A very interesting feature of today’s image sensors is their ability to cope with an overexposure. CCDs as well as CMOS image sensors do have anti-blooming means present in the pixels. Anti-blooming prevents overflow of electrons to neightboring pixels in the case of overexposure. In this blog the effect of the anti-blooming and especially the anti-blooming non-uniformity will be studied. It is quite common to have a large spread in the anti-blooming level, because the onset of the anti-blooming is depending on the threshold of a transistor. And it is known that thresholds can vary quite a lot from device to device. In a real application that is not a big deal, because the saturation level of most cameras (= definition of white in the image) is set below the anti-blooming level of the imagers, and any non-uniformity in anti-blooming is not visible.
An anti-blooming model was incorporated in the simulation tool and 100+ dark images were generated at various exposure times (between 0 s and 65 s). The result of this exercise in dark can be seen in the following four figures : Figure 1 contains the average dark signal (left axis) of the generated images 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 3 contains the average dark signal (left axis) of the generated images and its temporal 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 4 shows the dark current temporal noise versus the dark signal, based on the data shown in Figure 3.
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 is linear with the integration time, indicating that the dark current is responsible for the signal in dark. The relation between the dark signal and the exposure time (texp expressed in ms !) is also indicated in Figure 1. But the curve is showing a saturation indicating the anti-blooming capability of the sensor. The linear part of the pixel response is limited to about 70 % of the saturation level.
The FPN as a function of exposure time is shown on the right axis. As long as the response of the sensor is within the linear region, the FPN is composed only out of dark current non-uniformities, and the relation between the FPN and the exposure time is linear as well. The empirical relationship is shown in Figure 1 (texp expressed in ms). But the FPN curve reaches a maximum at the moment the first pixels reach saturation, the FPN starts to become a combination of dark current FPN and anti-blooming FPN. At the point that all pixels saturate, the FPN is composed only out of anti-blooming FPN. Notice that the onset of saturation coincides with the maximum level of FPN (in this particular case because the anti-blooming FPN is lower than the dark-current FPN at the onset of anti-blooming), and this is also the point at which the sensor’s output starts deviating from a linear curve.
From the two formulas shown, it can be deduced that the FPN component is 1/6.6 or 15.2 % of the dark signal in the linear region and becomes 4.9 % of the full-well level when the pixels are saturated.
Figure 2 : Dark FPN versus dark signal.
The corresponding “PTC” curve is illustrated in Figure 2 : the FPN versus the dark signal is shown. The slope of the curve is perfectly equal to 1, and its intersection with the horizontal axis is defined by the ratio of the FPN to the average dark current. Both parameters are not influenced by the anti-blooming behavior of the sensor. As could be learned from Figure 1, the onset of anti-blooming occurs at the maximum level of the FPN (in this particular example !), and this point corresponds to 103.255 DN = 1800 DN.
Figure 3 : Dark current and its temporal noise component as a function of the exposure time.
Figure 4 : “PTC” of the sensor with only dark-current shot noise.
Figures 3 and 4 are showing the dark signal with its temporal noise component, being the dark-current shot noise. Clearly visible is the strong influence of the anti-blooming means on the response of the sensor, as well as on its temporal noise component. In Figure 4 the PTC is shown. Its slope should be equal to 0.5, and the crossing with the horizontal axis is defining the conversion gain of the system. As can be expected, the latter is not influenced by the anti-blooming !
As long as the sensor behaves in the linear region, the temporal noise is only composed out of shot noise. But at the onset of saturation, the temporal noise starts to vanish, and ultimately the PTC curve completely collapses. This is due to the fact that a saturated pixel cannot hold any variation on its signal level ! At the moment all pixels are saturated the temporal noise should be equal to zero, because in the pixel model used in this simulation, the noise of the analog chain is not yet included.
Next to the conversion gain, also the onset of saturation as well as the full-well level of the sensor can be deduced. Anti-blooming starts at 1800 DN, and the saturation level is equal to 103.450 DN = 2818 DN.
Conclusion : a clear maximum can be observed in the noise versus signal curves. In the case of the FPN, only a maximum occurs if the anti-blooming FPN is lower that the dark-current FPN. In the case of the temporal noise, there is always a maximum present in the PTC curve corresponding to the moment the sensor reaches saturation. The following new parameters can be deduced from these curves : full well, onset of anti-blooming, anti-blooming FPN, next to the ones that were discussed in earlier blogs : dark current FPN, dark-current shot noise level, conversion gain.
Next time the analog signal processing chain will be (partly) included by means of the addition of a DC-offset .
Albert 2009-10-21