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:
With
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.
Final remarks: