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correlation time of the atmosphere,
The global velocity resolution is then:
σvsat =
σv =
λ
2 √ . (136)
N4πτc
σv 2 crlb +σv2 sat. (137)
Figure 68 illustrates the variation of σv with CNR for N = 100 and N = 10000.
Figure 68: Cramer Rao boundary for 100 averaged spectra (dark red) and 10000 averaged
spectra (light red). CNR is measured in narrow band (B = 1/τm)
For low CNR values, σv decreases as 1/CNR. Doubling the pulse energy divides by 2
the velocity resolution. For high CNR values, σv is constant. Spectral broadening comes from
specklefluctuationsinthesignal.Theonlywaytoreduceσv istoincreaseN.Forintermediate
CNR, σv varies as 1/ √ CNR. It is therefore equivalent to increase pulse energy or number of
pulses. In this region, σv depends only on the average laser power. Using a low energy, high
pulse repetition rate (PRF) laser is then equivalent to using a high energy, low PRF laser,
assuming the average power is constant. This is one for the reasons of the recent raise of
high PRF fiber lasers for pulsed Doppler lidars.
Range ambiguity The rate at which pulses are transmitted, the PRF limits the range over
which heights can be unambiguously determined. To avoid ambiguity between return signals,
the inter pulse period (IPP=1/PRF) must be longer than the round trip time of flight of the
pulse to the greatest height. For example, to measure without ambiguity up to 5 km, the
PRF needs to be less than 30 KHz,
5.3.5 Time-bandwidth tradeoffs
PRFmax = c
2Zmax
. (138)
Spatial resolution is proportional to pulse duration. The shorter the pulse, the smaller the
resolution. Velocity resolution is proportional to spectrum width and is smaller when the
spectrumisnarrow.Becausethespectrumwidthisinverselyproportionaltothepulseduration,
range resolution and velocity resolution are also inversely proportional.
116 DTU Wind Energy-E-Report-0029(EN)