APPLICATION OF THE RADON TRANSFORM TO OPTICAL PRODUCTION OF THE WIGNER DISTRIBUTION FUNCTION.

Roger L. Easton, Anthony J. Ticknor, Harrison H Barrett

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

The Wigner distribution function (WDF), a simultaneous coordinate and frequency representation of a signal, has properties useful in pattern recognition. Because the WDF is computationally demanding, its use is not usually appropriate in digital processing. Optical schemes have been developed to compute the WDF for one-dimensional (1-D) signals, often using acousto-optic signal transducers. Recent work has demonstrated the computation of 2-D slices of the 4-D WDF of a 2-D input transparency. In this latter case, the required 2-D Fourier transformation is performed by coherent optics. We demonstrate that computation of the WDF of real 2-D signals is susceptible to Radon transform solution. The 2-D operation is reduced to a series of 1-D operations on the line-integral projections. The required projection data are produced optically, and the Fourier transformation is performed by efficient 1-D processors (surface acoustic wave filters) by means of the chirp-transform algorithm. The resultant output gives 1-D slices through the 4-D WDF nearly in real time, and the computation is not restricted to coherently illuminated transparencies. This approach may be useful in distinguishing patterns with known texture direction. The optical setup is easily modified to produce the cross-Wigner distribution function, a special case of the complex, or windowed, spectrogram.

Original languageEnglish (US)
Pages (from-to)738-744
Number of pages7
JournalOptical Engineering
Volume23
Issue number6
StatePublished - Nov 1984

Fingerprint

Radon
radon
Distribution functions
distribution functions
Fourier transformation
Transparency
Optics
projection
Acoustic surface wave filters
spectrograms
acousto-optics
chirp
Digital signal processing
pattern recognition
Pattern recognition
central processing units
Transducers
transducers
textures
Textures

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

APPLICATION OF THE RADON TRANSFORM TO OPTICAL PRODUCTION OF THE WIGNER DISTRIBUTION FUNCTION. / Easton, Roger L.; Ticknor, Anthony J.; Barrett, Harrison H.

In: Optical Engineering, Vol. 23, No. 6, 11.1984, p. 738-744.

Research output: Contribution to journalArticle

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