What is the status of the CMOS pixel model so far ?  In Figure 1 the general overview of the pixel structure, the column circuit together with the chip-level programmable gain amplifier (PGA) and analog-to-digital converter (ADC) is shown. 

Figure 1: Basic configuration as used in the CMOS pixel model.

At this moment the following parameters are included in the model : dark current, dark current non-uniformities, influence of the temperature, anti-blooming capability, anti-blooming or saturation level non-uniformity, and in this blog the DC-offset introduced by the electronic circuitry will be included.  Because this DC-offset is equal for all pixels, it should not add any additional FPN.  Neither will it change the temporal noise, because the DC-offset is constant over time.  But the presence of such an additional DC value can deteriorate the PTC curves.  As will be shown, to construct the PTC curves the DC-offset needs to be subtracted from the obtained pixel signal.

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 :

-       Figure 2 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 3 shows the dark fixed-pattern noise versus the dark signal, based on the data shown in Figure 2.

-       Figure 4 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 5 shows the dark current temporal noise versus the dark signal, based on the data shown in Figure 4. 

 Figure 2 : Dark current and its FPN component as a function of the exposure time.

As can be seen in Figure 2, the average dark signal is still linear with the integration time, indicating that the dark current is responsible for the signal in dark.  The linear relationship between the dark signal and the exposure time (t_exp expressed in ms !) shown in Figure 2, holds for the linear part of the curve.  Notice that the expression as well as the curve show the presence of a DC-offset.  The curve of the fixed-pattern noise, shown on the right axis, is not influenced by this DC-offset. 

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.  As could be expected, neither of these values are influenced by the presence of the DC-offset.  

Figure 3 : Dark FPN versus dark signal, with and without the compensation of the DC offset.

The corresponding “PTC” curve is illustrated in Figure 3 : the FPN versus the dark signal is shown.  Notice the irregular behavior of the curve in the case the “measured” data is not compensated for the DC-offset.  The curve is no longer linear and is much steeper than expected.  But when the DC-offset is subtracted from the signal values (on the horizontal axis), again the “perfect” PTC is becoming available.  The value used for the DC-offsetcompensation is 512.04 DN as can be deduced from Figure 2.

 

 

 

 Figure 4 : Dark current and its temporal noise component as a function of the exposure time.

From Figure 4, showing the signal and the temporal noise as function of the exposure time, the same conclusion can be made as from Figure 2 : the presence of any DC-offset has no influence on the temporal noise component, only the absolute value of the signal is changed.

Figure 5 : “PTC” of the sensor, with and without the compensation of the DC offset.

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 10^3.450 DN = 2818 DN.

 

Conclusion : on one hand the presence of any DC-offset (being equal for all pixels) has no influence on the fixed-pattern noise, neither on the temporal noise behavior of the sensor.  On the other hand it needs to be compensated in the case PTC curves are to be generated.

 

Next time the effect of an extra gain (in the programmable gain amplifier) will be explored.

 

Albert 2009-11-02

This entry was posted on Tuesday, November 3rd, 2009 at 7:41 am and is filed under Uncategorized. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.