About lens distortion


Studying the manufacturers specifications of lenses and cameras we can see that in many cases the actual view angles obtained by measurement and listed in the specification do not coincide with the calculated view angles for an ideal lens, based on the lens focal length and the size of the image sensor.
For example, the specification of the lens T2314FICS3 (Computar) contains the following values:
With lens focal length of 2.3 mm and the size of the image sensor 1/3" real horizontal view angle is 113.30 deg., and the vertical view angle is 86.30 deg. But calculation gives lower values  92.40 deg. and 76.10 deg.
The form of the camera view area with this lens differs from the standard pyramid and therefore can not be accurately calculated by lens calculators or modeled by CCTV design programs of previous generation.
The cause of warping the view area is the Lens distortion. The Lens distortion arises from the fact that the optical magnification of a real lens is not constant over the entire field of view. Optical magnification varies depending on the distance from the center to the edges of the field of view.
Depending on whether the optical magnification of a lens is decreased or increased with distance from the center of the field of view, the barrel distortion and the pincushion distortion is distinguished.
The titles barrel and pincushion are associated with the distortion of the image. But the shape of the field of view varies oppositely the title. Thus, with the barrel distortion the image resembles a barrel, and the shape of the field of view resembles a pillow. With the pincushion distortion, the image resembles a pillow, and the shape of the field of view  a barrel.
Lens distortion leads to warping:
•  shape of view area and field of view; 
•  image from the camera; 
•  distribution of the pixel density. 
The Lens distortion should not be confused with the Perspective distortion (Fig. 7), which is natural on all images obtained with wideangle lenses. Perspective distortion does not change pyramidal shape of the view area, rectangular shape of field of view and distribution of the pixel density.
If by moving away from the center of the field of view the optical magnification decreases, then objects at the edges of the field of view seem compressed, and the pixel density decreases from the center to the edges, and the field of view is stretched to the edges. Real angles in this case are more than the calculated angles. This is called Barrel distortion. The Barrel distortion is most common and usual for wide angle lenses.
In particular, the lens T2314FICS3 has just the Barrel distortion. Let's consider a model of image from this lens, the model of field of view, view area projections built with and without simulating distortion. Position of the camera in both cases is constant.
Note the warping of distribution of the pixel density (Fig. 4). Barrel distortion increases the field of view, but reduces the pixel density, the farther from the center of the field of view, the stronger.

If by moving away from the center of the field of view the optical magnification increases, then objects at the edges of the field of view seem stretched, and the pixel density increases from the center to the edges, and the field of view is compressed to the edges. Real angles in this case are less than the calculated angles. This is called Pincushion distortion. The Pincushion distortion occurs seldom with teleobjective lenses.
Let's consider models built with and without simulating distortion. The models are given to illustrate the pincushion distortion, they are not associated with a certain model of lens. Position of the camera in both cases is constant.
Note the warping of distribution of the pixel density (Fig.14). Pincushion distortion decreases the field of view, but increases the pixel density, the farther from the center of the field of view, the stronger.

Modeling lens distortion in VideoCAD
Despite the complexity of internal calculations, simulation of lens distortion in VideoCAD is very easy. The lens distortion in VideoCAD is defined by a combination of calculated view angle and real view angle. The calculated view angles are calculated in the program from the lens focal length and format or the actual size of the image sensor.
The real angles are usually given in the specifications of cameras and lenses. If the angles are unknown, it is possible to get them by practical measuring.
To determine the lens distortion it is enough to set one of three real angles: horizontal, vertical or diagonal. It is preferable to set the horizontal angle. Missed real angles will be calculated by VideoCAD. For maximum accuracy, you can specify 2 or all 3 the real angles.

See more: Lens distortion, Modeling lens distortion, Measuring real view angles List/Range
See also: Specifying active area size of the image sensor