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Abstract
Taking advantage of broad response range and snap-shot operation mode, reconstructive spectrometers based on integrated frequency-modulation microstructure and computational techniques attract lots of attention. The key problems in reconstruction are sparse samplings related with the limited detectors and generalization ability due to data-driving principle. Here, we demonstrate abstractly a mid-infrared micro-spectrometer covering 2.5–5 μm, which utilizes a grating-integrated lead selenide detector array for sampling and a hierarchal residual convolutional neural network (HRCNN) for reconstructions. Leveraging data augmentation and the powerful feature extraction ability of HRCNN, a spectral resolution of 15 nm is realized. Over one hundred chemicals, including untrained chemicals species tested with an average reconstruction error of ∼1E-4, exhibit the excellent reliability of the micro-spectrometer. The demonstration of the micro-spectrometer promotes the development of the reconstructed strategy.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Spectrometers are a kind of momentous instruments applied throughout various fields including environmental sensing, on-site analysis, flora and fauna researches, clinical and biomedical examination, etc. [1]. Traditional spectrometers typically consist of mechanically movable modules (e.g., optical gratings or Michelson interferometers) and long path lengths, making themselves bulky [2,3]. After investigated by abundant researches, miniaturization has been an available vision for spectrometers and diverse micro-spectrometers have been developed therewith [4–8]. Recently, a new strategy for miniaturized spectrometers emerges, where original spectra are reconstructed from pre-calibrated information encoded within a group of detectors with individual response characteristics via computational techniques [9–14]. Benefiting from more readily available computer processing power and decrease in microprocessor cost, the reconstructive micro-spectrometers have attracted more and more attention all over the world [15]. Besides, the miniaturization paradigm can harness not only technological advances in hardware, but also the development of new computational approaches, especially the later. The smallest spectrometer so far up to now is the single-nanowire one with a footprint of 0.5 × 75 μm2 [16], followed by the black phosphorus one with a footprint of 16 × 9 μm2 [17], and the tunable van der Waals junction one with a footprint of 22 × 8 μm2 [18].
With the rapid development of artificial intelligence, diversified algorithms are utilized to reconstruct spectra, such as least-square method, regularization method, deep neural network (DNN), convolutional neural network (CNN), etc. [9–14,16–24]. Although these algorithms conveniently improve the performance of micro-spectrometers, they perform badly when the original signal collected to be reconstructed is sparse [9]. Benefiting from extraordinary local feature extraction ability, hierarchal residual CNN (HRCNN) has been applied in super-resolution imaging in which powerful reconstructive ability is demonstrated [25–29]. Deep learning system based on HRCNN algorithm can reconstruct spectra in real time with no need for iteration, leading to a significant reduction of computational power [30]. Another suspect faced by the reconstructive micro-spectrometers is their generalization ability due to the reconstructive principle. However, experimental data collecting is time-wasting and financially consuming. Data augmentation strategy is usually adopted to improve the generalization ability in deep learning [31], which is effective in spectrum reconstruction since the envelope feature of different chemical species is all Gaussian-like.
Herein, we report an MIR micro-spectrometer operating between 2.5–5 μm where HRCNN algorithm is utilized to reconstruct spectra first. Taking advantage of the excellent feature extraction ability of HRCNN and data-augmented skill in reconstruction, the micro-spectrometer shows excellent spectral resolution of 15 nm. A lead selenide (PbSe) MIR photon detector array integrated with ordinary metallic gratings is employed to collect raw spectrum data, meaning the proposed micro-spectrometer is with distinct extendibility and manufacturability. A series of property tests reveal fabulous reliability and anti-disturbance of the micro-spectrometer, owing to the unique reconstructive method. The demonstration of the HRCNN assisted micro-spectrometer expands and improves the reconstructive strategy of micro-spectrometers.
2. Operational principle
The operational process of the micro-spectrometer system is presented schematically in Fig. 1. In early-stage preparation, a primordial dataset of chemical absorption spectra (i.e., ground-truth spectra, measured using a commercial Fourier transform infrared spectrometer) is established deriving from Ref. [32]. All 700 liquid chemicals, with characteristic absorption peaks in the working waveband of our system and similar appearances (colorless, transparent, liquid), are included in the dataset, that are divided into three classes, i.e., benzene, alcohol, and acid, with numbers of 295, 267, and 138, respectively.
