# On-Chip Reconstructive Spectrometer Based on Parallel Cascaded Micro-Ring Resonators
## 4 Conclusions  
In this paper, we propose an on-chip spectrometer based on a programmable silicon photonic filter. By changing the transmission spectrum of the filter through control signals, multiple and different samplings of the input spectrum can be achieved. Combined with the ANN algorithm, the incident spectrum can be reconstructed from the sampled signals. This design realizes diverse sampling of the incident spectrum based on a single programmable filter with an adjustable number of sampling channels. This approach can significantly reduce the footprint of the device and offer clear advantages in terms of integration and  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Ref.** & **Footprint** & **Res** & **Bandwidth** & **Number of Sampling** & **Computing Time** \\  & **[um2]** & **[nm]** & **[nm]** & **Channels** & **[s]** \\ \hline
[19] & 520 \(\times\) 220 & 0.02 & 12 (2 spectral lines) & 64 & - \\
[21] & 35 \(\times\) 260 & 0.45 & 180 & 32 & 0.65 \\
[22] & 60 \(\times\) 60 & 0.04 & 100 & 2501 & - \\
[25] & 2000 \(\times\) 7600 & 0.03 & 125 & 256 & 9 \\
[26] & 1900 \(\times\) 3700 & 0.01 & 200 & 729 & 360 \\ Our work & 40 \(\times\) 100 (estimated) & 0.1\(\sim\)2 & 200 & 192–2187 & 0.033–1.93 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Performance comparison of reported filter-based computational spectrometers.  
hardware costs. The simulation results show that the proposed device can accurately reconstruct spectra with different characteristics in the wavelength range of 1450 nm to 1650 nm. Regarding the test set consisting of synthesized spectra, the proposed on-chip spectrometer achieves an average reconstruction error RMSE of 0.0051 and an average relative error \(\varepsilon\) of 0.0484 using only a limited number of sampling states (64). When the number of sampling states is increased to 729, the RMSE and relative errors \(\varepsilon\) are reduced to 8.912 \(\times\) 10\({}^{-6}\) and 2.2991 \(\times\) 10\({}^{-5}\), respectively. The resolution for dual narrow-peak spectra can reach 0.2 nm, which is limited by the resolution of the spectral pixels we set. Benefiting from the programmable nature of the silicon photonic filter, the chip can flexibly change the number of sampling channels, allowing users to configure the chip according to the application scenario. Our proposed integrated reconstructive spectrometer based on the programmable silicon photonic filter provides a new solution for chip-level spectrometers and has broad application prospects in fields such as miniature spectrometers and Lab-on-Chip.  
Conceptualization, [PERSON] ([PERSON]); simulation, [PERSON] ([PERSON]); results analysis and discussion, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); writing, [PERSON] ([PERSON]); supervision, B.H.; funding acquisition, B.H. and H.C. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Natural Science Foundation of China (Grant No. 62341508), the Youth Innovation Promotion Association of Chinese Academy of Sciences under Grant No.Y2022045, Shaanxi Qin Chuangyuan \"Scientist + Engineer\" Team Construction (Grant No.2024 QCY-KXJ-161). Data underlying the results presented in this paper are available from the authors upon reasonable request.  
I (Z.Z.) want to thank my wife and daughter for their great support.  
The authors declare no conflicts of interest.