The LSM simulates the performance of coherent and direct detection Doppler wind lidars as space-based or airborne remote wind sensors with an emphasis upon realistic representations of the atmosphere along individual line of sights. The current optical property data bases support 2.0518 mm coherent lidars and 0.355  mm, 0.532  mm and 1.06 mm direct detection lidars. Planned future upgrades to the optical property modules will support lidar wavelengths ranging from 0.3-1.6 mm range.

Coherent Signal Processing Models

The LSM has the option to use a narrow band signal to noise model or a consensus curve algorithm for signal processing of the lidar signal.

Poly-pulse Pair Method - Narrow Band SNR  (not available in the DLSM version 4.2)

There are several signal-to-noise (SNR) equations that have been suggested for use with Doppler lidar wind sounders. The narrow band SNR equation that the LSM uses is:

        c - speed of light (m/s)

      h₁ - heterodyne quantum efficiency

      h₂ - optical efficiency

      h₃ - beam shape factor

      h₄ - truncation factor

        J - fundamental laser energy per pulse (Joules)

        D - mirror diameter (m)

      t - pulse length (sec)

        ß - backscatter (m^-1 sr^-1)

        e^-2óa(r)dr - 2 way attenuation

        hn - photon energy (J)

        R - slant range (m)

      l - laser wavelength (m)

As with the lidar SNR equation, there are several radial or LOS velocity error estimates, s_los, that have been suggested for use with Doppler lidar wind sounders. While the Cramer-Rao Lower Bound may provide a limit to the extraction of a velocity estimate from a noisy signal, we have the option to chose the more conservative estimate based upon pulse pair autocorrelation processing of the Doppler signal. The following is derived from Eq. (6.22a) in Doviak and Zrnic (1984).

 s_los= (l/4p×f^0.5/2t) × (2p^1.5W + 16 p² W²/SNR_w + 1/SNR_w²)^0.5

where

       l - wavelength (m)

        V_max - maximum velocity measured

        f- sampling frequency = 2 × V_max/ l

        t- pulse duration (sec)

        W - normalized frequency spread of return signal (m/s)

        V_bw - uncertainty due to pulse bandwidth (m s^-1)

        V_atm - uncertainty due to turbulent eddies and windshear within the pulse volume

Phi-Capon Method 

A simplified version of the Effective Gaussian Signal Spectrum Model (Frehilch and Sharman, 2003; Frehilch, 1997; Frehilch, 1996) is used to estimate the performance of a coherent DWL for general conditions in the threshold regime of weak signals.

The wide band SNR equation used in the LSM is defined as 

SNRW = (p×h₁×h₂×h₃×h₄×h₅×J×D²×l²  ß×e^-2óa(r)dr)/(8×hn×2×V_max×R²)

where

      h₁ - heterodyne quantum efficiency

      h₂ - transmit optical efficiency

      h₃ - receive optical efficiency

      h₄ - mixing efficiency

      h₅ - coherent system margin

        J - fundamental laser energy per pulse (Joules)

        D - mirror diameter (m)

        ß - backscatter (m^-1 sr^-1)

        e^-2óa(r)dr - 2 way attenuation

        hn - photon energy (J)

        R - slant range (m)

      l - laser wavelength (m)

        V_max - signal velocity bandwidth.

An effective wideband SNR (db) is computed by accumulating all the samples in an user's defined grid volume.

SNRW_eff =  10×log10( (S(SNRW_i)²)^0.5)

The number of data samples per LOS range gate is given as

m = (2.0 * d * 2.0 * V_max) / (c  * l * 1E-6)

where

       l - wavelength (m)

        V_max - maximum velocity measured

        c - speed of light (m/s)

        d - range gate (m).

Thus the effective photons per LOS range gate is 

f = m * SNRW_eff.

The percentage of bad estimates described by the following fraction of random outliers is

B = exp(-(0.1*f/B₀)^a)

where

        B₀ - constant

      a - constant

The percentage of bad estimates is used to decided whether the DWL performance produces a failed attempt, false alarm or a good wind measurement. If B is greater than the user's entry of the gross error probability threshold, then it is considered a failed attempt. If the performance is considered to be a "good" performance, then the estimates have a random chance of producing a false alarm in which f is set to 0.1. The line of sight uncertainty spread for the "good" estimates  is defined as

s_los = C * (1.0 + (f*0.1/G₀)**e)**(-d) + m 

where

        s_los - the line-of-sight uncertainty (m/s).

        X - constant

        G₀ - constant

      e - constant

      d - constant

       m - constant

Direct Detection Signal Processing Models

The LSM has a double edge technique signal to noise model. Work is ongoing to add a fringe imager technique model in the near future.

Double Edge

A simplified version of the double edge technique model (Flesia and Korb, 1999;Korb et al., 1992) is used to estimate the performance of a direct detection DWL. The direct detection number of source photons reaching the beam splitter is defined as 

Nphotons = (p×h₁×h₂×h₃×h₄×h₅×h₆×J×C_l×D²×l×ß×e^-2óa(r)dr)/(4×Pk×c×R²)

where

      h₁ - detector quantum efficiency

      h₂ - transmit optical efficiency  

      h₃ - receive optical efficiency up to detector subsystem edge filters (monitor and edge filter, etc)

      h₄ - fraction of signal sent to each of the edge filters (beam split fraction)

      h₅ -  engineering adjustment factor

      h₆ -  edge filter throughput for source (aerosol or molecular) signal

        J - fundamental laser energy per pulse (Joules)

        C_l - wavelength conversion factor

        D - mirror diameter (m)

        ß - backscatter (m^-1 sr^-1)

        e^-2óa(r)dr - 2 way attenuation

         Pk - plank constant

        c - speed of light (m/s)

        R - slant range (m)

      l - laser wavelength (m)

The DLSM accumulates the photons and dark noise photon counts for the user's grid volume as follows

y = S((z*100.0) * d/ c)

g = S Nphotons * d 

where

        y - noise photocounts from the dark current in the detector

        z - dark current photocounts/s

          c - speed of light (m/s)

          d - range gate (m)

          Nphotons - number of source photons reaching the beam splitter

          g - accumulated source photons reaching the beam splitter

Assuming that aerosol/molecular ratio is very small and both edges have the same throughput, the effective SNR and LOS uncertainty along the edge are described as

SNR_e = g/(1.0 + (y/g))

s_los = (2/SNR_e)^**0.5 / e_s 

where

            SNR_e - effective SNR along the edge

          e_s  - edge sensitivity

        s_los - LOS uncertainty along the edge

The DLSM version 4.2 has no solar and cloud refection model. The effects are approximated by the following multiplier.

s_los = s_los * 1.10 

The DLSM 4.2 has an  photon count module that counts photons for aerosols (and clouds) and molecules at the primary mirror’s focus post atmospheric effects as follows

x₁ = S  (p×h₂×J×C_l×D²×l×ß_a×e^-2óa(r)dr)/(4×Pk×c×R²) * d 

x₂ = S  (p×h₂×J×C_l×D²×l×ß_m×e^-2óa(r)dr)/(4×Pk×c×R²) * d 

where

                   ß_a - aerosol backscatter (m^-1 sr^-1)

                   ß_m - molecule backscatter (m^-1 sr^-1)

                  x₁ - accumulated aerosol photons at the primary mirror’s focus post atmospheric effects

                  x₂ - accumulated molecule photons at the primary mirror’s focus post atmospheric effects

Fringe Imager 

A simplified version of the Fringe Imager model (Skinner and Hays, 1994) is used to estimate the performance of a direct detection DWL. 

(The Fringe Imager model is not currently available in the DLSM version 4.2)

Questions on the DWL Signal Models mailto: Dave Emmitt 

Last Updated: 02/07/2007