### Abstract

In situations where a large library of observed distributions of a function, such as temperature vs height, is available, these distributions may be used to form a set of empirical orthogonal functions. When sufficient observed distributions are not available, but when the general mathematical form of the distributions is known, a library may be constructed from the set of mathematical functions. A set of pseudoempirical orthogonal functions may then be constructed from this mathematical library. It is assumed that any distribution of the function may then be constructed from a linear sum of this pseudoempirical orthogonal set. This idea is employed to develop an inversion method using pseudoempirical orthogonal functions when a sufficient library of observations is not available. The technique employs a smoothing constraint as well as a positivity constraint, when warranted by the physical nature of the unknown.

Original language | English (US) |
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Pages (from-to) | 1243-1251 |

Number of pages | 9 |

Journal | Applied Optics |

Volume | 27 |

Issue number | 7 |

DOIs | |

State | Published - 1988 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

*Applied Optics*,

*27*(7), 1243-1251. https://doi.org/10.1364/AO.27.001243