The Theory
or How to create better images

Why combine?
How many frames?
Calibration: how to use dark, flat and bias frames

Which ISO speed?
The Calibration Process

Below you will find some simple information, however nothing can replace experience.
Some experts have decided to create an astrophotography dedicated web magazine which is full of precious, often hard earned knowledge.

Some past topics include Understanding noise in images, Drizzle discussion, Guiding imaging and much more.


Note: I am in no way related to this magazine or any advertisement that you may find in it.
I am only putting this banner because an issue is available for free and full of useful information.

Why combine?
The answer is simple: only to increase the Signal to Noise Ratio (SNR).

Is the resulting image more luminous? No.
Is the resulting image more colorful? No.

The goal of combing many images into one is only to increase the SNR. The resulting images are neither more luminous or more colorful but they contain much less noise which will let you stretch the histogram a lot more which will give you more freedom to bring back colors and details.

The example on the right shows the resulting image from a stack of 1, 2, 4, 16 and 32 images.

No calibration was done and some hot pixels are visible in some cases (no dark and bias subtraction, no flat division).

Mouse over the text to see the result of the stack for 
   1 image
   2 images
   4 images
   16 images
   32 images

You can see that the resulting image is not lighter or more colorful when the number of stacked light frames is increasing but is much smoother.


One Light Frame

How many frames?
The more, the better but above some threshold it is less efficient.

The signal to noise ration in increasing with the square root of the number of combined frames regardless of the exposure time of each frame.
This is true with all the combining methods (average, median, kappa-sigma clipping, auto-adaptive weighted average, ...) except entropy weighted average since this one in using the entropy to weight each pixel and thus is increasing the noise that is a big entropy contributor.

This means that if your base SNR is 1, when you combine 10 images the SNR increases by 3.16 (square root of 10). For 30 images it is 5.47, for 50 images it is 7.07, for 100 images it is 10, for 300 images it is 17.32.

As you can see to gain a 7 ratio 50 frames are needed between 1 and 50, but 200 frames are needed above 100.

Are 100 x 1 minute and 10x10 minutes giving the same result?
Yes when considering the SNR but definitely No when considering the final result.
the difference between a 10 minutes exposure and a 1 minute exposure is that the SNR in the 10 minutes exposure is 3.16 higher than in 1 minute exposure.

Thus you will get the same SNR if you combine 10 light frames of 10 minutes or 100 light frames of 1 minute. However you will probably not have the same signal (the interesting part). Simply put you will only get a signal if your exposure is long enough to catch some photons on most of the light frames so that the signal is not considered as noise.

For example for a very faint nebula you might get a few photons every 10 minutes. If you are using 10 minutes exposures, you will have captured photons on each of your light frames and when combined the signal will be strong.
If you are using 1 minute exposures you will capture photons only for some of your light frames and when combined the photons will be considered as noise since they are not in most of the light frames.

Can I combine two (or more) resulting images?
Absolutely, the square root rule applies with a small twist.

When combining two images the SNR increases by 1.414 (square root of 2).
If both images have the same SNR then this is the same as doing a single stack. That does not mean that the combination is giving the same image, just that the SNR will be the same.

However if one stack contains more light frames than the other, the SNR of the two stacks will be different and the SNR of the combination will be lower than the SNR of a single stack containing all the light frames.

Thus by combining the result of a 10x1 minute stack with a single 1 minute frame the SNR is roughly the same as the one obtained by combining 2 light frames. This is due to the fact that when combining two images the noise is additive and the best image is damaged by the worse image in the process.

Calibration: how to use dark, flat and bias frames
The calibration is the process consisting in subtracting the bias and dark signals and dividing by the flat signal.
The goal here is not to explain how to take dark, bias and flat frames (see here) but to better understand how to use them to get the best possible images.

A good idea
Everybody is saying that you must take dark, bias and flat frames to create great images, but if you are doing it the wrong way you can easily damage your nice light frames ending up with very disappointing results.

The good news is that it is really easy to get nice results. Here is why and how.

A common misconception
It is a common misconception to think that the number of dark, bias and flat frames is related to the number of light frames.
A lot of people are using very few (sometimes even only one) dark, bias and flat frames while they could get much better results by using a large number of dark, bias and flat frames with the same set of light frames.

Following the square root rule you will have much cleaner masters if you use a lot of frames to create them. Remember that you are trying to remove the dark and bias signals, not the noise that is coming with it.

For example when you subtract the master dark from each light frame you are adding the noise of the master dark to the noise of the light frame. The smaller the noise of the master dark, the less noise you will add to the light frame. This is also true for the master bias and the master flat.

In fact by using only a very small number of frames for the creation of the masters you can easily triple the noise of the calibrated light frame (bias and dark subtracted and flat divided) compared to the noise of the light frame before calibration.

You will then need 9 times (3 squared) more light frames to bring back the noise to the level you could have had by using noise free masters.

The example on the right shows the result of a stack of (mouse over the text to see the image)

32 light frames (no calibration)

32 light frames (2 darks, 2 flats and 2 biases calibration)

32 light frames (20 darks, 20 flats and 20 biases calibration)

As you can see increasing the number of dark, flat and bias frames is enhancing the resulting image making details more visible.

Stack of 32 light frames (no calibration)

This is the reason why you should use as many dark/bias/flat frames as possible. On the practical side, 20 frames is a minimum if you want to not add too much noise, and 50 to 100 will give you really nice and (almost) noise free masters..

A side note about hot pixels
Hot pixels are pixels that are not behaving normally. They are a very strong signal that is visible in each dark and each light frame.

Of course when you subtract one dark frame to one light frame you will remove the hot pixels which may give the false impression that the dark subtraction did its job.
However, at the same time the subtraction doubled the noise of the calibrated light frame and ruined it thoroughly.

Which ISO speed?
The question is common enough and the answer is simple: it doesn't matter...sort of.

In fact the ISO speed is just a setting of any DSLR, but since the CMOS or CCD chip is the same (you don't change it when changing the ISO speed, do you?) then the results are really the same.
This is not because you are using a higher ISO speed that you get more photons, it's just that the signal is more amplified (noise and all).

The good news is that you don't need to change the ISO speed to try to capture a fainter target. You just need to take longer exposures.

Of course it's a little more complicated than that since there is a good ISO speed for each DSLR.
However it depends on the characteristics of each sensor chip (readout noise and electronic noise) and is not simple to compute.
Christian Buil has computed the values for a few Canon DSLRs

DSLR Recommanded (Optimal) ISO Speed
Canon EOS 10D    400    (290)
Canon EOS 20D 1000  (1000)
Canon EOS 350D 800    (900)
Canon EOS 5D 1000  (1100)


The Calibration Process
The calibration process and how each set of files (lights, darks, flats,...)  is used is often perceived as a mystery but is in fact quite simple.

Below is the full calibration process when all the files are available:

Full Calibration Process (all files available)

However it is common and perfectly possible to properly calibrate without using dark flat frames. The calibration process in this case is described below:

Alternate Calibration Process I (no dark flat frames)

On the other hand if you are using dark flat frames you can also perfectly calibrate without using bias frames. Here's the process in that case:

Alternate Calibration Process II (no bias frames)

Any other combination leads to improper calibration so you should stick with one of these 3 possibilities.