## Archive for April, 2013

### How to Measure Non-Linearity ? (3)

Monday, April 22nd, 2013

After checking out the linearity of the sensor/camera with a gain set to unity, in this blog the linearity will be checked in the case the sensor/camera gain is set to 2 and 4.  In all three cases (gain = 1, 2 and 4) the linearity will be checked for an output swing of the sensor between 10 % and 90 % of the saturation level.  Figures 1-3 contain the obtained results.

Figure 1 : Camera output and INL for an output range between 10 % and 90 % of saturation and a sensor/camera gain setting equal to 1.

Figure 2 : Camera output and INL for an output range between 10 % and 90 % of saturation and a sensor/camera gain setting equal to 2.

Figure 3 : Camera output and INL for an output range between 10 % and 90 % of saturation and a sensor/camera gain setting equal to 4.

Some remarks :

–       All output signals in all figures have a fairly abrupt transition from their linear behaviour towards saturation.  This is due to the fact that the ADC is defining the maximum output signal and not the pixel or the source-follower.  This was already the case with the measurements presented in the previous blog with gain = 1.  So by increasing the gain of the sensor/camera, this saturation effect does not change,

–       All definitions used in this characterization of the INL are described in the previous blogs,

–       The results reported here come from an group of 50 x 50 pixels, and the graphs show the average non-linearity of these 2500 pixels,

–       The three graphs show (more or less) a similar behaviour of the non-linearity.  It should be noted that not only the gain of the sensor/camera is changed, but also the amount of light is changed by adapting the exposure time.  The light source itself is not changed.  Although the graphs have a different horizontal axis, all three of them :

• Cover different output swings of the photodiode,
• Cover different output swings of the floating diffusion,
• Cover the same output swing of the output amplifier.

With a bit of imagination, one can recognize that the INL shows more or less the same behaviour for all 3 situations and in all cases, and it remains fairly low, even if the gain is increased by a factor of 4.  This observation can lead to the conclusion that the non-linearity measured is not due to the non-linearity in the pixel, but most probably coming from the amplifier located in the (analog) output chain (a so-called V/V non-linearity).

Till now, the INL is characterized within 4 different sections of the output swing (1%-99%, 5%-95%, 10%-90%, 20%-80%) and for 3 different settings of the gain (1, 2 and 4).  All results are summarized in the table below.

 Gain Output swing (%) Max. INL (%) Min. INL (%) Average INL (%) St.Dev. (%) Offset (DN) 1 1-99 0.62 -0.74 0.68 0.21 2198 1 5-95 0.57 -0.38 0.47 0.16 2147 1 10-90 0.52 -0.33 0.43 0.16 2113 1 20-90 0.43 -0.35 0.39 0.14 1919 2 1-99 0.33 -0.42 0.38 0.16 1684 2 5-95 0.28 -0.44 0.36 0.16 1650 2 10-90 0.27 -0.47 0.37 0.14 1609 2 20-90 0.31 -0.41 0.36 0.13 1576 4 1-99 0.43 -0.25 0.34 0.16 1029 4 5-95 0.40 -0.25 0.33 0.14 1013 4 10-90 0.33 -0.22 0.27 0.11 982 4 20-90 0.22 -0.19 0.20 0.08 893

All data is coming from the same sensor and from the same group of pixels, but a lot of different numbers can be observed.  So the same conclusion can be made as last time : in the case of INL characterization, it is of crucial importance to specify all parameters and settings of the sensor/camera as well as the conditions for measuring/calculating the integral non-linearity.

What’s up next time ? Then the focus will be put on the INL of the individual pixels.

Albert, 22-04-2013.

### How to Measure Non-Linearity ? (2)

Tuesday, April 9th, 2013

Following-up on the previous blog with the definitions of non-linearity, this time the first results will be shown and discussed, focusing on the integral non-linearity or INL of the solid-state camera.

To perform the measurements, the amount of light coming to the sensor is changed by varying the exposure time under constant light conditions (green LEDs).  The amount of light that is coming to the sensor is not measured.  All evaluations are done with a camera without lens, and with a window containing 50 x 50 pixels.  Unless otherwise indicated, all results refer to the average value of these 2500 pixels.

In Figures 1-4, the measurements and calculations are shown which are obtained when the gain of the camera was set to 1.  The difference between the various figures is the sensor output range over which the INL is calculated : Figure 1 from 1 % to 99 % of saturation, Figure 2 from 5 % to 95 % of saturation, Figure 3 from 10 % to 90 % of saturation and Figure 4 from 20 % to 80 % of saturation.  All data about the INL are included in the figures.

Figure 1 : Camera output and INL for an output range between 1 % and 99 % of saturation.

Figure 2 : Camera output and INL for an output range between 5 % and 95 % of saturation.

Figure 3 : Camera output and INL for an output range between 10 % and 90 % of saturation.

Figure 4 : Camera output and INL for an output range between 20 % and 80 % of saturation.

Some remarks :

–       All output signals in all figures have a fairly abrupt transition from their linear behaviour towards saturation.  This is due to the fact that the ADC is defining the maximum output signal and not the pixel or the source-follower,

–       The output data of the camera is formatted into 16bits TIFF, the sensor has an ADC with 10 bits, and to convert the 10 bits into 16 bits, simply 6 bits are being added to every pixel output,

–       Max. INL indicates the maximum positive deviation of the camera output compared to the regression line drawn through the measurement points, Max. INL is expressed in % of the saturation level (= 216 – offset),

–       Min. INL indicates the maximum negative deviation of the camera output compared to the regression line drawn through the measurement points, Min. INL expressed in % of the saturation level (=216 – offset),

–       Average INL is the mean of the absolute value of the two foregoing parameters, Average INL is expressed in % of the saturation level (=216 – offset),

–       Standard Dev. is the standard deviation of all INL data points, Standard Dev. is expressed in % of the saturation level (=216 – offset),

–       Offset : refers to the offset of the camera output, found by extrapolating the regression line to an exposure time equal to zero seconds,

–       All parameters expressed as a percentage of the saturation level, can also be expressed in LSB, in that case 1 LSB of the sensor corresponds to about 0.1 %.

What can be learned from the four figures is the fact that all INL parameters are becoming better (= smaller) if the output range over which the INL is calculated, is becoming shorter or more limited.  This is not surprising because very often, the largest non-linearities of a sensor can be found in the lower range of its output and the higher range of its output.  This observation could give rise to the idea to limit the output range even further to calculation the INL …  So it should be clear that together with the INL specification, it is necessary to mention over which output range of the sensor/camera the INL is specified.

What’s up next time ? INL in combination with gain setting of the camera.

Albert, 09-04-2013.

### Announcement of FIRST IMAGING FORUM, Dec. 16th-17th, 2013.

Thursday, April 4th, 2013

Mark now already your agenda for the very first solid-state imaging forum.  It is scheduled for Dec. 16-17th 2013.  Again another conference ? NO, absolutely not.

The solid-state imaging forum will be a high-level, technical, short course focusing on one particular hot topic in the field of solid-state imaging.  The audience will be strictly limited to 30 people, just to stimulate as much as possible the interaction between the participants and speaker(s).  The subject of the first forum will be : “ADCs for Image Sensors”.  Only world-leading and independent expert(s) will be cont(r)acted to talk at the forum.  At this moment negotiations with a hotel in the Netherlands are taking place to have the forum close to the airport of Amsterdam.

More information will follow in the coming weeks or months, but I wanted to share this announcement with you as early as possible to make sure you can keep your agenda free on these days.

Albert,

04-04-2013.