The purpose of collimating is to get the best images of stars and other celestial objects.
Check the collimation by looking at a star. Use a magnification near 2X per millimeter of aperture (50X per inch).
Center the star in the field to avoid possible effects of aberration in your telescope.
If a telescope's collimation is perfect and the atmosphere is transparent and still enough, the focused image of a star will be very much like a circular dot of light.
If a telescope's collimation is imperfect, the focused image of a star will be bigger than a dot of light, and will tend to be elongated, like a comet.
If a telescope's collimation is perfect, the off-focus image of a star will be symmetrical and concentric diffraction rings,
and it will be equal inside and outside of the focus.
If a telescope's collimation is imperfect, the off-focus image of a star will be asymmetrical and eccentric diffraction rings,
and it might look different inside and outside of the focus.
The telescope will show "Coma" aberration, even at the field's center.
References:
Basic Star Testing (Stephen Tonkin. The Astronomical Unit - Tutorials)
Harold R. Suiter, Star Testing Astronomical Telescopes (Amazon Books)
The collimation (Astrophotography - Thierry Legault. High Resolution CCD Imaging)
The testing and precise adjustment of the collimation in a Newtonian telescope consists in finely adjusting the primary mirror
so that the diffraction pattern produced by a star a little out of focus is concentric.
See Collimating Newtonian Optics (in ARVAL)
For the user, collimating a Schmidt-Cassegrain telescope consists of adjusting the secondary mirror to obtain a perfect star test.
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