Spatial-Mode Selection for Local Mineral Absorption Spectroscopy

Abstract

Absorption-band depth measures the fractional decrease in mineral reflectance below its local continuum. Recovering this feature strength for a small mineral region supports quantitative comparisons between regions, but diffraction mixes its light with the surroundings. Conventional spectral fitting can separate mean contributions; it cannot remove background photon noise already recorded. We develop a quantum-inspired measurement framework that uses spatial-mode demultiplexing (SPADE) to retain the target absorption response while reducing background acceptance before detection. The framework connects finite mineral-region geometry and reference spectra to estimation precision. A loss-dependent design condition identifies when adding SPADE exposure improves on direct imaging (DI) under fixed-response Poisson measurements with unknown scene parameters. Joint inference from initial DI observations and both mode ports estimates target depth together with an unknown, spatially shared background spectrum. In equal-time simulations that include localization uncertainty, alignment time, calibration, and detector costs, this acquisition reduces depth root-mean-square error (RMSE) by 14\%--26\% across five absorption strengths relative to all-pixel DI with the same background freedom. These results use a supplied target feature shape and geometry, with target continuum slope fitted and curvature fixed. The analysis separates optical selectivity from parameter ambiguity and acquisition cost, providing a quantitative basis for spatial-mode receiver design in local mineral spectroscopy.

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BibTeX RIS

BibTeX

@misc{qian2026spatialmode,
  title = {{Spatial-Mode Selection for Local Mineral Absorption Spectroscopy}},
  author = {Qipeng Qian and Jialiang Jin and Shihao Wang and Yuntao Qian},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39221},
  eprint = {2610.39221},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39221},
}

RIS

TY  - UNPB
TI  - Spatial-Mode Selection for Local Mineral Absorption Spectroscopy
AU  - Qipeng Qian
AU  - Jialiang Jin
AU  - Shihao Wang
AU  - Yuntao Qian
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39221
UR  - https://arxiv.org/abs/2610.39221
AB  - Absorption-band depth measures the fractional decrease in mineral reflectance below its local continuum. Recovering this feature strength for a small mineral region supports quantitative comparisons between regions, but diffraction mixes its light with the surroundings. Conventional spectral fitting can separate mean contributions; it cannot remove background photon noise already recorded. We develop a quantum-inspired measurement framework that uses spatial-mode demultiplexing (SPADE) to retain the target absorption response while reducing background acceptance before detection. The framework connects finite mineral-region geometry and reference spectra to estimation precision. A loss-dependent design condition identifies when adding SPADE exposure improves on direct imaging (DI) under fixed-response Poisson measurements with unknown scene parameters. Joint inference from initial DI observations and both mode ports estimates target depth together with an unknown, spatially shared background spectrum. In equal-time simulations that include localization uncertainty, alignment time, calibration, and detector costs, this acquisition reduces depth root-mean-square error (RMSE) by 14\%--26\% across five absorption strengths relative to all-pixel DI with the same background freedom. These results use a supplied target feature shape and geometry, with target continuum slope fitted and curvature fixed. The analysis separates optical selectivity from parameter ambiguity and acquisition cost, providing a quantitative basis for spatial-mode receiver design in local mineral spectroscopy.
ER  -

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