Time-stretch spectroscopy device and time-stretch spectroscopy method

Abstract

Provided is a time-stretch spectroscopy device capable of restoring an original spectrum without using a high-speed modulation system or reception system even if temporally adjacent pulses overlap after stretching. This time-stretch spectroscopy device comprises: an optical modulator that performs intensity modulation in pulse units on a group of measurement light pulses, which are obtained by irradiating a measurement object having characteristics relating to light transmittance or reflectance with a group of light pulses; a pulse stretcher that performs time stretching on the group of measurement light pulses; and a signal processing device that, with the assumption that the measurement light pulses are sparse as data, performs a reconfiguration estimating pulse signal wavelength components corresponding to the stretched light pulses, which are obtained by individually time stretching the group of measurement light pulses, in light of a superimposition signal synthesized such that a temporal overlap occurs after the time stretching.

Description

Time stretch spectroscopy device and time stretch spectroscopy

[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.

[0002] Time-stretch spectroscopy is a technique for measuring objects 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 an 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. Another advantage of time-stretch spectroscopy compared to other techniques, such as Fourier transform spectroscopy, is its 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 number of measurement points per spectrum is N, the spectrum acquisition time interval is δτ, and 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). For example, assuming the number of measurement points N is 80 and the spectrum acquisition time interval δτ is approximately 12.5 ns, fR must be greater than approximately 6.4 GHz. However, the high cost of analog-to-digital converters with fR = 5 GHz or higher poses a major obstacle to practical application.

[0004] As a prior art technique for alleviating 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 then received using a low-speed receiving system, and 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 a high-speed optical intensity modulator and digital-to-analog converter with a bandwidth equivalent to that originally required for the receiving system (approximately 5 GHz).

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

[0006] R. Li, et al. ACS Photonics 2023, 10, 7, 2399-2406C. Lei, et al. IEEE Photon. J. 9, 1 (2017).

[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.

[0011] FIG. 1 is a conceptual block diagram illustrating a time stretch spectroscopy device according to an embodiment. FIG. 2 is a conceptual block diagram illustrating a modified time stretch spectroscopy device. FIG. 3 is a diagram illustrating a specific example of a time stretch spectroscopy device. FIG. 4a shows a group of measurement pulse light beams passing through a measurement object, FIG. 4b shows a group of measurement pulse light beams randomly intensity-modulated, FIG. 4c shows a superimposed signal captured by a photodetector, and FIG. 4d shows pulse signal wavelength components after decomposition by reconstruction processing. FIG. 5a is a diagram illustrating a numerical experiment assuming particle flow analysis, FIG. 5b shows a simulation of the transmission spectrum of a particle, FIG. 5c illustrates an example of a time-domain signal when the overlap ratio is 4, and FIG. 5d shows the RMSE between the reconstructed bead image and the original bead image as a function of the overlap ratio. FIG. 6 shows three different time (n ｔ = 15, 30, 45) ４ and OCS spectra alongside the ground truth. Fig. 7a shows the RMSE between the reconstructed and GT spectra, Fig. 7b shows the relative peak positions from GT, Fig. 7c shows the deviation of the mean linewidth from GT, and Fig. 7d shows the effect of SNR on the individual peak heights of the reconstructed spectra.

[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-optical element 21 or an electro-optical 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 a 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 has an arithmetic processing circuit 51, an interface circuit 52, a storage device 53, and a user interface device 54. The arithmetic processing circuit 51 is composed of a central processing unit (CPU) and the like, the interface circuit 52 includes a communication circuit and the like, the storage device 53 is a semiconductor storage device including RAM, ROM, flash memory and the like, and the user interface device 54 includes a display, a keyboard and other input / output devices. The arithmetic processing circuit 51 reads out a program stored in the storage device 53 and executes the program. Specifically, the arithmetic processing circuit 51 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 measurement pulse light after time stretching. That is, on the premise that each element constituting the group of measurement pulse light BP or the stretched pulse light EP is sparse as data, the arithmetic processing circuit 51 performs reconstruction to estimate 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 the wavenumber spectrum or frequency spectrum of the 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, which may be TwIST (Two-step iterative shrinkage / thresholding) or a machine learning model.

[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, which is the signal component, so as to minimize a predetermined loss function Φ(x). The loss function Φ(x) is, for example, Φ(x)=λ １ ||D ν x || １ +λ ２ ||D ｔ x || １ can be defined as, where || || １ Is L １ Norm, D. ν is the frequency differential, D ｔ is the differential in the time direction, and the value λ １ , λ ２ is a parameter determined in advance. By using such a loss function Φ(x), it becomes possible to obtain a better reconstruction result when the fluctuation in the time direction and the fluctuation in the frequency direction are different. In addition, the loss function Φ(x) is expressed as ||x|| １ In this case, 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), the reconstruction accuracy can be improved. Note that instead of directly reconstructing the vector x, the spectrum x in the case where the sample, i.e., the object to be measured (OB) does not exist in advance is reconstructed as follows: Ｂ Measure the difference x-x Ｂ In this case, the reconstruction becomes sparser, which can improve the reconstruction accuracy.

