Long time no see ?  Right !  The preparation of my new course (Hands-on Evaluation of Sensors and Cameras) got first priority and it took more time than expected.  But here we are again with the continuation of the PTC study.

When discussing the PTC in dark, several blogs were devoted on added pixel noise, column noise, row noise and output stage noise.  With the PTC in light, all these noise sources (called PORC noise : Pixel, Output, Row, Column) will be added at once.  All PORC components do contain fixed-pattern as well as temporal noise.  In this blog the focus will be put on the fixed-pattern components, next time the temporal noise will be discussed.

The hardcore fanclub of this blog should know by now the strategy of this study : 100+ light images are generated, the images have a size of 160 x 120 pixels.  Each set of 100+ images is taken at an exposure time that was varied from 0 s till 60 s.  So in total, several thousand of images were artificially generated and analyzed. (A computer can be very patient !) 

The result of this exercise can be seen in the following figures :

-       Figure 1 contains the average signal (left axis) of the generated images and its FPN noise component (right axis) as a function of the integration time (horizontal axis).

-       Figure 2 shows the fixed-pattern noise versus the signal, based on the data shown in Figure 1.  

-       Figure 3 contains the average signal on row level as a function of the integration time. 

-       Figure 4 shows the average signal on column level as a function of the integration time.   

Figure 1 : Output signal and its FPN component as a function of the exposure time.

 As can be seen in Figure 1 :

-       in the first part of the curve for small values of the exposure time, the average output signal is linear with the integration time.  The relation between the output signal and the exposure time (t_exp expressed in ms !) is also indicated in Figure 1,

-       also in the first part of the curve, the FPN linearly increases with the exposure time, indicating that the FPN is due to photo-generation and/or dark-current generation.  The empirical relationship of the linear part of the FPN is shown in Figure 1 (t_exp expressed in ms),

-       in the second part of the curve for larger values of the exposure time, the output signal reaches a saturation level due to the built-in anti-blooming capability of the pixels,

-       also in the second part of the curve, the FPN is constant, referring to the FPN due to the non-uniformities in saturation level.

From the two formulas shown in Figure 1, it can be deduced that the FPN component in the linear region (primarily PRNU) is 0.231/8.160 = 0.0283 or 2.83 % of the output signal.  The anti-blooming non-uniformities are equal to 141 DN.  In comparison to 3372 DN (saturation level in Figure 1) - 512 DN (offset) = 2860 DN saturation level, this is equal to 4.93 %.

Figure 2 : Light FPN versus output signal.

The corresponding “PTC” curve is illustrated in Figure 2 : the FPN (on a logarithmic vertical axis) versus the output signal (corrected for the offset and on a logarithmic horizontal axis) is shown.  From Figure 2, the following can be learned :

-       the minimum FPN on pixel level is equal to 10^0.320 DN = 2.09 DN.  This fixed-pattern noise is coming from the FPN generated by the pixel circuitry, the column circuitry and the row circuitry,

-       the slope of the curve should be equal to 1, because of the linear relationship between the (logarithmic of the) output signal and the (logarithmic of the) light FPN or PRNU.  The actual value of the slope is shown in Figure 2 and is a good match to the theory !

-       the intersection of the curve with the horizontal axis can deliver the amount of light FPN or PRNU present in the system : with an intersection at 1.493 DN, this gives PRNU = 1/10^1.493 = 0.0321 or 3.21 %.  This result is in good agreement with the number obtained from Figure 1,

-       saturation level : 10^3.456 DN = 2858 DN,

-       FPN at saturation level : 10^2.149 = 140.9 DN.

Comparing the numbers obtained from Figure 1 with the data of Figure 2, it can be concluded that they are almost equal to each other.  By itself this should not be surprising, because the two curves are based on the same data.

Figure 3 : FPN on row level as a function of the exposure time.

Figure 3 shows the FPN on row level : the average value of all pixels on each row is calculated, delivering an average row signal.  Next the standard deviation on the average row signals is calculated, resulting in the FPN on row level.  The graph of FPN versus the exposure time (expressed in msec and on a logarithmic scale) can be explained as follows :

-       for very low values of the exposure time, the FPN is dominated by the FPN introduced by the row circuitry, and this component is independent of the exposure time.  It can be found that the row FPN is equal to 10^-0.272 DN = 0.11 DN,

-       for larger values of the exposure time, the FPN proportionally increases with the exposure time.  In this region, the PRNU on pixel level is the dominant source of FPN, even if all pixels within a row are averaged.  The PRNU (on row level !) found is equal to 1/S_o at the moment the noise is equal to 1 DN.  This situation happens at an exposure time equal to 10^1.620 ms = 41.7 ms.  From Figure 1, it can be deduced that for an integration time of 41.7 ms a signal value equal to 340.2 DN can be found.  Or the row level FPN is equal to 1/S_o = 1/340.2 = 0.0029 = 0.29 %, which is a factor of 3.21 /0.29 = 11.1 lower than the same parameter on pixel level,

-       the FPN curve reaches a maximum and the FPN moves to a steady-state value of 10^1.061 DN = 11.51 DN due to the anti-blooming non-uniformities on row level.  This value is a factor 141/11.51 = 12.2 lower than the same parameter on pixel level.

Notice the reduction of the FPN (in the non-saturated region as well as in the saturated region) from pixel level to row level.  This value can be explained as follows : the row noise is obtained after averaging the noise of 160 pixel values into one row value : sqrt(160) = 12.6 !

Figure 4 : FPN on column level as a function of the exposure time. 

Figure 4 shows the FPN on column level : the average value of all pixels on each column is calculated, delivering an average column signal.  Next the standard deviation on the average column signals is calculated, resulting in the FPN on column level.  The graph of FPN versus the exposure time (expressed in msec and on a logarithmic scale) can be explained as follows :

-       for very low values of the exposure time, the FPN is dominated by the FPN introduced by the column circuitry, and this component is independent of the exposure time.  It can be found that the column FPN is equal to 10^0.284 DN = 1.92 DN,

-       for larger values of the exposure time, the FPN proportionally increases with the exposure time.  In this region, the PRNU on pixel level is the dominant source of FPN, even if all pixels within a column are averaged.  The PRNU (on column level !) found is equal to 1/S_o at the moment the noise is equal to 1 DN.  This situation happens at an exposure time equal to 10^1.631 ms = 42.8 ms.  From Figure 1, it can be deduced that for an integration time of 42.8 ms a signal value equal to 349.2 DN can be found.  Or the column level FPN is equal to 1/S_o = 1/349.2 = 0.0029 = 0.29 %, which is a factor of 3.21 /0.29 = 11.1 lower than the same parameter on pixel level,

-       the FPN curve reaches a maximum and the FPN moves to a steady-state value of 10^1.091 DN = 12.33 DN due to the anti-blooming non-uniformities on column level.  This value is a factor 141/12.33 = 11.4 lower than the same parameter on pixel level.

