## Abstract

An iterative method for determining slope in noisy lidar data is considered based on the use of a corrected (“shaped”) inverted function and an assumed behavior of the unknown function of interest (an “image function”). The method is utilized for extracting extinction-
coefficient profiles from data of multiangle measurements. The sequence and specifics of the retrieval procedure, results of simulations, and essentials of the practical retrieval of particulate extinction-coefficient profiles from signals of the elastic scanning lidar are considered. The methodology may be applicable when extracting the extinction-coefficient profiles from an elastic lidar operating in a multiangle scanning mode, a combined Raman elastic-backscatter lidar, or a high spectral resolution lidar operating in a fixed angular position.

© 2006 Optical Society of America

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### Equations (10)

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(1)
$${\tau}_{p\text{,2}}\left(0,h\right)=0.5\left[{\tau}_{u}\left(0,h\right)+{\tau}_{l}\left(0,h\right)\right],$$
(2)
$${\tau}_{u}\left(0,h\right)=\text{max}\left[{\tau}_{p\text{,}1}\left(0,{h}_{\text{min}}\right);\text{\hspace{0.17em}}{\tau}_{p\text{,}1}\left(0,{h}_{\text{min}}+\Delta {h}_{d}\right);{\tau}_{p\text{,}1}\left(0,{h}_{\text{min}}+2\Delta {h}_{d}\right);\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}};\text{\hspace{0.17em}}{\tau}_{p\text{,}1}\left(0,h\right)\right],$$
(3)
$${\tau}_{l}\left(0,h\right)=\text{min}\left[{\tau}_{p\text{,}1}\left(0,h\right);\text{\hspace{0.17em}}{\tau}_{p\text{,}1}\left(0,h+\Delta {h}_{d}\right);{\tau}_{p\text{,}1}\left(0,h+2\Delta {h}_{d}\right);\text{\hspace{0.17em}}\dots \text{\hspace{0.17em}};\text{\hspace{0.17em}}{\tau}_{p\text{,}1}\left(0,{h}_{\text{max}}\right)\right],$$
(4)
$${\kappa}_{p}{\left(h\right)}^{\left(i\right)}=\frac{I\left(h\right)}{B{\left(h\right)}^{\left(i-1\right)}},$$
(5)
$$B{\left(h\right)}^{\left(i\right)}=R{\left(h\right)}^{\left(i\right)}B{\left(h\right)}^{\left(i-1\right)},$$
(6)
$$I\left(h\right)=\left[{B}_{1}{\kappa}_{p}\left(h\right)\right],$$
(7)
$$P\left(h\right){h}^{2}=\left[C{\beta}_{\text{total}}\left(h\right)\right]{\left[T\left(0,h\right)\right]}^{2},$$
(8)
$${\xi}^{\left(i\right)}=\frac{1}{\Delta {\tau}_{p\text{,total}}}\sqrt{\frac{{\displaystyle \sum _{N}{\left[{\tau}_{p}{\left(0,h\right)}^{\left(i\right)}-{\tau}_{p\text{,}b}\left(0,h\right)\right]}^{2}}}{N}},$$
(9)
$${\tau}_{p}{\left(0,h\right)}^{\left(i\right)}={\tau}_{p}\left(0,{h}_{\text{min}}\right)+{\tau}_{p}{\left({h}_{\text{min}},h\right)}^{\left(i\right)},$$
(10)
$$I\left(h\right)=\frac{\left[C{\beta}_{\text{total}}\left(h\right)\right]}{\u3008C\u3009}-{\beta}_{m},$$