The coordinates on the sensor are expressed in a base of vectors called (u,v).
The distortion of a camera-lens system can be expressed by an operator that transforms the coordinates with distortion (u,v) into coordinates without distortion (u’,v’) or vice versa.
Therefore as a general rule we can write:
With A, a generic operator.
Classic modelling requires A to be a function:
The factor can be developed in series to divide the contributions of the different degrees of r.
To also take spurious effects into account, the equation can be redefined as:
The effects of the main coefficients are graphically shown as follows:
Determining the transformation values makes it possible to calculate and correct the distortion.