Stopping down by using an off-axis mask is a time honored way to beat seeing and to cut the dazzling light of the Moon and bright planets in large aperture scopes.

Stopping down is less popular today. This could be so because of drifting preferences. It is also a testament to learning how to use large Dobsonian mirrors in the dropping night time air by cooling them with fans.

The maximum diameter of an off-axis mask is set by taking the primary mirror’s diameter and subtracting the diagonal’s minor axis size then dividing the result by two. For example, a 16 inch with a 3.5 inch diagonal has a maximum off-axis mask diameter of (16 – 3.5) / 2 = 6.25 inches.

The light throughput is the inverse of the mask diameter to primary mirror diameter squared. Using the numbers from above, (off-axis mask diameter / primary mirror diameter) squared is (6.25 / 16) ^2 = 0.15 or 15% light throughput. That dims the Moon’s brightness by two magnitudes.

Everyone should make a black cardboard mask with a one inch off-axis hole. The Airy disk and rings look beautiful. But that costs resolution. Of course this resolution is wasted at low magnification.

What is the relationship between the off-axis mask’s resolution and the telescope’s magnification? What size should the off-axis mask be to resolve all that is possible at a particular magnification?

Since the eye's entrance pupil at best resolution is 1mm in size, the eyepiece's exit pupil is the factor that the primary mirror's aperture can be reduced. For example, an exit pupil of 6mm (the exit pupil is calculated by taking the eyepiece's focal length in mm and dividing by the primary mirror's focal ratio) means that the off-axis mask should be 1/6 the diameter of the primary, an exit pupil of 3mm means that the off-axis mask should be 1/3 the diameter of the primary. This leads to the conclusion that the smallest exit pupil to use with the maximally sized off-axis mask is 2-3mm.

There is also a very simple and easy to remember relationship between aperture and magnification with respect to resolution. And it is this: the telescope will resolve all that the human eye can see when the aperture in inches equals the magnification divided by 25. For example, at 100x, the off-axis mask should be at least 4 inches in diameter, 100 / 25 = 4.

For the 16 incher’s off-axis mask mentioned above, the optimal magnification is 6.25 * 25 = 156x.

That’s it! Now you can make those off-axis masks understanding the brightness reduction and the best fitting magnification (or what diameter to make the off-axis mask given a desired magnification).

Note: double star observing with smaller apertures can double even quadruple the optimum magnification, up to the seeing limit of the sky, in order to better see the Airy disk and rings.

Mel Bartels, 2013