flAirv = 2.44 x 656X10 , = 8x10~6 [radians], (Equ.1.7)
which corresponds to 1.6 seconds of arc. (Note that all measurements were converted to the same unit—meters. To convert from radians to degrees, multiply by 57.3; to convert from radians to minutes of arc, multiply by 3438; to convert to seconds of arc, multiply by 206,265.) The linear diameter of the Airy disk, dAiry, out to the first dark diffraction ring, is:
/i where A is the aperture and F the focal length of the telescope, and N is its focal ratio, F/A. The first term in the formula above is simply the angular diameter times the focal length of the telescope.
However, nearly half of the image-forming light is concentrated in the small, bright central core of the diffraction disk, a much smaller region defined by the diameter at which the light has fallen to half its central intensity. This region is the full-width at half-maximum (FWHM) of the diffraction disk, $FWHM . The angular diameter of the small, bright core of the point-spread function is:
and its linear diameter is:
where dFWHM is the FWHM of a perfect star image.
Assuming that the telescope has an//10 optical system, the FWHM of a perfect star image is:
JFWHM = 1.02 x 656xl0-9 x 10 = 6.7xl0~6 meters, (Equ. 1.11)
or 6.7 micrometers. The diameter of the FWHM of the diffraction disk is a realistic measure of the smallest detail contained in an astronomical image.
Note: The scientific unit for 10~6 meters is the micrometer. However, many engineers and technicians use a less formal term for micrometers: the micron. In this book, we use both the formal and the informal terms as they are normally used by engineers and scientists.
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