diffraction-limited spot size formula

In astronomy, a diffraction-limited observation is one that is only limited by the optical power of the instrument used, as opposed to seeing-limited, where the main limit is given by atmospheric effects.

Diffractionlimit formula

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For a given Numerical Aperture (NA), the resolution of microscopy for flat objects under coherent illumination can be improved using interferometric microscopy. Using the partial images from a holographic recording of the distribution of the complex optical field, the large aperture image can be reconstructed numerically[2].

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Space-based telescopes (such as the HST, or a number of non-optical telescopes) always work at their diffraction limit, if their design is free of optical aberration.

Radiotelescopes are frequently diffraction-limited, because the wavelengths they use (from millimeters to meters) are so long that the atmospheric distortion is negligible.

Diffraction-limited resolution

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Most optical telescopes on the Earth at ground level work at a much lower resolution than the diffraction limit, because of the distortion introduced by the passage of light through several kilometres of turbulent atmosphere. Traditionally, the large-size primary mirror of big ground-based telescopes was used to increase the flux from weak extra-galaxian objects rather than for improvement of resolution. [3]. Techniques such as speckle imaging can be used to obtain diffraction-limited images of bright objects. Some advanced observatories have recently started using adaptive optics technology, resulting in greater image resolution for faint targets, but it is still difficult to reach the diffraction limit using adaptive optics.

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The resolution of an optical imaging system like a microscope or telescope or camera can be limited by multiple factors like imperfections in the lenses or misalignment. There is however a fundamental maximum to the resolution of any optical system which is due to diffraction. An optical system with the ability to produce images with angular resolution as good as the instrument's theoretical limit is said to be diffraction limited.[1]

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The resolution of a given instrument is proportional to the size of its objective, and inversely proportional to the wavelength of the light being observed. For telescope with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of the Airy disc.

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