lits 
ele 
24° 
4° 
cal 
lon 
um 
jen 
the 
ind 
vas 
ng 
ich 
ere 
ues 
lits 
lial 
ere 
h), 
ital 
ind 
ind 
lir- 
of 
to 
ien 
"he 
1ge 
jon 
in 
Table 2 The radial lens distortion for each side vs. collimator shift angle. 
  
  
  
(by EFL) 
shift angle radial lens distortion(mm) 
H V SIDEI SIDEII SIDE III SIDE IV 
+a° + 4° 0009 0.005  -0.002  -0.005 
£12’ +8° -0.005 -0.004  -0.013 -0.011 
zig? +12 -0.049 -0.025 -0.066 -0.018 
+ 24° +16° -0.127  -0.053  -0.144  -0.043 
  
Table 3 The coefficients of radial lens distortion in each side obtained by 
  
  
collimator test. ( xE-3) 
coeff. SIDE I SIDE II SIDE II SIDE IV 
0.003546 0.003174 0.001178 0.004410 
-8.552213E-5 -1.996202E-4 
K, 
K, 
K, 277313757 
K, 
-4.344807E-5 -4.285227E-4 
2.024559E-6 -1.133125E-7  7.853835E-6 
-4.608873E-10 -8.256863E-9 
4.990564E-10 -4.291548E-8 
  
  
TIT T7173 
/ 
^A 
—120 
radial distortion (um) 
1 
| 
l 
/ 
// 
dd 
/ 
A 
H EFL 
  
  
—160 
l I 1 1 
0.0 3.8 7.7 11.7 16.0 
radial distance (mm) 
  
Fig.3 Radial lens distrotionby EFL and CFL 
Analytical Plumb Line Method 
Grid images are obtained by wide angle lens with 
35mm focal length through double exposures. 10 
plumb lines are imaged in first exposure and 7 
plumb lines in second exposure. We obtained radial 
and tangential lens distortion coefficients of Nikon 
F801 non-metric camera. 
SIMULATION TEST 
Using the coefficients obtained by the camera 
calibration, we performed the simulation test to 
examine the accuracy of results through the error 
correction. 
Table 4 Lens distortion coefficient of Nikon 801 
non-metric camera.( X E-6) 
  
  
  
  
  
  
  
  
Dis; radial distortion coeff. 
tance 
(m) K, K, K, 
0.5] 43.82876730|-0.03626487 |-0.00000921 
1.0) 53.17592457]-0.07958205|-0.00005170 
1.8| 42.51753570]/-0.03721015]-0.00001845 
Dis: tangential distortion coeff. 
tance 
(m) P P. P, 
0.5| -30.87500896/-17.43285964|-0.74695714 
1.0| -20.93058837| 7.74351767|-0.01338893 
1.8] 9.84737198| 25.69442983 |-0.28874270 
  
  
  
  
  
  
The 35 targets arrayed on the plane wall were 
photographed with 9 photos obtained at 0.5m, 
1.0m, 2.0m with the convergent angle 30° and 
normal case. The targets were rearranged for each 
object distance in order to be covered uniformly 
on the full film area. 
The standard deviations of results of two casese 
were compared between systematic error to be 
corrected and not to be through plumb line 
method and collimator method (Fig.5). It is noted 
that compared with uncorrected case, both methods 
have 2096-3096 decrease of standard deviations.