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 What are diffraction-limited optics?

A telescope’s circular aperture creates an optical pattern with incoming waves of light. This is known as the diffraction pattern: a bull’s eye with a bright, central area called the Airy disk surrounded by one or more diffraction rings.

Stars are so very far away that they will never show a real disk or ball shape in a telescope. Astronomers refer to them as "point sources"; they are imaged by telescopes as tiny diffraction patterns. How clearly a double star can be seen as double depends on the size of the diffraction pattern and Airy disk. (See the related Knowledgebase article on the Airy disk.) Extended objects (like planets, nebulae, galaxies and virtually anything else that might be viewed through a telescope) can be thought of as a large group of point-like sources, each with its own diffraction pattern and Airy disk. Planetary images and images of other extended objects are complex, blended diffraction patterns from each tiny point on the planet or extended object.

Resolution of any object, therefore, depends on how small a diffraction pattern appears with your scope. It also follows that the size of the diffraction pattern is what ultimately limits resolution of a telescope, since the pattern is due to the wave nature of light itself and cannot be designed out.

The basic measure of resolution is the Rayleigh criterion. It gives the angular size of the Airy disk (technically from the center out to the middle of the dark ring right around the central disk). This is equal to half the angular size θ in arc-seconds of a star’s image (since it appears as the Airy disk) as seen with a telescope of aperture D for a wavelength λ of light.

θ = 206265 (1.22λ / D)

Working out the numbers for an 8 in scope and yellow light in metric units (meters, 8 in = 0.2 m, yellow light = 5.7 x 10-7 m):

θ = 206265 (1.22λ/D) =  206265 (1.22  x  5.7 x 10-7 /0.2)  = 0.7 arc-sec

The optical quality of a telescope’s lenses or mirrors affects the diffraction pattern and the resolution. Optical errors are typically measured in wavelengths or waves of light. The benchmark or threshold for optical quality affecting the resolution in terms of the Rayleigh criterion is generally accepted as an error of ¼ wavelength. Such errors throughout the entire light path in the scope combine as the light arrives at the focal plane into wavefront errors.

Aberrations resulting in wavefront errors substantially less than ¼ wave won’t significantly affect a telescope’s resolution. Put another way, any further effort making the optics smoother or with a better figure won’t improve resolution.

When this is the case, the telescope’s resolving power is limited more by the diffraction of the light waves and the laws of physics than by any manufacturing process and the scope is said to have diffraction-limited optics.

Updated 11/11/13

Article Details
 Article ID: 1649
 Created On: Feb 21 2005 09:47 AM

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