The LSM simulates the performance of coherent  lidars as space-based  remote sensors CO₂ concentration with an emphasis upon a realistic representation of the atmosphere along individual line of sights. The MLSM version 1.0 optical property data bases supports DIAL wavelengths for a 2.053472 mm off line channel and 2.053208 - 2.0531997 mm on line channels. 

Coherent DIAL Signal Processing Model

The coherent wide band SNR equation used in for the coherent DWL is used for the coherent DIAL and is defined as 

SNR_W = (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. [Set to 1.0 for DIAL simulation]

The MLSM simulates  the user's prescribed DIAL system compared to what the same DIAL system would measure for a chosen Martian standard atmosphere. The current standard atmosphere is considered to be the median atmosphere. The measured and the standard atmosphere wideband signal to noises are accumulated for the on and off channels as follows

Pon_m = (S SNRwon_m(z))/N                   Poff_m = (S SNRwoff_m(z))/N

Pon_s = (S SNRwon_s(z))/N                       Poff_s = (S SNRwoff_s(z))/N

where

    SNRwon_m       - measured signal to noise for range gate, on channel

    SNRwon_s        - standard atmosphere signal to noise for range gate, on channel

    SNRwoff_m       - measured signal to noise for range gate, off channel

    SNRwoff_s        - standard atmosphere signal to noise for range gate, off channel

    Pon_m                   - accumulated measured signal for on channel

    Pon_s                     - accumulated standard atmosphere signal for on channel

    Poff_m                    - accumulated measured signal for off channel

    Poff_s                    - accumulated standard atmosphere signal for off channel

        N                    - Number of samples in the grid volume.

    T and B            -  top and bottom of the accumulation layer, respectively.

The MLSM output product is the vertical profile of the density of the CO₂ atmosphere to the density of the CO₂ Standard Atmosphere.

rCO_2m         - density DIAL measurement product of CO₂

rCO_2s         - density DIAL Standard Atmosphere product of CO₂

NASA/LaRC and SWA developed a first attempt representation of the DIAL CO₂ measurement error for the MLSM. This equation is ongoing review. Using the parameter, PHI, from the coherent lidar model the MLSM  estimates the percent error in making a CO₂ concentration as follows.

The 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.

Questions on the DIAL Signal Processing Models mailto: Dave Emmitt or Grady Koch 

Last Updated: 02/07/2007