[0018] Assuming that the overlap ratio R of the superimposed signal SS0 to be processed by the time stretch spectroscopy device 100 is acceptable at R=6.4, under the following conditions, Measurements can be made using a detector with a sampling rate of 1 GHz. 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 type of processing. That is, the time stretch spectroscopy device 100 may be configured such that the pulse stretcher 30 time-stretches the group of intensity-modulated 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 modulated 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, the mid-infrared range (e.g., 3 μm), and the second wavelength range is, for example, the near-infrared range (1 to 2 μm band). This technique is called up-conversion time-stretch spectroscopy. Note that the first wavelength range may be shorter than the second wavelength range, in which case it is called 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 target, 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 premise that each of the group of measurement pulsed light BP (i.e., each element that makes up the group of measurement pulsed light BP) or stretched 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 BP without using a high-speed modulation system or receiving system, and to restore individual pieces of spectral information included in the superimposed signal SS0, which is a group of measurement pulse light after time stretching, as pulse signal wavelength components PS.

[0024] 3 is a diagram showing a specific example of a time stretch spectroscopy apparatus 100. The time stretch spectroscopy apparatus 100 includes a pulsed light source 10 which is a pulsed 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. 4a). 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 the optical modulator 20 using a bias for each element pulse E′ (see FIG. 4b). This randomization improves the accuracy of spectral reconstruction using the compressed sensing algorithm (see Reference [2]). The group of measurement pulsed light BP passing through the optical modulator 20 is broadly stretched along the time axis by the pulse stretcher 30, and multiple adjacent stretched pulsed light EP are overlapped and combined, resulting in a superimposed signal SS0 captured by the photodetector 41 (see FIG. 4c). 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, thereby acquiring pulse signal wavelength components PS corresponding to a group of stretched pulsed light EP or stretched pulsed light EP0 (see FIG. 4d).

[0026] In the above explanation, a group of pulsed light IP is applied to the object to be measured OB before the modulation process by the optical modulator 20, but it is also possible to apply a group of pulsed light IP to the object to be measured OB after the modulation process by the optical modulator 20, and then perform pulse stretching.

[0027] The analytical formulation of the spectrum reconstruction process will be described below. The number of pulses and the spectrum 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 represented by x Ｂ (n ν ) and x ０ (n ν , n ｔ ) where n ν = 1, 2, ..., M or n ｔ= 1, 2, ... N are wavenumber and time indices. where T denotes the transpose of the vector. The linear measurement process is represented by the following equation: 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 converter circuit 42 and the variance of the pulse stretcher 30. In the reconstruction process, K is Here, 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 calculates the estimated value x as the answer to the inverse problem. ０ to provide. where x is the object to be estimated, When x ０ -x Ｂ is a variable corresponding to (the difference between the spectrum of the object to be measured OB and the baseline spectrum). ｎ and Φ is L ｎ The baseline term x represents the norm (n is a real number greater than or equal to 0) and the regularization function. Ｂ Although it seems unnecessary, including this term has been found to improve reconstruction. The inventors have investigated the L function of the first derivative of x, which is widely used in signal reconstruction problems (refs. [3, 4]). １ The total variation (TV) is adopted as the regularization function, which is a norm. The inventors have confirmed that asymmetric 2D TV is effective for this reconstruction problem. This regularization function or loss function is written as follows: Here, D ν and D ｔ is the matrix that calculates the difference between adjacent wavenumbers or time elements, and λ １ and λ ２ is the regularization coefficient. TwIST (reference [5]) was adopted as the reconstruction algorithm used in the reconstruction process.

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

[0029] As shown in Figure 5a, opaque particles (i.e., beads) flowing through a microfluidic channel were assumed to be spatially aligned, and 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 5b, 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 5c shows the time-intensity signal when the overlap ratio is 4. In this example reconstruction, we empirically used a regularization factor λ １ =10 －７／３ and λ ２ =10 －４／３ Figure 5d 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 measurements.

