t B2. Istanbul 2004
ch the camera must
iverted, however, the
ting engine can cause
vient to cowl exit of
ystems, the influences
and external air will
stics of the camera.
the most widely used
grammetric quality is
ith this aircraft, no
ir beneath the aircraft
of the temperature
can be extreme. The
) between the optical
aircraft. This change
n be represented as a
stant. Accordingly,
nd at the camera lens
for the open port
The ideal, but most
indowed port. The
specified by military
ication, the window
st be included as part
tion. When operating
nces of temperature
ized, the differences
erates a stress/strain
| image deformation,
nodeling during the
stem specification).
al step leading to a
n a national basis.
neasurement process
erior orientation, the
ion.
conducted over the
approach to camera
ed cameras.
sual C++ language.
The first program,
, was designed for
-oduction of files for
lon program. The
by computation of a
ir targets have been
it point, the program
ol, and selects only
photograph. This is
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
followed by automatic movement of the measurement mark to
the first of the imaged targets in the selected set of targets. At
this point, the observer can rapidly make the fine pointing.
record the image coordinates and is automatically directed to
the location of the next target image. The auto-location is
accurate to several pixels for a system of low distortion. After
all the reduced target list images have been brought forward for
fine pointing, the observer saves results and moves on to the
next photograph.
For processing of the film-based images, the film is first
scanned and the imaged fiducials are measured, followed by a
two-dimensional transformation into a fiducial coordinate
centered system. All subsequent image measurements on this
frame are transformed accordingly, resulting in photo
coordinates in a fiducial system but corrected for film
deformation. Digital image coordinates are measured directly
from the photo file, then transformed by a rigid-body
transformation to the photo center, resulting in conventional
photo image coordinate system.
Additional input files provide the GPS coordinates of the
antenna phase center, the survey coordinates of the targets, the
first approximations to parameters of both interior and exterior
orientation along with associated variance covariance files for
weight constraint purposes.
A right-handed coordinate system and right-handed rotations
are assumed in all cases. When all images on a given photo are
measured and transformed to photo coordinates, a final single
photo resection is computed, resulting in the angles relating the
photo coordinate system to the ground system of coordinates.
This transformation of coordinate systems proceeds from the
object space to the image space. Given the rotation matrix,
expressing the relationship of ground to camera coordinate
systems, its inverse is used to transform the photo parallel
offsets, GPS phase center to camera entrance node, into
corresponding components in the ground control system. The
exposure station then is computed by addition of the
transformed spatial offsets to the phase center coordinates of
the antenna.
For any given photo, final processing applies atmospheric
refraction correction using the Saastamoinen model (1972). The
final step applies the transformed spatial offsets, antenna phase
center to camera node, directly to the GPS coordinates for any
given exposure. Results of this program are data files
containing refined photo coordinates of targets (lens distortions
remain) and exterior orientation.
3.1.2 Camera Calibration Program The calibration program
titled “Bundle Adjustment with Self Calibration" (BASC) is
designed to use the files produced by the image measurement
program (PIC). Additional files used by the program include a
description of the camera including first approximations to the
interior orientation, target survey coordinates, and variance
covariance information for all parameters describing interior
and exterior orientation, image measurements and target
coordinates.
The mathematical model used is the SMAC model as defined
by the USGS, a model that represents focal length correction,
symmetrical and decentering distortion, and location of the
principal point.
In accord with this SMAC model, radial distortion is
expressed as: (8x, dy)
8x 2(x— x) (K, * K, + Kr + Ks ra.)
Sy = (y — Yp) (Ke + Ki P+ r+ Kr Ll)
Where: x, yp ^ photo coordinates of the principal point
P= (=x) *(y- yy
K coefficients representing radial, symmetrical
distortion
The distortion due to decentering of the compound
objective is expressed as: (Ax, Ay)
Ax - (I P5 PD) (P, (8° +2 x°)+ 2 P2x y)
Ay=(1+P,1) (2P,xy + PAT" +2 y°))
Where: P coefficients represent decentering distortion
The corrected photo coordinates are then:
Xe = X + OX + AX
Ye=y+ôy+Ay
Note that the K, represents a scalar term for photo coordinates.
Accordingly, it accounts for small differences in the chosen
value of focal length. This permits use of an arbitrary but close
approximation when using the nominal focal length associated
with the lens design in the computations.
3.2 Flight Test Verification
Flight testing of both digital and film-based cameras was
conducted concurrently with the development of the software
programs. This assured that all elements of the calibration
process could be identified and treated accordingly during
development of the programs. It also verified that digital
cameras. even with narrow fields of view, can be
accommodated by the in situ approach to aerial camera
calibration. In addition, these flight tests demonstrated the
contrast in results between a laboratory and in situ form of
calibration. These differences further justify the need for a
systems approach to aerial camera calibration.
3.2.1 Madison Test and Calibration Range The Madison
Range currently consists of about 100 targets located within a
1.6 km by 2.6 km region, 50 km west of Columbus, Ohio.
Target coordinates were measured by GPS methods with
elevations augmented by spirit leveling. Adjustment results
indicate that the internal accuracy of the network is better than
2 cm on each axis and includes the base station, MADI. The
base station is located a distance of 5 km from the range center
at the Madison County Airport. The range was constructed and
is maintained by the Office of Aerial Engineering of the Ohio