Notice the reduction of the FPN (in the non-saturated region as well as in the saturated region) from pixel level to column level.  This value can be explained as follows : the column noise is obtained after averaging the noise of 120 pixel values into one column value : sqrt(120) = 11.0 !

The total FPN on pixel level, found to be equal to 2.09 DN, contains the contributions of the pixel circuitry, the row circuitry (= 0.11 DN) and the column circuitry (= 1.92 DN).  Once the total FPN as well as the row FPN and column FPN are known, the contribution of the pixel circuitry to the total FPN can be calculated to be equal to (2.09² - 0.11² - 1.92²)^0.5 = 0.82 DN. 

Conclusion : it is amazing how much basic sensor information can be extracted from simple uniformly illuminated images without knowing the amount of light falling on the sensor.  This is one of the key advantages of the PTC : without doing any absolute measurement of the light input, the sensor can be easily characterized. 

What will be next ? The analysis of the temporal noise components in the presence of PORC (= pixel, output, row and column) noise.

Albert 2010-08-22

In the previous blog the dark current was combined with the light input.  But in the example described, the photo-generated signal was much larger than the dark-current generated signal.  If that is the case all parameters of the sensor could be simply extracted from the PTC.  As a kind of follow-on, in this blog the situation will be analyzed when the photo-generated signal is of the same size as the dark-current generated signal.  What can be learned from the PTC in such a case ?  In comparison with the previous blog, this time the light input is lowered by a factor 100, and as usual, 100+ dark images are generated.  The exposure time was varied from 0 s till 60 s.

The result of this exercise can be seen in the following figures :

-       Figure 1 contains the average signal (left axis) of the generated images and its FPN noise component (right axis) as a function of the integration time (horizontal axis).

-       Figure 2 shows the fixed-pattern noise versus the signal, based on the data shown in Figure 1.  

-       Figure 3 contains the average signal (left axis) of the generated images and its temporal noise component (right axis) as a function of the integration time (horizontal axis). 

-       Figure 4 shows the temporal noise versus the signal, based on the data shown in Figure 3.

 Figure 1 : Output signal and its FPN component as a function of the exposure time.

 As can be seen in Figure 1 :

-       in the first part of the curve for small values of the exposure time, the average output signal is linear with the integration time.  The relation between the output signal and the exposure time (t_exp expressed in ms !) is also indicated in Figure 1,

-       also in the first part of the curve, the FPN increases linearly with the exposure time, indicating that the FPN is due to photo-generation and/or dark-current generation.  The empirical relationship of the linear part of the FPN is shown in Figure 1 (t_exp expressed in ms),

-       in the second part of the curve for larger values of the exposure time, the output signal obtains a saturation level due to the built-in anti-blooming capability of the pixels,

-       also in the second part of the curve, the FPN is constant, referring to the FPN due to the non-uniformities in saturation level,

-       between the linear part and the saturated part of the FPN curve, a dip can be noticed.  This dip is the result of the transition from PRNU/DSNU dominated FPN to saturation-level dominated FPN.  As soon as the pixels go into the anti-blooming mode, the PRNU and DSNU effects become smaller, but as soon as the first pixels reach their saturated values, the non-uniformities in saturation take over to determine the total FPN.

From the two formulas shown in Figure 1, it can be deduced that the FPN component in the linear region (PRNU + DSNU) is 0.010/0.147 = 0.0680 or 6.8 % of the output signal.  By means of a single measurement, it is not possible to distinguish between PRNU and DSNU.  The anti-blooming non-uniformities are equal to 142 DN.  In comparison to 3380 DN (saturation level in Figure 1) - 512 DN (offset) = 2868 DN saturation level, this is equal to 4.95 %.

Figure 2 : Light FPN versus output signal.

 The corresponding “PTC” curve is illustrated in Figure 2 : the FPN versus the output signal is shown.  The “PTC” of the previous blog is included as a reference (dark coloured line).  From Figure 2, the following can be learned :

-       its slope of the curve remains equal to 1, because of the linear relationship between the (logarithmic of the) output signal and the (logarithmic of the) light and/or dark FPN.  The actual value of the slope is a good match to the theory !

-       the intersection of the curve with the horizontal axis (has shifted to the left, and) can deliver the amount of FPN present in the system : with an intersection at 1.152 DN, this gives a = 1/10^-1.152 = 0.0704 or 7.04 %.  This result is in good agreement with the number obtained from Figure 1.  Also in this case, it is impossible to distinguish between PRNU and DSNU based on a single measurement,

-       saturation level : 10^3.46 DN = 2884 DN,

-       FPN at saturation level : 10^2.15 = 141.2 DN.

Figure 3 : Output signal and its temporal noise component as a function of the exposure time.

 Figure 4 : “PTC” of the sensor.

Figure 3 shows the output signal with its temporal noise component, being the combination of the photon shot noise and the dark shot noise, as a function of the exposure time.  In figure 4 the Photon Transfer Curve is illustrated.  For comparison reasons, also the PTC of the previous blog is added into Figure 4.  The difference between the two curves is hardly noticabe !

The following parameters can be deduced from the PTC :

-       conversion gain : 1/10^0.810 = 0.153 DN/electron,

-       output level : 0.147·t_exp = 147 DN/pixel/second = 961 electrons/pixel/second at 30^oC (this is the temperature at which the images are being generated),

-       on-set of anti-blooming : 10^3.26 DN = 1819 DN = 11,889 electrons,

-       saturation level : 10^3.45 DN = 2818 DN = 18,418electrons.

Knowing the conversion gain and/or the output signal, also the FPN can be calculated to be equal to : 0.010·t_exp = 10 DN/pixel/second = 65 electrons/pixel/second at 30^oC.

Conclusion : it does not matter what the ratio is between PRNU and DSNU, it will not influence the Photon Transfer Curve because the PTC is based on the temporal noise parameters of the sensor.  If a similar analysis is done on the FPN, the story becomes different, because DSNU and PRNU both contribute to the overall FPN.

What will be next ? Then the PORC (= pixel, output, row and column) noise will be added on top of photo- and dark-current generation.  It will become more complex, more challenging but most of all, more interesting !

Albert 2010-07-12

When reading the pixels, they basically contain two types of signals : the photon-generated charge (with its FPN and temporal noise contribution) and the dark-current generated charge (with its FPN and temporal noise contribution).  In this blog the influence of these two signal components with their associated noise sources will be studied  To do so, the same structure as described earlier is used, and, at each chosen exposure time, 100+ dark images are generated.  The exposure time was varied from 0 s till 0.6 s.

The result of this exercise can be seen in the following figures :

-       Figure 1 contains the average signal (left axis) of the generated images and its FPN noise component (right axis) as a function of the integration time (horizontal axis).

-       Figure 2 shows the fixed-pattern noise versus the signal, based on the data shown in Figure 1.  

