November 24, 2014
The PiKon telescope has a magnification factor of about x160.
We’ve worked that out based on a standard 35mm film camera. A 50mm lens there gives a x1 magnification. A 100mm lens gives a x2 magnification. The focal length of the objective mirror in the PiKon is 800mm. So, for 35mm film that would give a magnification of x16. But the Raspberry Pi Camera sensor is just one tenth the size of a 35mm film frame. So effectively the magnification is increased by a factor 10 to x160.
Another way of thinking about the power of the telescope is the angle of field of view. If we place a 3.6mm wide sensor at the focal point of an 800mm lens, it subtends and angle of view of about a quarter of a degree. The moon subtends an angle of about half a degree at your eye ball, so we’d expect the PiKon to have a field of view that could capture about half of the moon. And that’s just what we get:
What is the limit of magnification?
The ultimate magnification of the PiKon is limited by something called Airy Disks. These are circular halos of light which surround a point image in the telescope. They are caused by defraction effects which depend on the size of the objective mirror and limit the ultimate useful magnification.
The rule of thumb is that maximum useful magnification is 60 times the size of the mirror (in inches) or 2.2 times (in mm). The PiKon prototype has a mirror diameter of 4.5 inches or 113mm, which means its maximum useful magnification is x270.