During the last blog about the study of the PTC (Photon Transfer Curve) I promised to continue with the gain of the on-chip PGA (Programmable Gain Amplifier). But in the mean time I changed my mind. The PGA gain will follow at a later stage. At this moment I would like to focus on the noise of the pixel : FPN (coming from some residual off-set) and the temporal noise (coming from remaining 1/f noise that is not cancelled by the CDS, Johnson noise in the pixel, and maybe kTC noise if not cancelled by CDS). The FPN due to dark current non-uniformities (DSNU) is already discussed in an earlier blog, while the FPN from light sensitivity non-uniformities (PRNU) will be addressed in a future one.
By means of the mathematical model 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 (notice that all noise sources are set to zero, except the dark current shot noise, the DSNU, pixel FPN and pixel temporal noise) :
- 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 3 contains the average dark signal (left axis), 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 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 these exposure times that do not saturate the pixel. This indicates 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 !) shown in Figure 1 holds for the linear part of the curve. Notice that the expression as well as the curve show the presence of the DC offset (introduced by the analog circuitry).
The curve of the fixed-pattern noise, shown on the right axis, is not influenced by this DC offset : for an exposure time of 0 s, the FPN is 0 DN as well.
From the two formulas shown, it can be calculated 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. The latter is representing the pixel non-uniformities in saturation.
Figure 2 : Dark FPN versus dark signal.
The corresponding “PTC” curve is illustrated in Figure 2 : the FPN versus the (dark) signal is shown. From this PTC curve several interesting parameters can be deduced :
- The DSNU can be found to be equal to : 1/100.814 = 0.153 or 15.3 % at 30oC,
- The pixel FPN (without DSNU) : 10-0.196 DN = 0.631 DN (after finding the conversion gain, this corresponds to 3.9 e-),
- The saturation non-uniformity : 102.140 = 138 DN (after finding the conversion gain, this corresponds to 862 e-).
Figure 3 : Dark current and its temporal noise component as a function of the exposure time.
Figure 3 is showing the signal and the temporal noise as function of the exposure time. Not really that much new information can be extracted from these graphs, except the minimum temporal pixel noise being equal to 1.63 DN.
Figure 4 : “PTC” of the sensor.
Figure 4 shows the real Photon Transfer Curve, in which the temporal noise is shown as a function of the signal. The curve clearly shows the part that is independent of the dark signal (with a slope of 0), the part that is directly depending on the dark signal (with a slope of 0.5) and the part showing a collapsing curve indicating the saturation of the pixels.
From the PTC curve the following parameters can be deduced :
- The conversion gain, being equal to 1/100.810 DN/e- = 0.155 DN/e-,
- The total temporal pixel noise (without any influence of the dark current) = 100.213 DN = 1.63 DN = 10.5 e-,
- The onset of anti-blooming = 103.32 DN = 2090 DN = 13480 e-,
- The saturation level of the pixels = 103.45 DN = 2818 DN = 18180 e-,
As could be expected : additional pixel noise is popping up in the flat part of the PTC curves. In these regions where the pixel noise is the dominant noise source (and where it is not overruled by dark-current shot noise or by saturation non-uniformities), its value can be easily deduced by means of the PTC curves.
Next time the effect of column noise will be investigated.
Albert 2009-12-19