Resolution and Robustness Bounds for Reconstructive Spectrometers
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908904290516992 |
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| author | Zhu, Changyan Lo, Hsuan Yu, Jianbo Wang, Qijie Chong, Y. D. |
| author_facet | Zhu, Changyan Lo, Hsuan Yu, Jianbo Wang, Qijie Chong, Y. D. |
| contents | Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance remain under-explored. We show that under a broad range of conditions, the noise-induced error for spectral reconstruction is governed by the Fisher information. We then use random matrix theory to derive a closed-form relation linking the variance bound to a set of key physical parameters: the spectral correlation length, the mean transmittance, and the number of frequency and measurement channels. The analysis reveals certain fundamental trade-offs between these physical parameters, and establishes the conditions for a spectrometer to achieve ``super-resolution'' below the limit set by the spectral correlation length. Our theory is confirmed using numerical validations with a random matrix model as well as full-wave simulations. These results establish a physically-grounded framework for designing and analyzing performant and noise-robust reconstructive spectrometers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20415 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resolution and Robustness Bounds for Reconstructive Spectrometers Zhu, Changyan Lo, Hsuan Yu, Jianbo Wang, Qijie Chong, Y. D. Optics Data Analysis, Statistics and Probability Reconstructive spectrometers are a promising emerging class of devices that combine complex light scattering with inference to enable compact, high-resolution spectrometry. Thus far, the physical determinants of these devices' performance remain under-explored. We show that under a broad range of conditions, the noise-induced error for spectral reconstruction is governed by the Fisher information. We then use random matrix theory to derive a closed-form relation linking the variance bound to a set of key physical parameters: the spectral correlation length, the mean transmittance, and the number of frequency and measurement channels. The analysis reveals certain fundamental trade-offs between these physical parameters, and establishes the conditions for a spectrometer to achieve ``super-resolution'' below the limit set by the spectral correlation length. Our theory is confirmed using numerical validations with a random matrix model as well as full-wave simulations. These results establish a physically-grounded framework for designing and analyzing performant and noise-robust reconstructive spectrometers. |
| title | Resolution and Robustness Bounds for Reconstructive Spectrometers |
| topic | Optics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2512.20415 |