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[sci.astro] General (Astronomy Frequently Asked Questions) (2/9)
Section - B.04 What is the resolution of a telescope?

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The _limiting_ resolution of a telescope can be no better than a size
set by its aperture, but there are many things that can degrade the
resolution below the theoretical limit.  Obvious examples are
manufacturing defects and the Earth's atmosphere.  Another interesting
one is the addition of a central obstruction (e.g., secondary mirror)
which degrades the resolution for most practical purposes even though
it _shrinks_ the size of the central diffraction disk.  The problem is
that even though the disk diameter decreases, the central disk
contains a smaller fraction of the incident light (and the rings
contain more).  This is why modest sized refractors often outperform
reflectors of the same size.

Giving a precise value for the resolution of an optical system depends
on having a precise definition for the term "resolution."  That isn't
so easily done; the most general definition must be based on something
called "modulation transfer function."  If you don't want to be
bothered with that, it's enough to note that in all but pathological
cases, the diameter (full width at half maximum in radians) of the
central diffraction disk will be very close to the wavelength in use
divided by the diameter of the entrance pupil.  (The often seen factor
of 1.22 refers to the radius to the first null for an _unobstructed_
aperture, but a different factor will be needed if there is a central
obstruction.)  In practical units, if the wavelength (w) is given in
microns and the aperture diameter (D) in meters, the resolution in
arcseconds will be:
  R = 0.21 w/D .

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