Diffraction Limited Beam Diameter
For a diffraction limited dish or telescope, the received beam diameter in the
far-field is given by:
D = ----------- meters
Wl = wavelength (656 nm),
R = range (10 light years = 9.461 x 1016 m),
d = beam diameter at exit of antenna (10 m).
Substituting the values in parentheses into the above equation:
D = 7.57 x 109 m = 0.051 A.U.
The radius of the Earth's orbit = 1 Astronomical Unit (A.U.) = 1.496 x 1011
This is also the Rayleigh criteria for the resolving power of a dish or telescope. The
extremely high pointing accuracy implied by this result should not be a problem for
advanced technological civilizations.
Clearly, a 10 m diameter optical telescope outside the atmosphere can resolve the
planetary systems of nearby stars since the Rayleigh resolution is about 1/20th of an
astronomical unit. The real problem, as will be shown later, is that the light reflected
from planets (in the visible spectrum) is typically more than 85 dB below that emitted by
their stars, so the dim planets are lost in the light of their stars.
For ease and uniformity of comparison calculations between microwave, infrared and
visible SETI systems, it is assume in most of the foregoing analysis that the planets are
not spatially resolved. This allows us to plot the Planck black body continuum background
level as a continuous function, such as is illustrated in graphs 9006-019,
9006-020 and 9006-021. The fact that
at visible and infrared wavelengths the planets are theoretically resolved and are
distinctly separated from the image of the star in the telescope's focal plane, means that
the levels of Planckian starlight in the background of SETI transmitters are actually much
less than indicated. In the two dimensional photodetector focal plane arrays which will be
described later, the light from the planet falls onto a different photodetector than the
light from the star. If it is assumed that in most cases it can be arranged that the
field-of-view of the planetary photodetector does not encompass any other stars, the
argument that Alien laser transmitters would be lost in the glare of their stars becomes
even less tenable.
The Columbus Optical SETI Observatory
Copyright (c), 1990