, K is TIFF2025128532000005.tif7163, where H is an L × NM matrix representing the variance, and G is an NM × NM diagonal matrix representing the intensity modulation. The matrix H is a simple mapping matrix consisting of 0 or 1. The compressed sensing algorithm used in the reconstruction process of this spectroscopy provides an estimated value x0 as the answer to the inverse problem. TIFF2025128532000006.tif10163where x_ is the object to be estimated, When it is TIFF2025128532000007.tif6163, it is x0-x B is a variable corresponding to the difference between the spectrum of the object under test (OB) and the baseline spectrum. n and Φ is L n The norm (n is a real number greater than or equal to 0) and the regularization function are respectively represented by the baseline term x B Although it seems unnecessary, including this term has been found to result in better reconstruction. We employ total variation (TV) as a regularization function, which is the L1 norm of the first derivative of x_, widely used in signal reconstruction problems (refs. [3, 4]). We have confirmed that asymmetric 2D TV is effective for this reconstruction problem. This regularization function or loss function is written as follows: TIFF2025128532000008.tif7163 where D ν and D tis a matrix that calculates the difference between adjacent wavenumbers or time elements, and λ1 and λ2 are regularization coefficients. The reconstruction algorithm used in the reconstruction process is TwIST (reference [5]).

[0028] To verify the method adopted in this study, the inventors first performed numerical experiments simulating the analysis of particulate flow based on 1D serial time-encoded amplification microscopy (STEAM), one of the best-known applications of time-stretch spectroscopy.

[0029] As shown in Figure 5(a), opaque particles (i.e., beads) flowing through a microfluidic channel were assumed to be spatially aligned. Their spatial profile was measured by a 1D spectral shower formed in the Fourier plane of a diffraction grating. The number of spectral elements examined was set to 64. Here, the overlap ratio, defined as the number of overlapping pulses (the ratio of the extended pulse duration to the pulse interval), was varied. The overlap ratio corresponds to the extended pulse width / pulse time interval. As shown in Figure 5(b), the flow rate was adjusted to measure the bead image with 64 pulses, which is proportional to the overlap ratio. Amplitude modulation or intensity modulation was performed with 256 gray levels. The signal-to-noise ratio (SNR) was set to 80 and is defined as the ratio of the standard deviation of the noise to the peak intensity of the baseline spectrum. Figure 5(c) shows the time-intensity signal when the overlap ratio was 4. For this example reconstruction, we empirically set the regularization factor λ = 10. -7 / 3 and λ2=10 -4 / 3 Figure 5(d) shows the root mean square error (RMSE) between the reconstructed and original bead images as a function of the overlap ratio. The simulation was repeated 10 times for each overlap ratio. The results show that our reconstruction works up to an overlap ratio of 8 with a root mean square error (RMSE) of approximately 0.05. This indicates that our technique allows an 8-fold increase in flow velocity, thereby improving the throughput of flow measurement.