-       Figure 3 contains the average signal (left axis) of the generated images and its temporal noise component (right axis) as a function of the integration time (horizontal axis). 

-       Figure 4 shows the temporal noise versus the signal, based on the data shown in Figure 3.   

Figure 1 : Output signal and its FPN component as a function of the exposure time.

 As can be seen in Figure 1 :

-       in the first part of the curve and for small values of the exposure time, the average output signal is linear with the integration time.  The relation between the output signal and the exposure time (t_exp expressed in ms !) is also indicated in Figure 1.

-       in the second part of the curve and for larger values of the exposure time, the output signal obtains a saturation level due to the built-in anti-blooming capability of the pixels.   

The FPN noise as a function of exposure time is shown on the right axis of Figure 1.  Because the FPN is composed only out of photon response non-uniformities and/or dark current non-uniformities, the relation between the FPN and the exposure time is linear as well, up till the point that the pixels go into anti-blooming.  The empirical relationship of the linear part of the FPN is shown in Figure 1 (t_exp expressed in ms).  From the two formulas shown, it can be deduced that the PRNU component is 0.243/8.177 = 0.02972 or 3.0 % of the output signal.

Figure 2 : Light FPN versus output signal.

 The corresponding “PTC” curve is illustrated in Figure 2 : the FPN versus the output signal is shown.  From Figure 2, the following can be learned :

-       its slope should be equal to 1, because of the linear relationship between the (logarithmic of the) output signal and the (logarithmic of the) light and/or dark FPN.  The actual value of the slope is a good match to the theory !

-       the intersection of the curve with the horizontal axis can deliver the amount of fixed-pattern noise present in the system : with an intersection at 1.507 DN, this gives a = 1/10^-1.507 = 0.0311 or 3.11 %.  This result is in good agreement with the number obtained from Figure 1.

-       saturation level : 10^3.46 DN = 2884 DN,

-       FPN at saturation level : 10^2.15 = 141.2 DN.

  Figure 3 : Output signal and its temporal noise component as a function of the exposure time.

 Figure 4 : “PTC” of the sensor.

Figure 3 shows the output signal with its temporal noise component, being the combination of the photon shot noise and the dark shot noise, as a function of the exposure time.  In figure 4 the Photon Transfer Curve is illustrated.  The following parameters can be deduced :

-       conversion gain : 1/10^0.814 = 0.153 DN/electron,

-       output level : 8.177·t_exp = 8177 DN/pixel/second = 53,444 electrons/pixel/second at 30^oC (this is the temperature at which the images are being generated),

-       on-set of anti-blooming : 10^3.26 DN = 1819 DN = 11,889 electrons,

-       saturation level : 10^3.45 DN = 2818 DN = 18,418electrons.

Knowing the conversion gain and/or the output signal, also the FPN can be calculated to be equal to : 0.243·t_exp = 243 DN/pixel/second = 1588 electrons/pixel/second at 30^oC.

Conclusion : comparing the “measured” and calculated data presented in this blog with the data obtained in the previous blog it will be clear that adding the dark current to the sensor does not influence the measured data.  Actually the reason is simple : the photon-generated components (signal, shot noise, PRNU) are much larger than the dark-current-generated components (signal, shot noise, DSNU).  But what happens to the PTC curve when the situation is considered where the photon-generated and dark-current generated signal components are of comparable size ?  If you want to know the answer to that question you have to wait till the next blog.

Albert 2010-06-28

After switching on the light in the previous blog, it is now time to take a closer look to the effect of the light fixed-pattern noise, also known as photo-response non-uniformity or PRNU.  To do so, the same structure as described earlier is used.  The light input (and its shot noise component) is unchanged, only the extra light FPN is added to the model. 

Again, at each chosen exposure time, 100+ dark images are generated.  The exposure time was varied from 0 s till 0.6 s. The result of this exercise can be seen in the following figures :

-       Figure 1 contains the average signal (left axis) of the generated images and its FPN noise component (right axis) as a function of the integration time (horizontal axis).  To find the FPN noise, all images were averaged on pixel level and the standard deviation on the resulting image was calculated.  This method allows obtaining the FPN, because the calculation is done on the averaged pixel signals and consequently, the temporal noise component is excluded (or at least strongly reduced). 

-       Figure 2 shows the fixed-pattern noise versus the signal, based on the data shown in Figure 1.  Figure 2 is very similar to the Photon Transfer Curve, keeping in mind that this time the FPN is shown.

-       Figure 3 contains the average signal (left axis) of the generated images and its temporal noise component (right axis) as a function of the integration time (horizontal axis).  Because only the temporal noise is shown in this graph, it is exactly the same curve as Figure 2 in the previous blog,

-       Figure 4 shows the temporal noise versus the signal, based on the data shown in Figure 3.    

 Figure 1 : Output signal and its FPN component as a function of the exposure time.

 As can be seen in Figure 1,

-       in the first part of the curve for small values of the exposure time, the average output signal is linear with the integration time, indication the increase of output signal under the influence of a larger amount of photons impinging the pixel.  The relation between the output signal and the exposure time (t_exp expressed in ms !) is also indicated in Figure 1.

-       in the second part of the curve for larger values of the exposure time, the output signal obtains a saturation level due to the built-in anti-blooming capability of the pixels.   

The FPN noise as a function of exposure time is shown on the right axis.  Because the FPN is composed only out of photo response non-uniformities, the relation between the FPN and the exposure time is linear as well, up till the point that the pixels go into anti-blooming.  The empirical relationship of the linear part of the FPN is shown in Figure 1 (t_exp expressed in ms).  From the two formulas shown, it can be deduced that the PRNU component is 0.243/8.112 = 0.02995 or 3.0 % of the output signal.

Figure 2 : Light FPN versus output signal.

The corresponding “PTC” curve is illustrated in Figure 2 : the FPN versus the output signal is shown.  The measured signal of the pixel, S_tot (expressed in DN, digital number) can be written as :

                                               S_tot = k · N_o

with k being the overall gain [DN/electron] of the image sensor and N_o [electrons] the number of optically-generated electrons.  The total noise at the output of the sensor, n_tot, is related to the noise in the pixel by (all noise sources are set to zero, except the photo-current shot noise and the light FPN) :

                                                n_tot = k ·(n_o² + n_PRNU²)^0.5

with n_o and n_PRNU being the photon shot noise and the Photo Response Non-Uniformity (PRNU) or light FPN respectively.  In the case only FPN is considered (as shown in Figure 2 because the temporal noise is averaged out), the relation between n_PRNU and N_o is :

                                               n_PRNU = a · N_o

with a being a constant.  By combining the aforementioned formulas, the relation between the measured signal S_tot and its measured noise component n_tot can be written as :

                                               n_tot = k · a · N_o = k · a · (S_tot/k) = a · S_tot

or :      

                                               log(n_tot) = log(a) + log(S_tot).

