The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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quantified and the number of pixels is n). A) Generating a 
normal one-dimensional simulation coefficients array whose 
size is 1 x « for every quantitative level, so the entire array’s 
size is 256 xn . B) Looking for simulation coefficient 
according to the DN values and the pixel’s position. C) The 
simulated image is generated by multiplying the simulation 
coefficients. It must be noted that the calibration accuracy in 
every radiance level should be set separately according to the 
user’s requirement. 
The Equation 2 is generated from Equation 1. 
RA = 
f^iDN-DN) 2 
t -i 
DN 
¿(kDN-kDN ) 2 
r „-1 
kDN 
(2) 
It means that the calibration accuracy of the corrected average 
row data is unchangeable no matter multiplying a constant or 
not, so a normal one-dimensional array whose mathematical 
expectation is 1 and standard deviation is the required 
calibration accuracy is generated. When a uniform image 
multiplies this array, the calibration accuracy is changeless. The 
two-dimensional simulation array is acquired by generating 256 
one-dimensional arrays for all quantified levels. 
If all quantified levels’ calibration accuracy could be acquired, 
the actual image done with relative radiance correction can be 
simulated. In this paper, all levels’ accuracy is set to be the 
same value as enough data about accuracy can’t be gotten, so 
the simulation results are the worst under the specification. It is 
different from the actual situation that the calibration accuracy 
is different in different radiance level. 
PSNR is used to evaluate the influence of calibration accuracy 
objectively. The image quality will be better if PSNR is higher. 
3.2 Simulation program validation 
If the incident light is uniform, all output DN values after 
correcting should be same in the ideal circumstances. However, 
they vary in 2~3 DN because of calibration error and the 
histograms obey normal distribution approximately. The 
relation between corrected and expected values is unfixed for a 
pixel in every radiance level. The simulation program was 
compiled based on the above analysis and the calibration results 
shown in Table 1 are used as inputs to validate the simulation 
method. The simulation results are shown in Fig.4 and Fig. 5. 
Fig.4. Simulation result in B2 
Fig.5. Simulation result in different level 
The simulation results are consistent with the statistical results 
according to Fig. 2-5. The simulation program is proper. 
3.3 The influence on image quality under relative 
calibration accuracy 
Some common images are used as the ideal images. Fig. 6 is 
used as an input image to analyze the influence on image 
quality under different relative calibration accuracy. Its size is 
512X512. After generating simulation array according to the 
input accuracy, the program checks up the simulation 
coefficient by pixel serial number and DN value in the image. 
The simulation results are acquired by multiplying the 
simulation coefficients. The simulation results in different 
accuracy are shown in Fig.7, 8, and 9. 
Fig. 6 Input image