GOBO projection for 3D measurements at highest frame rates: a performance analysis

Abstract

Aperiodic sinusoidal patterns that are cast by a GOBO (GOes Before Optics) projector are a powerful tool for optically measuring the surface topography of moving or deforming objects with very high speed and accuracy. We optimised the first experimental setup that we were able to measure inflating car airbags at frame rates of more than 50 kHz while achieving a 3D point standard deviation of ~500 µm. Here, we theoretically investigate the method of GOBO projection of aperiodic sinusoidal fringes. In a simulation-based performance analysis, we examine the parameters that influence the accuracy of the measurement result and identify an optimal pattern design that yields the highest measurement accuracy. We compare the results with those that were obtained via GOBO projection of phase-shifted sinusoidal fringes. Finally, we experimentally verify the theoretical findings. We show that the proposed technique has several advantages over conventional fringe projection techniques, as the easy-to-build and cost-effective GOBO projector can provide a high radiant flux, allows high frame rates, and can be used over a wide spectral range.

Fig. 1

Schematic illustration of a GOBO projection-based 3D sensor. Definitions of some of the variables that are listed in Table 1 by means of a a top view of the camera-projector-camera arrangement and b an exemplary GOBO wheel with aperiodic binary fringes

Fig. 2. 3D point cloud completeness p and standard deviation σ_3D when using varying GOBO wheel parameters to project aperiodic sinusoidal patterns (upper row) and phase-shifted sine-like patterns (lower row).

a, d p and σ_3D as functions of randomly varied parameters c, σ_blur, n, ω, and e. b The minimum standard deviation σ_3D, which is shown for each of the five parameters. c, e A camera image of the projection of the optimal GOBO pattern onto a plane. f The 3D point standard deviation σ_3D as a function of the number of aperiodic sinusoidal patterns (solid lines) and phase-shifted sine-like patterns (dashed lines) that are used for reconstruction

Fig. 3. Experimental investigation.

a A photograph of the sensor that is used. b, c The measured and e, f simulated dependency of the 3D point standard deviation σ_3D and point cloud completeness p on the degree of projector defocusing, which is approximated by a Gaussian blur with standard deviation σ_blur, and the rotational speed ω of the GOBO wheel. d A detailed view of the GOBO wheel of the sensor that is shown in a. Undesired opaque spots, which may negatively affect the measurement accuracy, are clearly recognisable

Fig. 4

High-speed 3D measurement of the impact of a 40-bar nitrogen jet on a 400 × 400 mm² pillow that is attached to a polystyrene plate. a Snapshots of the recorded process at five points in time. b Camera images of the GOBO-projected aperiodic sinusoidal fringes, which are recorded with a resolution of 512 × 408 px at a frame rate of 55.2 kHz. c Reconstructed point clouds at a 3D rate of 5.5 kHz (see also Supplementary Video S2)

Fig. 5. Block diagram of the simulation framework.

According to the parameters c and n, a part of a GOBO wheel is generated (1). Based on the parameters σ_blur, ω, and e, subpatterns of the rotating GOBO wheel are determined (2). The subpatterns that are related to a pattern are projected onto a plane and the corresponding camera images are rendered (3). After computing the disparity map (4) and reconstructing the 3D point cloud (5), the standard deviation σ_3D and completeness p are estimated