From Figure 2, the following can be learned :

-       its slope should be equal to 1, because of the linear relationship between the (logarithmic of the) output signal and the (logarithmic of the) light FPN.  The actual value of the slope is a good match to the theory !

-       the intersection of the curve with the horizontal axis can deliver the constant a mentioned in the formulas and indicating the amount of FPN present in the system : with an intersection at 1.499 DN, this gives a = 1/10^-1.499 = 0.0317 or 3.17 %.  This result is in good agreement with the number obtained from Figure 1.

-       saturation level : 10^3.45 DN = 2818 DN,

-       FPN at saturation level : 10^2.149 = 140.2 DN. 

Figure 3 : Output signal and its temporal noise component as a function of the exposure time.

 Figure 4 : “PTC” of the sensor with only photon shot noise.

Figure 3 shows the output signal with its temporal noise component, being the photon shot noise, as a function of the exposure time.  In figure 4 the Photon Transfer Curve is illustrated.  These two figures are basically the same as in the previous blog because they only contain the temporal noise component and that has not changed by adding light FPN.  That means that also the same parameters can be deduced :

-       conversion gain : 1/10^0.812 = 0.154 DN/electron,

-       output level : 8.112·t_exp = 8112 DN/pixel/second = 52,675 electrons/pixel/second at 30^oC (this is the temperature at which the images are being generated),

-       on-set of anti-blooming : 10^3.26 DN = 1820 DN = 11,816 electrons,

-       saturation level : 10^3.45 DN = 2818 DN = 18,301electrons.

Knowing the conversion gain and/or the output signal, also the FPN can be calculated to be equal to : 0.243·t_exp = 243 DN/pixel/second = 1578 electrons/pixel/second at 30^oC.

Conclusion : after obtaining the 100+ images with light two calculations took place : averaging and standard deviation (variance) calculation.  Averaging first and then calculation of the standard deviation results in the characterization of the FPN.  Standard deviation (variance) calculation first followed by the averaging results in the characterization of the temporal noise.  

Next time the dark current with its DSNU will be added.

Albert 2010-06-14

In the various blogs published over the last couple of months, many aspects of using noise as a measurement tool were discussed.  Up to now, all evaluations were done based on images that were generated in dark.  From this blog onwards, “the light will be switched on” !  Several output values of the sensor signal need/can be generated by means of a light input.  And that is what is going to be studied in this and the coming blogs.  To study the effect of a light input on the Photon Transfer Curve the same strategy will be followed as the one in the case with the dark current as input :

-       changes in (average) output signal will be realized by means of changing the exposure or integration time,

-       a step-by-step approach to study the influence of the different noise sources and/or artifacts,

-       a similar sensor architecture will be used, as shown in Figure 1. 

Figure 1 : Architecture of the (hypothetical) sensor used in the noise model.

The pixel is based on a pinned-photodiode in combination with a transfer gate (TX), reset transistor (RST) and addressing transistor (RS), each column contains the bias current source, the circuitry to perform the correlated-doubling sampling, the programmable gain amplifier (PGA) and an analog-to-digital converter (ADC) are included.

In a first experiment, only the light input and its shot noise component are added to the model, all other noise sources are set to zero.  At each chosen exposure time, 100+ images were generated.  The input to the pixels was provided by means of a light source dumping 150,000 photons/s on each pixel.  The latter has a quantum efficiency of 33 %.  The exposure time was varied from 0 s till 0.6 s, the latter makes sure that the pixels can be fully saturated under the given input condition.

The result of this exercise can be seen in the following two figures :

-       Figure 2 contains the average signal (left axis) of the generated images and its photon shot noise component (right axis) as a function of the integration time (horizontal axis).  To find the noise, the standard deviation/variance on pixel level was calculated, and next the obtained variances were averaged.  This method allows obtaining the temporal noise, because the calculation is done on pixel level and consequently, FPN is excluded.  So every point on the curves is the result of all pixels in 100+ images,

-       Figure 3 shows the photon shot noise versus the  signal, based on the data shown in Figure 2.  Because the noise shown is the temporal noise, Figure 3 is the original PTC (described by Jim Janesick in his book “Photon Transfer, SPIE Press, 2007”).

Figure 2 : Output signal (red) and temporal noise (blue) as a function of exposure time.

As can be seen in Figure 2, the average signal is linear with the integration time.  The relation between the output signal and exposure time (t_exp expressed in ms !) is indicated in Figure 2 as well. The temporal noise, as a function of exposure time, is shown on the right axis.  Because the noise model only contains the light input signal, the temporal noise component represents the photon shot noise.

The corresponding “PTC” curve is illustrated in Figure 3 : the temporal noise versus the output signal is shown.

Figure 3 : PTC of the sensor with only photon shot noise.

 The measured signal of the pixel, S_tot (expressed in DN, digital number and corrected for the offset) can be written as :

                                               S_tot = k · N_o

with k being the overall gain [electrons/DN] of the image sensor and N_o [electrons] the number of electrons generated in every pixel.  The total temporal noise at the output of the sensor, n_tot, is related to the noise in the pixel by (all noise sources are set to zero, except the photon shot noise) :

                                                n_tot = k · n_o

with n_o being the photon shot noise.  The relation between n_o and N_o is determined by the Poisson statistics :

                                               n_o = N_o^0.5.

By combining the aforementioned formulas, the relation between the measured signal S_tot and its measured noise component n_tot can be written as :

                                               n_tot = (k · S_tot)^0.5

or :      

                                               log(n_tot) = 0.5 · log(k) + 0.5 · log(S_tot).

From the PTC curve, the following can be learned :

-       its slope should be equal to 0.5, because of the square-root relationship between the output signal and the photon shot noise,

-       the intersection of the curve with the horizontal axis can deliver the gain of the overall system : a value of 0.810 is found, which can be converted into a gain of 0.155 DN/electron,

-       the sensor goes into anti-blooming mode at a signal value equal to 10^3.26 DN = 1820 DN,

-       the sensor saturates at 10^3.45 DN = 2818 DN.

From Figure 2, it can be seen that the relationship between output signal and the exposure time (expressed in ms) is equal to :

8.107 · t_exp + 511.90.  

Taking into account the conversion gain, this can be translated in an output signal equal to 52,300 electrons/pixel/s.  To check this value : the quantum efficiency put into the simulation tool is 33 %, and with an input signal of 150,000 photons/pixel/s, the expected output signal has to be 50,000 electrons/pixel/s.

Next time, the light fixed-pattern noise will be added to the noise model and its effect on the PTC curve will be investigated.

Albert 2010-05-31

It is amazing to see how many people are attracted to my web-site since I am posting the material about the noise simulations and noise evaluations.  Recently I got a few suggestions to expand the model I built.  Although it is difficult to indicate when I can work on it, I can promise that the following artifacts will be included in the simulation tool :

-          Non linearity of the pixel/floating diffusion/source follower,

-          Shading of the dark current,

-          Column and row defects.

