Quality time with the fractious fourier family

H. H. Barrett

Research output: Contribution to journalConference articlepeer-review

5 Scopus citations


The Fourier family comprises a wide variety of mathematical transforms, some of them well established in the image-science community, some lesser known but deserving of more recognition. The goal of this paper is to survey the genealogy of this family and to show some possibly non-obvious applications of each member. Three central premises run through the discussion: (1) There can be no science of imaging without a scientific approach to the evaluation of image quality; (2) Image quality must be defined in terms of the information that is desired from the image and the method of extracting that information; (3) Digital images are discrete data obtained from a continuous object. These considerations will lead us to rely on rather different members of the Fourier family than the ones most often encountered in polite imaging society.

Original languageEnglish (US)
Pages (from-to)9-21
Number of pages13
JournalProceedings of SPIE - The International Society for Optical Engineering
StatePublished - 2001
Externally publishedYes
EventOptical Processing and Computing: A Tribute to Adolf Lohmann - Orlando, FL, United States
Duration: Apr 17 2001Apr 18 2001


  • Detectability
  • Digital imaging
  • Fourier analysis
  • Image quality
  • Wigner distribution function

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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