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# Chasing the curve

April 2012: Learn the limits of combining images to reduce noise.
RELATED TOPICS: ASTROIMAGING
Most fairy tales have their origin in the ancient past, but a select few have modern roots. In astrophotography, one such tale goes something like this: “If we just take enough frames of our subject matter and average them together, all the noise in our image will go away.”

Similarly, we get recommendations to take “hundreds of dark frames” in the hope that we will have a “pure” master dark, the better to create a perfect picture.

Ain’t gonna happen.

Looking at the graph at left, we notice something interesting. The level of noise does drop dramatically with the averaging of multiple frames at first, but then something strange happens: The curve begins to level out. Specifically, the improvement is substantial up to 16 frames, but after 25 frames, the improvement basically ends.
Combining a number of dark frames decreases noise initially, but after about 16 frames, the improvement fades as the noise level slowly approaches (but never reaches) the asymptotic boundary. Astronomy: Roen Kelly, after Tony Hallas
We call this boundary an “asymptote” — a certain number that a changing value approaches but never arrives at. Put another way, there comes a time beyond which further data collection achieves nothing in terms of noise reduction.

Related to this is the signal-to-noise formula: The improvement of signal to noise equals the square root of the number of frames combined. Four frames will thus double the signal over the noise, 16 frames will have a fourfold increase, and, theoretically, 25 frames will see a fivefold increase. Remember that at 25 frames, we’re getting close to the asymptotic boundary, beyond which noise doesn’t improve. Plus, the difference between four times and five times improvement is slim to begin with. Adding nine more frames accomplishes basically nothing.

In my experiments, I couldn’t see any improvement after combining nine dark frames. Indeed, comparing the results of a three-frame dark and a 40-frame dark revealed no visible difference when I combined the light frames as a mean (average). See the photo comparison at right for a visual reference.
The rate of return for noise reduction diminishes quickly in the author's experiments. Note that the apparent noise level is identical between a three-frame dark (at left) and a 40-frame dark. Tony Hallas
Mixed in with all of this is the darkness of your sky, the nature of your subject matter, the accuracy of your tracking, the noise characteristics of your camera, and the optical integrity of your imaging device — all of which will have an effect on your final noise level. It’s a lot to handle.

Remember, you can’t take infinite frames. Make each one count, so that when you combine them to reduce noise, you bring as much as you can to the table. It is thus better to take the longest exposures that your equipment and sky will allow.

After image processing, use noise-reduction software on what noise remains to create the illusion of infinite data. That’s how to get a real-life happy ending.
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