Three-dimensional (3-D) measurement systems based on coded-light techniques are conventionally limited by the projection speed, which is typically in the range of a few 100 Hz, resulting in 3-D frame rates of 1 to 60 Hz. We propose to use an array projector for 3-D shape measurements, which enables much higher projection frame rates of up to the 100-kHz range. In contrast to previous setups, it does not project well-known phase-shifted sinusoidal fringes and Gray code patterns, but aperiodic sinusoidal fringes. This new technique, based on sine-shaped fringes with spatially and temporally varying offset, amplitude, period length, and phase shift, allows accurate 3-D measurement of objects, even with sharp edges, high slope, or varying surface properties, at high speed up to the kilohertz range. This paper explains the 3-D measurement principle and the basic design of an array projector that projects aperiodic sinusoidal fringes. It verifies the consistency between specified and projected patterns and points out the results of the setup’s characterization, e.g., of its high-speed capability. Furthermore, first 3-D shape measurements at a projection frame rate of 3 kHz resulting in a 3-D frame rate of <330 Hz are presented and evaluated.