ons. Due to 
cameras are 
trology. As 
racy of the 
of a simple 
tion of very 
requires an 
ation model 
asks. This 
of distortion 
and Rollei 
00 pixels in 
uch as the 
ies of 0.01 
| have been 
using self- 
. In theory, 
y networks 
imately 1 : 
,000 image 
sed by the 
and precise 
e not yet 
because the 
al accuracy 
ld suggest. 
'e routinely 
'grammetric 
tes that the 
indicator of 
latively few 
independent 
coordinates, 
theodolite 
. Although 
d with such 
is of object 
  
  
stability and consistency of target location measurement, 
many independent tests have indicated a significantly 
degraded external accuracy when compared to internal 
precision. 
Clearly, systematic or stochastic errors remain in the 
model for the optical and electronic components of still 
video cameras or the target location algorithms for image 
measurement. Because there are many possible sources 
of error, the best approach to the problem is one of 
elimination. One area of valid research is the common 
use of a simple lens model which assumes radial lens 
distortions are constant with respect to the distance 
between the lens and the target. This paper will 
concentrate on initial research toward the evaluation of 
an extended lens model. The intent of the research is the 
isolation of the effects of variation of distortion with 
focus distance and distance within the object space. 
2. VARIATION OF DISTORTION 
2.1 Variation with Focus Distance 
An image is considered to be in focus at a specific 
distance, known as the focus setting or focus distance for 
the camera lens. The plane of best focus in the object 
field is a plane parallel to the image plane. 
It is well known that lens distortion varies with lens 
focus. A change in the focus distance for a typical 
camera with a simple lens system is achieved by a 
change in the principal distance, which changes the 
image magnification produced by the camera lens. The 
change in the principal distance results in a change in 
lens distortion which is proportional to the principal 
distance and the focus distance. 
Magill (1955) developed a formula for the computation 
of lens distortion at any specified focus distance, or 
magnification, based on two other determinations of lens 
distortion profiles. The computation uses a scale factor 
derived from the focal length and focus distances : 
o = Os drs + ( 1 - og) ÔTs, (1) 
where 
org — required lens distortion at focus distance s 
Org = predetermined lens distortion at focus 
distance s, 
Ors, = predetermined lens distortion at focus 
distance s, 
The scale factor og is derived from : 
= $9385814251 sam (2) 
S $9 - Sj ST 
  
535 
where 
s, S,, s,= distances from the camera to specified 
focus planes in the object space 
focal length of the camera (the principal 
distance at infinity focus) 
f 
The focal length of the camera may not be known, other 
than the nominal value given by the manufacturer. The 
principal distance at a specified focus distance can be 
computed using the thin lens formula : 
1 1.4 
t omcRL (3) 
S e 
where 
Cz principal distance 
This formula can be re-arranged to conveniently give the 
focal length as a function of the principal distance and 
focus distance : 
f. XS (4) 
c+s 
A focal length value averaged from the two 
predetermined calibrations can be computed to provide 
the maximum accuracy. Once the focal length is known, 
the principal distance corresponding to the required focus 
distance used in Magill’s formula can be computed using 
equation (3). Other parameters required for a full 
specification of the camera calibration, such as the 
principal point location, may be determined by 
averaging, or perhaps linear or non-linear prediction 
from a series of calibrations at different focus distances 
(Wiley and Wong, 1995). 
The optimum accuracy of the new distortion parameters 
will be gained if the two pre-determined lens distortion 
profiles are as far apart in distance as possible. One set 
of profiles should be obtained at a focus distance of 
infinity, and a second set of profiles obtained at as short 
a focus distance as possible. 
In practical terms, the predetermined profiles will 
generally be derived from a targeted test range 
calibration, a straight (or plumb) line calibration, or a 
combined test range and straight line calibration of the 
camera lens (Shortis et al 1995a). The proximity of the 
near focus distance calibration will be limited by field of 
view and depth of field considerations. The far focus 
distance calibration can generally be conducted at 
infinity focus, but again field of view may be a 
consideration. At the near focus distance the target or 
line density may be very low, whilst at the far focus 
distance the target array or straight lines may cover only 
a small portion of the image format, reducing the 
effectiveness of the calibrations. 
Shortis et al (1995a) showed that the combination of 
target array and straight line calibrations realises 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996