Lucky Imaging Theory

Lucky imaging gives us amateurs the possibility of shooting deep space targets at resolutions hitherto only seen in multi million dollar professional observatories. The basic premise behind lucky imaging is explained in the first five minutes of my video: £700 vs £7,000,000: Astrophotography Shoot Out

Benefits

 

DRAWBACKS

  • Only works with scopes that can resolve stars to better than 3 arcseconds FWHM (see a list of scopes that can do this here).

  • You throw away more than half of the subs so you need to spend more than twice as long gathering data to catch the same number of photons

  •  Lucky imaging techniques struggle to resolve the dim bits. If you are interested in going ‘deep’ regular imaging techniques are prefereable.

 

The Enemy

In the UK the atmosphere wobbles around so much that when we look into space it blurs everything we see by 1 to 3 arc seconds (depending on the weather). This isn’t a problem for small telescopes.  A perfect small 72mm refractor can’t resolve anything smaller than 1.6 arcseconds anyway and most refractors aren’t perfect. But when the fatness of your telescope grows and its potential resolution increases then  assuming your mount isn’t wobbling all over the place then the atmosphere becomes your biggest source of blurriness. INCREDIBLY us nerds have found a way to reduce the atmospheric blur by employing a technique known as lucky imaging.

 

Below, the atmosphere giving Jupiter (as seen through Big bertha with a green filter) a good wobble 

By choosing just the lucky less wobbly frames and stacking them (and adding the data from the red and blue channels) the above produced this much sharper image of Jupiter.

Lucky Imaging 

Lucky imaging relies on the fact that the amount of blurriness the atmosphere delivers varies from one moment to the next. So over the course of a minute you might get a few patches of relative calm. This can help us.  If during that minute you shoot 60 x 1 second exposures rather than say a single 60second exposure  then you will discover that  the shots taken during the calm periods will be crisper than the shots taken when the atmosphere is more wobbly. If you then only stack the sharpest images which were shot at a lucky moment of atmospheric calm and throw away the blurry images your resulting stacked image will be much sharper than the single 60 second exposure. The shorter your exposures and the more subs you throw away the sharper your final image will be. Lucky imaging makes it possible for  us amateurs  to resolve details smaller  than 1 arc second (and maybe even smaller than that). So lucky imaging is really exciting. Of course because we are throwing away a lot of frames lucky imaging requires us to image for longer to catch the same number of photons. So the sharpness comes at a price and that price is noise.

Lucky imaging has been used for 20 years on the bright planets but now thx to very sensitive low read noise CMOS cameras we’re able to lucky image dim deep space too. 

My first attempt at lucky imaging

In my first attempt at lucky imaging I used 5 second exposures with my little 6inch Newtonian – the ‘Red Devil’. As you will see later it turns out 5 seconds is too long an exposure length for real lucky imaging although it still makes a difference. Even with these overly long exposures the signal was so weak that my shot of M106 was very noisy in all but the core of the galaxy. The noise was further increased by the fact that i threw 50% of my least sharp subs away. The more subs you throw away the more the noise increases but at the same time the more the sharpness of the final image increase. I personally think its worth it as the detail in M106’s  core is GOBSMACKING😉

Solving the noise problem

To reduce the noise in images shot with the lucky imaging technique you need to collect more photons. You could simply throw less subs away but that’ll reduce your sharpness. You could buy a bigger, fatter scope so you collect more photons per second but that costs more money (see best lucky imaging rigs). Or you could collect more photons by simply shooting the target more often but in the UK clear skies tend not to last. I decided that the best way to reduce the noise was to persuade as many amateurs as possible to shoot the same target and share their data with me 😜

And that led to the biscuit setting up The Big Amateur Telescope (aka The BAT): an international band of amateurs who all shoot the same target and share their data. The BAT is also a place where fellow nerds delve deeper into lucky imaging theory.  Below  is some of what we have found out so far.

