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We present the first application of balanced heterodyne detection, established in quantum optics, to Brillouin spectroscopy in biological tissues. The balanced detection cancels out a large part of the influence of the laser noise. The center wavelength is 1064nm and the frequency resolution is 30MHz. The frequency resolution and the accessible frequency range are only limited by the measurement time and the laser tuning range (30GHz), respectively. In this way, we were able to measure the Brillouin shift in acetone, water, gummy bears, glass, and even porcine eye lenses.