[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 of 2912.06 to 2932.99 cm. －１ The MIR spectrum covering the frequency range of 9400 cm －１ Difference frequency generation by a periodically poled lithium niobate (PPLN) crystal pumped by a continuous wave laser (wavelength 1.064 μm) produces 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: Here, G, LPF, D ２ , 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 x ０ / x Ｂ A method called the alternating direction method of multipliers (reference [6]) with a sparsity constraint of 0.03 cm is used. The spectral resolution is 0.03 cm. －１ To avoid large ripple artifacts on the sharply filtered spectrum, the baseline spectrum x with smooth bandpass filtering is set to Ｂwas assumed. where ν is the wave number and the parameter is ａ =2914.53cm －１ , ν ｂ =2929.53cm －１ , σ=1.5 cm －１ is set to

[0031] １２ CH ４ 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: Here, n ｔ is the index of the measured spectrum, and T ＣＨ４ and T ＯＣＳ is CH ４ and the transmittance of OCS. The sample, i.e., the object to be measured OB, is ｔ When = 1, CH ４ consisting of n ｔ When = 60, it consists of OCS. CH ４ The / OCS transmittance 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 transmittance of the OCS at three different times (n ｔ The reconstructed spectra for λ = 15, 30, 45 are shown alongside the noise-free ground truth (GT). The top half of the chart shows the GT, and the bottom half of the chart shows the reconstructed spectra. The reconstructions are １ = 0 and λ ２ =10 －４／３ It 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 CH ４ Ten simulations were performed for the stationary spectrum of v ａ ≦ν≦ν ｂ 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 of 1000 sq m (Fig. 7b). We evaluated the peak position and linewidth by fitting to a Gaussian distribution using the Levenberg-Marquardt method implemented in the Scipy library (Ref. [8]). As shown in Fig. 7b, 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% (Fig. 7c).

[0034] Finally, we evaluated the effect of SNR on the individual peak heights of the reconstructed spectrum (Fig. 7d). In Fig. 7d, the dotted line indicates the GT. In this analysis, the peak 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 SNRs as low as 10. However, we observed a tendency to underestimate peak heights regardless of the SNR, which became more pronounced for higher peaks. This results in an RMSE lower limit in the high SNR region, as shown in Figure 7a. This tendency is also observed in simple simulations that do 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] While 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, and 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, etc.

[0039] Google Scholar Crossref , CAS 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 Some, IEEE Signal Process. Mag. 25, 21 (2008). https: / / doi.org / 10.1103 / PhysRevLett.91.101212 , Google Scholar Crossref , CAS 3. L. 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. JM Bioucas-Dias and MAT Figueiredo, IEEE Trans. Image Process. 16, 2992 (2007) 6. Chan SH, Wang XR, and Elgendy OA, IEEE Trans. Computing. Imaging 3, 84–98 (2017). 7. Gordon IE, Rothman LS, Hargreaves RJ, et al., J. Quant. Spectrosc. Radiation. Transfer 277, 107949 (2022). 8. P. Virtanen, et al. Nat. Methods 17, 261 (2020). 9. JL Wu, YQ Xu, JJ Xu, XM Wei, AC Chan, AH Tang, AK Lau, BM Chung, HC Shum, and EY Lam, KK Wong, and KK Tsia, Light Sci. Appl. 6, e16196 (2017). https: / / doi.org / 10.1103 / PhysRevLett.101.1101 , Google Scholar Crossref , CAS 10. A. Kawai, K. Hashimoto, T. Dougakiuchi, VR 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 LV Gool, IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit. (IEEE, 2022) p. 17502.

[0040] This application claims priority based on Japanese Patent Application No. 2024-025241, filed on February 22, 2024, the entire disclosure of which is incorporated herein by reference.

Claims

1. A time stretch spectroscopy device comprising: an optical modulator that performs intensity modulation on a pulse-by-pulse basis on a group of measurement pulse lights obtained by irradiating a group of pulse lights onto a measurement target having characteristics related to optical transmittance or reflectance, a pulse stretcher that time-stretches the group of measurement pulse lights, and a signal processing device that performs reconstruction to estimate 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.

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

3. 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 device according to claim 1, wherein the signal processing device estimates the wavelength components of each pulse signal from the superimposed signal using a machine learning model.

6. The signal processing device calculates the L of the signal component of each measurement pulse light. ｎ The time stretch spectroscopy apparatus of claim 1 , wherein a loss function including a norm is minimized.

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

8. The time stretch spectroscopy device according to claim 1, further comprising a wavelength converter for converting the wavelength of said group of measurement pulsed light from a first wavelength region to a second wavelength region.

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 time stretch spectroscopy method comprising the steps of: performing intensity modulation on a pulse-by-pulse basis on a group of measurement pulse lights obtained by irradiating a measurement target having characteristics related to optical absorptance or reflectance with the group of pulse lights; time stretching the group of measurement pulse lights; and reconstructing the group of measurement pulse lights by estimating wavelength components of the pulse signals corresponding to the stretched pulse lights 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.

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