Optics

Error-free depiction of the field of view

Lens distortion

Distortion is a rotationally symmetric image error that increases from the centre of the image towards the edges.

This results in a local change in image scale within the image plane, which can be very annoying in metrology applications.

As the magnification increases towards the edges of the image field, a square is distorted into a pincushion shape. The opposite is called barrel distortion.

Various types of distortion

Wide-angle retrofocus lenses (focal length greater than the lens focal length) tend to have barrel distortion, and telephoto lenses (length less than the lens focal length) tend to have pincushion distortion.

Determination of optical distortio

The percentage of maximum distortion is measured from the centre to the corners of the image, as this is where the maximum distortion occurs.

In a very simplified way, the increase in error can be described as a linear increase from the centre of the image to the edge.

If the error is smaller than the pixel size of the camera sensor, it cannot be detected by measurement.
The human eye is only able to detect distortion when the geometric error is greater than two percent. For many applications, this may be far too high! It is worthwhile to measure the distortion!
This error occurs with many common lenses, especially wide angle lenses. It can usually be corrected by sophisticated lens design, but this is very expensive in the case of wide-angle lenses.

How optical distortion occurs

A non-symmetrical design of the lens construction and an aperture in front of and behind the optical centre of the lens causes image distortion. The image can be distorted into a barrel or pincushion shape.

The rear diaphragm arrangement of a non-symmetrical lens design results in pincushion distortion.
The front diaphragm arrangement of an asymmetric lens design results in barrel distortion.

Especially with zoom lenses, this error can become very large at long focal lengths, as the lens groups are shifted, but not necessarily the aperture position.

Creation of pincushion distortion

Creation of barrel distortion

Correction options and tips for machine vision

Improvement by the user: Subsequent software correction (non-linear image correction by image transformation) can further optimise the image.
Use of high quality corrected lenses with improved lens design
Use of longer focal length lenses when a longer working distance can be achieved as an alternative to wide angle lens designs.
Avoid compromising zoom lenses
Stopping down the lens cannot correct this error

Applications using extreme optic distortion

Distortion is annoying in almost all applications. However, the extreme fisheye perspective of a very short focal length makes it possible to view the sidewalls of a cavity from a very close distance.

Typical applications include the inspection of bores, bearings, threads, etc.

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