Designing Cassegrain type telescopes with spreadsheet

Published 22.2.2013

Here I will demonstrate use of spreadsheet for designing a Cassegrain type reflective telescope.

Designing a reflective telescope system with paraxial optics is really easy, since there is no refraction involved. Pre-design calculations offer final solutions in most cases. Here I will demonstrate use of spreadsheet for designing a Cassegrain type reflective telescope.

Cassegrain type reflective telescope has primary concave mirror and a convex spherical mirror. The shape of the primary and secondary mirrors determine further classification. A Classical Cassegrain has a parabolic main mirror and a hyperbolic secondary mirror, whereas in a Ritchey-Chretien, both mirrors are hyperbolic. A Dall-Kirham type telescope has an elliptical primary and a spherical secondary.

Next I will show step by step the calculations for a Ritchey-Chretien type Cassegrain telescope by using a spreadsheet (xls, updated Apr. 17th 2013). The steps are repetitive until suitable values can be achieved.

First step is to determine final focal ratio of the system. In the sheet, it is expressed as a combination of primary mirror focal ratio and the magnification factor of the secondary mirror (steps 1 and 2). First they will be set to the desired value, but later they must be adjusted to reduce astigmatism. Generally,as the magnification approaches the value of 3, the field will flatten out. Unfortunately the conic constant of the secondary mirror drops sharply, making the manufacture of such a small hyperbolic mirror difficult.

The next step is to decide physical characteristics, such as aperture (step 3) and obstruction ratio between the secondary and primary (step 4). Also the distance from the reflective surface of the primary to the desired image plane can be inserted (step 5), keeping in mind the thickness of the primary mirror.

The spreadsheet calculates the required radii and distances at this point, but the formed image is still quite blurry, because the calculations were done to spherical surfaces. The conic constants will be inserted next (in steps 6 and 7). The fastest way of determining appropriate values for zero spherical and comatic aberrations is to adjust the value of secondary conic (step 7) so that comatic aberration is zero (or near a desired value). Then the conic of the primary is directly the negative value of the spherical aberration.

At this step an overall inspection can be done with an optical design software such as Zemax or Code V, or even one of the free ones such as Oslo-LT or MODAS, as the paraxial design might benefit from optimization most design software offers (i.e. Zemax dummy layer effect). However, if one would like to examine other values for conics and astigmatism, tiny adjustments (on the scale of one tenth) can be made to the values of focal ratio of the primary and magnification of secondary, and repeat the process from the start. Optical design includes compromising image quality for a flatter field or more manufacturable components.