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PH507
Professor Michael Smith
MULTIMEDIA ASTRONOMY
School of Physical Sciences
Convenor Prof. Michael Smith
Taught in Spring Term
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PH512
ECTS Credits 7.5
Kent Credits 15 at Level H
Resolution: please read Chapter 1 (pdf file)
Angular resolution
Ignoring blurring of the image by turbulence in the atmosphere
(atmospheric seeing) and optical imperfections of the telescope,
the angular resolution of an optical telescope is determined by the
width of the objective, termed its "aperture" (the primary mirror,
or lens.)
The Rayleigh criterion for the resolution limit αR (in radians) is
given by
αR = 1.22λ / D,
The angular diameter of the` Airy Disk, to the first
dark diffraction ring is
αAiry = 2.44/ D,
where λ is the wavelength and D is the aperture.
The factor 1.22 is derived from a calculation of the position of the
first dark ring surrounding the central Airy disc of the diffraction
pattern.
If one considers diffraction through a circular aperture, then the
calculation involves a Bessel function -- 1.220 is approximately
the first zero of the Bessel function of the first kind, of order one
(i.e. J1), divided by π (3.14159). This factor is used to
approximate the ability of the human eye to distinguish two
separate point sources depending on the overlap of their Airy
discs:
PH507
Professor Michael Smith
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For visible light (λ = 550 nm), this equation can be rewritten:
αR = 138 / D.
Here, αR denotes the resolution limit in arcseconds and D is in
millimeters.
In the ideal case, the two components of double stars can be split
even if separated by slightly less than αR. This is taken into
account by the Dawes limit
αD = 116 / D.
Essentially: the larger the aperture, the better the angular
resolution
It should be noted that the resolution is NOT given by the
maximum magnification (or "power") of a telescope. Telescopes
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Professor Michael Smith
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marketed by giving high values of the maximum power often
deliver poor images.
For large ground-based telescopes, the resolution is limited by
atmospheric seeing. This limit can be overcome by placing the
telescopes above the atmosphere, e.g., on the summits of high
mountains, on balloon and high-flying airplanes, or in space.
Resolution limits can also be overcome by adaptive optics or
speckle imaging for ground-based telescopes.
Recently, it has become practical to perform aperture synthesis
with arrays of optical telescopes. Very high resolution images can
be obtained with groups of widely-spaced smaller telescopes,
linked together by carefully controlled optical paths, but these
interferometers can only be used for imaging bright objects such
as stars or measuring the bright cores of active galaxies.