[0030] Next, we conducted a numerical experiment of mid-infrared (MIR) gas-phase molecular spectroscopy to demonstrate high-resolution time-stretch spectroscopy with a dynamically changing complex spectral profile. Here, we simulated up-conversion time-stretch infrared spectroscopy (UC-TSIR). In UC-TSIR, the spectrum of a mid-infrared femtosecond pulse interacting with a sample, i.e., an object under test (OB), is converted to a spectrum in the telecommunications region for time stretching and detection. We investigated the frequency range from 2912.06 to 2932.99 cm. -1 The MIR spectrum covers the frequency range of 9400 cm -1 Difference frequency generation from a periodically poled lithium niobate (PPLN) crystal pumped by a continuous-wave laser (wavelength 1.064 μm) produced a frequency of approximately 6450 cm -1 It was assumed that the light was upconverted to a wavelength of 1.55 μm. The repetition rate of the illumination pulsed light IP was set to 80 MHz, and the measurement pulsed light BP was stretched at 19.8 ns / nm (corresponding to an overlap ratio of 8) using an optical fiber 31. It is important to note that in gas-phase molecular spectroscopy, near-field propagation effects are expected, which inherently distort the stretched spectrum. This effect can be included in the calculation by incorporating the mathematical model expressed as follows: TIFF2025128532000009.tif6163TIFF2025128532000010.tif14163Here, G, LPF, D2, and H hil denotes the transmittance spectrum, low-pass filtering, second-order dispersion, and Hilbert transform. After resolving the overlapping spectra, the spectral distortions are corrected using a post-processing method described in [1]. In this method, the transmittance x0 / x B A method called the alternating direction method of multipliers (reference [6]) with a sparsity constraint of is used. The spectral resolution is 0.03 cm. -1To avoid large ripple artifacts on the sharply filtered spectrum, we set the baseline spectrum x with smooth bandpass filtering, expressed as B was assumed. TIFF2025128532000011.tif25163 where ν is the wave number and the parameter is ν a =2914.53cm -1 , ν b =2929.53cm -1 , σ=1.5cm -1 is set to

[0031] 12 CH4 molecules and 16 O 12 C 32 Sixty consecutive spectra of the mixture with S molecules were measured, whose concentration changed rapidly during the measurement. The total transmittance is expressed as: TIFF2025128532000012.tif10163where n t is the index of the measured spectrum, and T CH4 and T OCS is the transmittance of CH4 and OCS. The sample, i.e., the object to be measured OB, has n t When n = 1, it consists of CH4 t = 60, which consists of OCS. The CH4 / OCS transmission ratio was calculated using the HITRAN database (Ref. [7]). The pressure, temperature, and interaction length were set to 10 Torr, 296 K, and 50 mm, respectively. The SNR of the time-domain signal was assumed to be 80, as evaluated as realistic in Ref. [1]. Figure 6 shows the transmission ratios for three different time periods (n t The reconstructed spectra for λ1 = 0 and λ2 = 10 are shown alongside the noise-free ground truth (GT). The top half of the chart shows GT, and the bottom half of the chart shows the reconstructed spectra. The reconstructions are -4 / 3It has been found that this method performs well with the regularization term. When the changes in the time domain are much slower than the corresponding changes in the wavenumber domain, as in this example, the regularization in the time domain is important. In comparison, the contribution of the regularization term in the wavenumber domain is negligible and can be omitted.

[0032] To evaluate the effect of SNR on the accuracy of the reconstruction, we repeated the reconstruction at different SNRs (Fig. 7). For each SNR condition, we randomly selected different modulation patterns and performed the reconstruction at 10 Torr, 296 K, and 50 mm. 12 Ten simulations were performed for the steady-state spectrum of CH4. Figure 7(a) shows the a ≦ν≦ν b The RMSE between the reconstruction and GT spectra is shown in Fig. 1. The results show that the RMSE remains around 0.02 until the SNR drops to 46.5, demonstrating robustness to noise.

[0033] The inventors investigated the effect of SNR on the peak position and linewidth of the absorption line in the reconstructed spectrum. -1 We used a large, isolated absorption line. We evaluated the peak position and linewidth by fitting to a Gaussian distribution using the Levenberg-Marquardt method implemented in the Scipy library (reference [8]). As shown in Figure 7(b), we observed that the standard deviation of the peak position relative to the GT was one order of magnitude smaller than the spectral resolution of the system. Similarly, the deviation of the average value of the linewidth from the GT did not exceed 2% (Figure 7(c)).

