| article: Thoughts about Image Calibration for low dark current, unregulated Amateur CCD Cameras to increase Signal-To-Noise Ratio (SNR) |
The first look at the raw image of a digital CCD imager as it comes right out of the camera is disappointing.
The whole picture seems to be noisy and grainy.
While there are many sources of noise in a CCD image many authors regard the dark noise as the most painful one and the most important noise to take care of.
As Richard Berry wrote:
"Like a Mantra tell yourself: I love dark frames. I love to take dark frames. I need to take dark frames."
Dark frames is the most important single issue an Amateur should take care of. ... You sould take dark frames with at least the same exposure time as your light frames. For best results take 5 times longer dark frames as light frames.
I am respecting the work of Richard Berry very much and in fact I learned a lot from his several books.
However I want to show that under certain circumstances it is possible to improve the overall SNR of an image by not taking dark frames at all!
These circumstances are
- Low dark current in the order of 0.1 electrons/pixel/sec at 10 degree Celcius ambient temperature.
- Not actively regulated (not constant) temperature at the CCD chip
A perfect example for such a digital CCD camera is the Starlight XPress HX916.
But the considerations are quite similar to all the Starlight cameras and some of the high-priced imagers.
The calculations below are done with the specification of exactly that model.
They will be compared to the SBIG ST-8e with a typical dark current of 1 electrons/pixel/sec.
Keep in mind that the latest models of SBIG have reduced dark current as well.
Click here for a comparison of many common and astronomical CCD and CMOS cameras..
Some Theory about the Noise in a CCD Frame
Let's first have a look at a formula which is accepted by professionel astronomers to give a good estimation of the SNR under certain observation circumstances:
The CCD Equation:
|  |  | The signal from the object of interest, i.e. a star. The photons entering one pixel of the CCD must be multiplied by the QE of the CCD camera to calculate the detected electrons.
Because the flux of photons is given per second of time we can also write:
S(star) = flux * exposure time |  | The signal from the object again, but now as the Photon Noise. It describes the uncertainty of the incoming light from the object because this light is generated randomly. |  | This term describes the noise introduced by incoming photons of the sky background. Again the number of photons must be multiplied by the QE of the CCD camera to calculate the detected electrons. |  | The noise by the Dark Current. A Dark Frame includes the electrons generated by the dark current plus the Bias Noise and Offset Level (positive offset to prevent negative values during readout) plus the Readout Noise. It can simply be recorded by covering the telescope so that no light can enter the CCD. It is strongly depending on the temperature of the CCD chip. |  | This term describes the readout noise introduced by the camera electronics. Unlike the other noises this noise is not Poisson distributed but it behaves like shot noise. Hence it must be squared. |
With this formula the SNR of a CCD image (in one pixel) can be estimated quite well. Note, that the Spatial Noise is not regarded here and that the Bias Noise is included in the noise of the Dark Frame.
For more detail see Howell, 2000 |
Let us now have a look at the typical noise distribution in a CCD dark frame.
As we have seen from the CCD equation the dark frame is actually containing the signal from the dark current plus the signal of the bias of the electronics (offset) plus the readout noise.
Now in a camera with low dark current, the dark frame's noise is actually dominated by the bias and/or readout noise.
A typical dark frame produced by the HX916 after 300 seconds at 10 degree ambient temperature could look like that:
- dark noise: 30 electrons / pixel
- readout noise: 12 electrons / pixel
- bias noise / offset level: 1300 electrons / pixel
The dark frame is by far dominated by the bias noise and the bias offset level.
The bias frame values are having a range from appr. 1200 to 1600 electrons with a slight vertical gradient.
The highest population of values is around 1300.
Hence it is not possible to just subtract one single pedestal value.
Finally the dark noise is in the order of the readout noise.
The dark noise part in the dark frame is very much depending on the temperature.
While the various CCD chips are slightly different in their response to temperature there is a good first guess:
For every 6 Kelvin of temperature change the dark noise is changed by factor 2.
In a CCD camera with unregulated temperature at the chip this has serious consequences.
It means that every light frame should be bracketed by darkframes to keep the temperatures as close as possible.
Every one of these light frames should later be corrected by the combination of both dark frames.
For a very good final frame we might want to use 50 or 100 light frames.
That means ending up with a very lengthy and boring task of image reduction.
Furthermore, the dark frames of unregulated cameras cannot be stored for later use because the actual temperature at the CCD chip is usually not known.
