Volumetric Calibration Refinement of a Multi-Camera System Based on Tomographic Reconstruction of Particle Images
Abstract
:1. Introduction
2. Methodology of Calibration Refinement
2.1. The Shape of a Particle Reconstruction with Camera Mismatch
2.2. Cross-Correlation of Original Images with Back-Projected Images
2.3. Ensemble Averaging of Correlation Maps from Snapshots
2.4. Correction Steps
2.5. Typical Iterative Correction Performance
2.6. Treating Larger Mismatch with Image Pre-Processing Using Gaussian Blur
3. Numerical Assessment
3.1. Influence of Particle Image Diameter and Seeding Density
3.2. Influence of Errors on All Cameras
3.3. Performance Tests with Synthetic Velocity Data
4. Performance Tests with Experimental Data
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Cam #1 | Cam #2 | Cam #3 | Cam #4 | |
---|---|---|---|---|
Camera size full width × height (px) | 250 × 250 | 250 × 250 | 250 × 250 | |
Camera alpha α | α1 = −45° | α2 = 0° | α3 = +45° | |
Camera beta β | β1 = 0° | β2 = 0° | β3 = 0° | |
Camera pixel size (µm) | 10 | 10 | 10 | |
Magnification (mm/vx) | 1/10 | 1/10 | 1/10 | |
pixel to voxel ratio | 1 | 1 | 1 | |
Lens configuration | Ideal telecentric | Ideal telecentric | Ideal telecentric | |
Initial mapping function | Ideal rectilinear | Ideal rectilinear | Ideal rectilinear | |
Initial camera error translational | Δpx = +3 | - | - | |
Initial camera error rotational | Δγ1 = 0° | - | - | |
Refined mapping and LOS equation | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z |
Cam #1 | Cam #2 | Cam #3 | Cam #4 | |
---|---|---|---|---|
Camera size full width × height (px) | 800 × 500 | 800 × 500 | 800 × 500 | 800 × 500 |
Camera alpha α | α1 = 0° | α2 = +45° | α3 = 0° | α4 = −45° |
Camera beta β | β1 = −45° | β2 = 0° | β3 = +45° | Β4 = 0° |
Camera pixel size (µm) | 10 | 10 | 10 | |
Magnification (mm/vx) | 1/10 | 1/10 | 1/10 | 1/10 |
pixel to voxel ratio | 1 | 1 | 1 | 1 |
Lens configuration | Ideal pinhole | Ideal pinhole | Ideal pinhole | Ideal pinhole |
Initial mapping function | Ideal rectilinear | Ideal rectilinear | Ideal rectilinear | Ideal rectilinear |
Initial camera error translational (px) | Δpy = +5 | Δpy = +5 | Δpx = −3 | Δpx = −3 |
Initial camera error rotational | Δγ1 = 0° | - | - | - |
Refined mapping and LOS equation | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z |
Cam #1 | Cam #2 | Cam #3 | Cam #4 | |
---|---|---|---|---|
Camera size full width × height (px) | 1280 × 800 | 1280 × 800 | 1280 × 800 | 1280 × 800 |
Camera alpha α | α1 = −33.75° | α2 = −11.25° | α3 = 11.25° | α4 = 33.75° |
Camera beta β | β1 = 0° | β2 = 0° | β3 = 0° | β4 = 0° |
Camera pixel size (µm) | 20 | 20 | 20 | 20 |
Magnification (mm/vx) | 1/10 | 1/10 | 1/10 | 1/10 |
pixel to voxel ratio | 1:1.1 | 1:1.1 | 1:1.1 | 1:1.1 |
Lens configuration | Zeiss 100 mm | Zeiss 100 mm | Zeiss 100 mm | Zeiss 100mm |
Initial mapping function | Soloff | Soloff | Soloff | Soloff |
Initial camera error translational | unknown | unknown | unknown | unknown |
Initial camera error rotational | unknown | unknown | unknown | unknown |
Refined mapping and LOS equation | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z | 3rd order X,Y 2nd order Z |
Appendix B
Appendix C
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Particle Density ppp | Angular Displacement of Cam #1 and Cam #3 | Noise Level Variance | Initial Correction Step of Cam 1 (from +3 px Error-Shift) | Minimum Number of Ensemble Additions to Achieve Peak Position within 0.1 px Radius | Iterations to Correct Cam #1 Down to 0.1 px Offset |
---|---|---|---|---|---|
0.001 | ±45° | 0 | −1.1 | 4 | 5 |
0.003 | ±45° | 0 | −1.0 | 6 | 7 |
0.005 | ±45° | 0 | −0.8 | 10 | 9 |
0.008 | ±45° | 0 | −0.4 | 20 | 13 |
0.010 | ±45° | 0 | −0.3 | 22 | - |
0.001 | ±22° | 0 | −0.6 | 4 | 10 |
0.001 | ±45° | 0.00 | −1.1 | 3 | 5 |
0.001 | ±45° | 0.01 | −0.6 | 6 | 7 |
0.001 | ±45° | 0.02 | −0.5 | 10 | 10 |
0.001 | ±45° | 0.03 | −0.6 | 20 | - |
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Bruecker, C.; Hess, D.; Watz, B. Volumetric Calibration Refinement of a Multi-Camera System Based on Tomographic Reconstruction of Particle Images. Optics 2020, 1, 114-135. https://doi.org/10.3390/opt1010009
Bruecker C, Hess D, Watz B. Volumetric Calibration Refinement of a Multi-Camera System Based on Tomographic Reconstruction of Particle Images. Optics. 2020; 1(1):114-135. https://doi.org/10.3390/opt1010009
Chicago/Turabian StyleBruecker, Christoph, David Hess, and Bo Watz. 2020. "Volumetric Calibration Refinement of a Multi-Camera System Based on Tomographic Reconstruction of Particle Images" Optics 1, no. 1: 114-135. https://doi.org/10.3390/opt1010009