In this article we present the simulation and experimental implementation of a camera-based sensor with low object-space numerical aperture that is capable of measuring the distance of multiple object points with an accuracy of 8.51 µm over a range of 20 mm. The overall measurement volume is 70 mm × 50 mm × 20 mm. The lens of the camera is upgraded with a diffractive optical element (DOE) which fulfills two tasks: replication of the single object point to a predefined pattern of K spots in the image plane and adding a vortex point spread function (PSF), whose shape and rotation is sensitive to defocus. We analyze the parameters of the spiral phase mask and discuss the depth reconstruction approach. By applying the depth reconstruction to each of the K replications and averaging the results, we experimentally show that the accuracy of the reconstructed depth signal can be improved by a factor of up to 3 by the replication approach. This replication method (also called multipoint method) not only improves accuracy of depth reconstruction but also of lateral position measurement. Therefore, the presented concept can be used as a single camera 3D position sensor for multiple points with high lateral as well as depth resolution.