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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 .

User Contributions:

1
Keith Phemister
Sep 13, 2024 @ 11:23 pm
Copied from above: If the Universe were infinitely old, infinite in extent, and filled
with stars, then every direction you looked would eventually end on
the surface of a star, and the whole sky would be as bright as the
surface of the Sun.
Why would anyone assume this? Certainly, we have directions where we look that are dark because something that does not emit light (is not a star) is between us and the light. A close example is in our own solar system. When we look at the Sun (a star) during a solar eclipse the Moon blocks the light. When we look at the inner planets of our solar system (Mercury and Venus) as they pass between us and the Sun, do we not get the same effect, i.e. in the direction of the planet we see no light from the Sun? Those planets simply look like dark spots on the Sun.
Olbers' paradox seems to assume that only stars exist in the universe, but what about the planets? Aren't there more planets than stars, thus more obstructions to light than sources of light?
What may be more interesting is why can we see certain stars seemingly continuously. Are there no planets or other obstructions between them and us? Or is the twinkle in stars just caused by the movement of obstructions across the path of light between the stars and us? I was always told the twinkle defines a star while the steady light reflected by our planets defines a planet. Is that because the planets of our solar system don't have the obstructions between Earth and them to cause a twinkle effect?
9-14-2024 KP

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