Apodization

Source: Wikipedia, the free encyclopedia.
Airy disk

In

mathematical function. The function may represent 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.

Apodization in electronics

Further information: Window function

Apodization in signal processing

The term apodization is used frequently in publications on

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 brick-wall filters, in order to reduce the pre- and post-ringing that the latter introduces.[1]

Apodization in mass spectrometry

During oscillation within an Orbitrap, ion transient signal may not be stable until the ions settle into their oscillations. Toward the end, subtle ion collisions have added up to cause noticeable dephasing. This presents a problem for the Fourier transformation, as it averages the oscillatory signal across the length of the time-domain measurement. The software allows “apodization”, the removal of the front and back section of the transient signal from consideration in the FT calculation. Thus, apodization improves the resolution of the resulting mass spectrum. Another way to improve the quality of the transient is to wait to collect data until ions have settled into stable oscillatory motion within the trap.[2]

Apodization in nuclear magnetic resonance spectroscopy

Apodization is applied to NMR signals before discrete Fourier Transformation. Typically, NMR signals are truncated due to time constraints (indirect dimension) or to obtain a higher signal-to-noise ratio. In order to reduce truncation artifacts, the signals are subjected to apodization with different types of window functions. [3]

Apodization in optics

Modifying how much a lens transmits as a function of the lateral position, leads to a slightly wider and weaker focus, but at the same time removes the rings around it, thus limiting imaging artifacts.

In optical design jargon, an apodization function is used to purposely change the input intensity profile of an

optical system
, and it 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 imaging

Since side lobes of the Airy disk are responsible for degrading the image, techniques for suppressing them are utilized. If the imaging beam has Gaussian distribution, when the truncation ratio (the ratio of the diameter of the Gaussian beam to the diameter of the truncating aperture) is set to 1, the side-lobes become negligible and the beam profile becomes purely Gaussian. [4] [page needed]

In

grating lobes can be reduced by activating ultrasonic transducer elements using variable voltages in apodization process.[5]

Apodization in photography

Most camera lenses contain diaphragms which decrease the amount of light coming into the camera. These are not strictly an example of apodization, since the diaphragm does not 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).

Some lenses use other methods to reduce the amount of light let in. For example, the Minolta/Sony STF 135mm f/2.8 T4.5 lens however, has a special design introduced in 1999, which accomplishes this by utilizing a concave neutral-gray tinted lens element as an apodization filter, thereby producing a pleasant

SEL-100F28GM) based on the same optical Smooth Trans Focus principle.[7]

Simulation of a Gaussian laser beam input profile is also an example of apodization.[citation needed]

Photon sieves provide a relatively easy way to achieve tailored optical apodization.[8]

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.

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 modeled 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 its transmission, results in an alteration in the associated diffraction pattern.

See also

  • Apodization function

References

  1. ^ Robjohns, Hugh (August 2016). "MQA Time-domain Accuracy & Digital Audio Quality". soundonsound.com. Sound On Sound. Archived from the original on 10 March 2023.
  2. PMID 27553853
    .
  3. ^ NMR data processing: Phase correction, Scaling of first point, 9 July 2021, retrieved 2022-01-17
  4. OCLC 756724023.{{cite book}}: CS1 maint: others (link
    )
  5. doi:10.1093/bjaceaccp/mkr030
    .
  6. ^ ""Bokeh-Gigant": Fujinon XF 1,2/56 mm R APD (aktualisiert)". 2001-11-30.
  7. ^ "Neu von Sony: E-Mount-Objektive 100 mm F2.8 STF GM, FE 85 mm F1.8; Blitz HVL-F45RM". Photoscala (in German). 2017-02-07. Archived from the original on 2017-02-11. Retrieved 2017-02-10.
  8. ^ Hewett, Jacqueline (2007-06-01). "Photon sieves benefit space telescopes". Optics.org. Retrieved 2007-06-05.
  9. ISBN 978-0-201-11609-0
    . Section 11.3.3.
  10. ^ FIRST RESULTS FROM VERY LARGE TELESCOPE NACO APODIZING PHASE PLATE: 4 μm IMAGES OF THE EXOPLANET β PICTORIS b* The Astrophysical Journal (Letter)
  11. ^ Planet hunters no longer blinded by the light. spacefellowship.com Note: this article includes several images of such a phase plate
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