If you have more suggestions or shortcomings you would like to see discussed, feel free to drop me a mail or add a comment to the blog. 

Another request I got is to make the data of the simulations available.  Apparently some people want to play around with the images.  It is too complicated and too much work to make available all images used so far.  But the images that are being used to generate the graphs shown in the last two blogs (all noise sources integrated in the model and the sensor operated in dark) can be downloaded here.

In the directory you can download (170 MB), you will find 48 files containing images and 1 file containing information.  Every image file contains 100 images.  Every image has 160 pixels (H) and 120 pixels (V).  Every image file is the result of 100 images generated at a fixed integration time.  The 100 images at each integration or exposure time are written in a single file line after line, all images one after another.  So :

-          Line 1 of the file contains 160 pixel values of the first line of the first image,

-          Line 2 the second line of the first image,

-          Line 3 the third line of the first image,

-          …

-          Line 120 the last line of the first image,

-          Line 121 the first line of the second image,

-          Line 122 the second line of the second image,

-          Line 123 the third line of the second image,

-          …

-          Line 240 the last line of the second image,

-          …

-          Line 12000 (being the last line in the file) contains the 160 pixel values of the last line of the 100^th image.

The filename of each image contains also the data of :

-          W(idth) of each image : number of pixels, being equal to 160

-          H(eight) of each image : number of pixels, being equal to 120

-          G(ain), mostly set to 1,

-          t(ime) : exposure time expressed in ms,

-          T(emperature), expressed in deg.C, mostly set to 30

-          ph(otons) impinging on the sensor, being 0 in case of dark images,

-          n(umber) of images at every exposure time, mostly fixed at 100.

The directory contains in total 48*100 = 4800 images, and 48*100*160*120 = 92,160,000 pixels.  All data is being expressed in digital numbers (DN), the data is taken after the ADC of the imaging system.

Good luck with the calculations/simulations.

Albert.

5^th CMOS Imager Workshop, Duisburg, May 4-5, 2010.

DAY 2

Boyd FOWLER (Fairchild Imaging, Milpitas, CA) : “Scientific CMOS Image Sensor”

The specific sensor architecture and sensor operation was explained, but that part of the talk was very similar to the one presented last year in Toulouse.  The most interesting details came when Boyd discussed the performance of the device.  He compared the high gain channel with the low gain channel, both in rolling shutter mode as well as global shutter mode.  Worthwhile to mention is the mean noise performance of the various modes :

-          Read noise of 1.5 e- high gain channel in rolling shutter mode (100 MHz),

-          Read noise of 9.2 e- low gain channel in rolling shutter mode (100 MHz),

-          Read noise of 1.9 e- high gain channel in rolling shutter mode (290 MHz),

-          Read noise of 10.3 e- low gain channel in rolling shutter mode (290 MHz),

-          Read noise of 4.8 e- high gain channel in global shutter mode (100 MHz),

-          Read noise of 13.3 e- low gain channel in global shutter mode (100 MHz),

-          Read noise of 5.7 e- high gain channel in global shutter mode (290 MHz),

-          Read noise of 14.7 e- low gain channel in global shutter mode (290 MHz).

The pixel is a 5T cell that can be operated with CDS in the rolling shutter mode, but without CDS in the global shutter mode (digital CDS is performed off-chip).  That is the explanation why the rolling shutter mode is that much superior over the global shutter mode.  Together with all these numbers, several histograms about noise distribution and dark current distribution are shown.  At the end of the talk, images were shown of the colour version of this device, as well as of the BSI-ed version.  QE levels over 90 % were reported (if the appropriate anti-reflective coating was applied). 

Alex KRYMSKI (Alexima, CA) : “Design of CMOS imagers : Selected Circuits & Architectures”

The focus of the presentation was a series of useful circuits and architectures that were created over the last decade.  If you tell people that you will talk about useful circuits, you inherently admit that there exists something like useless circuits as well, and indeed Alex did.  He even showed examples of useless circuits.

Examples of useful circuits were : clamping source follower input and output, dynamic source follower, driving rows from both sides, multiple ADCs per column of the imager, multiple busses in the pixel array, pipelining top-bottom and block-memory readout.  Together with circuit diagrams, Alex explained the working principles of the circuits and illustrated the concept with products in which these circuits are applied.  Also the device for which he and his co-workers received the 2003 Walter Kosonocky Award was highlighted.

Guy MEYNANTS (CMOSIS, Antwerp, Belgium) : “CMOS image sensors for industrial applications”

The outline of Guy’s talk :

-          High speed imaging and other requirements for industrial imaging,

-          CIS architectures with analog architectures for the fastest, customized imagers, (conclusion about this chapter : analog offered the highest speed so far, mainly obtained by parallelism, but there are limited capabilities to further speed up),

-          CIS architectures with on-chip ADC for easy-to-use and easy-to-integrate imagers, (great overview of the various ADC architectures was given),

-          Case study : 2 Mpixel imager at 340 fps with global shutter and CDS.  A new shutter type implemented with an 8T pixel was shown with a parasitic light sensitivity of 1/60,000.  Taken into account a pixel size of 5.5 um, this is an amazing performance. 

Walter RUETTEN (Philips Research, Aachen, Germany) : “Solid-State X-ray Imaging”

The talk started with an overview of the various X-ray detection systems : Screen-film system, image intensifiers, fully digital solid state detector systems, photoconductors and scintillators.  A parameter that is not that often used in (consumer) digital imaging is the Detective Quantum Efficiency.  Although in the medical imaging field, the DQE is a very important characteristic.  Walter explained the definition as well as the importance of DQE.  A nice example based on numbers and figures (that is what engineers like to see) explained the typical noise issues in an X-ray system.

The second part of the talk was concentrating on monolithic silicon detectors : large area CMOS image sensors, 3 sides buttable that allow to build very large detectors (40 cm x 40 cm).  A first test chip of such a detector is available with high speed readout architecture implemented.  With this test chip most features of the large area detector can be tested.  The very first X-ray experiments show at least the same or even better DAE with higher resolution compared to the commercially available detectors.

What the future going to bring in medical imaging ?   A potential next step could be spectral imaging in which the energy of the X-ray can detected (“colour X-ray”).  Apparently an interesting “X-ray future” ahead of us.

Werner BROCKHERDE (Fraunhofer IMS, Duisburg, Germany) : “Solid-State ToF Sensors”

3D imaging is a hot topic these days.  A typical sensor architecture used to detect the third dimension is ToF : time of flight.  ToF can be realized by three approaches : direct time measurement, continuous wave modulation, pulse modulated light.  All three principles were explained, compared and benchmarked.  At IMS, the pulse modulation technology is explored.  A major issue in 3D imaging is the speed of the pixels, measurements need to be done at the “speed of light” and pixels need to be emptied within the same timescale.  To come to this point, photogate pixels and pinned photodiode pixels with a built-in lateral drift field are developed.  Examples and results of both architectures are shown in the talk.

