This concept of calibration provides a basis for systematically conducting calibration of photographic 
systems. 
"Many procedures intended for calibration have been devised and are currently in use. With few 
exceptions, however these schemes fall short of Eisenhart's concept of calibration. Such calibration 
procedures may well yield superior results in terms of the fit of the mathematical model to the 
observations. If the procedures are not conducted within the expected ranges of operational 
circumstances, the results do not represent realistic characteristic properties of the measurement 
procedure as intended. In many applications, a serious compromise in measurement accuracies will result 
using the results from such calibrations." /Merchant 1971/. 
It is noted that the concept of measurement system calibration - or, for short, system calibration 
- requires an arbitrary standard of comparison. Such a standard for photogrammetric purposes is a 
testfield with known well-defined points. Photographs over three such testfields were available for 
the investigation. 
In the case of vertical photography over a practically plane testfield - the three testfields all 
fall into this category - an almost strict linear dependency exists between the following paired 
elements of interior and exterior orientation: 
a. principal point coordinate (x,) and exposure station coordinate (X) 
b. principal point coordinate (Yo) and exposure station coordinate (Yo) 
c. calibrated focal length camera constant (£.) and the terrain clearnace (H - h) 
It is clear that computational problems will arise as calibration is attempted when such geometry is 
given. For vertical photography, which is the conventional aerial case and the case at hand, there are 
basically two alternative approaches which have been suggested to supress these unfavorable high 
correlations existing between interior and exterior elements of orientaion, the determination of the 
exposure station coordinates during the flight mission and the "Method of Mixed Ranges" proposed by 
Merchant. Neither approach was available to us. Hence, the principal point coordinates and calibrated 
focal lengths determined for the used cameras with camera calibration procedures were held, and only 
the parameters defining lens distortion were determined. There was no need to consider either shear 
factor or differential scale change for the image coordinates corrected by means of the réseau. 
System calibration within the context of this paper includes into the determination of system 
distortion the distortion of the lens, the effects of the camera port window, of dimensional changes of 
lens/camera components caused by changes in the ambient conditions, uncorrected film deformation and 
deviation of the emulsion from the intended recording surface, and photogrammetric refraction. 
SELF-CALIBRATION 
Self-calibration is the name commonly used for an approach to a photogrammetric triangulation | 
procedure with a configuration permitting the recovery of parameters defining the geometric-optical ; Í 
parameters of the employed camera system; in this approach all image points contribute to the I Lm > 
determination of the parameters, while only-the given control points do_so in laboratory and system 
calibration. 
Self-calibration had been used at DBA Systems, Inc. since 1965 in a bundle adjustment program used 
to calibrate parabolic radio reflectors by means of terrestical photographs. /Brown 1974/. the first | 
paper dealing with self-calibration of aerial photographs presented at a meeting of the International MN 
Society of Photogrammetry was that by Bauer and Müller given at the congress in Ottawa in 1972. - Since | | 
that time, self-calibration has enjoyed an ever increasing attention in photogrammetry. After the 1976 
congress, a "Working Group Compensation of Systematic Errors of Image and Model Coordinates" was |.  -— — 
established to study "1. Component calibration, 2. Testfield calibration, 3. Self-calibration and 4. 
Other possible methods". The results achieved by the working group are presented in /Kilpelà 1980/ and 
show that the members of the group concentrated on self-calibration. Some results for system 
(testfield) calibrations and component calibrations are reported as well but the report does not 
include a comparison of system and self-calibration results. | 
From appendix A of /Kilpeld 1980/ the follcwing self-calibration-parameter sets were selected: 
Parameter set a proposed by Brown: 
dx = a,x + ayy + a3xy + a ye * acx?y + ag xy? + a, x?y? * X(a 42 - y?) * a x^ y? + 2y 502° - y^) 
+ x(a; (x? T y2) + a; (x? + y2)? + a, g(x? + y2)3) 
+ y(a, ç (x* + y?) T aj; (x? T y^»? + 8, 5x? + v2)3) 
Parameter set b proposed by Ebner: 
dx = byx + byy - b(2x? — 4B2/3) 4 b,xy + bs(y? - 2B2/3) + byx(x2 - 282/3) + bg(x? - 282/3)y 
+ by; (x? - 28%/3) 
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