Multiple-beam Interference Spectroscopy: Instrument Analysis and Spectrum Reconstruction
Spectroscopie de l'interférométrie à ondes multiples : analyse instrumentale et reconstruction du spectre
Résumé
Hyperspectral imaging systems based on multiplebeam interference (MBI), such as Fabry-Perot interferometry, are attracting interest due to their compact design, high throughput, and fine resolution. However, unlike dispersive devices, the desired spectra in interferometric devices are reconstructed from the measured interferograms. Although the response function of MBI devices is modeled by the Airy function, existing reconstruction techniques are often constrained to the Fourier-transform spectroscopy, which is tailored for two-beam interference (TBI). Those approaches pose limitations for MBI and are susceptible to non-idealities like irregular sampling and noise. To address these challenges, we propose to use inversion techniques with prior knowledge that rely on a transfer matrix that embeds more accurately the real-world conditions of the device in the theoretical model, for which we also propose an analysis of the discretization of the continuous model and the ill-posedness of the problem. We frame our proposed solution as a unified formulation of both MBI and TBI spectroscopy, smoothly transitioning from the classical physical interpretation to a numerical system analysis of this forward matrix representation. Consequently, we extend the range of existing solutions for spectrum reconstruction, framing them as a classic optimization problem. Specifically, we employ a Bayesian framework incorporating prior knowledge, such as sparsity constraints. Experiments on simulated and real data demonstrate the framework’s flexibility and noise robustness compared to conventional algorithms. An implementation of the code is available at https://github.com/mhmdjouni/inverspyctrometry.
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