Fig. 1: Principle of FTBM.

a, In Brillouin scattering a small portion of the incident light (dark red, upwards-pointing arrow) interacts with thermal phonons intrinsically present in the sample. This gives rise to a scattered light (Brillouin) spectrum with two symmetrical peaks on the side of the main laser line with shift and width as indicated. B, Brillouin; ν_B, Brillouin shift; Δν_B, Brillouin linewidth. b, Conceptual schematic of FTBM: the sample is illuminated with a light-sheet (side-view only here); an objective lens collects the scattered light and a rubidium cell suppresses the elastically scattered light without affecting the Brillouin signal. After going through a Michelson interferometer, a tube lens forms the image of the sample on the sensor; a reference beam is also introduced to provide a reference for determining the optical phase (see Supplementary Note 2). sCMOS, scientific complementary metal–oxide–semiconductor. BS, beam splitter; c, speed of light. c,d, Comparison of sampling the interferogram (that is, the intensity I on the detector versus the time delay \(\tau\) between the two arms of the Michelson interferometer) between standard Fourier-transform spectroscopy (c) and our approach (d). In the standard approach, the full interferogram is sampled according to the Nyquist–Shannon criterion, requiring ~10⁶ points (red dots) to achieve the necessary spectral resolution of ~500 MHz. I, intensity. d, In our approach the interferogram is only locally sampled, with much fewer points, to reconstruct the amplitude (A, blue dashed line) of the envelope, while the local phase (ϕ) is used to determine its sign; our approach requires only ~100 points. sign_n, sign of the envelope. Insets: in both cases the full spectrum can be reconstructed by performing the Fourier transform of the samples; however, the spectrum is centred at the laser frequency \({\nu }_{\rm{L}}\) in the standard approach, whereas it is centred at zero in our approach.