Ulrich SEGER (Robert Bosch, Germany) : “Imaging sensors for driver assistance applications”

It should be clear that vision systems and intelligent cameras can add a lot of functionality to driver assisted applications.  Near IR vision can help a lot in detecting obstacles, etc.  Several of these examples are known.  In this talk, Ulrich highlighted a couple of issues that were encountered with the CMOS image sensors used.  A first example was sun-burn-in.  Too heavy sunlight focused on the image sensor could generate some nasty burn-in effects, showing up as FPN.  This effect was corrected by changing/adapting the processing of the micro-lenses on top of the image sensor.  A second issue was the drift of the FPN after the camera was assembled.  This effect had to do with the UV damage introduced during the assembly process.  

These two examples show that the harsh automotive environment can put extra constraints and requirements on the imagers/cameras when used for automotive purposes. 

Martin WENDLER (Pilz, Ostfildern, Germany) : “Safe CMOS camera system for three-dimensional zone monitoring”

The very last talk of the workshop was focusing on the application of a logarithmic CMOS image sensor with a global shutter to protect a 3D zone of an industrial environment.  The safety requirements of such an applications are extremely high, and for that reason a camera is needed with an imager that complies with :

-          High dynamic range (120 dB),

-          Triggerable global shutter,

-          Logarithmic characteristic curve.

Interesting talk to hear the discussion of an image sensor and its requirements presented by the customer.

5^th CMOS Imager Workshop, Duisburg, May 4-5, 2010.

DAY 1

Holger VOGT (Fraunhofer IMS, Duisburg, Germany) : “Devices and technologies for CMOS Imaging”

The first talk on the first day gave an good introduction to the workshop.  In the first part of the talk several CMOS detectors were reviewed (photodiode, buried photodiode, pinned photodiode and photogate pixels).  Special attention was given to the effect of emptying the pixels at higher speed and how to introduce a lateral drift field in the pixels.  At the end of the talk several projects and topics were illustrated that form part of the IMS research portfolio.  Examples are  :

-          Colour by metal grids,

-          Colour by depth sensing in the silicon,

-          The low noise double modified internal gate pixel,

-          SPADs,

-          BACKSPAD (back-side illuminated SPAD) and,

-          Uncooled Bolometers. 

Nice opening of the workshop because of the wide overview, with a bit of publicity for the Fraunhofer IMS institute.  But they deserve it, because they are the organizer of the workshop.

Lindsay GRANT (ST Microelectronics, Edinburg, UK) : “CMOS image sensors and technology”

In the mean time I have heard several presentation of Lindsay, and they all come down to a very broad overview of the CMOS technologies needed for mobile imaging.  And if you have heard a few of them, you get a very good insight in how rapidly this technology is evolving.  The topics addressed in this talk are too many to list here, but (for me) the main ones are :

-          0.9 um pixel size on the roadmap, 1.1 um in demo,

-          Progress in pixel modeling (optical and device physics),

-          Pixel optics,

-          Colour improvements,

-          Back-side illumination and crosstalk,

-          SNR performance metric.

In his last sheet he tried to show us : “What’s next ?”  In short :

-          The pixel race continues,

-          Front-side illumination will remain cost/performance competitive,

-          Sensor image quality assessment will continue to a topic in active research.

At the end of the talk Lindsay acknowledged the late Peter Denyer for his inspiring leadership.

Mark ROBBINS (e2v, Chelmsford, UK): “Electron Multiplying CCDs”

The EM-CCD is intended for imaging in a photon starved environment where all sources of noise must be minimized.  EM-CCD reduces the effect of charge to voltage conversion noise and noise from the video chain.  After a short description of how the EM-CCD works, Mark spent quite a bit of time on the introduction of the noise factor and on the dependency of the gain as a function of temperature and gate voltage.  He showed nice results for the EM-CCD in the photon counting mode.  In the last part of the talk, the Rose criterion was introduced to quantify the visibility of a feature in a noisy image.  The theory was illustrated with images under extreme low light level conditions.  As can be expected, the ultimate low-light level sensor will be the EM-CCD in combination with back-side illumination.   Interesting to notice that up to this point in the workshop, all speakers were referring to BSI.

Frank ZAPPA (Politecnico di Milano, Milano, Italy) : “SPADs”

In the overview presentation about SPADs, Frank addressed the following topics :

-          Single photon counting and timing, such as PMTs, special CCDs (EM-CCD, I-CCD), SSPD, SPAD

-          Single photon avalanche diode,

-          Circuital modeling, static as well as dynamic,

-          Devices structures with focus on planar versus reach-through,

-          Processing technologies with focus on custom versus CMOS,

-          Circuits : monolithic versus smartchips, detection as well as counting chips,

-          Arrays for single-photon imaging.

As a conclusion, Frank stated that SPAD detectors and arrays, microelectronics and instrumentation are available, know-how is present for custom development, and commercial products based on SPADs are available on the market.

Gerhard LUTZ (PNSensor, Munich, Germany) : “Silicon Radiation Detectors”

Sometimes one forgets that there is much more than CCD or CMOS image sensors to detect radiation, but Gerhard put us back with two feeds on the ground.  He discussed the basic detection process of radiation in semiconductors, reviewed the basic principles of semiconductor detectors such as the reverse biased diode, the semiconductor drift chamber and the DEPFET detector-amplifier structure.  It was quite funny to see the presentation of the good old junction CCDs, never thought that still some products were made out of this technology.  But the more you think about, the more intriguing the devices are.   The same is true for the DEPFETs.  These unique devices are able to satisfy a variety of different requirements depending on specific applications.  More sophistic variations of this structure have been invented, their functioning has been proven by simulations and by measurements of finished devices.   

Albert THEUWISSEN (Harvest Imaging, Bree, Belgium) : “Noise : you love it or you hate it”

A simulation and evaluation tool is described.  The simulation tool accepts the specification of an image sensor as input and creates images.  One of the main applications of this simulation software is the study of the various noise sources present in an imager/camera.  The artificial images created can be the input for the evaluation tool.  But also images generated by a real camera can be used as the input for the evaluation tool.  During the presentation an example was shown of the combination simulation-evaluation of images.  Also real images generated by a CMOS camera were analyzed.  During the talk the main focus was on images created in dark.  Even without any light input several important noise contributions can be measured/analyzed.  The algorithms applied in the evaluation tool will be part of the new training course that will be offered by Harvest Imaging later this year.  

Pierre MAGNAN (ISAE, Toulouse, France) : “Ionization effects in CMOS imagers”

In the first part of the presentation the theory of the different defects and artifacts that can be generated by radiation were discussed.  It was clearly shown how complex the physics are behind radiation effects in CMOS image sensors.   Attention was given to :

-          The generation of electron-hole pairs in the various materials involved,

-          Charge transport in the silicon dioxide,

-          Charge trapping in silicon dioxide,

-          Radiation induces interface traps.

