We previously presented a technique calibrating a multiaperture array projector (MAAP) for performing high-speed three-dimensional (3-D) surface topology measurements with aperiodic sinusoidal fringe structured illumination. Although a stereo-camera setup used to be required for triangulation, the presented MAAP calibration technique re-enables photogrammetric 3-D measurements to be made using a single CCD or CMOS camera. For such a monocular-view photogrammetric system, intrinsic camera calibration, intrinsic projector calibration, and extrinsic system calibration are vital to obtain high-measurement performance. However, there is currently no such technique that can comprehensively perform the required extrinsic system calibration when using an MAAP and a single-camera setup. A comprehensive optimization-based method is proposed and the resulting measurement performance is evaluated. With the new calibration technique, we are able to achieve a surface standard deviation of ∼50  μm.