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A Faraday rotation spectroscopy (FRS) technique is presented for measurements on the micrometer scale. Spectral acquisition speeds of about two orders of magnitude faster than state-of-the-art modulation spectroscopy setups are demonstrated. The experimental method is based on charge-coupled-device detection, avoiding speed-limiting components, such as polarization modulators with lock-in amplifiers. At the same time, FRS spectra are obtained with a sensitivity of 20 µrad () over a broad spectral range (525–800 nm), which is on par with state-of-the-art polarization-modulation techniques. The new measurement and analysis technique also automatically cancels unwanted Faraday rotation backgrounds. Using the setup, Faraday rotation spectroscopy of excitons is performed in a hexagonal boron nitride-encapsulated atomically thin semiconductor WS2 under magnetic fields of up to 1.4 T at room temperature and liquid helium temperature. An exciton g-factor of −4.4 ± 0.3 is determined at room temperature, and −4.2 ± 0.2 at liquid helium temperature. In addition, FRS and hysteresis loop measurements are performed on a 20 nm thick film of an amorphous magnetic Tb20Fe80 alloy.