Filter diameter

Minimum filter size to avoid vignetting

In principle, a filter diameter must always be at least as large as the chip diagonal. The further away a filter is from the chip, the larger its diameter must be. This also applies to smaller aperture values. The smaller these are (i.e. the “faster” a telescope is), the larger the filter must be. This is because the beam path widens towards the telescope aperture. In the following, this will be illustrated using principle sketches of three telescope types. It will be shown that the second ray theorem is sufficient for determining the minimum filter size.

AB – requested length by which the filter radius must be larger
SA – distance filter to chip
SC – telescope focal length
CD = 0.5*telescope aperture – 0.5*chip diagonal

Refractor / telephoto lens

Principle sketch for determining a vignetting-free filter for a refractor

Newtonian telescope

Principle sketch for determining a vignetting-free filter for a Newtonian telescope

Schmidt-Cassegrain telescope

The main planes of a Schmidt-Cassegrain telescope are usually not known and are often not directly located next to the optical components. In addition, the light paths are folded at the non-planar mirror surfaces, making it difficult to create a ray theorem diagram for the edge beams of the chip edge. Instead, the center rays are used in the principle sketch. The small angular deviation (resulting from the shift of the starting point 'S' to the optical axis), which is of little consequence with the long focal lengths, is accepted.
However, the same calculation steps are used as for the other telescopes, as the principle that the length of half the chip diagonal is subtracted from the length of half the aperture does not change.

Principle sketch for determining a vignetting-free filter for a Schmidt-Cassegrain telescope (Source for the concept of focal length: https://www.cloudynights.com/topic/777522-beginner-question-about-focal-length/?p=11197866)

Example calculation to determine the minimum filter size

Given:

telescope aperture: 130 mm
chip diagonal: 43.3 mm (full frame)
SC – telescope focal length: 364 mm
SA – distance filter to chip: 27 mm
CD = 0.5*telescope aperture – 0.5*chip diagonal = 43.35 mm

AB is the required length by which the filter radius must be greater than the chip diagonal. The minimum filter diameter required is therefore: