Here are the formulas, how to calculate the basic optical parameters of a cassegrain telescope. First we have to declare the sign conventions we will use:
All Cassegrain telescopes consist of a concave primary mirror with a small secondary mirror inside the focus of the primary; the secondary redirects starlight toward the primary. The image, in most cases, lies behind the primary. The convex secondary multiplies the focal length by a factor M. This factor M is termed secondary magnification, and is defined:
The focal length of the system is:
We can calculate the basic parameters seen in the picture with the formulas below:
Where f1 is the focal length of the primary, f2 is the focal length of the secondary (it is a negative value because of the conventions), and d is the separation. b is the back focus of the system, and bfl is the back focal length.
The focal surface has a radius of curvature:
Where RF is the radius of curvature of the focal surface, r1 is the radius of curvature of the primary and r2 is the radius of curvature of the secondary.
The sagitta of the mirror is: (sagitta is the height of the mirror at a given radius.)
where z is the sagitta, h is the radius where we calculate the height of the mirror, r is the radius of curvature of the mirror, SC is the conic constant (explained later).
The conic constant, or Schwarzschild constant defines the shape of a conic section.
where e is the eccentricity of the conic section.
We will use the dimensionless quantities defined by Schwarzschild:
The third-order Seidel Coefficients for a two-mirror Cassegrain are:
To simplify the formulas above, we will use additional quantities:
Since the spherical aberration is zero; Acass = 0, we can calculate the different conic constants of the primary and secondary mirrors.
For the classical Cassegrain, the primary is parabolic SC1 = − 1, so the secondary is:
For the Ritchey-Chrétien, both spherical aberration and coma are eliminated, so