Signal-to-noise ratio trade-offs associated with coarsely sampled Fourier transform spectroscopy

Abstract

We derive the spectral signal-to-noise ratio (SNR) trade-offs associated with coarsely sampled Fourier transform spectroscopy using a step-and-integrate measurement scheme. We show that there is no SNR penalty in the shot noise limit and a slight SNR benefit in the detector noise limit for the case of coarse sampling to achieve the same spectral resolution as a baseline Nyquist sampling scenario, where the total detector integration time is the same for both sampling cases.

Near-common-path interferometer for imaging Fourier-transform spectroscopy in wide-field microscopy

“…5 (A). This observation is in line with the theoretical simulations presented by Thurman and Fienup [33]. Figure 5(B) shows de-noised recovery of the same spectrum using TwIST along with sparsity priors.…”

“…To validate this point, we have demonstrated full-field Raman imaging using the proposed design. We also experimentally demonstrated that under-sampled interferogram acquisition can speed up Raman imaging by an order of magnitude at an expense of SNR as proven theoretically in [33]. However, we further demonstrated that low SNR Raman spectra can be de-noised using sparsity priors.…”

“…Therefore, the interferogram can be under-sampled without risking aliasing [13]. This is also known as coarsely sampled Fourier-transform spectroscopy [33]. Thus, 10 times under-sampled interferograms were taken (at 1.32 μm step size) by scanning 290 OPD positions.…”

Wide-field spatiospectral interferometry: theory and imaging properties

“…5. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]; and h•i is the ensemble average, equivalent to the time average from start time t a to end time t b defined by…”

“…Conversely, the range of recovered wavenumbers is κ max because only positive values of κ are physical. In fact, due to system transmissivity and detector limitations, the interferometer's bandpass is less than κ max , suggesting 0 < κ min < κ max ; knowledge of the bandpass can be exploited, provided the measurements have an adequate signal-to-noise ratio, thus allowing the delay line sampling to be relaxed as for FTIS [12].…”