Accurate single image depth detection using multiple rotating point spread functions

Abstract

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.

Field evaluation of a novel holographic single-image depth reconstruction sensor

“…Subsequently, the position, where the reference image stack is acquired, is called calibration position. In a former publication we have shown, that the on-axis performance of the measurement principle is very good [10]. The mean standard deviation of three measurements was 𝜎 = 8.51 µm within a measurement range of 20 mm.…”

“…Simulations and experiments show, that the two rotating spots, created by the double-helix, form a tail, whose length is growing with the angle of rotation. More information regarding the simulations can be found in [10]. This tail makes it difficult to evaluate the rotation angle using the CoGs of both spots.…”

“…The ratio between measurement range and accuracy reached by those techniques ranges between 280 and 560. In this contribution we address the question, to which extent the formerly published single-image depth reconstruction method [10] can be used as a single image 3D position sensor. Therefore, field measurements are carried out to investigate its off-axis performance.…”

Holographic single-image depth reconstruction

“…In total three measurements with different number of equidistant measurement points are carried out. The mean standard deviation of all three measurements is = 8,51 µm and the signals show good reproducibility[6].…”

“…Simulations and experiments show, that the two rotating spots, created by the double-helix, form a tail, whose length is growing with the angle of rotation. More information regarding the simulations can be found in [6]. The tail formation is shown in Fig.…”