High-precision Brillouin frequency shift extraction using a double-stage orthogonal VIPA-based spectrometer

VIPA-based Brillouin spectrometers have been widely used in Brillouin microscopy systems for extracting the Brillouin frequency shift. Enhancing the measurement precision of Brillouin shift is essential for high-resolution 3D imaging. In this work, we propose a novel 2D dispersion model for a double-stage orthogonal VIPA-based spectrometer based on the angular spectrum of plane waves. Using the derived dispersion equation, the Brillouin frequency shift can be determined through quadratic and cubic function approximations. To validate the proposed dispersion model, we develop a confocal Brillouin system by leveraging the double-stage orthogonal VIPA-based spectrometer to measure the Brillouin frequency shifts of pure water and methanol samples. The results show that the Brillouin measurements of water and methanol present good robustness and high precision at different integration times of EMCCD camera. The standard deviation of the Brillouin shift is <5.0 MHz and the line width of histogram is <10 MHz when the camera integration time exceeds 0.1 s under a laser power of 10 mW. The proposed method features instantaneous self-calibration and eliminates the need for standard samples to determine Brillouin shifts, thereby significantly shortening the measurement time. This study is crucial for the future development and application of 3D elastography of biological tissues utilizing the Brillouin microscopy technique.