Apodization
Encyclopedia
Apodization literally means "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.
analyzer to smooth the discontinuities at the beginning and end of the sampled time record.
or transmission profile that approaches zero at the edges.
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, 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.
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.
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 a change of the diffraction pattern.
Apodization in signal processing
An example of apodization is the use of the Hann window in the Fast Fourier transformFast Fourier transform
A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
analyzer to smooth the discontinuities at the beginning and end of the sampled time record.
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 illuminationor transmission profile that approaches zero at the edges.
Apodization in photography
The diaphragmDiaphragm (optics)
In optics, a diaphragm is a thin opaque structure with an opening at its center. The role of the diaphragm is to stop the passage of light, except for the light passing through the aperture...
of a photo camera
Camera
A camera is a device that records and stores images. These images may be still photographs or moving images such as videos or movies. The term camera comes from the camera obscura , an early mechanism for projecting images...
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, which accomplishes this by utilizing a concave neutral-gray tinted lens element as apodization filter, thereby producing a pleasant Bokeh
Bokeh
In photography, bokeh is the blur, or the aesthetic quality of the blur, in out-of-focus areas of an image, or "the way the lens renders out-of-focus points of light."...
. The same optical effect can be achieved combining depth-of-field bracketing with multi exposure
Multiple exposure
In photography, a multiple exposure is the superimposition of two or more individual exposures to create a single photograph. The exposure values may or may not be identical to each other.-Overview:...
, as implemented in the Minolta Maxxum 7's STF function.
Simulation of a Gaussian
Gaussian beam
In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity distributions are well approximated by Gaussian functions. Many lasers emit beams that approximate a Gaussian profile, in which case the laser is said to be operating on the fundamental...
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 diffractionFresnel diffraction
In optics, the Fresnel diffraction equation for near-field diffraction, is an approximation of Kirchhoff-Fresnel diffraction that can be applied to the propagation of waves in the near field....
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 a change of the diffraction pattern.