/ he International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
photogrammetric applications established by several 
organizations such as ASPRS, NMAS, etc (Madani, et. al, 
2004). These results have been achieved despite the smaller 
base-to-height ratio of the DMC by the higher image coordinate 
accuracy resulting from a better radiometric quality, and in 
particular, by better system geometry. However, some DMC 
users and research institutions have indicated that there is still a 
very small systematic error left in the DMC virtual images 
which leads to a lower vertical accuracy of determined object 
points of the large scale engineering projects. 
In this study, two methods for modelling the remaining 
systematic errors in the so-called virtual image plane of the 
DMC imagery are analyzed: bundle adjustment with collocation 
trend refinement of the image residuals and self-calibrating 
bundle adjustment. 
These two approaches are analyzed on several DMC test blocks 
having different GSDs. The ImageStation Automatic 
Triangulation (ISAT) software is modified to generate 
correction grids by collocation technique, as well as to import 
correction grids created by significant additional parameters of 
self-calibration bundle adjustment programs. The Post 
Correction Grid ON/OFF enabled status is controlled by the 
ImageStation Photogrammetric Manager “Edit Camera” dialog. 
Grid group and grid names can be any ANSI strings; the camera 
name must correspond to that in the camera file. These ISAT 
modifications also allow verifying the quality of these 
correction grids before they are used in generating new 
“distortion free” virtual images by DMC’s Postprocessing 
software (Madani, 2008). 
Figure 2. Edit Camera dialog 
2. DMC ERROR BUDGET EVALUATION 
Lens-Chip distortion of each PAN camera contains about 93% 
unstable “linear” (magnification, shift) part and about 7% 
relatively stable “nonlinear” part. Magnification (focal length 
change) and shift (principle point change) of each PAN camera 
must be fully compensated (directly or indirectly) in the 
platform orientation of the 4 PAN cameras. The uncompensated 
“nonlinear” part is the primary source of the systematic error, 
which directly propagates into virtual image rectification (VIR) 
camera space and affects platform orientation. The upper limit 
for the uncompensated distortion is about 2[um], which 
corresponds to about 8% of the total nonlinear distortion 
(24[umj). The estimated variation of the uncompensated 
nonlinear part with temperature is only 0.25[um]. So, the 
primary error source is a very stable constant term (Madani, 
2008, Dorstel 2007). 
Platform orientation, which is responsible for refinement to the 
relative orientation of 4 PAN cameras and compensation for the 
“linear” part of the lens-chip distortion, is sensitive to 
uncompensated nonlinear error. However, a constant systematic 
effect from the primary error source on platform orientation 
produces a constant systematic response. Error in platform 
orientation that propagates to VIR image space as 4-quadrant 
perspective distortion is the secondary error source. In total, 
about 35% of the systematic error in VIR space is due to 
primary error source and 65% is due to secondary error source. 
The minimal reliable estimate of the systematic distortion 
present in the DMC virtual panchromatic imagery by averaging 
all image residuals from block adjustment within a cell-grid 
placed on the camera frame is about 0.5[um], The maximal 
observed distortion estimate is about 3-5[um], while random 
image feature measurement error due to radiometric noise is 
2[um], 
The unknown portion of the total systematic error in image 
space propagates into object space, causing block shape 
deformation (bending, twisting, wobbling, or similar). It is 
contributing to an increase in discrepancy on the vertical 
component of the check points by 3-4 times over the 
undistorted values achieved by the properly calibrated cameras 
or bundle block adjustment of DMC photos with 4-quadrant- 
based self-calibration. For example, for project “Rubi” (Alamus, 
2006) with GSD of 10[cm], the Z residual is about 20[cm] 
versus 5[cm] when the cumulative image distortion is removed. 
For reference, direct effect of 3[um] in image space contributes 
to only 0.6[cm] in object space for a single photo of this project 
scale; therefore, the rest of Z-distortion comes from the 
accumulated error causing block deformation. This 
deformation is visible as a “banana curve” in Z-residuals of 
GPS observations along a strip with the relaxed statistical 
weights. 
3. SYSTEMATIC ERROR COMPENSATION 
Traditionally, cameras are calibrated in laboratories and their 
systematic distortions are modelled to a considerable extent, but 
they always leave some kind of residual systematic errors due 
to their own limitations. Different camera calibration methods 
are used to model these residual systematic errors (Madani, 
1985): 
■ Pre-calibration (Laboratory) 
■ On-the-job (Test Field) calibration (Camera intrinsic 
model) 
■ Self-calibration (Physical and Geometric models) 
■ A posteriori interpolation treatment of image residuals 
(Correction grid by Collocation) 
In the following sections, only self-calibration and a posteriori 
interpolation techniques are briefly discussed. 
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