Al-Hanbali, Nedal
There are a total of twenty-two parameters to be solved for. These parameters consist of: two sensor parameters (related
to the Pixel-Size and the Pixel-scale), nine internal parameters (related to the internal geometry of the scanner), four
interior orientation parameters (05, $o, 60, and 9$), one scale factor and six exterior orientation parameters (Xe, Y»,
Zo, ©, ®, and K). For more details regarding the mathematical model, collinearity equations, distortion model, and the
expected precision see Al-Hanbali (1998) and Al-Hanbali et. al. (1999).
5 THE CALIBRATION RESULTS
In imaging metrology, the calibration process of determining precisely the interior geometry of a camera is essential to
produce accurate and reliable three-dimensional information from measurements made on two-dimensional imagery.
The observations of the LSS are used to define a three-dimensional object space scene or points based on the LSS
interior orientation parameters and internal parameters. However, these coordinates are only defined with respect to the
camera space coordinate system. To link the camera space coordinate system with the object space coordinate system,
the exterior orientation parameters of LSS have to be determined and, hence, the object space datum is required. Special
adjustment procedure with a suitable target field has been followed to determine a good set of calibrated parameters, see
Al-Hanbali (1998 and 1999).
5.1 Precision of Absolute and Relative Measurements
Figure 8 shows the lab testing results to measure absolute and relative measurements, along the X-, Y- and Z- axes, at
depth distances ranging from 0.65 m to 1.95 m. The RMS (root mean square) values of the relative coordinate
measurements, are similar to the expected precision values calculated based on the variance values of the observations
used in the least squares adjustment Al-Hanbali (1998 and 1999).
| ——x-axis —B-- Y-axis Z-axis | | —e— X -axis —&-— Y-axis Z-axis |
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Precision of absolute
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Precision of relative
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Figure 8: The RMS values of the absolute and relative measurements at depth distances ranging from 0.65 m to 1.95 m.
The RMS values of the absolute measurements along the X-, Y- and Z-axes are nearly equal and similar in behavior, at
depth distances less than 1.25 m. However, in the case of relative measurements, only the X-axis and the Z-axis are
nearly similar and equal for depth distances that are less than 1.25 m. The Y-axis has better RMS values. This may
indicate that most of the systematic errors of the Y-axis are eliminated. Finally, the accuracy of the relative
measurements shows a drastic improvement in comparison to the accuracy of the absolute measurements.
3,2 Precision of Deformation Measurements
Figure 9 shows the deformation errors along X, Y and Z-axes. The errors are the difference between introduced
movements of targets mounted on translation stage ditributed over the field of view of the LSS. The movements are
calculated based on the calibrated parameters. The RMS values of the errors for a depth distance of 1.2 metre (Figure
8a) are: +0.023 mm, +0.074 mm, and +0.041 mm along the X-, Y- and Z-axes, respectively. The RMS values of the
errors for a depth distance of 1.5 metre (Figure 8b) are: +0.032 mm, +0.125 mm, and +0.092 mm along the X-, Y- and
Z-axes, respectively.
The movements for the depth distance of 1.2 m are introduced ranging from 0.25mm for the first epoch up to to 25 mm
for epoch 10 (Figure 9a). Similarly, the movements for the depth distance of 1.5 m are introduced ranging from 0.25mm
for the first epoch up to 50 mm for epoch 10 (Figure 9b). The absolute and relative measurement results, using
calibrated parameters, show that the LSS has better RMS values and mean errors for the calibrated depth distances
14 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000.
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