### Abstract

The term planar projection refers to the integral of a three-dimensional (3-D) function over a plane, as opposed to the line integrals that form the basic data set of computed tomography. Planar projections arise naturally in nuclear imaging when a slit aperture is used, in imaging with nuclear spin resonance, and in time-domain scattering studies. If an appropriate set of translations and rotations of the plane of integration is carried out, a complete data set is generated and a reconstruction of the 3-D object is possible. Various reconstruction algorithms are discussed and compared to the more familiar case of computed tomography. Another potential application of planar projections is in general 3-D data processing, where it should be useful to preprocess the data by generating a set of planar integrals, even if the original data have nothing to do with projections. This has the effect of reducing 3-D operations such as convolutions and correlations to one-dimensional (1-D) operations, which are more readily performed. After a subsequent reconstruction from the filtered projections, the final 3-D result is equivalent to that which would have been obtained by 3-D operations. Several incoherent optical systems for performing the projection and reconstruction operations are described.

Original language | English (US) |
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Pages (from-to) | 179-190 |

Number of pages | 12 |

Journal | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 373 |

DOIs | |

State | Published - Feb 27 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

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