Chapter 5 ______________________________________________________ Functional Description
VAISALA _______________________________________________________________________ 75
Return Signal Strength
The instantaneous return signal strength is in general form (the Lidar
equation):
∫
′
′
−
⋅
⋅
⋅
⋅
=
z
z
d
z
e
z
z
A
c
Eo
z
0
)
(
2
2
r
)
(
2
)
(
P
σ
β
where
Pr(z)
=
The instantaneous power received from distance z [W = Watt]
E
O
=
The effective pulse energy (taking all optics attenuation into
account) [J = Joule = Ws = Watt - second]
c
=
The speed of light [m/s = meters per second]
A
=
The receiver aperture [m
2
]
z
=
The distance in question [m]
ß(z)
=
The volume backscatter coefficient at distance z [m
-1
srad
-1
, srad =
steradian]
e
z dz
z
−
′
′
∫
2
0
σ
( )
=
The two-way atmospheric transmittance, accounts for the
attenuation of transmitted and backscattered power by extinction
at various distances (z') between transceiver and distance in
question (z). The expression equals 1 in clear atmosphere (i.e.,
with no attenuation).
Height Normalization
Assuming a clear atmosphere, it can be seen that the power is
inversely proportional to the square of the distance or height, that is,
the strength of a signal from 10000 ft is generally one-hundredth of
that from l000 ft.
The height-square dependence is eliminated by multiplying the value
measured with the square of the height (height normalization). Noise,
however, being height-independent from a measurement point of
view, will then be correspondingly accentuated with increasing height.
Backscatter Coefficient
The volume backscatter coefficient, ß(z), of the Lidar Equation
represents the portion of light which is reflected back towards the
ceilometer from a distance z (for example, by water droplets). It is
