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The range resolved lidar power can be represented as (Piironen, 1994),

where

P(r) | = | lidar power incident on receiver from range r, W; |

= | laser pulse energy, J; | |

c | = | speed of light, m s; |

A | = | area of the receiver, m; |

= | aerosol scattering cross-section per unit volume | |

from range r, m; | ||

= | molecular scattering cross-section per unit volume | |

from range r, m; | ||

= | extinction cross-section
per unit volume from range r, m; | |

= | analytical molecular backscatter phase function, sr ; | |

= | aerosol backscatter phase
function from
range r, sr ; | |

M(r) | = | multiply-scattered return
from range r, W; |

b | = | background signal, W; |

and the range is determined relative to the time, *t*, following the
transmitted pulse, such that

Multiple scatter is reduced by limiting the system field of view. However, it is an important feature in the measurement and is a topic under investigation (Eloranta and Piironen, 1992). System optical characteristics and measurement of the background signal are determined through calibration. Nonetheless, there remain four unknowns in Equation 21: aerosol and molecular cross-sections per unit volume, aerosol backscatter phase function, and extinction cross-section. The column optical depth, , is related to the extinction cross-section as

Measurement of individual optical properties is not possible with a single channel lidar due to the inherent coupling of extinction cross-section with the aerosol and molecular backscatter cross-sections. However, it can be accomplished with the separation of Equation 21 into individual molecular and aerosol equations,

and

respectively; where multiple scattering and the background contribution have been assumed to be negligible.

Sun Aug 11 10:02:40 CDT 1996