Plate scale

The plate scale of a telescope connects the angular separation of an object with the linear separation of its image at the focal plane

Plate scale can be derived using this image assuming that the angle is very small (so that tan(theta) is approximately theta).

If focal length ${\displaystyle f}$ is measured in mm, the plate scale in radians per mm is given by angular separation θ and the linear separation of the image at the focal plane s, or by simply the focal length f:

${\displaystyle p={\frac {\theta }{s}}={\frac {1}{f}}\ ,}$

since

${\displaystyle {s}{=}{f}{\theta }\ .}$

Plate scale is usually expressed in arc-seconds per mm:

${\displaystyle p={\frac {206265}{f}},}$

where f is in mm,[1] or expressed in arc-seconds per pixel after further division through the pixel scale.