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Apodization (e.g., apodizing an image) is a method of improving an observation by physically manipulating the diffraction of the incoming electromagnetic radiation. The term is also used for a mathematical process to do an equivalent operation during subsequent image processing.
Generally, the larger a telescope's aperture, the clearer the image, but the exact portions of the full image that are obscured depend upon both the aperture's size and its shape, and there are cases where a reduction in the aperture's size clears up some portions of the image, and the shape of this reduced aperture also affects precisely what's obscured. A telescope's default aperture is generally as large as the physical telescope allows and one of the few possible methods of further clearing up specific image details is the clever use of masking to reduce the aperture's size, and (optionally) changing the aperture's shape.
An example is nullifying, to some extent, the confusion of an image due to Airy disks, by combining a telescope's image with that from a smaller aperture, which can be from the same telescope, but with a mask. By this means, the extent of the confusion can be reduced, and two very close objects can be resolved, even though the telescope's angular resolution indicated by the Rayleigh criterion would suggest they are not discernible, especially when one source is much brighter than the other. Adjusting the shape of the aperture can also have useful effects.
Apodization is now a common mechanism of coronagraphs. Early ones often blocked the circular region comprising the Sun, in order to view the corona, but current goals also include acquiring an image of a specific location that is difficult to image because it is a short angular distance from the Sun or a star; various shapes of stops are used specifically to gather image data regarding the chosen target location.
The star-like shape of the starshade design, which aims to limit the diffraction of the star's light that would direct some of the unwanted light into the telescope, is classified as apodization.