Dawes criterion

Superposition of two diffraction images that can just be resolved according to Dawes

The Dawes criterion describes the resolving power of a human observer , which is limited by diffraction , when viewing narrow double stars through a telescope . It is named after the British astronomer William Rutter Dawes .

definition

The criterion is based on the relationship found empirically by Dawes between the diameter  d of a circular telescope opening in inches and the angular distance of a double star that is just about to be separated. The light source is then resolved as two separate stars when the light intensity between the sources shows a dip of at least 5%. The minimum angular distance in arc seconds is calculated using the numerical equation : ${\displaystyle \alpha }$

${\displaystyle \alpha ={\frac {4{,}56}{d}}}$

Here it is assumed that it is a sun-like yellow double star whose light has an approximate wavelength of . ${\displaystyle \lambda =550\;\mathrm {nm} }$

With a telescope with an opening of two inches (a good 5 cm), a double star with an angular distance of 2.3 arc seconds can be perceived separately.

For any wavelength , and in radians , the Dawes criterion is: ${\displaystyle \lambda }$ ${\displaystyle \alpha }$

${\displaystyle \alpha =1{,}02{\frac {\lambda }{d}}}$

application

Telescopes with aperture shading can achieve greater angular resolutions because the size of the first diffraction disks is reduced. The formula no longer applies to large telescopes, since it is not diffraction but rather seeing that limits the resolution.

Compared to the empirical Dawes criterion for human vision, the formal Rayleigh criterion underestimates the resolving power by a factor of 1.22: with the Dawes criterion the two diffraction disks overlap so much that almost no depression can be seen between the maxima, while with the Rayleigh criterion the depression is about 26%. Modern image processing allows double stars to be measured even if they overlap even more.

See also

• Rayleigh criterion

Individual evidence

1. ^ Dawes, WR, Catalog of Micrometrical Measurements of Double Stars . In: Memoirs of the Royal Astronomical Society, Vol. 35, p.137 1867, bibcode : 1867MmRAS..35..137D
2. ↑ ^{a b} T. Stewart McKechnie: General Theory of Light Propagation and Imaging Through the Atmosphere . Springer, 2015, p. 409 ( limited preview in Google Book search).
3. ↑ Jingquan Cheng: The Principles of Astronomical Telescope Design . Springer Science & Business Media, 2010, p. 10 ( limited preview in Google Book search).