# Difference between revisions of "Fisheye Projection"

From PanoTools.org Wiki

m (1 revision(s)) |
|||

(14 intermediate revisions by 3 users not shown) | |||

Line 1: | Line 1: | ||

− | + | in a fisheye projection the distance from the centre of the image to a point is proportional to the equivalent spatial angle. | |

− | |||

− | |||

− | |||

− | + | Taken from a posting of [[Helmut Dersch]]: | |

+ | <pre> | ||

+ | The focal length f of common fisheye lenses corresponds | ||

+ | quite simple to the angle of view theta and the | ||

+ | radial position R of a point on the slide: | ||

− | + | R = 2 * f * sin( theta/2 ) | |

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

So for 90 degrees, which would be the maximum | So for 90 degrees, which would be the maximum | ||

− | theta of a | + | theta of a 180 degree lens, f=8mm, you get |

− | R = 11.3mm, which is the radius of the image circle. | + | R = 11.3mm, which is the radius of |

+ | the image circle. | ||

This projection model applies to the Nikon 8mm | This projection model applies to the Nikon 8mm | ||

Line 27: | Line 20: | ||

Some older Nikon lenses (e.g. the 7.5mm) try to | Some older Nikon lenses (e.g. the 7.5mm) try to | ||

− | approach a linear mapping (theta in rad) | + | approach a linear mapping |

− | + | ||

+ | R = f * theta (theta in rad). | ||

+ | |||

and succeed more or less. | and succeed more or less. | ||

− | |||

For most practical applictions, you won't see a big | For most practical applictions, you won't see a big | ||

difference between the two. | difference between the two. | ||

Btw, a rectilinear lens has a mapping | Btw, a rectilinear lens has a mapping | ||

− | + | ||

+ | R = f * tan( theta ) | ||

+ | </pre> | ||

We can assume that most newer fisheyes follow the first mapping scheme. | We can assume that most newer fisheyes follow the first mapping scheme. | ||

Line 41: | Line 37: | ||

Complete text of the mail can be found at W.J. Markerink's [http://www.a1.nl/phomepag/markerink/fishyfaq.htm page about fisheye analysis] | Complete text of the mail can be found at W.J. Markerink's [http://www.a1.nl/phomepag/markerink/fishyfaq.htm page about fisheye analysis] | ||

− | More information on | + | More information on fisheyes and their distortions in this [http://www.coastalopt.com/pdfs/FisheyeComparison_SPIE.pdf PDF from coastal optics] |

− |

## Revision as of 20:49, 22 April 2005

in a fisheye projection the distance from the centre of the image to a point is proportional to the equivalent spatial angle.

Taken from a posting of Helmut Dersch:

The focal length f of common fisheye lenses corresponds quite simple to the angle of view theta and the radial position R of a point on the slide: R = 2 * f * sin( theta/2 ) So for 90 degrees, which would be the maximum theta of a 180 degree lens, f=8mm, you get R = 11.3mm, which is the radius of the image circle. This projection model applies to the Nikon 8mm and the Sigma 8mm (which actually has f=7.8mm). This is also what you get when you look into a convex mirror. Some older Nikon lenses (e.g. the 7.5mm) try to approach a linear mapping R = f * theta (theta in rad). and succeed more or less. For most practical applictions, you won't see a big difference between the two. Btw, a rectilinear lens has a mapping R = f * tan( theta )

We can assume that most newer fisheyes follow the first mapping scheme.

Complete text of the mail can be found at W.J. Markerink's page about fisheye analysis

More information on fisheyes and their distortions in this PDF from coastal optics