----------- Your trusted
source for independent sensor data- Photons to Photos------------------------ Last revised:
2022-02-19
---------------------------------- Dark Current Non-Uniformity
--------------------------------------------------------- By Bill Claff
Introduction
Most digital image sensors work roughly as follows.
A percentage of the visible photons that strike the silicon create an electron
hole. We often refer to that percentage as Quantum Efficiency (QE).
Over the course of the exposure a charge builds up in the pixel which is
essentially a capacitor.
The maximum charge that can be (reliably) held is called the Full Well Capacity
(FWC) which is usually stated in electrons.
When the pixel is read the charge is first converted to a voltage. The number
of (milli-)volts per electron is called the conversion gain.
Then, typically, the voltage is amplified in proportion to the ISO setting and
converted to a Digital Number (DN) by an Analog to Digital Converter (ADC).
Ultimately we assume that the measurement in DN is proportional to the number
of photons that was incident on the
pixel.
However, there are other electrons that accumulate in the pixel, mostly due to
heat.
Even at relatively short exposure times some sensors will show an effect that
is often called "amp glow".
Normally this is along one edge or in one corner of the sensor near some
internal heat source.
This effect is well controlled in most cameras but can be detected as a slight
gradient on careful examination of dark frames.
During long exposures, regardless of how evenly heat is distributed, electrons
will accumulate at the pixel even in the absence of light.
Some cameras seem to mitigate this effect using information from the optical
black pixels.
The accumulation of a charge in the pixel in the absence of light is called
Dark Current. Dark Current can be problematic for astro-photography in
particular.
As we will see Dark Current does not affect all pixels equally and it is the
non-uniform effect of Dark Current that this article explores.
We will examine the behavior in depth on a Nikon D7200.
Dark Current Signal
Given the mechanism for how Dark Current accumulates we
would expect dark frame signal level to increase in proportion to exposure
time.
Here's a look at average signal versus exposure time for Nikon D7200 black
frames:
Note that the x-axis is logarithmic; 12 is 4096 seconds which is over 1 hour.
Signal looks unaffected through 32
seconds and does rise over time.
The data point at 9 looks a bit low but we should also remember that Dark
Current is temperature dependent and perhaps the camera was cooler for that
shot.
Let's take a closer look at the exposure that were 60
seconds or longer:
Although the line is not perfectly straight correlation is good and the offset
of 599.6DN is in close agreement with the Nikon D7200 Black Level of 600DN.
So it does appear that Dark Current causes signal to increase in proportion to exposure time and that the effect on signal is negligible up to 30 seconds or so.
Dark Current Noise
Dark Current arrives randomly and so there is shot noise
associated with it. Therefore we expect observed read noise to increase with
Dark Current.
Using the accumulation rate from the above fit as well as read noise at
1/8000sec and gain we can predict the expected effect.
Observed noise significantly exceeds the expected value. To investigate further
let's look at maximum Signal as a function of time:
It look as though the maximum starts to rise at about 1/30sec, dropping
abruptly at 1/4sec and then continuing to rise.
The abrupt drop at 1/4sec is mandatory signal processing (noise reduction) that
is applied at longer exposures.
Regardless of the noise reduction the fact that both Noise and the maximum
signal rises over time is a bit surprising.
The behavior of maximum signal gives us some insight and
further investigation of the histograms reveals that increased exposure time
results in long tails of unusually high values.
For example, the z-score histograms over a huge range of exposure times look
normal (they should have the shape of a Normal Distribution) and are
substantially identical:
Dark Current Non-Uniformity (DCNU)
Dark Current Non-Uniformity (DCNU) results from pixels not
behaving identically (uniformly) to stray electrons.
The number of pixels affected by DCNU is fairly high and results in a
significant effect on the observed read noise for long exposures.
Nikon D7200 Study
To better understand what is happening we will examine a relatively small portion (32x32 pixels) of the Nikon D7200 sensor over time.
Here are the Signal values for 5 pixels from the sample
region chosen as representative:
Note that two pixels show a strong rise in Signal over time while the other
pixels do not.
A closer examination (reduced y-axis) of the same data shows that even the less
affected pixels do rise some over time.
Let's characterize the more affected pixels as "DCNU-affected" and
the other pixels as "normal".
Here is a 3D view of the entire region of interest:
The peak in the rear actually goes up to 16384DN.
So while most pixels appear well behaved (normal) a significant number are
DCNU-affected.
To characterize the number of DCNU-affected pixels let's
look at the count of the z-scores that exceed 8 as a function of exposure time.
At out longest exposure time about 1 pixel in every 120 is DCNU-affected.
To see the effect at more normal exposure times let's show
the data using a logarithmic y-axis:
Once again we see the effect of the mandatory signal processing that starts at
exposures of 1/4sec and longer.
Conclusion
Although the Nikon D7200 was examined in depth I also looked at data for about 20 other camera models from various manufacturers and saw similar trends.
DCNU is not often investigated and rarely cited as the
reason for observed behavior.
For example, most astro-photographers are well aware of Dark
Current but are probably unaware of DCNU.
DCNU is probably the chief reason that dark frames need to be taken at a
particular exposure rather than simply scaling from some known exposure.
It's not uncommon for people to attribute the effect of DCNU as "hot pixels"; while they may have a similar appearance the underlying mechanism is quite different.
I'm left wondering, and currently assume, that mandatory raw
signal processing such as that on the Nikon D7200, is motivated by the need to
keep DCNU under control.
It's evident that by 1/8sec the number of DCNU-affected pixels is starting to
rise and without this signal processing I suspect they would be quite
noticeable at longer exposures.