Improve Temporal Fourier Transform Profilometry for Complex Dynamic Three-Dimensional Shape Measurement
<p>Schematic diagram of phase unwrapping based on reference plane; (<b>a</b>) Wrapped phase of the measured object; (<b>b</b>) Unwrapped phase of the reference plane; (<b>c</b>) 100th row of the wrapped phase and the unwrapped phase of the reference plane; (<b>d</b>) Value of the order K; (<b>e</b>) Unwrapped phase of the measured object; (<b>f</b>) Reconstructed result of measured objects.</p> "> Figure 2
<p>Schematic diagram of self-made grating disc design.</p> "> Figure 3
<p>Schematic diagram of our proposed mechanical projection system.</p> "> Figure 4
<p>Computational framework of our proposed 3-D reconstruction method.</p> "> Figure 5
<p>System calibration process: (<b>a</b>) Photograph of the standard block; (<b>b</b>) Absolute phase of the standard block; (<b>c</b>) Four fitted absolute phase planes based on the standard block’s absolute phase.</p> "> Figure 6
<p>Accuracy analysis of our proposed method. (<b>a</b>) Four positions of the ceramic standard flat in the measured field; (<b>b</b>–<b>e</b>) Error distribution of standard flats of the four positions.</p> "> Figure 7
<p>Measurement of the isolated objects by this proposed method. (<b>a</b>) One captured sinusoidal image of the measured scene; (<b>b</b>) Wrapped phase of the measured scene; (<b>c</b>) Absolute phase of the measured scene; (<b>d</b>) Reconstructed result of measured scene.</p> "> Figure 7 Cont.
<p>Measurement of the isolated objects by this proposed method. (<b>a</b>) One captured sinusoidal image of the measured scene; (<b>b</b>) Wrapped phase of the measured scene; (<b>c</b>) Absolute phase of the measured scene; (<b>d</b>) Reconstructed result of measured scene.</p> "> Figure 8
<p>Comparative experiments about isolated object; (<b>a</b>) False unwrapped phase by FTP; (<b>b</b>) False unwrapped phase traditional TFTP; (<b>c</b>) Three-dimensional diagram of false unwrapped phase by FTP; (<b>d</b>) Three-dimensional diagram of false unwrapped phase traditional TFTP.</p> "> Figure 8 Cont.
<p>Comparative experiments about isolated object; (<b>a</b>) False unwrapped phase by FTP; (<b>b</b>) False unwrapped phase traditional TFTP; (<b>c</b>) Three-dimensional diagram of false unwrapped phase by FTP; (<b>d</b>) Three-dimensional diagram of false unwrapped phase traditional TFTP.</p> "> Figure 9
<p>Pulse frequency captured by oscilloscope</p> "> Figure 10
<p>Measurement on the impact process scene. (<b>a</b>–<b>e</b>) Sinusoidal image of representative impact process; (<b>f</b>–<b>j</b>) 3-D reconstructions at the corresponding moments (Visualization 1).</p> ">
Abstract
:1. Introduction
2. Principle and Equipment
2.1. Temporal Fourier Transform Profilometry Method
2.2. Three-Dimensional Phase Unwrapping Based on Reference Plane
- (1)
- For the deformed fringe pattern captured by camera, 1-D Fourier transform, spectrum filtering and inverse Fourier transform are performed along the time axis on each pixel, getting the 3-D wrapped phase distribution data of a measured dynamic object.
- (2)
- Calculating the unwrapped phase of the reference plane measured on the same system.
- (3)
- Choosing one wrapped phase of the tested object at sampling time t1, in which, the object’s corresponding height changes within a suitable range. And comparing 2π with the phase difference between and to get the multiple integer K for each pixel, which must satisfy the following condition
- (4)
- Adding 2Kπ to to get its unwrapped phase
- (5)
- Taking as the benchmark of the 3-D phase unwrapping and performing the 1-D phase unwrapping along the temporal axis, then finally obtaining the 3-D unwrapped phase distribution.