Then the question was answered : and what is going to be the influence on the CIS performance parameters of all these beautiful artifacts ?  I can be expected, in the first place the dark current will increase, but also the light response will be changed, unfortunately the light response will become lower.    

Pierre ended his talk with some ideas about how to make a design radiation hard.

We continue with the integration of all noise sources in one sensor.  Last blog the focus was on the FPN, this blog will highlight the temporal noise effects on the PTC.  The hypothetical device contains the following noise components (the same numbers as already mentioned in previous blog) :

-       dark current : 220 e^-/s at 22 ^oC,

-       dark current non-uniformity : 30 e^-/s at 22 ^oC,

-       dark current doubling temperature : 8  ^oC,

-       saturation non-uniformity : 5 %,

-       DC offset : 125 mV,

-       output amplifier noise : 0.3 mV,

-       temporal row noise : 6 e^-,

-       fixed-pattern row noise : 3 e^-,

-       repetition frequency : 16 lines,

-       temporal column noise : 8 e^-,

-       fixed-pattern column noise : 12 e^-,

-       temporal pixel noise : 10 e^-,

-       fixed pattern pixel noise : 3 e^-,

-       defects pixels : 15 pixels stuck at “1” and 15 pixels stuck at “0”,

-       RTS pixels : 160 pixels.

At various exposure times, 100+ dark images were generated by the simulator.  The exposure time was varied from 0 s till 65 s, the latter makes sure that the pixels can be fully saturated with dark current.

As far as the temporal noise is concerned, the result of this exercise can be found in this blog.  Figure 1 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).  These curves are generated after correction of the defect pixels (see previous blog).  The latter has no effect at all on the temporal noise characteristics of the sensor.  But after correction the offset that comes with the output signal has changed a bit.

To find the noise shown in Figure 1, the standard deviation for every pixel was calculated based on the pixel values in the generated images, next for each integration time, all the noise values calculated were averaged.  This method allows to obtain the temporal noise without any influence of the fixed-pattern noise, so every point on the curves is the result of all pixels in 100+ images.

 Figure 1 : Dark signal (red) and temporal noise (blue) as a function of exposure time.

In Figure 1, clearly noticeable are the DC offset of the output signal (512 DN at zero exposure time and after the correction of the defects) and the onset of anti-blooming (when the noise reaches a maximum value).  Notice the relative large noise level at very short exposure times, indicating the minimum noise at pixel level (2.78 DN at 30 ^oC).  The output signal is linearly increasing with exposure time, indicating that the dark current is filling up the pixels, but the temporal noise is not linear with the exposure time.  The quadratic relation between dark current shot noise and generated electrons in dark is responsible for this non-linear noise curve.

Figure 2 illustrates the temporal noise versus the dark signal, based on the data shown in Figure 1 (after correction of the defect pixels and after subtracting the DC offset signal).  Actually, this is a similar curve as the PTC described for the first time by Jim Janesick.  The original PTC was done with light input, here only the dark current is used to increase the output signal of sensor, but the basic idea is exactly the same.

Figure 2 : “Photon Transfer Curve” of the sensor in dark.

This “PTC” curve shows three characteristic regions, and from each region interesting parameters can be deduced :

-       The part with a slope = 0, representing the temporal noise at very low exposure times.  This noise is coming from the nearly-empty pixel, the column and the row circuitry, the output amplifier.  In this case the total noise on pixel level is equal to 10^0.443 = 2.77 DN,

-       The part with a slope = 0.5, representing the increasing temporal noise due to the dark current.  From the data shown in Figure 2, it can be calculated that the extrapolation of this part of the curve gives a value equal to 0.760, the conversion gain can be deduced to be equal to 1/10^0.760 = 0.17 DN/e^-, (how to come to the value of 0.760 is up to the reader to find out),

-       The part representing a collapsing curve, the onset of anti-blooming at 10^3.26 = 1819 DN, and the saturation level at 10^3.45 = 2818 DN.

The curve shown is a very powerful tool in the analysis of the noise behavior, not just because it gives the values of important parameters, but it also includes a very efficient test to check if the measurements are done correctly.  The slope of the dark-current temporal noise should be equal to 0.5 !  

Nevertheless the curve does not give any value about the temporal noise introduced by the column and/or row circuitry.  In the case of the fixed-pattern noise, it was quite easy to find the contributions from the row and column circuitry, in the case of the temporal noise, this is not that easy !

In summary, the following data could be extracted from the measurements (the value put into the simulator are shown between brackets) :

-       conversion gain : 0.17 DN/e^- (0.16 DN/e^-)

-       start of anti-blooming : 1819 DN (1960 DN)

-       temporal pixel noise : 2.77 DN (2.56 DN)

-       saturation level : 2818 DN (2800 DN)

Now that the conversion gain is know, all parameters (including the ones obtained in the previous blog) can be converted to the charge domain.  The following numbers can be found (the value put into the simulator are shown between brackets) :

-       dark signal at 30 ^oC : 382 e^-/s (400 e^-/s),

-       dark signal non-uniformity at 30 ^oC : 17.4 % (16 %),

-       total FPN on pixel level : 12.2 e^- (12.7 e^-),

-       row FPN : 2.9 e^- (3 e^-),

-       column FPN : 11.2 e^- (12 e^-),

-       pixel contribution to FPN : 3.0 e^- (3 e^-),

-       temporal pixel noise : 16.4 e^- (16 e^-),

-       saturation pixel FPN : 794 e^- (875 e^-),

-       onset anti-blooming : 10,767 e^- (12,250 e^-),

-       saturation level : 16,578 e^- (17,500 e^-),

-       dynamic range at 30 ^oC : 60.1 dB (61 dB).

The values obtained from the images and the input parameters of the simulator are almost equal to each other.  The parameters dealing with the saturation levels deviate a bit more than the others, this is partly due to the limited amount of data point in this region.  The overall analysis described here shows again the power of the PTC tool !

This blog concludes the discussion about the PTC in dark.  Fortunately or unfortunately, the PTC story has not yet come to an end.  Next time we switch on the light.

Albert 2009-04-22

In this blog we are going to combine all foregoing theory about noise sources into one single image sensor.  In the first part (of two) the focus will be on the fixed-pattern noise analysis.  The hypothetical device contains the following noise components :

-       dark current : 220 e^-/s at 22 ^oC,

-       dark current non-uniformity : 30 e^-/s at 22 ^oC,

-       dark current doubling temperature : 8  ^oC,

-       saturation non-uniformity : 5 %,

-       DC offset : 125 mV,

-       output amplifier noise : 0.3 mV,

-       temporal row noise : 6 e^-,

-       fixed-pattern row noise : 3 e^-, repetition frequency : 16 lines,

-       temporal column noise : 8 e^-,

-       fixed-pattern column noise : 12 e^-,

-       temporal pixel noise : 10 e^-,

-       fixed pattern pixel noise : 3 e^-,

-       defects pixels : 15 pixels stuck at “1” and 15 pixels stuck at “0”,

-       RTS pixels : 160 pixels.