Fig. 1. The operational scheme of the micro-spectrometer. Here, a schematic of the detector array (as the hardware) and a magnified schematic of a detector unit are involved. Every unit is comprised of a PbSe detector, an air layer, a dielectric layer, and a grating.
To begin with, light irradiated from an electrically modulated infrared source (EMIRS200) passes through an analyte and then illuminates onto the PbSe detector array (i.e., hardware). The analyte is selected from the chemicals in the dataset, with a known ground-truth spectrum. Every unit in the array contains a PbSe detector integrated with a grating (i.e., filter) made of gold (Au). Besides, a dielectric layer and an air layer are located between the detector and the grating, as shown in Fig. 1. The dielectric layer with a thickness of 1.35 μm is made of SU-8 photoresist, and the air layer with a thickness of 0.5 μm can be achieved with sacrificial layer technology. There are 250 units in the array, and all portions except the grating are the same for different units. The thickness, the duty cycle, and the length in y direction of all gratings are fixed as 0.1 μm, 89%, and 500 μm, respectively, yet the period linearly varies from 1.75 μm to 3.8 μm in x direction. After receiving the incident infrared light, one detector unit generates a photocurrent value Ii, and thus a series of values [I1, I2, …, InD] (nD represents the number of the detector units) can be collected from the array, as shown in Fig. 1. The step for acquiring the series of photocurrent values is the sampling, and it is virtually implemented here with the following equation:
where R(λ) is the response spectrum of the PbSe detectors, P(λ) is the radiation spectrum of EMIRS200, T(λ) is the transmission spectrum of the corresponding grating, A(λ) is the ground-truth spectrum of the analyte in the container, respectively. Thereinto, R(λ), P(λ), and T(λ) will be presented in Section 4. To resolve the background problem, a two-step measurement is adopted. Before the analyte is put into the container, a series of current signals IBn (n = 1, 2, …, nD) are attained by the sampling; after putting the analyte into the container, another series of signals ISn (n = 1, 2, …, nD) are also output from the detector array. The differences between the two series of signals are then input into the HRCNN for spectral reconstructions after normalization. After the samplings is finished, the obtained results are divided into two parts according to the proportions of the three classes: one is named as training set with 600 chemicals from which 100 spectra are randomly selected for validation; the other is named as test set with 100 chemicals. In order to guarantee the performance of the HRCNN model, the training set is augmented into five times as large as the initial one by translation operation. Next, the samplings in the training set are input into the HRCNN model referred to the enhanced deep super-resolution (EDSR) network to be trained for spectral reconstructions [33]. The reconstruction procedure of the HRCNN is introduced in Section 3. During this step, the mean square error (MSE) is used as the loss function, and it is expressed as:3. HRCNN presentation
Figure 2(a) shows the framework of the HRCNN, and the spectral reconstruction procedure is described below. Firstly, the inputted sampling data are processed in a one-dimensional convolutional layer for extending the network depth from 1 into 64. The general operation of one-dimensional convolutions is displayed in Fig. 2(b), where the kernel and its overlap in the input are multiplied respectively and then added to acquire the output. The step size of the convolution operation is 1.
Fig. 2. (a) The flowchart of the HRCNN. (b) The operational rule of one-dimensional convolutions. (c) The internal framework of the GSRM in the HRCNN.
After the convolution, the obtained data are input into a globally scaled residual module (GSRM) for feature extraction. Figure 2(c) shows the detailed structure of the GSRM, which contains two independent branches. In one of the branches, 16 locally scaled residual modules (LSRMs) are involved. The GSRM extracts the shallow and deep features of the input signal through the convolution kernel and the 16 residual modules. For each LSRM, the inputted data are divided into two portions: one of them are processed in a convolution, a rectified linear unit (ReLU), and another convolution in succession; the remaining are of skip connection and output without any processing. The data are output from an LSRM after adding the output ones of the two portions. Going through the LSRMs one after another, the data are processed in a convolution and then output from this branch. In the other branch, the data are of skip connection without going through any process. The output data from the two branches are added and then output from the GSRM.