[0034] Finally, we evaluated the effect of SNR on the individual peak heights of the reconstructed spectrum (Fig. 7(d)). In Fig. 7(d), the dotted line indicates GT. In this analysis, the peak height at 2917.64 cm in the reconstructed transmission spectrum was -1 , 2927.43cm -1 , and 2922.91 cm -1We calculated the average peak heights of the three absorption lines in the NMR spectrum. The results show that our method can reconstruct peak heights even at a low SNR of 10. However, we observed a tendency to underestimate peak heights regardless of the SNR, which became more pronounced as the peaks became taller. This resulted in a lower RMSE limit in the high SNR region, as shown in Figure 7(a). This tendency was also observed in simple simulations that did not consider near-field propagation distortion, so this underestimation is not caused by post-processing for distortion correction.

[0035] In conclusion, we propose a compressive time-stretch spectroscopy method that can resolve overstretched overlapping pulses and overcome the limitations of the trade-off between acquisition speed, spectral resolution, and spectral bandwidth. The method operates via a simple pulse-by-pulse intensity modulation and a reconstruction algorithm that applies compressed sensing based on total variation (TV) regularization. We numerically tested the method for applications involving complex temporal and spectral fluctuations, such as particulate flow analyzers and gas-phase molecular spectroscopy. We demonstrated its operation using an overlap ratio of 8 with a realistic single-shot SNR of less than 100 (Ref. [1]). Our technique is expected to lead to improvements in acquisition speed, spectral resolution, and / or spectral bandwidth. For example, unprecedented acquisition speeds exceeding GHz can be achieved using a high-repetition-rate mode-locked laser. Furthermore, this technique can be effectively applied to time-stretch spectroscopy operating in wavelength regions such as visible light (Ref. [9]) and mid-infrared light (Ref.

[10] ), where available detector bandwidths are narrow compared to the telecommunications region. The inventors hope to further improve the reconstruction accuracy through the use of machine learning techniques that have been demonstrated in the field of compressed spectral imaging (Reference

[11] ).

[0036] [Variations and Others] Although the present invention has been described above based on the embodiments, the present invention is not limited to the above embodiments. For example, the central wavelength, pulse repetition frequency, sampling rate, optical bandwidth, number of measurement points, etc. of the measurement light used in the example of the time stretch spectroscopy device 100 are merely examples and can be selected taking into consideration the properties of the object under test OB and the measurement pulsed light BP obtained from it. In this case, for example, the pulse repetition frequency may not be constant but may fluctuate, but the data processing device 50 monitors the timing of the pulse emitted from the pulse light source 10 and the intensity modulation rate by the optical modulator 20.

[0037] The recovery algorithm for the vector x performed by the data processing device 50 is not limited to the loss function Φ(x) exemplified as equation (4), and various models suitable for pulse stretch spectroscopy can be used.

[0038] The intensity modulation of the measurement pulsed light BP by the optical modulator 20 is not limited to random modulation, but may be regular. In this case, the data processing device 50 monitors the intensity modulation rate by the optical modulator 20 for each pulse. Note that random modulation tends to make it relatively easy to estimate and reconstruct each pulse signal wavelength component PS regardless of the properties of the measurement pulsed light BP.

[0039] [References] 1. K. Hashimoto, T. Nakamura, T. Kageyama, VR Badarla, H. Shimada, R. Horisaki, and T. Ideguchi, Light: Sci. Appl. 12, 48 (2023). 2. EJ Candes and MB Wakin, IEEE Signal Process. Mag. 25, 21 (2008). 3. LI Rudin, S. Osher, and E. Fatemi, Phys. D 60, 259 (1992). 4. X. Yuan, in Proc. IEEE Int. Conf. Image Process. (IEEE, 2012), p. 2539. 5. J. M. Bioucas-Dias and M. A. T. Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007) 6. S. H. Chan, X. R. Wang, and O. A. Elgendy, IEEE Trans. Comput. Imaging 3, 84-98 (2017). 7. I.E. Gordon, L.S. Rothman, R.J. Hargreaves, et al., J. Quant. Spectrosc. Radiat. Transfer 277, 107949 (2022). 8. P. Virtanen, et al. Nat. Methods 17, 261 (2020). 9. J. L. Wu, Y. Q. Xu, J. J. Xu, X. M. Wei, A. C. Chan, A. H. Tang, A. K. Lau, B. M. Chung, H. C. Shum, and E. Y. Lam, K. K. Y. Wong, and K. K. Tsia, Light Sci. Appl. 6, e16196 (2017). 10. A. Kawai, K. Hashimoto, T. Dougakiuchi, V. R. Badarla, T. Imamura, T. Edamura, and T. Ideguchi, Commun. Phys. 3, 152 (2020). 11. Y. Cai, J. Lin, X. Hu, H. Wang, X. Yuan, Y. Zhang, R. Timofte, and L. V. Gool, IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. (IEEE, 2022) p. 17502.

