Diffraction Limited Beam Diameter

9006-002

9006-002a

For a diffraction limited dish or telescope, the received beam diameter in the far-field is given by:

    (1.22).Wl.R
D = -----------  meters
         d

where:

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 m.

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.

9006-002b

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