Considering that one-dimensional spectral data has linear characteristics compared with two-dimensional image data, the HRCNN employs a linear interpolation (LERP) for upsampling. As shown in Fig. 2(a), the data size is linearly enlarged into 2 times after processed by the upsampling, Next, a convolution is implemented to recover the network depth back into 1. Finally, the data are processed in a linear full connected network (FCN) to keep the data size of the output consistent with that of the ground-truth spectrum. The network above is featured by a much deeper structure (54 layers in total compared to 9 layers or less in Refs. [22–24]) that can better utilize the features in the training data, and the hierarchal residual structure that will significantly address the so-called degradation problem and the calculation complexity.
The HRCNN was trained using the Adam optimizer with an initial learning rate of 1E-5. All the preprocessing and training/test of the HRCNN were performed with PyTorch libraries. All spectral reconstructions were performed on a server computer with eight NVIDIA 2080Ti graphics processing card.
4. Results and discussion
4.1 Performance of the detector array
The operation of the proposed micro-spectrometer is based on the PbSe detector array, and it has been developed successfully by standard micro-nano technologies before the hardware design. Figure 3(a) shows a processed array of 8 × 8 PbSe elements, and unit size is 640 × 500 μm2. The responsivity (R) of the array is characterized with a blackbody response measurement setup, including a standard blackbody source, a low-noise current amplifier SR570, and a lock-in amplifier SR830 at a chopped frequency of 1000 Hz. The blackbody responsivity (Rbb) is obtained from the following equation [34]:
where Ipc is measured photocurrent, Tb = 500 K is the blackbody temperature, Td = 300 K is the background temperature, σ = 5.67 × 10−12 W/(cm2·K4) is the Stefan-Boltzmann constant, Ab = 19.63 mm2 is the blackbody exit aperture area, Ad = 500 × 500 μm2 is the effective photosensitive area, and L = 30 cm is the distance between the aperture and the detector array. The color-scale mapping for responsivity of the PbSe detector array is plotted in Fig. 3(b), and good uniformity is demonstrated. The response spectra of the PbSe detectors are also measured, and the employed setup is composed of a grating monochromator (Omni-λ 300), a calibration globar illuminant, SR570, and SR830 at a chopped frequency of 377 Hz. All the measured spectra show nearly the same curves with a cutoff wavelength of ∼5 μm, one of which is presented in Fig. 3(c). The above response spectrum is R(λ) in Eq. (1), and P(λ) in there is also given in Fig. 3(c).Fig. 3. (a) Front view of an 8 × 8 PbSe detector array. (b) The color-scale mapping for responsivity of the array. The axis labels represent the row or column numbers of pixel of the detector array, corresponding to the shown structure in (a). (c) The response spectrum of the PbSe detectors, and the radiation spectrum of EMIRS200. (d) The simulated transmission spectra of some gratings employed in the micro-spectrometer, and the FWHM versus resonant wavelength.
The transmission spectra of the gratings in Fig. 1 are simulated by a commercial software, FDTD Solutions. The relative dielectric constants of Au, SU-8 and PbSe utilized in the simulations are from the Palik model, a constant of 2.46, and derived from Ref. [35], respectively. The boundary conditions in x and y directions are periodic, and that in z direction is perfectly matched layer. The polarization of the incident light is along x direction, and the transmission monitor is placed in the middle of the air layer. The simulations are performed on a discrete mesh with a spacing of one twentieth of the minimum structure size, and the stop criterion is set as 1E-5. Some of the simulated transmission spectra are displayed in Fig. 3(d), and the respective full widths at half maximum (FWHMs) are labelled therewith. All the resonant wavelengths range in 2.5–5 μm, within the response band of the PbSe detectors shown in Fig. 3(c). Herein, the dynamic range is defined as the ratio between the largest and the smallest value of the transmission, and it is calculated to be ∼7662:1 according to the transmission spectra shown in Fig. 3(d).
