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d charge 
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(7) 
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viewing 
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0.216 
In order to compensate for saturation non-linearity of 
the imager response it was assumed that this non-linearity 
represents the loss of the detector responsivity with rising 
bias voltage and, therefore, it is primarily a function of the 
detected signal level. 
The pixel-by-pixel correction for offset and saturation 
non-linearities of IR imager response is achieved 
according to the following algorithm: 
1. Based on the experimental signal measurements for a 
wide range of blackbody temperatures and values of 
the optical integration time, the detected signal can 
be approximated by an exponential function of optical 
integration time, tin, for each temperature, T;, of the 
calibration source, as: 
i 
S detected _ al 2 int = a; (8) 
2. For N various radiative fluxes corresponding to N 
various temperatures, T;, of the calibration blackbody 
source the intensity of the incident on IR detectors 
radiative flux is characterized by the ratio of the 
detected signal, S(Ti, tin), to the value of optical 
integration time, tint, as: 
S(T; me) i zd] uM 
Lint (9) 
Paz DC 
1 
3. The linearized signal corrected for off-set at zero 
integration time can now be expressed as function of 
the detected signal and the intensity of the incident 
radiative flux as: 
as detected 
ot int 
WS 
0X fin 5 Ay 9 
iii 
= = af. (ma ai 
where index k is determined from the following 
condition (assuming that Fy are sorted in the 
ascending order): 
S linear = 
(10) 
FF » S Ft Fy 
2 Lint 2 
  
(11) 
The radiative flux intensities used for M-WIP 
calibration, F;, are stored in the ascending order 
along with corresponding coefficients a;' and a; in the 
correction table for each pixel. During the on-line M- 
WIP temperature measurements these tables are 
searched according to the criteria given by Eq. (11). 
Once the appropriate flux level, Fx, has been 
determined, the corresponding correction coefficients 
a," and as“ are then used for signal linearization 
according to Eq. (10). 
Figure 4. illustrates the correction for saturation non- 
linearity resulting from application of the above algorithm 
to the signals detected by M-WIP through 4500nm filter 
illuminated by the blackbody source at 600?C. 
81 
2.0 ————————— 
1.7: = 
15 - " 
glinearza, a Jf; 
12- 2 int wd .* 
WW ad 
1.0 - i 
wl 
0.7 - / 
0.5 - 
detected. aot: 
pa | S =a,e“2'int+a, 
Detected Signal x10° [electron/pixel] 
  
  
  
0.0 i | 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 
Integration Time [s] 
Fig. 4. Saturation non-linearity correction. 
Calibration of M-WIP System 
The experimental M-WIP system includes a least- 
squares-based calibration algorithm [1-3] for evaluation of 
effective values of peak filter transmissions (t9) and center 
wavelengths (Ag) based on the detection of radiation 
emitted by the pre-calibrated blackbody source over a 
wide range of temperatures: 
min 2. 
TA, Hal Oi 
where: 
<1 bem. 3 
8, ^S Toho) 2T, A02 
T — i-th temperature of reference blackbody source, 
Oo, = AS, = ve — rms signal noise (rms electrons/pixel 
A seven-filter experimental M-WIP system was 
initially calibrated according to Eq. (12) against a 
reference blackbody source over a temperature range from 
450?C to 900?C. It should be noted that the initial 
calibration did not include the compensation for 
saturation non-linearity of the imager response. This 
calibration resulted in an effective radiometric uniformity 
correction of all camera pixels used for the M-WIP 
measurements. However, due to self-compensation for 
non-linear response of the imager by the calibration 
algorithm, the initial calibration resulted in a shift of the 
effective center wavelengths of the filters in the range of 28 
to 358 nm as compared to manufacturer specifications (see 
column II of Table 1). In order to study this effect, the M- 
WIP "calibration" was also performed on the basis of the 
simulated signal with various values of "offset" and 
"saturation" non-linearities. It was found, as illustrated in 
column III of Table 1, that "offset" non-linearity of 2.5% 
of Qmax at zero optical integration time (ie. tint=0) and 
"saturation" non-linearity of 8% at 50% of Qmax results 
in similar shifts in effective center wavelengths of IR 
filters as was obtained for the experimental data not 
compensated for imager non-linearity. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B1. Vienna 1996