Apodization (e.g., Apodizing an image) is a method of improving an observation by physically manipulating the Diffraction of the incoming Electromagnetic Radiation (EMR). The term is also used for a mathematical process to do an equivalent operation during signal processing.
An example is nullifying to some extent the distortion of an image due to Airy Disks, by combining a telescope's image with that from a smaller Aperture, e.g., reusing the same telescope with a mask. By this means, the extent of the distortion can be reduced, and two very close objects can be resolved, which the telescope's Angular Resolution suggested by the Rayleigh Criterion would rule out, especially when one source is brighter than the other. Adjusting the shape of the aperture can also have useful effects.
The star-like shape of the Starshade design, which is designed to limit diffraction of the star's light to the center of the shadow, is termed apodization.
Imaging Fourier Transform Spectroscopy (IFTS)