2.3. High-speed Measurement System and Framework of the Proposed Method
2.4. System Calibration
3. Experiments and Results
3.1. Accuracy Analysis
3.2. Comparative Experiments on Isolated Objects
3.3. Measurement of an Impact Process
4. Discussion
- A new absolute phase of an isolated, steep object can be recovered from a new distorted sinusoidal fringe pattern. For a dynamic measured scene, compared with FTP, TFTP can also get new height information from each new distorted fringe pattern, and the motion error is avoided. Moreover, TFTP does not filter in the spatial domain but in the temporal domain, avoiding the spectral overlapping caused by the information loss of some pixels in the spatial domain and the smoothing effect of spatial Fourier regarding steep objects. The absolute phase recovery, pixel-by-pixel, is realized by introducing the unwrapping phase of the reference plane and unwrapping the 3-D wrapped phase distribution along the temporal axis. The difference is, for the TFTP method, data processing operations should be carried out after all the deformed fringe patterns are acquired.
- TFTP have a better performance in the dynamic measured scene. In the improved TFTP method, a new 3-D reconstruction result can be obtained from each new deformed fringe pattern. Compared with the PMP method and temporal phase unwrapping method, the improved TFTP will not cause a motion error in high-speed measurement. Nevertheless, in the TFTP method it is expected that the sampling theorem must be satisfied in the temporal domain because of the use of Fourier fringe analysis along the temporal axis (at least four sampling points per period to avoid spectrum overlapping). In other words, although the measured scene is isolated in the spatial domain, it is still continuous on each pixel along the temporal axis under a high-speed recording. When projecting N-step phase-shifting fringe patterns, it is required that N must be more than or equal to 4 to ensure that each period has four sampling points (In this paper, we adopt the nine-step phase-shifting). Once the sampling theorem in the temporal domain is not satisfied, the accuracy of the TFTP method will be affected. Therefore, for objects with complex dynamic distributions, the reconstruction accuracy of the TFTP method is between those of the FTP method and PMP method. In short, TFTP has a better performance on the dynamic measured scene and high-speed device can offer a better guarantee of the continuity in temporal domain.
- A fast, low-cost and flexible structured light pattern sequence projector is presented. In this paper, we presented a self-made mechanical projector to offer a better guarantee of the sampling theorem for the TFTP method. Our self-made projector generates sinusoidal fringe by the defocusing method and can reach the projection speed of thousands of frames per second. The signal part on the dics can accurately feedback the phase-shifting information and control the camera to capture the corresponding deformed pattern simultaneously. In addition, the dics is easy to change according to different measurement scenarios. In the measurement process, the measuring speed of the device is only limited by the shooting speed of the high-speed camera. Moreover, it is worth reminding that the sinusoidal feature generated from the defocused binary pattern will be affected by the defocusing degree, which is a common limitation of the binary defocusing method. So, if the measured height’s change exceeds the measurable depth range of the current binary defocusing, this proposed method will produce reconstruction error or even lead to failure.
- The different spatial frequencies are adopted to match the measured process with different complexities. It is a simple and effective method by introducing the reference plane to assist the absolute phase recovery of the 3-D wrapped phase distribution. According to the nature of the principle, the height change of the measured object must have one moment within the phase change of 2π corresponding to the height change range during the measurement. However, it is worth mentioning that the period of the projected sinusoidal fringe in the spatial domain does not affect the accuracy of the TFTP method (even the single-period sinusoidal fringe can be used). We can choose different spatial frequencies according to different measurement scenarios. For a special measured scene, in which the depth change at each moment in the measurement process is large, we can adopt the large period fringe projection to guarantee feasibility of 3-D phase unwrapping based on the reference plane.
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Conflicts of Interest
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Liu, Y.; Zhang, Q.; Zhang, H.; Wu, Z.; Chen, W. Improve Temporal Fourier Transform Profilometry for Complex Dynamic Three-Dimensional Shape Measurement. Sensors 2020, 20, 1808. https://doi.org/10.3390/s20071808
Liu Y, Zhang Q, Zhang H, Wu Z, Chen W. Improve Temporal Fourier Transform Profilometry for Complex Dynamic Three-Dimensional Shape Measurement. Sensors. 2020; 20(7):1808. https://doi.org/10.3390/s20071808
Chicago/Turabian StyleLiu, Yihang, Qican Zhang, Haihua Zhang, Zhoujie Wu, and Wenjing Chen. 2020. "Improve Temporal Fourier Transform Profilometry for Complex Dynamic Three-Dimensional Shape Measurement" Sensors 20, no. 7: 1808. https://doi.org/10.3390/s20071808
APA StyleLiu, Y., Zhang, Q., Zhang, H., Wu, Z., & Chen, W. (2020). Improve Temporal Fourier Transform Profilometry for Complex Dynamic Three-Dimensional Shape Measurement. Sensors, 20(7), 1808. https://doi.org/10.3390/s20071808