“The adventure is not to see new things, but to see things with new eyes.” — Marcel Proust

For a ground-based telescope, the mount moves the telescope to point to a particular object and then track the object throughout a observation.

Transit or ‘drift-scan’ telescopes do not track but observe a particular region toward the zenith all the time. The spin of the Earth brings different parts of the sky within the FoV of such a telescope.

Ground-based telescopes have two main types of mounts: altazimuth and equatorial.

Altazimuth: rotate the the vertical axis to different azimuths, and horizontal axis to different altitudes.

Equatorial: rotate the polar axis (pointed toward the north celestial pole) to different hour angles, and the declination axis to different declinations. The hour angle is the sidereal time minus the right ascension (RA). So the mount directly tracks the RA and DEC.

Equatorial mount is simpler for pointing and tracking, but more expensive and clumsy in terms of construction. All ground-based telescopes above a diameter of 5 m use altazimuth mount.

Advantage of altazimuth mount is that the gravitational load does not vary with pointing direction in this case. But the main disadvantage is the complex tracking. Both the axes have to moved simultaneously with varying speed as a function of time.

Almost all modern telescopes are reflecting telescopes.

In prime focus telescopes, the astronomer or her remote-controlled detectors or instruments are located at the focal plane of the paraboloid primary mirror. As the detectors block parts of the light going to the primary mirror, this configuration works well only if the size of the detectors is small compared to the primary mirror. For mirrors larger than around 3.5 meters, the instruments are located in a prime focus cage.

For focused images, the central obstruction has minimal effect, but out-of-focus images have a ‘doughnut’ shape. The support structure of the prime focus cage, that connects it to the side of the optical tube, also creates ‘diffraction spikes’ on very bright stars.

The length of the coma effect for these telescopes, $L_c = \theta/16\mathcal{R}^2$ and for astigmatism $L_a=\theta^2/2\mathcal{R}$ where $\mathcal{R}$ is the focal ratio $f/D$ and $\theta$ is the angular distance of the image from from the optical axis.

An alternative to prime focus is Newtonian focus, where the light is reflected away from the focal plane to the side of the tube where the detectors and instruments are located. Light is redirected using a diagonal mirror at the focal plane. Professional astronomers do not really use Newtonian anymore, they prefer Cassegrain.

Neither the prime focus nor the Newtonian designs are good enough for modern professional astronomy because they require placing the astronomer or the instruments directly at the focal plane which is challenging, especially when the focal length is large. Also any weight at the focus creates a variable torque on the optical tube.

The Cassegrain and Gregorian designs are shown above. In Cassegrain design, a convex hyperboloid secondary mirror is placed in front of the paraboloid primary so that the virtual focus of the secondary mirror coincide with the focus of the primary mirror. Light is collected at the second focus of the hyperboloid at $F'$. The Gregorian uses the same method with the exception that the secondary is a concave ellipsoid.

The parameters of a two-mirror telescope are defined in reference to the above diagram. Final power

$$ P = \frac{1}{f} = P_1 + P_2 - dP_1P_2 $$

where $P_1$ and $P_2$ are the powers of the primary and secondary, respectively. Three dimensionless parameters describe the final focal length $f$, the distance between the primary and secondary $d$, and the back focal distance $z_F$. The respective dimensionless parameters are

$$ m = \frac{P_1}{P} = \frac{f}{f_1} = -\frac{s_2'}{s_2} $$

$$ k = \frac{y_2}{y_1} = 1-\frac{d}{f_1} $$

$$ \beta = \frac{z_F}{f_1} $$

where $\beta$ is positive if the focus is behind the primary, and $m$ and $k$ are positive for aCassegrain and negative for a Gregorian. Only two of these parameters might be enough as

$$ k = \frac{1+\beta}{1+m}. $$

The tube of the Cassegrain is much shorter than a Newtonian which means Cassegrain is much cheaper to build. A Gregorian is longer than a Cassegrain but still shorter than a Newtonian.

The conic constants of the two mirrors $K_1=-1$ (paraboloid) and

$$ K_2 = -\left(\frac{m+1}{m-1}\right)^2 $$

which is determined by the requirement that SA should be zero.