Now it is getting interesting : what is the effect of defect pixels on the PTC ? The processing engines present in today’s cameras are very powerful and the vendors tell us that you get these processors almost for free. On the other hand, also memory is quasi free of charge (till the moment that you need some), so defect pixels are massively corrected in consumer as well as in professional cameras. The translates in the fact that more and more defects are tolerated in the imaging arrays. And then the questions arises : what is the effect of defect pixels on the PTC ? Actually the answer is pretty simple : because the defects can be seen as a kind of FPN, they do not influence the classical photon transfer curve based on temporal noise. But as will be shown in this blog, the defects really disturb the analysis of the FPN parameters !
By means of the mathematical model 100+ dark images were generated at various exposure times (between 0 s and 65 s). The hypothetical imager used to create these images is corrupted with 0.15 % of defect pixels (half of them are stuck at “1”, half of them are stuck at “0”).
The result of this exercise in dark can be seen in the following two figures :
- Figure 1 contains the average dark signal (left axis), and its fixed-pattern noise component (right axis) as a function of the integration time (horizontal axis). (See previous blogs to learn how the calculation of the fixed-pattern noise is done.)
- Figure 2 shows the dark fixed-pattern noise versus the dark signal, based on the data shown in Figure 1.
Figure 1 : Dark current and its FPN component as a function of the exposure time.
As can be seen in Figure 1, the average dark signal still is linear with the integration time, at least for the exposure times that do not saturate the pixel. This indicates that the dark current is responsible for the signal in dark. The linear relation between the dark signal and the exposure time (texp expressed in ms !), shown in Figure 1, holds for the linear part of the curve. The expression, as well as the curve, shows the presence of a DC offset. Remark that this DC offset is slightly increased to 515 DN, compared to 512 DN in the previous blogs, due to the presence of the stuck-at-“1” defects. Otherwise the there are no major changes compared to the results obtained earlier.
The curve of the fixed-pattern noise, shown on the right axis, depicts a very interesting feature : the FPN is relatively high for an exposure time of 0 s, much higher than in the foregoing blogs. This is due to the presence of the defect pixels. When the exposure time increases the FPN is first of all slightly decreasing, reaches a minimum and next increases towards it highest value at the onset of saturation. This strange behavior can be explained by the fact that at very low exposure times the FPN due to the dark current is negligible, but starts to increase for values of the exposure time > 0 s. Small values of the dark-current FPN added to the defect pixel FPN makes the overall value of the FPN smaller, till the moment that also the dark-current FPN contribution becomes larger and larger. From that moment the overall FPN starts increasing again. So in summary, the FPN curve is gradually determined by the defect pixels (0 s < texp < 2 ms), a combination of defects pixels and dark current FPN (2 s < texp < 6 ms), the dark-current FPN (6 s < texp < 23 ms), a combination of dark-current FPN and anti-blooming FPN (23 s < texp < 40 ms), and ultimately by the anti-blooming FPN (texp < 40 ms).
Figure 2 : Dark FPN versus dark signal.
The corresponding “PTC” curve is illustrated in Figure 2 : the FPN versus the (dark) signal is shown. As can be seen, the FPN at low signal level is completely “overruled” by the defects. A pixel FPN equal to 101.946 DN is found. It will be very difficult to extract any other FPN parameter from this curve, because the sensor has too many defects.
But after software-correction of the defects pixels (simply by replacing a defect by the average value of its 8 neighbors) this “PTC” curve changes into an almost perfect curve that allows to extract the following characteristics :
- The DSNU can be found to be equal to : 1/100.822 = 0.151 or 15.1 % at 30oC, (the latter is the temperature at which the simulations are performed,
- The saturation non-uniformity : 102.138 = 137 DN,
- Saturation level : 103.45 = 2818 DN.
In conclusion : “The more you play with the PTC, the more secrets get unfold” !
Next blog will focus on the noise contribution of the RTS pixels.
Albert 2010-03-05