Apodization

Apodization is an optical filtering technique. 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.

Airy disk

Apodization in electronics
Further information: Window function

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 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. 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.[1]

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 imaging

Since side lobes of the Airy disk are responsible for degrading the image, techniques for suppressing them are utilized. In case 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.[2] The measured beam profile[3] of such imaging system is shown and compared to the modeled beam profile[4] in the Figure on the right.

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 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.[5] 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.[6]

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.[7]

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.[8][9][10] 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.

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See also
  • Apodization function

References
  1. Savaryn, John P.; Toby, Timothy K.; Kelleher, Neil L. (September 2016). "A researcher's guide to mass spectrometry-based proteomics". Proteomics. 16 (18): 2435–2443. doi:10.1002/pmic.201600113. PMC 5198776. PMID 27553853.
  2. Handbook of optical and laser scanning. Marshall, Gerald F., Stutz, Glenn E. (2nd ed.). Boca Raton, Florida: CRC Press. 2012. ISBN 9781439808795. OCLC 756724023.CS1 maint: others (link)
  3. Ahi, Kiarash; Shahbazmohamadi, Sina; Asadizanjani, Navid (2018). "Quality control and authentication of packaged integrated circuits using enhanced-spatial-resolution terahertz time-domain spectroscopy and imaging". Optics and Lasers in Engineering. 104: 274–284. Bibcode:2018OptLE.104..274A. doi:10.1016/j.optlaseng.2017.07.007.
  4. Ahi, K. (November 2017). "Mathematical Modeling of THz Point Spread Function and Simulation of THz Imaging Systems". IEEE Transactions on Terahertz Science and Technology. 7 (6): 747–754. Bibcode:2017ITTST...7..747A. doi:10.1109/tthz.2017.2750690. ISSN 2156-342X.
  5. ""Bokeh-Gigant": Fujinon XF 1,2/56 mm R APD (aktualisiert)". 2001-11-30.
  6. "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.
  7. Hewett, Jacqueline (2007-06-01). "Photon sieves benefit space telescopes". Optics.org. Retrieved 2007-06-05.
  8. E. Hecht (1987). Optics (2nd ed.). Addison Wesley. ISBN 978-0-201-11609-0. Section 11.3.3.
  9. FIRST RESULTS FROM VERY LARGE TELESCOPE NACO APODIZING PHASE PLATE: 4 μm IMAGES OF THE EXOPLANET β PICTORIS b* The Astrophysical Journal (Letter)
  10. 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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