K3's Astronomy - Telescope resolution
"When I consider your heavens, the work of your fingers, the moon and the stars which You have set in place, what is Man that You are mindful of him?" -- Psalm 8:3,4

The resolution of the telescope is limited because of wave nature of light. The limitation is caused by diffraction of light. Amount of diffraction depends on input aperture of the telescope (diameter of objective for refractors or diameter of primary mirror for reflectors) and wave length of light emitted by source of light. Diffraction causes that star image is not pin-point when looking through a telescope, but it has certain diameter - it is called airy-ring. The less the input apperture is the greater diameter of the star image is. Furthermore, the diffraction causes that diffraction rings appear around the star image. The intensity of the rings is falling down in direction out from the star center. It is illustrated in the star image (the diffraction rings are emfasized):

Not zero diameter of star image and diffraction rings cause that images of 2 stars, which are very close to each other, overlap. This limited the minimum angular distance of double-star components, which can be resolved through the telescope. It is given by Rayleigh criterion. The Rayleigh criterion for resolution indicates how close two points can be brought together before they can no longer be distinguished as separate. Here is example:

Resolving power of telescope according to Rayleigh criterion is (for green light wave length 550nm):

For planar objects the situation is more complicated - each point of source of light is creating its own image. The result image is integration of all partial points' images. When we have planar white object with 1 black line, the line can be visible in telescopes with smaller resolution power, than the angular dimension of the black line is. But the contrast of the line will be reduced. If the white object contains 2 black lines, which are closer than the resolution power of the telescope is, the observer will not be able to distinguish them. The principle is similar to resampling the picture in graphics program. Here is an example:

Full size Resampled to half size Resampled image magnified to 200%

All lines are visible in the resampled image, but the closer lines cannot be distinguished. The black color of single lines has changed to silver - reduced contrast.
This explain how it is possible to see Cassini division in Saturn's rings through the 3.5" telescopes (resolving power 1.27), although its angular size is about 0.5".

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Last Update: 30.7.2001