Motion-induced error reduction for high-speed dynamic digital fringe projection system

TL;DR

This work tackles motion-induced errors in phase-shifting profilometry by exploiting motor encoder data and the pinhole models of the camera and projector to perform pixel-level corrections. The method sequentially applies camera-pixel correction, phase-shift error correction, and geometry-based phase unwrapping, enabling accurate 3D measurements with only three fringe patterns even under non-uniform motion. Experimental results on a motorized stage show substantial reductions in phase-error metrics and distortion, achieving RMSEs on the order of a few tenths of a millimeter and robust texture maps for complex geometries. The approach is computationally light and suitable for real-time PSP, with potential extensions to explicitly estimate inter-frame motion to handle arbitrary moving systems.

Abstract

In phase-shifting profilometry (PSP), any motion during the acquisition of fringe patterns can introduce errors because it assumes both the object and measurement system are stationary. Therefore, we propose a method to pixel-wise reduce the errors when the measurement system is in motion due to a motorized linear stage. The proposed method introduces motion-induced error reduction algorithm, which leverages the motor's encoder and pinhole model of the camera and projector. 3D shape measurement is possible with only three fringe patterns by applying geometric constraints of the digital fringe projection system. We address the mismatch problem due to the motion-induced camera pixel disparities and reduce phase-shift errors. These processes are easy to implement and require low computational cost. Experimental results demonstrate that the presented method effectively reduces the errors even in non-uniform motion.

Figures (7)

• Figure 1: Conceptual illustration of the method for removing $2\pi$ discontinuities in a wrapped phase map using the minimum phase map determined from geometric constraints an2016pixel.
• Figure 2: Illustration of the rotation of the reference plane. The blue plane is the original reference plane, the red plane is the rotated reference plane and the purple line is the intersection line located at the center of the original reference plane.
• Figure 3: Flowchart of our proposed method.
• Figure 4: Photograph of our experimental system setup.
• Figure 5: Measurement results of a sphere while the PSP system is in uniform motion (associated with Visualization 1). (a) Texture map obtained using conventional phase-shifting method, (b) the corresponding 3D result, and (c) error map (mean: 0.176 mm, standard deviation: 0.537 mm, RMSE: 0.565 mm); (d) Texture map obtained only using camera pixel correction in our proposed method, (e) the corresponding 3D result, and (f) error map (mean: -0.313 mm, standard deviation: 0.987 mm, RMSE: 1.035 mm); (g) Texture map obtained using our proposed method, (h) the corresponding 3D result, and (i) error map (mean: 0.011 mm, standard deviation: 0.337 mm, RMSE: 0.337 mm).