Explanation of Symbols

[0040] 100...time stretch spectroscopy device, 10...pulse light source, 20...optical modulator, 21...acousto-optic element, 22...electro-optic element, 30...pulse stretcher, 30...pulse stretcher, 31...optical fiber, 40...signal input device, 41...photodetector, 42...A / D conversion circuit, 50...data processing device, 51...arithmetic processing circuit, 52...interface circuit, 53...storage device, 54...user interface device, 60...signal processing device, 80...wavelength converter, 142...oscilloscope, 150...computer, BP...measurement pulse light, BP01, BP02...measurement pulse light, E, E'...element pulse, EP, EP0...stretched pulse light, IP...pulse light, OB...object to be measured (measurement target), PS...pulse signal wavelength component, SS0...superposed signal, SS...digital superposed signal

Claims

1. an optical modulator that performs intensity modulation on a group of measurement pulsed light beams obtained by irradiating a measurement target having characteristics related to light transmittance or reflectance with the group of pulsed light beams, in pulse units; a pulse stretcher that time-stretches the group of measurement pulse beams; a signal processing device that performs reconstruction by estimating each pulse signal wavelength component corresponding to each stretched pulse light obtained by individually time-stretching the group of measurement pulse lights from a superimposed signal that is synthesized so that temporal overlap occurs after time stretching, on the assumption that each measurement pulse light is sparse as data; A time stretch spectroscopy apparatus comprising:

2. The time stretch spectroscopy device according to claim 1 , wherein the pulse stretcher time stretches the group of intensity-modulated measurement pulse lights.

3. 2. The time stretch spectroscopy apparatus of claim 1, wherein the pulse stretcher is an optical fiber having chromatic dispersion.

4. The time stretch spectroscopy device according to claim 1 , wherein the optical modulator is either an acousto-optical element or an electro-optical element.

5. The time stretch spectroscopy apparatus according to claim 1 , wherein the signal processing device estimates the wavelength components of the pulse signals from the superimposed signal using a machine learning model.

6. The signal processing device is configured to: ｎ The time stretch spectroscopy apparatus of claim 1 , wherein a loss function including a norm is minimized.

7. The time stretch spectroscopy device according to claim 1 , further comprising a pulsed light source that emits the group of pulsed lights to be irradiated onto an object to be measured, thereby causing the object to generate the group of measurement pulsed lights.

8. a wavelength converter for converting the wavelength of the group of measurement pulse light from a first wavelength region to a second wavelength region; The time stretch spectroscopy apparatus of claim 1 , comprising:

9. The time stretch spectroscopy device according to claim 1 , wherein the optical modulator randomly amplitude-modulates the group of measurement pulsed lights on a pulse-by-pulse basis.

10. a step of performing intensity modulation on a group of measurement pulsed light beams obtained by irradiating a measurement target having characteristics related to optical absorptance or reflectance with the group of pulsed light beams, in pulse units; time-stretching the group of measurement pulse beams; a step of estimating and reconstructing each pulse signal wavelength component corresponding to each stretched pulse light obtained by individually time-stretching the group of measurement pulse lights from a superimposed signal synthesized so that temporal overlap occurs after time stretching, on the assumption that each measurement pulse light is sparse as data; Time stretch spectroscopy comprising:

Images