### 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 language | English (US) |
---|---|

Pages (from-to) | 738-744 |

Number of pages | 7 |

Journal | Optical Engineering |

Volume | 23 |

Issue number | 6 |

State | Published - Nov 1984 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Optical Engineering*,

*23*(6), 738-744.

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

Research output: Contribution to journal › Article

*Optical Engineering*, vol. 23, no. 6, pp. 738-744.

}

TY - JOUR

T1 - APPLICATION OF THE RADON TRANSFORM TO OPTICAL PRODUCTION OF THE WIGNER DISTRIBUTION FUNCTION.

AU - Easton, Roger L.

AU - Ticknor, Anthony J.

AU - Barrett, Harrison H

PY - 1984/11

Y1 - 1984/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0021521605&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021521605&partnerID=8YFLogxK

M3 - Article

VL - 23

SP - 738

EP - 744

JO - Optical Engineering

JF - Optical Engineering

SN - 0091-3286

IS - 6

ER -