These parameters were used as input for the device simulator and based on the overall sensor concept as shown in Figure 1. 

 Figure 1 : Architecture of the hypothetical sensor used in the noise model.

The pixel is based on a pinned-photodiode in combination with a transfer gate (TX), reset transistor (RST) and addressing transistor (RS), each column contains the bias current source, the circuitry to perform the correlated-doubling sampling, an on-chip level programmable-gain amplifier (PGA) and an analog-to-digital converter (ADC) are included.

At various exposure times, 100+ dark images were generated by the simulator.  The exposure time was varied from 0 s till 65 s, the latter makes sure that the pixels can be fully saturated with dark current.

As far as the fixed-pattern noise is concerned, the result of this exercise can be found in this blog.  Figure 2 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).  To find the noise, all images at a particular integration time were averaged (to cancel the temporal noise), and next the standard deviation was calculated.  This method allows to obtain the fixed-pattern noise, so every point on the curves is the result of all pixels in 100+ images,

 Figure 2 : Dark signal (red) and fixed-pattern noise (blue) as a function of exposure time.

Clearly noticeable is the DC offset of the output signal (515 DN at zero exposure time), the onset of anti-blooming (when the noise reaches a maximum value), and the FPN at saturation.  Notice the relative large FPN at very short exposure times, as well as the fact that for increasing integration times the FPN first goes down, and next increases with the exposure time.  For very small values of the exposure time, the FPN behavior is dominated by the presence of the defect pixels.  To exclude the influence of the defect pixels, the defect pixels were software-corrected in the images.   The result of the foregoing calculation of average value and FPN in dark after the cancellation of the defect pixels is shown in Figure 3. 

Figure 3 : Dark signal (red) and fixed-pattern noise (blue) as a function of exposure time, after correction of the defect pixels.

After correction of the defect pixels, the curve showing the average dark signal as a function of the exposure time is hardly changed.  Only the DC offset is lowered to 512 DN.  On the other hand, the FPN as a function of the exposure time is altered especially for very low exposure times.  This time the FPN is nearly a linear function of the exposure time as well.  The ratio between average dark signal and FPN is 0.008/0.065 = 12.3 %.  From the same curve also the onset of anti-blooming as well as the FPN at saturation can be deduced.

The relation between dark signal and exposure time, as well as between dark FPN and exposure time are shown in Figure 3 (t_exp expressed in ms !).  Both expressions hold for the linear part of the curves.  It can easily be learned that the dark signal is equal to 65 DN/s at 30 ^oC.

Figure 4 illustrates the dark FPN versus the dark signal, based on the data shown in Figure 3 (after correction of the defect pixels).

Figure 4 : “PTC” of the fixed-pattern noise.

 This simple “PTC” curve shows three characteristic regions, and from each region several interesting parameters can be deduced :

-       The part with a slope = 0, representing the FPN at very low exposure times.  This FPN is determined by the (empty) pixel, the column and the row circuitry.  In this case the total FPN on pixel level is equal to 2.04 DN,

-       The part with a slope = 1, representing the FPN generated by the dark current.  From the equation shown in Figure 4, it can be calculated that the extrapolation of this part of the curve gives a dark signal non-uniformity (DSNU) equal to 0.174,

-       The part representing a collapsing curve, the onset of anti-blooming at 1819 DN, the saturation level at 2818 DN and the saturation non-uniformity of 134.9 DN.

The curve shown is a very powerful tool in the analysis of the FPN, not just because it gives the values of important parameters, but it also includes a very efficient test to check if the measurements are done correctly !  The slope of the dark-current FPN should be equal to 1 !  (The curve shown in Figure 4 is very similar to the original Photon Transfer Curve described by Jim Janesick). 

Nevertheless the curve does not give any value about the column and/or row FPN.  These parameters need to be evaluated separately.  Figures 5 and 6 show the results.  In Figure 5, the row FPN is shown as a function of the exposure time, while in Figure 6, the column FPN is shown as a function of the exposure time.

 Figure 5 : Row FPN as a function of exposure time. 

Figure 6 : Column FPN as a function of exposure time.

The curves look very similar to each other :

-       a first part with slope = 0, indicating a FPN that is independent of the exposure time.  The values obtained (0.502 DN for the row noise and 1.905 DN for the column noise) indicate the real FPN contributions of respectively the row and column circuitry,

-       a second part that increases with the exposure time,

-       and finally a last part with a saturation part for both the row FPN (at 12.33 DN) and the column FPN (at 15.38 DN).  These values represent the FPN values present in the saturated signal.  In the case of the pixel FPN at saturation, a value equal to 134.9 DN was found.  In principle the row FPN at saturation should be equal to 134.9 DN/sqrt(number of columns) = 134.9/sqrt(160) = 10.7 DN.  The column FPN at saturation should be equal to 134.9 DN/sqrt(number of rows) = 134.9/sqrt(120) = 12.3 DN.

The total pixel FPN is found from Figure 4, being 2.04 DN.  From Figures 5 and 6, it is found that the row and column contributions are respectively 0.502 DN and 1.905 DN.  That means that the contribution from the pixels themselves is equal to (2.04² – 0.50² – 1.90²)^0.5 = 0.51 DN.

In summary, the following data could be extracted from the measurements (the value put into the simulator are shown between brackets) :

-       dark signal at 30 ^oC : 65 DN/s (64 DN/s),

-       dark signal non-uniformity at 30 ^oC : 17.4 % (16 %),

-       total FPN on pixel level : 2.04 DN (2.07 DN),

-       row FPN : 0.50 DN (0.48 DN),

-       column FPN : 1.91 DN (1.92 DN),

-       pixel contribution to FPN : 0.51 DN (0.48 DN),

-       saturation pixel FPN : 135 DN (140 DN),

-       saturation row FPN : 12.3 DN (11.1 DN),

-       saturation column FPN : 15.4 DN (12.8 DN),

-       onset anti-blooming : 1819 DN (1960 DN),

-       saturation level : 2818 DN (2800 DN).

The values obtained from the images and the input parameters of the simulator are almost equal to each other.  The deviation between the two sets of numbers is in all cases < 10 %, for most of them < 5 % and for a few even < 2 %.  There is a clear explanation why the measured data of some parameters is higher than their theoretical values, but it is left up to the reader to find the root cause for these differences ….  After all, the reader has to put some effort in the PTC story as well ….

Next time, a similar exercise will be done on the same imager but then focusing on the temporal noise.  Something to look forward to ?!

Albert 2009-04-07