We report on microelectromechanical systems (MEMS)-actuated 32 × 32 optical phased arrays (OPAs) with high fill-factors and microsecond response time. To reduce the mirror weight and temperature-dependent curvature, we use high-contrast-grating (HCG) mirrors comprising a single layer of sub-wavelength polysilicon gratings with 400 nm thickness, 1250 nm pitch, and 570 nm grating bar width. The mirror has a broad reflection band and a peak reflectivity of 99.9% at 1550 nm wavelength. With 20 × 20 μm2 pixels and 2 μm, the OPA has a total aperture of 702 × 702 μm2 and a fill factor of 85%. The OPA is electrostatically controlled by voltage and has a total field of view of ± 2°, an instantaneous field of view (beam width) of 0.14°, and a response time of 3.8 μs. The latter agrees well with the mechanical resonance frequency of the HCG mirror (0.42 MHz).