Optical scanning apparatus includes a triangular prism, having first and second side faces and a base. A transmitter directs a beam of optical radiation into the prism through the first side face, which refracts the beam so that the optical radiation is incident on and reflects from the base within the prism at a reflection angle that is greater than a total internal reflection (TIR) angle of the prism and exits the prism through the second side face. At least one scanning mirror is positioned to intercept and reflect the beam back into the prism while scanning the beam over an angular range selected such that after refraction of the scanned beam at the second side face, the scanned beam is incident on the base at a transmission angle that is less than the TIR angle and is transmitted out of the prism through the base.