4.2 Reconstruction performance
The ground-truth and the reconstructed spectra of three chemicals (belonging to different classes) in the test set are displayed in Fig. 4(a)–(c). Both peaks and intensities of the ground-truth and the reconstructed spectra are almost fully accordant. It is worth mentioning that the variation of the average MSE is traced during the training, as displayed in Fig. 4(d). Within 500 epochs, the average MSE can converge into ∼1E-4 and then keep stable, indicating that the HRCNN model is trained adequately. To evaluate the generalization of the reconstruction results, a 5-fold cross validation of the dataset is conducted. The evolutions of the average MSE during the trainings and the average-MSE variation of the test sets in the cross validation are also displayed in Fig. 4(d). The average MSE of the test sets varies very little in the whole cross validation, indicating that the results are truly generalizable instead of simply cherry-picked. The ground-truth and the reconstructed spectra of three worst (with MSE above 4E-4) in the test set are presented in Fig. 4(e). It is obvious that the elaborate information of the ground-truth spectra is still well restored. Moreover, the reconstruction comparison of the HRCNN, auto-encoder DNN (AE-DNN), CNN, and regularized least squares (RLS) algorithms is presented in Fig. 5, in which the performance of the HRCNN is apparently better than the others. The flowcharts of the AE-DNN and the CNN algorithms are presented in Appendix I. The excellent reconstruction performance reveals that the HRCNN used in this work can capture the fine details of the ground-truth spectra perfectly.
Fig. 4. (a)–(c) The ground-truth and the reconstructed spectra of three chemicals in the test set. They are expressed as R#benzene, R#alcohol, and R#acid, respectively, and their MSE values are labelled therein. (d) The average MSEs versus epoch during the trainings in the 5-fold cross validation (#0 represents the regular training, #1–#5 represent the cross validation); inset: the average MSE of the test sets in different folds. (e) The three reconstructed spectra with MSEs above 4E-4.
Fig. 5. The spectral-reconstruction comparison of the HRCNN, AE-DNN, CNN, and RLS algorithms through the three chemicals.
To further evaluate the performance of the proposed micro-spectrometer, the spectral resolution is explored. The method for acquiring the resolution simulates that in traditional spectrometers. A spectrum imitating two monochromatic lights is simulated with a spectral interval of 0.6 nm for reconstruction, which contains two peaks with an interval of 15 nm. The simulated and the reconstructed spectra using the HRCNN are shown in Fig. 6(a), where the two peaks are well resolved after the reconstruction. Thus, the spectral resolution of 15 nm is demonstrated. The interval is then gradually narrowed until it cannot be recognized, and thus the resolution is gained. To imitate monochromatic lights, the two peaks of the simulated spectrum in Fig. 6(a) are very sharp. In this case, the peak mismatch between the simulated and the reconstructed spectra would not influence the MSE clearly, such that the MSE keeps almost unchanged even when the interval is below the spectral resolution of 15 nm. The simulated spectrum is also reconstructed using AE-DNN and CNN algorithms respectively, as displayed in Fig. 6(b). It is clearly seen that the two peaks vanish in the reconstructed spectra, indicating that the spectral resolution of the AE-DNN and CNN algorithms cannot rival that of the HRCNN. Figure 6(c) shows the spectral resolution comparison of the micro-spectrometer with other infrared spectrometers, the filter structures of which include black phosphorus, plasmonic structure, linear variable filter (LVF), Micro Electro Mechanical Systems (MEMS) Fabry-Perot Interferometer (FPI), and random photonic chip [17,20,36–38]. Here, the spectrometers in Refs. [17,20,36] are reconstructive ones, and those in Refs. [37,38] have been in commercialization. As can be clearly seen, the resolution of the micro-spectrometer is close to the commercial one in Ref. [37] (10–16 nm in 1.75–2.15 μm), superior to that in Refs. [38] (30 nm in 1.5–5 μm), [20] (40 nm in 2.2–3.8 μm), and [17] (90 nm in 2–9 μm). The outstanding resolution shows a brilliant advantage of the presented HRCNN for spectral reconstructions. As stated in previous articles, the spectral-reconstruction performance can be further improved by increasing the numbers of the spectra in the training set and the detector units [14,17,20]. In addition, the detection limit (DL) of the micro-spectrometer is also analyzed in Appendix II.
Fig. 6. (a) The simulated and the reconstructed spectra using the HRCNN for acquiring the spectral resolution of the micro-spectrometer. (b) The reconstructed spectra using the AE-DNN and CNN algorithms. (c) The spectral resolution comparison of the micro-spectrometer with other infrared spectrometers.
