Figure 1.
Laser line displayed horizontally in the image: (a) complete image taken by the camera; (b) laser line section obtained from the complete image.
Figure 1.
Laser line displayed horizontally in the image: (a) complete image taken by the camera; (b) laser line section obtained from the complete image.
Figure 2.
Laser line detection procedure in image: (a) part of the laser line detection for each pixel; (b) pertinent histogram for a pixel column with each pixel’s light intensity value.
Figure 2.
Laser line detection procedure in image: (a) part of the laser line detection for each pixel; (b) pertinent histogram for a pixel column with each pixel’s light intensity value.
Figure 3.
Laser triangulation system. The calibration processes consist of identifying extrinsic and intrinsic parameters of both elements followed by the measurement process for the image. Here, and correspond to laser point p taken in the image and projected in the pattern following unitary vector u, for both the camera coordinates () and world coordinates (), with a transformation matrix R,d. Additionally, and correspond to laser parameters.
Figure 3.
Laser triangulation system. The calibration processes consist of identifying extrinsic and intrinsic parameters of both elements followed by the measurement process for the image. Here, and correspond to laser point p taken in the image and projected in the pattern following unitary vector u, for both the camera coordinates () and world coordinates (), with a transformation matrix R,d. Additionally, and correspond to laser parameters.
Figure 4.
Flow chart for experiments, with each block divided into different phases. Each output obtained in camera and laser calibrations is used as an input for block measurements. For camera calibration, the final outputs are the intrinsic parameters, which are the focal length (f), centre of distortions (Cx, Cy), and calibration parameters (K1, K2, P1, P2). Both N and L are triangulator calibration parameters defining the laser position in space.
Figure 4.
Flow chart for experiments, with each block divided into different phases. Each output obtained in camera and laser calibrations is used as an input for block measurements. For camera calibration, the final outputs are the intrinsic parameters, which are the focal length (f), centre of distortions (Cx, Cy), and calibration parameters (K1, K2, P1, P2). Both N and L are triangulator calibration parameters defining the laser position in space.
Figure 5.
Laser calibration in the coordinate measurement machine (CMM) and the three-dimensional (3D) pattern for laser line detection. The 3D pattern position is obtained by the CMM stylus and the laser is calibrated by displaying the laser line onto its surface while the camera captures images.
Figure 5.
Laser calibration in the coordinate measurement machine (CMM) and the three-dimensional (3D) pattern for laser line detection. The 3D pattern position is obtained by the CMM stylus and the laser is calibrated by displaying the laser line onto its surface while the camera captures images.
Figure 6.
Main layout for experiments, including a camera and laser with a carbon fiber rod, along with the Thorlabs stage. At the bottom of the image, a block measurement is displayed in the camera.
Figure 6.
Main layout for experiments, including a camera and laser with a carbon fiber rod, along with the Thorlabs stage. At the bottom of the image, a block measurement is displayed in the camera.
Figure 7.
Triangulation system in the CMM and camera calibration with a marker in the CMM stylus. The marker goes through different positions, while the camera obtains images for each position in space.
Figure 7.
Triangulation system in the CMM and camera calibration with a marker in the CMM stylus. The marker goes through different positions, while the camera obtains images for each position in space.
Figure 8.
A virtual pyramid for camera calibration with 1000 points (10 × 10 × 10), which is displayed in an internal software to obtain intrinsic and extrinsic parameters.
Figure 8.
A virtual pyramid for camera calibration with 1000 points (10 × 10 × 10), which is displayed in an internal software to obtain intrinsic and extrinsic parameters.
Figure 9.
Gauge block measurement on Thorlabs stage to ensure alignment. Another block is placed to ensure a flat and reflective surface (such as the 30 mm block).
Figure 9.
Gauge block measurement on Thorlabs stage to ensure alignment. Another block is placed to ensure a flat and reflective surface (such as the 30 mm block).
Figure 10.
Maximum error and linearity for calibration combinations in block measurements between reference heights and obtained heights.
Figure 10.
Maximum error and linearity for calibration combinations in block measurements between reference heights and obtained heights.
Figure 11.
Measurement combination distribution for ten different camera calibrations, with each calibration divided into different measurements.
Figure 11.
Measurement combination distribution for ten different camera calibrations, with each calibration divided into different measurements.
Figure 12.
Histogram of all combinations for 30 mm height measurement: (a) histogram for maximum error values; (b) histogram for linearity values.
Figure 12.
Histogram of all combinations for 30 mm height measurement: (a) histogram for maximum error values; (b) histogram for linearity values.
Figure 13.
Comparative measurements between experimental and Monte Carlo analysis, with similar shapes obtained for maximum error and linearity.
Figure 13.
Comparative measurements between experimental and Monte Carlo analysis, with similar shapes obtained for maximum error and linearity.
Table 1.
Block characteristics, such as nominal value, deviation, and uncertainty.
Table 1.
Block characteristics, such as nominal value, deviation, and uncertainty.
