What's `photon shot noise' ?

What's in a name?

As I was thinking of starting an imaging blog, I decided that the first `content' to be created would have to be the blog's name. I wanted to use something memorable, perhaps a bit unusual. As with many aspects of this blog, I'm following in the footsteps of a good friend who writes an astro-imaging blog called Cilice Astrophotography. Both of us have been experiencing / suffering / celebrating this hobby for a while now. A mutual friend (who's a visual observer) sometimes calls us the `hair-shirt monks', due to the often-ridiculous levels of penitent devotion that are required to get good image data and to process the images. Cilice Astro's `About' page links here, which pretty well sums up the attitude that one needs in order to become an imager.

Since hair-shirt-related names were out, I found myself searching for an interesting-sounding name from the science and craft that is `imaging'. I decided on Photon Shot Noise.

To make a long story short, PSN is something that a beginning imager can see as a goal, as in `ooh, finally, my images have very little noise from my equipment! They just have the photon shot noise from the sky!' Eventually, an aspiring imager realizes that this is but one step on a long journey, and that all sorts of further efforts and gyrations will be necessary. Imaging is like climbing an endless mountain, on which one must climb up and over one false summit after another, chasing an ever-elusive goal. That goal? An image that is as free as possible of `noise' and other visually distracting flaws. And, further, an image that has been processed so as to make the most of the data, displaying those data in the clearest / most aesthetically pleasing / most scientifically useful manner possible.

Okay, so an astro-imager is on a never-ending quest for lower- and lower-noise images. But just what is `noise' in an image, and why is it so bad? Isn't `noise' related to sound, and not images? This is a long and detailed subject, but here's a quick overview:

Noise in an image is best seen if you take your digital camera - probably in your phone, and that's fine - and take a picture in a low-light setting. If you look closely at the image, you'll see that it looks grainy. Commonly, there are small colored dots all through the image, and they distract you from seeing the real details in the scene. To an observational astronomer, a camera-sensor designer, an imaging-software programmer, or a signal-processing engineer, those distracting little dots are called noise. The real details in the scene are called the signal. If you have a lot of signal and not much noise, that's good, and we call that a high signal-to-noise ratio (SNR). If, on the other hand, you have a lot of distracting little noise dots, and the details of the scene are weak relative to the noise, then you have  a low signal-to-noise ratio. That's bad.

Anyone who's taking a picture, whether it's someone taking a snapshot with their cell phone, or an astronomer imaging a distant galaxy, needs a high SNR in order to get a good-looking image. No one likes grainy pictures, unless it's for some specific artistic effect. The astronomer, whether a researcher or an amateur, is cursed with three big problems:

1) The object they're shooting is almost always faint. This means the signal is small - and that makes it hard to get a high SNR.

2) The equipment they're using creates electronic noise, which shows up as those distracting little noise dots. (If you had some low-performance audio equipment, it might generate things like hiss or static in its circuits, which you would also call noise.)

3) Even if your equipment didn't generate noise, the sky itself is going to introduce noise into your image. This is the photon shot noise. It comes from many sources, but here's the remarkable thing:

At any time, every part of the scene you're looking at is flickering up and down in brightness, and it's NOT due to problems with your eyes or your camera! Let's say you have a telescope with a digital camera attached, and it's pointed at a `blank' piece of sky, with a lot of dark background between the sparsely-scattered stars. Even that `blank' background sky is flickering a bit in brightness, and the `flicker' is different at every point on the sky. The tiny bit of light coming from every `blank' part of the sky comes from several sources, such as a faint, permanent aurora in the Earth's atmosphere, from sunlight scattered off of dust between the planets in our solar system, and from the faint, unresolved light of dim, distant stars, galaxies, and quasars. That tiny bit of light is never quite the same from moment to moment (or from point to point on the scene), and the variation is the PSN.

Here's the really crazy part: Every natural process that generates light has this slight `flickering' built into it. Anything generating photons - the little particles that make up light - does it at a slightly non-constant rate. The reasons for this run quite deep, and many people have gotten Nobel prizes for investigating the physics involved. It's called quantum physics or quantum mechanics, and it was first developed in the early 20th century. A famous example, closely tied up with this strange `natural flickering', is Heisenberg's `uncertainty principle'.

So, imagine that you're a beginning imager. You have all these problems with noise coming from your equipment. Eventually you learn how to reduce this noise to the smallest possible level. You're done, right? Nope! Now you've still got the photon shot noise to deal with - that's the `natural flickering' I've been talking about. Oh brother, does that mean the quest for low-noise images is hopeless? No, fortunately. But it does mean there's a lot of work left to do. Two main ways of `beating down' the PSN are to:

1) Go to a darker site, where there is less PSN from human-made light pollution, and

2) Take longer and/or more images of the same object, and combine them with software.

If you become an astro-imager, once you get proficient with your gear, your life will revolve around these last two items. Have a nice life! Prepare to drive a lot of miles, unless you already live in a remote area, and prepare to lose a lot of sleep! As my friends and I like to say, get ready to put on the hair shirt!

The topic of noise in images is quite detailed - here is some further reading:

Craig Stark's article on SNR

More of Craig Stark's articles on image noise

A tutorial from Nikon's remarkable `Microscopy U' site (see also the similar site from Olympus)

Chapters 2 and 6 in The Handbook of Astronomical Image Processing by Berry and Burnell - this is something of a `bible' for amateur astro-imagers.