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Apodization is an optical filtering technique, and its literal translation is "removing the foot". It is the technical term for changing the shape of a mathematical function, an electrical signal, an optical transmission or a mechanical structure. In optics, it is primarily used to remove Airy disks caused by diffraction around an intensity peak, improving the focus.
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Apodization in signal processing
The term apodization is used frequently in publications on Fourier transform infrared (FTIR) signal processing. An example of apodization is the use of the Hann window in the Fast Fourier transform analyzer to smooth the discontinuities at the beginning and end of the sampled time record.
Apodization in digital audio
An apodizing filter can be used in digital audio processing instead of the more common brickwall filters, in order to avoid the pre-ringing that the latter introduces.
Apodization in optics
In optical design jargon, an apodization function is used to purposely change the input intensity profile of an optical system, and may be a complicated function to tailor the system to certain properties. Usually it refers to a non-uniform illumination or transmission profile that approaches zero at the edges.
Apodization in photography
The diaphragm of a photo camera is not strictly an example of apodization, since the stop doesn't produce a smooth transition to zero intensity, nor does it provide shaping of the intensity profile (beyond the obvious all-or-nothing, "top hat" transmission of its aperture).
The Minolta/Sony Smooth Trans Focus 135mm f/2.8 [T4.5] lens, however, is a special lens design introduced in 1999, which accomplishes this by utilizing a concave neutral-gray tinted lens element as apodization filter, thereby producing a pleasant bokeh. The same optical effect can be achieved combining depth-of-field bracketing with multi exposure, as implemented in the Minolta Maxxum 7's STF function.
In 2014, Fujifilm announced a lens utilizing a similar apodization filter in the Fujinon XF 56mm F1.2 R APD lens.
In 2017, Sony introduced the E-mount full-frame lens Sony FE 100mm F2.8 STF GM OSS (SEL-100F28GM) based on the same optical Smooth Trans Focus principle.
Simulation of a Gaussian laser beam input profile is also an example of apodization.
Photon sieves provide a relatively easy way to achieve tailored optical apodization.
Apodization in astronomy
Apodization is used in telescope optics in order to improve the dynamic range of the image. For example, stars with low intensity in the close vicinity of very bright stars can be made visible using this technique, and even images of planets can be obtained when otherwise obscured by the bright atmosphere of the star they orbit. Generally, apodization reduces the resolution of an optical image; however, because it reduces diffraction edge effects, it can actually enhance certain small details. In fact the notion of resolution, as it is commonly defined with the Rayleigh criterion, is in this case partially irrelevant. One has to understand that the image formed in the focal plane of a lens (or a mirror) is modelled through the Fresnel diffraction formalism. The classical diffraction pattern, the Airy disk, is connected to a circular pupil, without any obstruction and with a uniform transmission. Any change in the shape of the pupil (for example a square instead of a circle), or in its transmission, results in an alteration in the associated diffraction pattern.