# Multi-Wavelength Digital-Phase-Shifting Moire Based on Moire Wavelength
## 4 Conclusions  
Multi-wavelength digital-phase-shifting moire was demonstrated using moire wavelength determined by calibration over the full working depth. The method is the first to compute multiple moire wavelengths in calibrations over the full working depth and employ them in heterodyne multi-wavelength phase unwrapping in digital moire. Furthermore, the moire wavelength calibration  
Figure 16: Wrapped phase maps: (**a**) \(\Phi_{1}\), (**b**) \(\Phi_{2}\).  
Figure 14: Moiré pattern generation: (**a**) Original captured image of double-hemisphere object with binary grid of 8-pixel pitch, (**b**) generated image with moiré pattern and high-frequency grid lines, and (**c**) moiré pattern after grid removal.  
Figure 17: (**a**) Extended continuous phase map \(\Phi_{12}\) with extended beat wavelength \(\lambda_{12}\), (**b**) unwrapped phase map \(\varphi\), and (**c**) point cloud representation of double-hemisphere object.  
Figure 18: Sample cross-section of measured points of double-hemisphere object and true semicircles.  
Figure 15: Moiré pattern generation: (**a**) Original captured image of double-hemisphere object with binary grid of 10-pixel pitch, (**b**) generated image with moiré pattern and high-frequency grid lines, and (**c**) moiré pattern after grid removal.  
determines a moire-wavelength to height relationship that is used in pixelwise refinement of the moire wavelength and height during 3D reconstruction. This is the first time that this is applied in multi-wavelength digital moire. The method has been demonstrated in 3D surface-shape measurement of an object with surface discontinuities and spatially isolated objects.  
In the multi-wavelength digital-phase-shifting moire, the extended noisy phase map is used as a reference to unwrap the phase map with the shorter wavelength, and thus achieve a less noisy and more accurate continuous phase map. Only a single pattern has to be projected and thus single image captured to compute each phase map with different wavelength in order to perform digital-phase-shifting moire temporal phase unwrapping. Only two captured images are required for two-wavelength phase unwrapping and three captured images for three-wavelength phase unwrapping. The number of projected and captured images required is one third of that for standard heterodyne temporal phase unwrapping by fringe projection. Decreasing the number of required projected and captured images would be advantageous in the image data acquisition process to enable fast measurement of dynamic objects, either moving or deforming. A further advantage for fast image data acquisition for measurement is that the projected grid is binary, which allows fast projection of patterns of different grid periods.  
Conceptualization, F.M. and J.K.; methodology, F.M. and J.K.; software, F.M.; experiments and analysis, F.M.; writing--original draft preparation, F.M.; writing--review and editing, F.M. and J.K.; supervision, J.K.; project administration, J.K.; funding acquisition, J.K.  
This research was funded by the Natural Sciences and Engineering Research Council of Canada and the University of Waterloo.  
The authors declare no conflict of interest.