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Radial Distortion Correction

Modern camera lenses are relatively free of geometric distortion. However, there is always a small remaining amount even with the most expensive lenses.



Radial Distortion:

Radial distortion is most visible when taking pictures of vertical structures having straight lines which then appear curved. This kind of distortion appears most visibly when the widest angle (shortest focal length) is selected either with a fixed or a zoom lens.  It may be adequately corrected by applying a simple polynomial transformation due to the 19th century mathematician and astronomer Philipp Ludwig von Seidel (1821-1896) published by him in 1856 which requires three constants affecting the image content as a function of the distance from the center and symmetrical about it, hence the name radial distortion. A very complete discussion with full mathematical background, is given in this link

Calibration:

These constants may be computed by photographing a structure or a target containing known straight lines, both vertically and horizontally. They depend on the focal length of the lens relative to the length of the diagonal of the image sensor and vary from lens to lens. For cameras with interchangeable lenses, separate calibration is required for each lens and for a selection of typical focal lengths relative to a given camera. For a less expensive digital camera with a non-interchangeable lens, calibration is required only for a selection of focal lengths.

This programme accesses a database called PTLens.dat to correct distortion. To use recent entries in the database you must purchase a license from the Purchase page at http://epaperpress.com/ptlens. Updates to the database may be found on the Download page at same site. Instructions for installing the license in RadCor are in a readme file that accompanies the license. If you have any questions about the database contact Tom Niemann (http://epaperpress.com/whoami).

Because of the many cameras and lenses on the market which are constantly being added to, it is not possible to have a profile for every camera and every lens. Therefore, this programme offers simple tools for calibrating any camera-lens combination if a suitable image is available. Here, this process is called manual correction..

Chromatic Aberration:

Some cheaper cameras have distortion which varies with colour.  This is chromatic aberration. In this programme, a facility is offered for selection of the correction constants for the red, green and blue components of a colour calibration image in the chromatic correction option.

In addition to radial distortion and chromatic aberration, there are other types of lens distortion which affect the quality and geometry of an image which are not radially symmetric.  This type of distortion (tangential) is not corrected in this programme, since it is usually small compared with that due to radial lens distortion at the typical image resolutions of digital cameras. Perspective distortion, which is introduced by the camera pointing obliquely at the subject of interest, will be addressed in another programme.

Vignetting:

If the distribution of light at the sides of the image is not the same as nearer to the center, these portions of an image appear to be darker. The programme can correct for simple symmetrical radial vignetting sometimes present at very wide angles or when lens hoods are used.