## Abstract

An experimental method for determining the presence and the level of systematic distortions in lidar data is considered. The method has been developed on the basis of two years of field experiments with the Fire Sciences Laboratory elastic scanning lidar. The influence of multiplicative and additive distortion components is considered using numerical experiments and is illustrated with experimental data.
The examination method is most applicable for short wavelengths at which the atmospheric molecular component in clear atmospheres is large enough to stabilize the Kano–Hamilton multiangle solution, based on the assumption of horizontal atmospheric homogeneity.

© 2007 Optical Society of America

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### Equations (19)

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(1)
$$\u3008P\left(r\right)\u3009={P}_{\mathit{total}}\left(r\right)-\u3008BGR\u3009=Cq\left(r\right)\beta \left(r\right)D\left(r\right){r}^{-2}\times \mathrm{exp}\left[-2\tau \left(0,r\right)\right]+B\left(r\right)\text{,}$$
(2)
$$y\left(r\right)=\mathrm{ln}\left[C\beta \right]+\mathrm{ln}\text{\hspace{0.17em}}q\left(r\right)+\mathrm{ln}\text{\hspace{0.17em}}D\left(r\right)+\mathrm{ln}\left[1+B/P\left(r\right)\right]-2\tau \left(0,r\right)\text{.}$$
(3)
$${q}_{\mathit{eff}}\left(r\right)=q\left(r\right)D\left(r\right)\left[1+B/P\left(r\right)\right]\text{.}$$
(4)
$$\u3008{P}_{j}\left(h\right)\u3009{\left(h/\mathrm{sin}\text{\hspace{0.17em}}{\phi}_{j}\right)}^{2}=\left[{P}_{j\text{,}\mathit{total}}\left(h\right)-\u3008BG{R}_{j}\u3009\right]{\left(h/\mathrm{sin}\text{\hspace{0.17em}}{\phi}_{j}\right)}^{2}=C{q}_{j}\left(h\right){\beta}_{j}\left(h\right){D}_{j}\left(h\right)\mathrm{exp}\left[-2{\tau}_{j}\left(0,h\right)\right]\times \left(1+{B}_{j}/{P}_{j}\left(h\right)\right)\text{,}$$
(5)
$${y}_{j}\left(h\right)=\mathrm{ln}\lfloor \u3008{P}_{j}\left(h\right)\u3009{\left(h/\mathrm{sin}\text{\hspace{0.17em}}{\phi}_{j}\right)}^{2}\rfloor \text{,}$$
(6)
$${y}_{j}\left(h\right)=A\left(h\right)+\mathrm{ln}\lfloor {q}_{j\text{,}\mathit{eff}}\left(h\right)\rfloor -2\tau \left(0,h\right){x}_{j}\text{.}$$
(7)
$$A\left(h\right)=\mathrm{ln}\left[C\beta \left(h\right)\right]\text{,}$$
(8)
$${q}_{j\text{,}\mathit{eff}}\left(h\right)={q}_{j}\left(h\right){D}_{j}\left(h\right)\left(1+{B}_{j}/{P}_{j}\left(h\right)\right)\text{.}$$
(9)
$${\left[T\left(0,h\right)\right]}^{-2}=\mathrm{exp}\left[2\tau \left(0,h\right)\right]\text{.}$$
(10)
$${\left[T\left(0,h\right)\right]}^{-2}=a+bh$$
(11)
$${\kappa}_{\mathit{total}}\left(h\right)=\frac{d\tau \left(0,h\right)}{dh}=\frac{0.5b}{a+bh}\text{.}$$
(12)
$${\kappa}_{\mathit{total}}\left(h=0\right)={\kappa}_{p\text{,}\mathit{neph}}+{\kappa}_{m}\left(h=0\right)\text{.}$$
(13)
$${\tau}_{\mathit{int}}\left(0,h\right)=\frac{{\kappa}_{\mathit{total}}\left(h=0\right)}{\eta}\left[1-\mathrm{exp}\left(-\eta h\right)\right]\text{,}$$
(14)
$$\xi ={\displaystyle \sum _{\left(\Delta {h}_{\mathit{int}}\right)}{\left[\tau \left(0,h\right)-{\tau}_{\mathit{int}}\left(0,h\right)\right]}^{2}}\text{,}$$
(15)
$${\kappa}_{\mathit{total}}\left(h\right)={\kappa}_{\mathit{total}}\left(h=0\right)\mathrm{exp}\left(-\eta h\right)\text{.}$$
(16)
$${\tau}_{\mathit{max}}\left(0,h\right)=\mathrm{max}\left[\tau \left(0,{h}_{\mathit{min}}\right);\text{\hspace{0.17em}}\tau \left(0,{h}_{\mathit{min}}+\Delta {h}_{d}\right);\text{\hspace{0.17em}}\tau \left(0,{h}_{\mathit{min}}+2\Delta {h}_{d}\right)\text{; \hspace{0.17em} \u2026 \hspace{0.17em} ; \hspace{0.17em}}\tau \left(0,h\right)\right]\text{,}$$
(17)
$${\tau}_{\mathit{min}}\left(0,h\right)=\mathrm{min}\left[\tau \left(0,h\right);\text{\hspace{0.17em}}\tau \left(0,h+\Delta {h}_{d}\right);\text{\hspace{0.17em}}\tau \left(0,h+2\Delta {h}_{d}\right)\text{; \hspace{0.17em} \u2026 \hspace{0.17em} ; \hspace{0.17em}}\tau \left(0,{h}_{\mathit{max}}\right)\right]\text{.}$$
(18)
$${\tau}_{sh}\left(0,h\right)=\frac{1}{2}\left[{\tau}_{\mathit{min}}\left(0,h\right)+{\tau}_{\mathit{max}}\left(0,h\right)\right]\text{.}$$
(19)
$$\epsilon =\frac{{\displaystyle {\int}_{{h}_{min}}^{{h}_{max}}\left[{\tau}_{max}\left(0,h\right)-{\tau}_{min}\left(0,h\right)\right]dh}}{2{\displaystyle {\int}_{{h}_{min}}^{{h}_{max}}{\tau}_{sh}\left(0,h\right)dh}}\text{.}$$