An apparatus (10) for structured illumination microscopy (SIM) comprises a pulsed femtosecond MiTai laser (11) operable to generate a pulsed beam. The beam pulses are directed on to a specimen (12) via an optical arrangement including a beam steering apparatus comprising a pair of acousto-optic deflectors AODx, AODy, each operable to vary the deflection angle of the beam in response to variation in the frequency of an applied acoustic deflection signal,and an acousto-optic modulator AOM. The frequency of the acoustic deflection signals applied to the AODs and/or the frequency of the acoustic compensation signal applied to the AOM in the present invention is dynamically modulated. This dynamic modulation can increase the effective AODxy scan angle in each direction by about 4 mrads (equivalent to a 15% increase in the area of the field of view). Furthermore, dynamic modulation of the compensation frequency also improves the evenness of the illumination over the field of view.