Some guessing about the temperature seems to be possible but subtracting a bad dark frame might introduce more noise than it actually should decrease.
So we finally might end up with 50% exposure time spent for acquiring dark frames.
At least.
That means losing 50% of the exposure time for the light frame.
But the more exposure of the light frame the better the SNR!
On the other hand we have seen that the dark frame is dominated by bias noise.
So: Why not just subtracting a bias frame instead of a dark frame and using the free time to expose light frames?
The bias frame of a healthy camera is very stable over time, so it can be reused for several months.
Because of noise considerations a master bias frame should be combined from as much bias frames as light frames will be taken.
In my case I took 100 bias frames (for each binning mode used).
The exposure time is 0 seconds so the work can be done quickly and during the day.
If there is no pollution by cosmics we should use the mean (or average) combination method.
This is giving a slightly better SNR for random noise.
If there are cosmics the median or Sigma-Kappa combination is the better choice because they will reject the cosmics.
Example calculations
This is an estimation of the final SNR after image reduction with dark frame correction (red) and with master-bias frame correction (green).
The first case is a SBIG ST-8e.
Under perfectly dark skies as well as under little light polluted skies it is dramatically better to invest 50% of the exposure time into dark frames.
Obviously this is the case Richard Berry talked about in his book about astronomical image processing.
Now to the HX916. The best case is regarded here with -2 degree Celsius ambient temperature which is lowering the dark current by appr. factor 4.
The situation is just the other way round!
The investment of valuable exposure time into dark frames instead of light frames is reducing the final SNR dramatically!
The results at 10 degree Celsius ambient temperature are quite typical for nights in central europe from spring to fall.
Again dark frames are a waste of time respectively SNR.
The results at 16 degree Celsius ambient temperature which is a warm summer night in central europe.
Still taking dark frames cannot improve the SNR.
For higher temperatures and very dark skies we slowly reach the point to consider dark frames.
But the improvement will be very small.
So I think it is obvious that dark frames should not be a topic for these cameras - especially under some light polluted skies.
Conclusion
It should be obvious now that dark frame correction is not useful for low-dark-current CCD cameras.
But by only using the master-bias frame for image correction there will be no correction for thermal hot pixels.
This can be solved in different ways.
1. Using flat-frames of similar exposure time should correct for these pixels in some degree.
It might be a problem to match the exposure times though.
You needed a light box for the frame with very low lighting conditions and you will lose exposure time for supporting frames again.
Additionally correcting the thermal hot pixels by a drak frame is more accurate.
So this method is not recomended.
2. Median or Sigma-Kappa frame combination methods together with a little drift between guide scope and main scope are able to detect these pixels and will not add them to the final frame.
For sure this is not suitable for off-axis guiders.
3. If these pixels are rare you can replace these pixels with its neighbour pixels in the final image.
My HX916 has only one thermal hot pixel.
Remeber that a fully exposed thermal hot pixel is containing close to nothing of information about the object.
So replacing it by its neighbour does not mean to lose too much information.
4. Applying a median filter with 3x3 before combining the images.
Please use the link below to find real astro photos taken with that method:
master-bias corrected only
Comment by Rick Krejci 06.03.2003:
Fantastic article on using darks for the SX cameras! This is something I have been preaching (and doing) for over a year now. And I've found it's even more the case with the SXV-H9, as it's more sensitive but no more thermally active.
I've done informal, more subjective studies myself, but I'll be glad to have your study as a great reference!
Comment by Joaquin Ferreiros 09.12.2003:
Fine article. I have tried this technique with my Cookbook 245-LCD and it works!. With master bias subtraction + flat fielding, only the hot pixels remained on deep sky images. To eliminate hot pixels I suggest the following method which I have just used successfully with AIPwin software:
1- Obtain a master dark frame by median filtering several long exposure darks.
2- Subtract the master bias from the master dark, obtaining a thermal frame
3- On AIP win, invert the thermal frame (click: enhance-pixel ops-invert), so that hot pixels will be black and the rest of the frame will be white .
4- Stretch the resulting image, looking first at the histogram, so that only the dark pixels are black, and the rest of the image is white.
5- Go to “defect correction” and click: calibrate-defect correction-copy image to defect map-classify defects-save defect map. In this way, you have a defect map, which you should load (load defect map), and apply defect correction when processing your images, so eliminating the hot pixels.
I hope this suggestion will be of interest, specially for low noise CCD cameras such as SXV-H9. Soon, I will have one on these cameras!
|
|
|