Best Exposure Length

The graph above shows us that even  at a comparitively long 0.3 frames per second (3.33 second exposure) we will start to see the benefits of lucky imaging (if you were to stack  just 10% of your 3 second subs you should see a 40% improvement in sharpness). This is the kind of sub length I would recommend for deep space lucky imaging. If you have one of the new low read noise cmos cameras, and if the target you are shooting is bright enough, you may be able to go much shorter. If you are able to shoot 0.1second subs (and still successfully stack them) then by throwing away 90% of them you may be able to double the sharpness of your image.

This remarkable graph taken from a physcis paper by N.M. Law, C.D. Mackay, and J.E. Baldwin tells us how much sharper our images will get when we reduce our exposure time AND how much sharper our images will get when we keep 1/10/50 and 100% of the subs.

Best Percentage of Subs to Stack

From the graph above i would suggest that stacking around 10% of your subs is a good place to start. But this isn’t just theory. Bat member MrCrazyPhyscist has run his own real world tests with his C14 and ASI1600MM and come out with similar results.

Best Pixel Scale

Based on the fact that the best seeing we get in the UK tends to be about 1arcsecond and we’re trying to do better than the seeing, I would recommend you pixel scale to be 0.5 arc seconds per pixel or smaller. I appreciate that lots of nerds will want to talk about  over sampling. I personally think that kind of talk is old school. After all you don’t worry about oversampling when you are shooting the planets (or at least not in the same way). And please dear reader bear in mind that planetary photographers are able to shoot details 10times sharper than the Dawe’s limit of their scopes… and us deep space lucky imagers are trying to do the same.

 

Seeing

This graph from those clever professional nerds N.M. Law, C.D. Mackay, and J.E. Baldwin  also shows us how seeing affects the results of stacking fewer frames. When the seeing is bad reducing the % improves the results greatly but its also worth noting that the better the seeing the bigger the effect of lucky imaging.

This is what N.M.Law says about this graph (good luck!)

Fig. 4. The factors by which FWHM and FWHEF (full width at half enclosed flux) are improved at slow frame rates (12FPS),
at three seeings. Obtained from linear fits to figure 3 and similarly derived results for the FWHEF. Starting at the leftmost point
of each line, datapoints correspond to selecting frames at the 1%, 2%, 5%, 10%, 20%, 30%, 40%, 50%, 75% and 100% levels
respectively

Best Gain Setting

This is an easy one. Check out the read noise vs gain graph for your particular camera and choose a gain setting that gives you near as damn it the least read noise. For my ZWO asi2600mm its a gain of 350 (out of 400). You don’t need to think twice about all the dynamic range we’re loosing with these high gains bc our lucky imaging  shots are so short we’ll never fill our wells up anyway.

Best Targets

The best targets for lucky imaging are bright ones!!! That’s because we loose so many photons through throwing away 90% of our subs  we need to make up for it by having lots of photons to begin with.

Like planetary photography it also makes a huge difference shooting targets that are directly overhead. This is so important that its almost not worth bothering to shoot any target that is lower than 70 degrees.

lucky imaging atmospheric dispersion

And the final consideration in my opinion is contrast. This isn’t directly to do with lucky imaging but sharpening techniques such as wavelets of deconvolution allow us to pull out signifinatly more detail and these sharpening techniques work very well on high contrast targets.

Best Wavelengths

Short wavelengths of light like Ultra violet get disturbed by the atmosphere far more than longer wavelengths of light like red or infra red. It’s clear that when lucky imaging we must block out the UV light. I have a UV cut filter which I’m planning on using. But is it enough. Is it possible that just shooting in infra red will actually give us the sharpest results. If you look at my shot of Jupiter you can clearly see how much sharper Jupiter becomes as the wavelengths get longer. I think this is a good area for experimentation. It maybe longer exposures in just red and ir yield better results than shorter exposures in luminance… when I find out I’ll tell you! If you are interested you should really be a member of The BAT already!

Jupiter shot with a blue filter

Jupiter shot with a red filter

Jupiter shot with an ir filter