Barrel distortion

Wine-glass lenses create non-uniform distortion of their background

Barrel distortion simulation

Pincushion distortion simulation

In geometric optics and cathode ray tube (CRT) displays, distortion is a deviation from rectilinear projection, a projection in which straight lines in a scene remain straight in an image. It is a form of optical aberration.

Although distortion can be irregular or follow many patterns, the most commonly encountered distortions are radially symmetric, or approximately so, arising from the symmetry of a photographic lens. The radial distortion can usually be classified as one of two main types:

• barrel distortion, in which image magnification decreases with distance from the optical axis. The apparent effect is that of an image which has been mapped around a sphere. Fisheye lenses, which take hemispherical views, utilize this type of distortion as a way to map an infinitely wide object plane into a finite image area.

• pincushion distortion, in which image magnification increases with the distance from the optical axis. The visible effect is that lines that do not go through the centre of the image are bowed inwards, towards the centre of the image. In photography, this aberration is often seen in older or low-end telephoto lenses.

A mixture of both types, sometimes referred to as moustache distortion, is less common but not rare. It starts out as barrel distortion close to the image center and gradually turns into pincushion distortion towards the image periphery. It is observed with certain retrofocus lenses, also more recently on large-range zooms such as the Nikon 18-200mm.

[edit] Software correction

Radial distortion is modelled by a function D(r) that affects each point v in the projected plane relative to the principal point p,

where D(r) is normally a non-linear scalar function and p is close to the midpoint of the projected image. Barrel projections are characterized by a positive gradient of the distortion function , whereas pincushion by a negative one.

Software can correct those distortions by warping the image with a reverse distortion.

[edit] Calibrated

Calibrated systems work from a table of lens/camera transfer functions:

• PTlens is a Photoshop plugin or standalone application which corrects complex distortion
• DxO Labs' Optics Pro can correct complex distortion, and takes into account the focus distance

[edit] Manual

Manual systems allow manual adjustment of distortion parameters:

• Photoshop CS2 and Photoshop Elements (from version 5) include a manual Lens Correction filter for simple (pincushion/barrel) distortion
• The GIMP includes manual lens distortion correction (from version 2.4).
• Hugin can be used to correct distortion,[1] though that is not its primary application

[edit] See also

• Anamorphosis
• Distortion
• Vignetting

[edit] References

• Paul van Walree. "Distortion". Photographic optics.