Keystone effect

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Illustration of the Keystone Effect

The Keystone effect is caused by attempting to project an image onto a surface at an angle, as with a projector not quite centered onto the screen it is projecting on. It is a distortion of the image dimensions, making it look like a trapezoid. In the typical case of a projector sitting on a table, and looking upwards to the screen, the image is larger at the top than on the bottom. Some areas of the screen may not be focused correctly as the projector lens is focused at the average distance only.

[edit] Theory behind Keystone

The distortion suffered by the image depends on the angle of the projector to the screen, and the beam angle. The distortion (on a two-dimensional model, and for small focus angles) is given by:

$\frac {\cos(\epsilon - (\alpha/2))} {\cos (\epsilon + (\alpha/2))}$

where $ε$ is the width of the focus, and

$α$ is the angle between the screen axis and the central ray from the projector

From the formula is clear that there will be no distortion when $α$ is zero, or perpendicular to the screen. See a derivation of this formula at Derivation of the equation to combat Keystone

[edit] Solving the problem

The problem arises for screen projectors that don't have the depth of focus necessary to keep all lines (from top to bottom) focused at the same time. The problem can be solved by:

Move the projector more to the center of the screen, if this does not interrupt vision.
Tilt the screen in a small angle.
Use some type of software on the projector (or computer controlling the projector). Well known video card producer NVidia delivers a package called NVKeystone with most of their software solutions.