- Brillouin spectroscopy is an emerging tool in biomedical imaging and sensing. It is capable of assessing the high-frequency viscoelastic longitudinal modulus with microscopic spatial resolution. Nonlinear Brillouin spectroscopy based on impulsive stimulated Brillouin scattering offers a number of significant advantages over conventional spontaneous and stimulated Brillouin scattering. In this report, we evaluate the accuracy of Brillouin shift measurements in spontaneous and nonlinear Brillouin microscopy by calculating the Allan variance for both CW excited spontaneous Brillouin measurements and nonlinear Brillouin scattering measurements made with both nanosecond and picosecond pulse excitation. We find that impulsive stimulated Brillouin spectroscopy is superior to spontaneous Brillouin spectroscopy in terms of the accuracy of such measurements and demonstrate its application for assessing tiny changes in Brillouin frequency shifts associated with low concentrations of biologically relevant solutions.