Nominal L (mm) | Deviation to Nominal D (µm) | Length Variation F (µm) | Uncertainty U (µm) |
---|
10 | −0.03 | 0.09 | 0.09 |
20 | 0.04 | 0.08 | 0.10 |
30 | 0.25 | 0.12 | 0.11 |
40 | 0.18 | 0.09 | 0.12 |
50 | 0.12 | 0.05 | 0.13 |
60 | 0.22 | 0.09 | 0.14 |
70 | 0.26 | 0.18 | 0.16 |
80 | 0.21 | 0.25 | 0.16 |
90 | 0.18 | 0.10 | 0.17 |
100 | 0.14 | 0.17 | 0.18 |
Table 2.
Summary of experiments.
Table 2.
Summary of experiments.
Nº Test | Objective | Results |
---|
1 | Camera calibration of CMM | Extrinsic and intrinsic camera parameters |
2 | Laser calibration of CMM | Intrinsic laser parameters () |
3 | Height measurement | Ceramic gauge block heights |
Table 3.
Mean value and standard deviation for both maximum error and linearity.
Table 3.
Mean value and standard deviation for both maximum error and linearity.
Nº Block | Maximum Error | Linearity |
---|
(mm) | σ (mm) | (mm) | σ (mm) |
---|
0 | 0 | 0 | 0.0012 | 0.0075 |
1 | 0.0391 | 0.0158 | 0.0131 | 0.0088 |
2 | 0.0537 | 0.0285 | 0.0016 | 0.0124 |
3 | 0.0758 | 0.0414 | −0.0025 | 0.0125 |
4 | 0.1009 | 0.0555 | −0.0035 | 0.0163 |
5 | 0.1316 | 0.0695 | 0.0010 | 0.0199 |
6 | 0.1462 | 0.0831 | −0.0105 | 0.0226 |
7 | 0.1703 | 0.0961 | −0.0125 | 0.0247 |
8 | 0.2002 | 0.1088 | −0.0088 | 0.0280 |
9 | 0.2341 | 0.1197 | −0.0009 | 0.0308 |
10 | 0.2842 | 0.1296 | 0.0229 | 0.0332 |
Table 4.
Calibration and measurement influence on repeatability.
Table 4.
Calibration and measurement influence on repeatability.
| Maximum Error Deviation | Linearity Deviation |
---|
| mm | % | mm | % |
---|
Camera calibration | 0.10600 | 56.910 | 0.00116 | 58.617 |
Laser calibration | 0.07430 | 39.901 | 0.00078 | 39.228 |
Measurement | 0.00595 | 3.200 | 0.00004 | 2.155 |
Table 5.
Covariance (correlation and probability) values for experimental data.
Table 5.
Covariance (correlation and probability) values for experimental data.
Experimental | | | | |
---|
R | p | R | p | R | p | R | p |
---|
| - | - | - | - | - | - | - | - |
| 0.987 | 0 | - | - | - | - | - | - |
| 0.986 | 0 | 1 | 0 | - | - | - | - |
| −0.280 | 0.006 | −0.270 | 0.007 | −0.270 | 0.007 | - | - |
Table 6.
Covariance (correlation and probability) values for Monte Carlo analysis (3D: 20 µm; image: 0.1 pixel).
Table 6.
Covariance (correlation and probability) values for Monte Carlo analysis (3D: 20 µm; image: 0.1 pixel).
Monte Carlo | | | | |
---|
R | p | R | p | R | p | R | p |
---|
| - | - | - | - | - | - | - | - |
| 0.851 | 0 | - | - | - | - | - | - |
| 0.839 | 0 | 1 | 0 | - | - | - | - |
| 0.369 | 0 | 0.269 | 0.007 | 0.269 | 0.008 | - | - |
Table 7.
Comparison between experimental and Monte Carlo covariance matrices (3D: 20 µm; image: 0.1 pixel).
Table 7.
Comparison between experimental and Monte Carlo covariance matrices (3D: 20 µm; image: 0.1 pixel).
Experimental | | | | | Monte Carlo | | | | |
---|
| 1.21 E − 07 | 1.93 E − 07 | 1.74 E − 07 | −3.69 E − 06 | | 2.03 E − 07 | 1.31 E − 07 | 1.16 E − 07 | 5.96 E − 06 |
| 1.93 E − 07 | 3.16 E − 07 | 2.85 E − 07 | −5.81 E − 06 | | 1.31 E − 07 | 1.17 E − 07 | 1.05 E − 07 | 3.31 E − 06 |
| 1.74 E − 07 | 2.85 E − 07 | 2.57 E − 07 | −5.26 E − 06 | | 1.16 E − 07 | 1.05 E − 07 | 9.35 E − 08 | 2.89 E − 06 |
| −3.69 E − 06 | −5.81 E − 06 | −5.26 E − 06 | 1.49 E − 06 | | 5.96 E − 06 | 3.31 E − 06 | 2.89 E − 06 | 1.29 E − 06 |