## Archive for September, 2013

### How to Measure Full Well Capacity (1)

Friday, September 27th, 2013

The next parameter to be characterized is the full well capacity of the sensor.  But before any measurement or characterization can be done it is important to make clear what is the definition of the full well capacity (FWC).  To come to that point, let’s treat two different situations, the first one in which the ADC is setting the saturation of the sensor and the second one in which the ADC is not setting the saturation of the sensor.

1)    Saturation of the sensor is larger than maximum value of the ADC.  In such a case, most of time the camera/sensor designer is setting the maximum value of the ADC such that the complete ADC range covers the linear part of the sensor’s output response.  An example of a camera in which the ADC defines the maximum output level of the system is shown in Figure 1.

Figure 1 : Sensor output value as a function of exposure time, under a constant illumination level.

Shown is the sensor output as a function of the exposure time with a constant illumination level (at this stage of the discussion, the exact value of the light input is not important for this measurement, as long as it stays constant, so that various setting of the camera and/or sensor can be compared with each other).  On the right axis the integral non-linearity is shown as well.  As can be observed, the transition from a monotonically increasing output value to saturation goes pretty abruptly.  This is a clear indication that the ADC defines the saturation level.  Moreover, the value of the saturated output is equal to 216 – 1 = 65535 DN (216 is coming from the TIFF format).

For this example, the definition of the full well capacity is equal to the saturation level (of the ADC) minus the offset at zero seconds exposure time, or 65535 – 2106 = 63429 DN.  Taking into account the conversion gain of the sensor (3 DN/electron, for the TIFF format it is 64x larger than what can be measured at the output of the sensor), this results in a FWC = 19820 electrons.

2)    Saturation of the sensor is smaller than maximum value of the ADC.  In this case, the FWC needs a clear definition : is FWC referring to the saturation level of the sensor/camera, or is FWC referring to the maximum linear part of the sensor’s output swing ?  The former can be referred to a FWCsat, while the latter can be indicated by FWClin.  But then the question arises : how to define the linear part of the sensor’s output swing ?  Very often, FWClin is defined at the point where the deviation of the sensor’s output and an ideal straight line is maximum 3 %, or at the point where the sensor’s output is linear up to 97 % or better.  An example of a camera in which the ADC maximum output value is larger than the saturation level of the sensor is shown in Figure 2.

Figure 2 : Sensor output value as a function of exposure time, under a constant illumination level.

Shown on the left vertical axis is the sensor output as a function of the exposure time with a constant illumination level (the exact value of the light input is not important for this measurement, as long as it stays constant), shown on the right vertical axis is the corresponding integral non-linearity (INL).  As can be observed, the transition from a monotonically increasing output value to saturation goes smoothly.  This is a clear indication that the ADC is NOT defining the saturation level of the system.

For this example, the definition of the full well capacity at saturation is equal to the saturation level minus the offset at zero seconds exposure time, or 51880 – 1602 = 50278 DN.  Taking into account the conversion gain of the sensor (1.5 DN/electron), this results in a FWCsat = 33518 electrons.

But as mentioned before, this is only half of the story, because the sensor’s response is very nonlinear close to saturation.  For that reason the linearity (INL) of the sensor is characterized and plotted in Figure 2 as well.  At the point where the real output characteristic deviates 3 % from its regression line, the FWClin is defined.  In this example, the following number can be found : 45860 – 1602 = 44258 DN, translating in FWClin = 29505 electrons.

It should be clear that this last number is very much depending on the definition of FWClin.  If the 3 % deviation is shifted to 1 %, the value for the FWClin will become smaller, or if the 3 % deviation is shifted to 5 %, the opposite becomes valid.

Note : the data shown in Figures 1 and 2 are obtained from the same sensor, with the same light input.  The difference between the two measurements is a difference in camera setting, such that the analog gain of the sensor and the reference voltage of the ADC result in an overall camera gain difference of a factor of 2.