The influence of external noise levels on spectral reconstructions is studied as the reviewer suggested. The average MSE versus signal-to-noise ratio (SNR) is plotted in Fig. 7(a). As SNR decreases, the average MSE approximately exponentially increases. Figure 7(b)–(d) shows the reconstructed spectra of R#benzene with different SNRs. The basic information of the ground-truth spectra is still restored even under a relatively low SNR of 20 dB. For the generalization characterization of the micro-spectrometer, some substances including oils, phenols, and minerals, are employed into the spectral reconstructions using the well-trained HRCNN. The reconstructed results are presented in Fig. 8, where the reconstruction quality is satisfying. This is due to the similarity between the abstract features of these substances and those in the training set. Hence, the HRCNN performs well to these substances even they are not in the training set, such that it has good generalization performance. The above results uncover the excellent generalization ability of the micro-spectrometer benefiting from the utilization of the HRCNN.
Fig. 7. (a) The average MSE as a function of SNR. (b)–(d) The reconstructed spectra of R#benzene with different SNRs.
Fig. 8. The ground-truth and the reconstructed spectra of (a) oils, (b) phenols, and (c) minerals using the well-trained HRCNN.
5. Conclusion
In conclusion, an HRCNN-assisted MIR micro-spectrometer is designed and abstractly realized, of which the hardware is a grating-integrated PbSe detector array. Benefiting from the powerful local feature extraction ability of the employed HRCNN model, outstanding reconstruction results are demonstrated in 2.5–5 μm range. The spectral resolution of the micro-spectrometer is achieved as 15 nm. The spectra of 100 chemicals are well restored with an average error of 1E-4. Moreover, the reconstruction qualities keep outstanding as ever even with the introductions of untrained chemicals. The high performance of the proposed micro-spectrometer manifests that the combination of HRCNN-based super-resolution algorithm and frequency-modulation microstructure is a promising strategy in the realization of micro-spectrometers.
Appendix I
The flowchart of the AE-DNN algorithm is displayed in Fig. 9(a). In the AE-DNN, the encoder includes four FCN layers and Sigmoid activation function, and it gradually maps the features of the input signal into a high-dimension implicit encoding. The decoder is composed of three FCN layers and Sigmoid activation function, in which the high-dimension implicit features are gradually reduced into the data size of the output spectra. In this way, the spectral reconstructions are realized. The difference between the AE-DNN and the HRCNN is that the former directly uses the activation function to encode and decode through multi-layer linear mapping, yet the later uses residual convolution kernels to extract features. The flowchart of the CNN algorithm is displayed in Fig. 9(b). The CNN algorithm mainly uses multiple convolution kernels to extract the characteristics of the input signal, and then reconstructs spectra through the FCN layers. The convolution network is to extract the characteristics of the input signal through the convolution kernels. Compared with the direct linear mapping of the AE-DNN, the CNN can extract more-abundant signal features. However, the calculation amount is also multiplied. In the HRCNN, the convolution is adjusted into the residual one, and thus the network weight can be calculated by extracting residual features. Hence, the network depth increases with avoiding the problems such as network bloat and gradient disappearance.
Appendix II
Referred to the Non-Dispersive Infrared (NDIR) gas measurement systems, the DL of the micro-spectrometer can be expressed by the following equation [36]:
where Δf is the signal bandwidth, and D* is the specific detectivity of the infrared detector. I’ is the change in transmitted radiant power for 1 ppm of gas concentration, and it can be obtained for given concentrations as: where I1 and I2 are the transmitted radiant powers at the concentrations c1 and c2, respectively. Besides, the values of I1 and I2 are related to the spectral radiant power of the infrared radiation source, the detector area, the transmission spectrum of the used filter, the absorption coefficient of the analyte, and the light path of the system. Hence, the lower DL of our micro-spectrometer depends on the spectral radiant power of the infrared radiation source and the light path when the detector array is certain. Since our purpose is spectrometer miniaturization, the radiant power and the light path are limited. Therefore, the lower DL cannot match with traditional spectrometers. However, it is sufficient to meet the requirements of ordinary application scenarios, such as wilds and mobile occasions.Funding
National Natural Science Foundation of China (11933006, 61805060, 61871164, U2141240); Zhejiang Provincial Natural Science Foundation of China (LGF21F050001); Hangzhou Key Research and Development Program (20212013B01); Hangzhou Science and Technology Bureau (TD2020002); National Science and Technology Key Laboratory Foundation (6142401200201); China Postdoctoral Science Foundation (2021M703334); Research Funds of Hangzhou Institute for Advanced Study (B02006C019019, 2022ZZ01007).
Acknowledgments
The fabrication of the devices was performed at the Micro-Nano Fabrication Center, Zhejiang University.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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