Fig. 1. Experimental setup of all-fiber reconstructive spectrometer based on PDM technology. SMF, single-mode fiber; PBS, polarization beam splitter; PMF, polarization-maintaining fiber; MMF, multimode fiber; OL, objective lens; ATT, attenuator.

Fig. 2. Representative output speckles corresponding to (a) horizontally, (b) vertically polarized incidences. (c) The differential speckle. The white subscript in the low right corner indicates the image contrast value.

Fig. 3. (a) Reconstructed spectra of two spectral lines separated by 2 pm via TM, PDM, and DPDM approaches. The inset graph reveals the reconstructed details. The spectral reconstruction errors of TM, PDM, and DPDM are 0.0108, 0.0036, and 0.0009, respectively. (b) Reconstructed spectrum of broadband signal with an FWHM of 0.5 nm via TM, PDM, and DPDM approaches. The spectral reconstruction errors of TM, PDM, and DPDM are 0.1977, 0.1050, and 0.0287, respectively. The blue solid-line curve indicates the reconstructed spectrum. The red dashed-line curve indicates the ground truth.

Fig. 4. Reconstruction errors of spectra with varying Lorentzian FWHM using TM (vertical polarization), TM (horizontal polarization), PDM (vertical polarization and horizontal polarization), and DPDM.

Fig. 5. (a) Reconstructed spectra of a set of narrow spectral lines (FWHM = 0.1 nm) across the entire working range using the DPDM method. (b) Reconstructed spectrum (green solid line) for a continuous random signal (black dotted line) using the DPDM method.