41. Parameterizing the Return Signal 
Waveform processing algorithms parameterize the return signal 
resulting from the interaction of the transmitted laser pulse with 
the intercepted surface, and identify the response from the 
multiple targets encountered within the footprint. The SLA 
detector output voltage is continuously sampled by a high 
speed, 8-bit digitizer. Upon detection of a backscatter return 
by the ranging electronics, the digitizer time series is sampled 
and stored, yielding a waveform record of received laser 
backscatter energy. The digitizer memory is sampled so as to 
record detector output voltage beginning slightly before the 
ranging electronic's detection of the backscatter return and 
extending in time to include the maximum range of within- 
footprint heights expected for land surfaces. Thus a time series 
of the complete backscatter return for land surfaces is recorded. 
Returns are modeled as a single Gaussian function, or as the 
combination of several Gaussian peaks when measurement of 
multiple ranges from a single return is required. In this 
manner, the vertical extent and approximate height distribution 
of intercepted surfaces can be derived from the return signal. 
Most of the waveforms are single peaked and can be fit by a 
single Gaussian function, characterized by its maximum 
amplitude, location of this maximum amplitude in time with 
respect to the ranging electronics detection time, and its half 
width. When complex surfaces are intercepted within the 
footprint (as with the presence of complex surface topography, 
clouds, vegetation, buildings), multiple returns are present in 
the waveforms and multi-Gaussian functions are used to model 
these more complex waveforms. 
In brief, the waveform processing steps consist of: 
D Identifying and processing only shots that are 
classified as valid surface returns form land and ocean 
based on a comparison of the laser bounce point 
elevation (orthometric height) to a reference surface 
(5 minute resolution Terrain Base Digital Elevation 
Model for land returns, and mean sea level for ocean 
returns). 
ID Determining the noise baseline and calculating noise 
mean and standard deviation, establishing a 
waveform threshold level for signal above noise. 
IIT) Identifying start and end of signal above waveform 
threshold. 
IV) Identifying saturated returns. 
V) Subtracting mean noise level from the signal. 
VD Characterizing the basic properties of the signal. 
VII) Scaling waveform engineering units to physical units 
(detector output voltage vs. time) based on scaling 
factors and calibration constants. 
   
       
      
      
   
  
   
   
    
    
   
  
   
    
   
   
    
  
   
   
    
    
   
    
   
   
   
      
    
    
   
    
   
    
     
    
   
  
     
   
   
  
  
   
   
     
     
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
VIII) Identifying returns to be excluded from processing 
based on anomalous characteristics. 
IX) Smoothing the signal. 
X) Establishing initial estimates for peak positions, 
amplitudes and half-widths based on the first and 
second derivatives of the signal, with exception 
handling for saturated returns. 
XD Applying constrained function fitting to obtain first 
estimates of peak amplitudes, with exception 
handling for saturated returns. Editing peaks based 
on their amplitude and proximity (zero amplitude 
peaks are eliminated), with exception handling for 
saturated shots. 
XII) Re-evaluating peak's significance if necessary, and 
solving for peak amplitude, location, and half-width. 
XIII) Deriving distances from the start of the waveform 
signal to: 1) centroid of all peaks, 2) centroid of the 
last peak. 
For our purpose, a Gaussian peak is defined as follows: 
F(x) = A(0) * TE ; (2) 
where zZ sa : (3) 
AQ) 
F is the analytical function representing the model, and the 
parameters to be solved are: 
A(0)= Gaussian peak maximum amplitude 
A(1)= location in the time axis 
A(2)= 1-sigma deviation from its mean 
X; is the independent variable, Y; is the observations 
(independent variables), and ERR; are the 1-sigma uncertainties 
in the observations. The residuals are calculated in the 
following manner: 
Residuals = (Y; - F(X;)) | ERR, (4) 
If ERR are the 1-sigma uncertainties in Y, then the total chi- 
squared value will be: 
2 
2 Yi -F(i) 
es re 3 
X : ERR, | (5) 
SLA uses the IDL routine MPFIT to fit Gaussian distributions 
to the waveform. This is a recently-added, user-supplied IDL 
routine authored by Craig B. Markwardt, NASA/GSFC Code 
622, which uses the The Levenberg-Marquardt technique as a 
particular strategy to iteratively search for the best fit in the 
   
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