How to calculate CCD Gain, Read Noise and Dark Current

[MarkS]

The procedure for calculating gain and read noise is at the bottom of this page:
http://www.astrosurf.org/buil/20d/20dvs10d.htm

Some comments:
* Make sure you are shooting raw frames - not jpgs.
* Take a bias frame (very fast shutter speed in the dark) to use in step (2)
* Step (3) is only needed if you are using a colour camera
* Step (8 ) - the variance is the square of the standard deviation
* Step (9) - the gain calculated is only approximate.  The true gain is only obtained as the slope of the curve in step (10)
* Step (10) - when he says repeat for many values of S he means take two (flat) images at each of many (short) exposure times but, of course, never let the CCD saturate.
* Step (10) - in practice you are likely to find the "straight line" is slightly non linear because of limitations in the electronics.  RON is "Read Out Noise" of course!


For my Canon EOS 300D at ISO 800 I obtained the following:
Gain = 1.3e/ADU
Read noise = 13e

Once you have the gain and read noise it is time to calculate dark current at a particular temperature.  I've never found a description of how to do this on the web so this is my own technique.
Take two (raw not jpg) dark frames at each of the following exposure times:
1min, 5min, 10min, 20min

I use the following relationships:

mean pixel value (electrons) = bias(t) + dark_current*t
variance pixel value = read_noise_variance + variance(dark_current*t)

t is the exposure time
I have written bias(t) because the bias of many cameras (e.g. both Nikon & Canon) is time & temperature dependent.  They subtract the average value of unlit pixels on the CCD from the total image and then maybe add an offset (128 in the case of the Canon EOS 300D)

Note that variance(dark_current*t) = dark_current*t
because thermal noise is a Poisson process - assuming we are calculating dark current in electons and not ADUs.

So we can write: pixel variance = read_noise_variance + dark_current*t 


Now to the calculations:
1) Take the two 1min frames and subtract one from the other.
2) Multiply by the gain (to convert the units to electrons)
3) Calculate the standard deviation of an area of the difference frame, well away from any amp glow effects.
4) Square the standard deviation to get variance
5) Divide by two (because the initial subtraction of 2 frames doubled the variance)
6) Subtract the square of the read noise (in my Canon case 13*13=169)
The resulting value is the number of electrons that have accumulated due to dark current

Repeat steps 1-6 for each exposure time and plot a graph of the value obtained in step 6 against exposure time.  This graph should be more or less a straight line and it's slope is the dark current.

Alternatively, divide the result at step 6 by the exposure time to get a rough estimate of dark current.

For my Canon ESO 300D at 22C (room temperature) I obtain almost exactly 1 electron/sec i.e. 60 electron/min

At fridge temperature (4C) I obtained approx 8 electron/min

I haven't yet done this in the freezer!

[MarkS]

I've grabbed myself an EOS 350D off Ebay:

For the Canon EOS 350D at ISO800 and an ambient temperature of 22C I get:
Gain 1.1e/ADU
Read noise  5.5e (RMS)
Dark current 0.5e/sec

The equivalent figures for the EOS 300D were:
Gain 1.3e/ADU
Read noise  13e (RMS)
Dark current 1e/sec

The figures agree suprisingly well with those at http://www.pbase.com/terrylovejoy/read_out_noise_in_dlsrs but note the gain will be different because they used ISO400.

This indicates that the 350D is a definite improvement over the 300D.

[MarkS]

I repeated the experiment on my newly acquired second-hand EOS 350D at beer fridge temperature 6C .

Gain 1.1e/ADU
Read noise  6e (RMS)
Dark current 0.06e/sec   (i.e. 3e/minute)

These figures agree well with the 22C figures and demonstrate an approximate halving of dark current for every 6C reduction in ambient temperature.

So on a Winter's night at Tuesnoad, the light pollution will be the main limiting factor.  At the Dec-07 DSC I measured the Tuesnoad background flux to be around 10/e/pixel/minute.

[JohnP]

Mark - looks very promising - can't wait to see some images. Is this the camera you are planning on modifying? John

[MarkS]

Yes, I'll definitely mod the 350D!  But I'll mod the 300D first as a trial run.  Assuming that goes well, I'll mod the 350D afterwards - otherwise I'll send it away to be modded.

I'm still waiting for Baader replacement filters to come back into stock ...