Explained in this blog is the measurement of FWC based on linearity measurements.  Again it can be learned that the values obtained for the FWC strongly depend on the exact definition of the full well capacity.  Lesson to take away : if the FWC is specified in an image sensor’s datasheet, first ask yourself “How is the FWC defined ?”.

See you next time !

Albert, 27-09-2013.

### Playing Time (3)

Monday, September 9th, 2013

Once more thanks for all the reactions.

I checked the reactions again this morning, and it is clear that the right answer/suggestion came from David San Segundo Bello (imec).  Already in one of the very first reactions, he mentioned a possible drift of the LED light source due to an AC variation on top of the DC voltage.  Afterwards Guy Meynants (CMOSIS) repeated the answer of David, but also added to it the method to check it out, namely by means of noise measurements.  That actually completed the story.  So I think it is fair to give both guys a bottle of wine.

Albert, 09-09-2013.

### Playing Time (2)

Friday, September 6th, 2013

It was surprising to see the amount of reactions on the previous “Playing Time” blog.  Thanks for all the remarks, questions, suggestions, also through the www.image-sensors-world.blogspot.com web-site.

Remember what the issue was : measurements were done with a constant LED light input at two different settings :

–       gain = 1, exposure time = 42.24 ms, 100 images, and,

–       gain = 4, exposure time = 10.56 ms, 100 images.

A constant switch between the two settings was realized, and in total 21 (times 100 images) measurements were done to check the reproducibility.  Based on the numbers shown, one would expect the same output in all situations.

A first issue, being the offset that does not scale with the gain, was corrected by subtracting the (measured seperately) offset for all measurements.  A second issue, being the incorrect ratio of gain setting (theory 1:4, reality 1:3.8) was corrected, and then the final result is shown in Figure 1.

Figure 1 : Sensor output values (corrected for the offset and corrected for incorrect gain setting) as a function of measurement number (each dot represents the average value of a 50×50 ROI of 100 images).

To find the root cause of the fluctuations fo the output signal, the temporal noise on pixel level is calculated, this excludes the FPN of the pixels.  The result of the measurement is shown in Figure 2.

Figure 2 : Noise calculations of the measurements performed in Figure 1 (each dot represents the average value noise value of a 50×50 ROI of 100 images).

Notice that, although the output signal in both cases is expected to be the same, that is not the case for the noise !  The temporal noise is dominated by photon shot noise and if the cases of “gain = 1” are set as the references, then the photon shot noise (expressed in electrons) for the cases of “gain = 4” is a factor of 2 less in the charge domain (4 times less photons).  But with a gain setting that is 4 times higher, the temporal noise in the digital domain becomes a factor of 4 higher.  Compared to the cases of “gain = 1”, the noise in the digital domain of the cases of “gain = 4” will be factor of 2 higher.  This is pretty much the case for the measurements (proving that the measurements and calculations were done right).

If the noise of the “gain = 4” cases is reduced by a factor of 2, and if then the noise results are plotted together with the output signals of the sensor, Figure 3 is generated.

Figure 3 : Measured output signal (corrected where needed) and calculated temporal noise (adapted where needed) of the measurements performed.

With a bit of imagination, a similar pattern that was present in the measurements of the output signal can be found in the calculated temporal noise.  There is enough correlation between both to conclude that the changes in the output signal was coming from the light source, because the fluctiations are reflected in the (photon) shot noise results as well.  (After some experiments, it was found that the power supply for the LEDs was causing the issues, because its output voltage was not stable over time.)

This exercise illustrates the power of using noise measurements as a diagnostic tool !

Albert, 06-09-2013.

### Status Imaging Forum “ADCs for Imagers”

Tuesday, September 3rd, 2013

Due to the large interest for the first Imaging Forum “ADCs for Imagers”, two sessions are now scheduled : the first one on 16 & 17 Dec. 2013, the second one on 19 & 20 Dec. 2013.  Unfortunately a few people had to cancel their pre-registration, so a few seats (for both sessions) are back available for those who still are interested.  Please notice that a third session will not be organized.  In the year 2014, another forum will be planned, but with another subject !

Albert, 3-9-2013.