The percentage change in image width (or height, for horizontal distortions) necessary to prevent keystoning can be calculated as follows:
angle A is the full beam angle (not the half angle as is sometimes quoted!) of the lantern or projector
angle B is the deviation of the projector from horizontal (-ve if pointing up, +ve if pointing down)
Points to Note
- With a gobo inserted most lanterns are no longer capable of delivering the full beam angle quoted.
- Always select the largest gobo size that will fit in your lantern- for example CCT Silhouettes can accept 'A' or 'B' size gobos, but when using a 'B' size gobo the effective beam angle will be significantly less.
- If the screen is not vertical, then angle B is the deviation from a line perpendicular to the surface of the screen
This equation can also be used to calculate horizontal distortions. Note that in any case the projector or lantern is assumed to be on the centreline of the projection surface in the direction which is not being distorted.
You can read the derivation of this equation here
In deriving this, it has been assumed that the distance between the projector and the screen at the centre of the beam is the same as the distance between the projector and the screen at the edge of the beam.
For small beam angles (upto about 25°) this assumption will not present a problem.
However for wide angle projectors, the equation will not compensate adequately for spherical distortions.