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ASTRO: OT, How to measure DSNU, Dark Shot noise, Read Noise, Camera Gain, Full Well capacity and so on using empirical data



 
 
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Old February 9th 08, 03:45 AM posted to alt.binaries.pictures.astro
Richard Crisp[_1_]
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Default ASTRO: OT, How to measure DSNU, Dark Shot noise, Read Noise, Camera Gain, Full Well capacity and so on using empirical data

http://www.narrowbandimaging.com/dar...urves_page.htm

Characterization of Certain Camera Parameters via Dark Transfer Curve


Dark Transfer Curves (DTC): what they are and what we learn from them
(Richard Crisp, www.narrowbandimaging.com, 8 February 2008)


What is a Dark Transfer Curve?
A Dark Transfer Curve is an application of the Photon Transfer analysis
method pioneered by Jim Janesick and Tom Elliott of JPL for the specific
task of assessing the characteristics and performance of electronic imaging
systems such as CCD cameras. The tool permits empirical data to be reduced
and plotted in a particular way so that critical system performance
parameters can be readily extracted.

To make a DTC plot you end up plotting the following data that is measured
from a camera system:

1) Total noise (Dark Shot Noise + Dark Fixed Pattern Noise + Read Noise)
vs Signal
2) Dark Fixed Pattern Noise vs Signal
3) Dark Shot Noise vs Signal

The things we learn from the DTC a

1) Camera conversion gain (e- / DN)
2) Read noise ( in DN or absolute units such as e-)
3) DSNU factor
4) Full well capacity (if you take long enough exposures)
5) And the data can permit you to calculate the dark current Quality
factor (the room temperature dark current/unit-area) and doubling
temperature

How to do it:
Take a collection of identical pairs of dark exposures with varying signal
levels from very low (like a bias frame) to very high (near full well). You
will need very accurate offset values so the best thing to do is to overscan
the horizontal shift registers if a CCD is used. For a CMOS sensor you
cannot take overscan data so a collection of bias frames
veraged together can give you the pixel by pixel offset values.

Data reduction:
The first thing is to determine the offset and subtract that from the raw
signal. I use Excel to do that as I will be making many calculations with
columns of numerical data. Then you need to measure the Standard Deviation
of a region of the image. The more pixels in the sample window, the more
accurate is the result. I use 100 x 100 (10,000 pixels) and that gives a
statistical accuracy of (sqrt(2/#-pixels). For 10,000 pixels the accuracy is
therefore in the 1.4% error range and is a convenient size to use on most
sensors.

The next thing is to difference pairs of identical dark frames. This results
in removal of the Dark Fixed Pattern noise and the standard deviation of
this difference is equal to sqrt(2) * the remaining noise, which is Dark
Shot Noise and Read noise in a quadrature sum.

Using the expression for the quadrature adding of uncorrelated noise
sources, you can compute the Dark Fixed Pattern Noise for each Signal level
in a separate column
Then the Total Noise, the quadrature sum of the Dark Shot Noise and Read
Noise, and the Dark Fixed Pattern noise can be plotted on LOG LOG scale
versus Signal. The units will be in DN (also known as ADU in the amateur
astronomy community). A sample Excel Spreadsheet layout is shown below:



The Y intercept of the Total Noise is the Read Noise. Once the read noise is
known you can again use the quadrature formula to isolate the Dark Shot
Noise and that is added to the DTC plot: again plotting noise against
signal. The final plot will look like this:



Interpretation
There are two major curves on the plot of interest: the Dark Shot Noise and
the Dark Fixed Pattern noise. The slope of the Dark Shot noise will always
be ½ when plotted on LOG LOG scale. The Slope of the Dark Fixed Pattern
Noise will always be 1: again when plotted on LOG LOG scales. The DSNU is
measured directly from the plot: it is the X intercept of the extrapolated
Slope=1 portion of the Dark Fixed Pattern Noise curve. It is dimensionless
(or expressed in percentage).

The Kadc (camera gain) is measured directly as well: it is the X intercept
of the Slope = ½ portion of the Dark Shot Noise Curve. It will have
dimensions of e- / DN. If the dark integrations are long enough, you can
observe full well being approached as the slope of the curves will show a
change on the high signal level end of the curves.

If you record the integration times and temperatures when the data is
collected you can also calculate the Dark Figure of Merit (a room
temperature measurement of e-/sec/pixel) or (e-/sec/cm^2) and that number
can be used along with the energy gap equation to
predict the dark current at any operating temperature. The energy gap
equation is more accurate than the doubling temperature method but that can
give good results over a comparatively small temperature excursion from the
reference temperature.

Additionally if you have dark integrations at other temperatures and
exposure times you can calculate the doubling temperature as well. So there
are a number of important parameters that can be learned from these plots.

Related Technology
The technique of plotting noise against signal can be also used to create
Photon Transfer Curves. Instead of Dark Exposures you use light exposures.
Many things can be learned from those plots including:

1) Read Noise
2) Signal Shot Noise
3) Signal Fixed Pattern Noise
4) Camera gain (Kadc)
5) Full Well
6) The effectiveness of flat fielding (are you improving the image by
applying flats or not?)
7) And a host of other parameters of interest.

I will write up a few examples of how to use this powerful tool in the near
future as time permits.

Richard Crisp

8 February 2008


www.narrowbandimaging.com














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