Because of the radial distortion and the eccentricity r' 0 we obtain an assym- 
metric radial distortion 
Ar = dr — dr$ 7.2.5 
and a so called tangential distortion 
At = dt — dt$ 7.2.6 
When formulas 7.2.1—7.2.4 are substituted in 7.2.5 and 7.2.6 we obtain 
, , y/*-rV sin 2 W-fio) 
Ar = dr 
— dr o cos 
At = 
dr dr'<] 
r o sin (/5—Po) 
7.2.7 
7.2.8 
The so called tangential distortion At in formula 7.2.8 is exactly the same as 
that obtained from the formula given in [1] page 156. 
Most methods for determination of radial distortion use symmetrically loca 
ted points. If the method refers to a center point which is not the principal point 
as indicated above, this provides 1) assymmetric radial distortion, Ar in for 
mula 7.2.7 and 2) so-called tangential distortion, At in formula 7.2.8. The rea 
son for this is the eccentricity of the center point and has nothing to do with the 
camera design. 
By introducing the point of best symmetry the assymmetric radial distortion 
is converted to radial distortion. If measurements were exact, this point is exact 
ly the same as the principal point of the ’’ideal” camera. 
In some calibration methods these effects are determined and the maximum 
value of the so-called tangential distortion is given in the calibration certifi 
cate. This may not be a characteristic cf the camera but rather of the method 
of calibration. If dr 0 = 0 and dr from formula 5.2.1 is introduced into 7.2.8, 
we obtain an expression corresponding to that in 5.3.3. This means that there 
exists a relation between radial and tangential distortions. 
I