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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.
