68 
ndet 
,m 
Where: 
i = scan index 
j = sample index 
ndet = no. of detectors per focal plane (default = 16) 
nscan = no. of scans (default = 32) 
nsamp = no. of samples (default = 512) 
eq_source = raw uniform image from detector k, band m (DN) 
~ bias = average response value to shutter for sample j, from scan i, detector k, band m (DN) 
G = gain for detector k, band m (DN/radiance) ** 
r = average EAR for detector k, band m (radiance) 
r_avg = average EAR across all detectors in a band m (radiance) 
** Each detector gain is currently implemented as a nominal constant value across all scans. 
Shutter data collected at the same time as the equalization source image was extracted from the calibration data and 
averaged to provide estimates of the offset bias for each pixel on each individual scan. The best results (i.e. minimized 
streaking and striping) were achieved when using the extraction technique described below. 
Subtracting the appropriate bias allowed for computation of the signal counts, which when divided by the detector gain, 
yielded radiance. The radiance values were averaged over samples and scans to produce an average EAR for a detector. 
After all detectors in a band had been processed, the average EAR across the band was also calculated. The ratio of these 
average radiance values, r_avg and r, became equalization coefficients which were used to equalize imagery. 
Once the coefficients had been calculated, they were applied both to the remainder of the image from which they were derived 
and to other images produced by the same sensor using the following processing steps: 
For each reflective band, m, and each detector, k : 
  
(input, .-bias, ) | men (3) 
  
output byte, — i | (output, ) -239-..., 05| (4) 
P max 
Limit output byte between 0 and 255 
Where: 
input = raw input image from detector k, band m (DN) 
output = corrected radiance image from detector k, band m (floating point radiance) 
output_byte = byte scaled output radiance image from detector k, band m 
Rmax = Maximum radiance for band m (radiance) 
The average bias was again computed on an individual scan basis and removed. 
5. BIAS REMOVAL 
Enough emphasis cannot be placed on the proper calculation and removal of scan dependent bias levels. Most of the visible 
residual striping in TM imagery was found to be due to the incomplete compensation of the individual bias associated with 
each scan. Early in the study it was assumed that subtracting the proper average dark shutter value from the image pixel 
values inthe same scan would eliminate scan to scan bias variations causing striping. However, use of the averaging window 
specified in the Long Term Parameter File (see window w2 in Figure 1) provided with the images for determining average dark 
responses actually induced striping. A variety of averaging windows was tried before the final windows, w6 and w7, were 
selected for their minimization of striping. The key ingredient in selecting the proper window was to avoid readings obtained 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences’, Zurich, March 22-24 1995