Micro Fourier Transform Profilometry ($μ$FTP): 3D shape measurement at 10,000 frames per second (1705.10930v1)

Abstract: Recent advances in imaging sensors and digital light projection technology have facilitated a rapid progress in 3D optical sensing, enabling 3D surfaces of complex-shaped objects to be captured with improved resolution and accuracy. However, due to the large number of projection patterns required for phase recovery and disambiguation, the maximum fame rates of current 3D shape measurement techniques are still limited to the range of hundreds of frames per second (fps). Here, we demonstrate a new 3D dynamic imaging technique, Micro Fourier Transform Profilometry ($\mu$FTP), which can capture 3D surfaces of transient events at up to 10,000 fps based on our newly developed high-speed fringe projection system. Compared with existing techniques, $\mu$FTP has the prominent advantage of recovering an accurate, unambiguous, and dense 3D point cloud with only two projected patterns. Furthermore, the phase information is encoded within a single high-frequency fringe image, thereby allowing motion-artifact-free reconstruction of transient events with temporal resolution of 50 microseconds. To show $\mu$FTP's broad utility, we use it to reconstruct 3D videos of 4 transient scenes: vibrating cantilevers, rotating fan blades, bullet fired from a toy gun, and balloon's explosion triggered by a flying dart, which were previously difficult or even unable to be captured with conventional approaches.

• The paper presents a μFTP method that captures dense 3D point clouds at 10,000 fps using only two projected patterns.
• It employs micro variations in spatial sinusoids to eliminate phase ambiguity and achieve high-resolution single-shot phase recovery.
• Experimental results show superior depth accuracy (<80 μm) and low temporal uncertainty, enabling analysis of rapid transient events.

Overview of Micro Fourier Transform Profilometry (μFTP)

The paper presents the Micro Fourier Transform Profilometry (μFTP) as an innovative approach to high-speed 3D shape measurement, achieving remarkable frame rates and depth accuracy by leveraging advanced fringe projection techniques. Unlike traditional methods, μFTP allows for capturing dense 3D point clouds at a frame rate of 10,000 frames per second (fps), using just two projected patterns, setting it apart in the domain of rapid transient event analysis.

Key Contributions and Methodology

μFTP essentially builds upon the Fourier Transform Profilometry (FTP) by introducing micro variations in frequency across multiple spatial sinusoids. This subtle adaptation allows for the elimination of phase ambiguity while enhancing the fidelity of rapid phase acquisition. The cornerstone of the technique is its ability to encode phase information within a single, high-frequency sinusoidal pattern, making it essentially a single-shot method capable of producing high temporal resolution reconstructions.

The framework of μFTP is implemented with a high-speed fringe projection system, comprising a Digital Light Processing (DLP) apparatus alongside a high-speed CMOS camera. This setup facilitates synchronized image capture and binary pattern switching at unprecedented speeds, optimizing the projection and imaging capabilities far beyond traditional DLP projectors limited by mechanical constraints.

The detailed computational framework underlying μFTP handles phase recovery, unwrapping, compensation for errors, and system calibration. These processes enable accurate and unambiguous 3D reconstructions, maintained even in scenarios presenting complex surface textures or significant object motion.

Experimental Evaluation and Results

The paper rigorously evaluates μFTP across several experimental scenarios illustrative of transient phenomena—vibrating cantilevers, rotating fan blades, a bullet fired from a toy gun, and balloon explosions. Critical results demonstrate μFTP's superiority in capturing dynamic 3D shapes without motion artifacts. A standout finding is the depth accuracy, maintained below 80 μm, along with temporal uncertainties kept below 75 μm over a substantial measurement volume, which underscore the system's reliability and accuracy.

Additionally, μFTP proves capable of tracking rapid movements with high precision. The experiments showcase its utility in accurately measuring and analyzing fast and complex geometric changes across diverse domains like solid mechanics and material science.

Implications and Future Directions

The implications of μFTP are broad and significant. Practically, it bridges the gap between high-speed 2D photography and 3D sensing, offering an unmatched tool for capturing intricate dynamics at kilohertz scales. Its potential for application in fields requiring real-time high-speed data acquisition and analysis—such as biomechanics and fluid dynamics—is noteworthy.

Theoretically, μFTP's single-shot approach to encoding phase information lays a foundational framework that could inspire future research into optimizing and extending computational imaging techniques. The concept has potential for adaptation across various imaging methodologies, including microscopy and ghost imaging, where rapid phase and spatial data capture could enhance analytical capabilities.

Further optimizations, particularly in computational processing, are likely to boost μFTP's adoption and applicability. With potential improvements leveraging GPU-based accelerations, real-time processing of 3D video data from a high-speed camera setup becomes plausible, opening newer frontiers for μFTP integration in live analytical applications.

In summary, the μFTP presents a technically robust and empirically verified advancement in high-speed 3D measurement, with the versatility and accuracy necessary for addressing challenging imaging scenarios in both industrial and academic settings.