Astrophotography in the digital age   Leave a comment

I’ll discuss the optics of ‘image stacking’ shortly, but first, some eye candy. Here are some recent images: Saturn with (from lower left) Titan, 74 Vir and 72 Vir-

The globular cluster M53 (which we have shown already) and M3:

The globular cluster M13 in Hercules:

And this, which I am calling the Nikonian Deep Sky Survey:

The goal of this image was to see how far I could push my imaging equipment- let’s see how it does. The lens used was a 400mm f/2.8 lens, and the camera setting was 0.8 s seconds acquisition time at ISO 3200- how that translates to electronic gain is unclear, but it’s pretty high- there’s a lot of noise present:

The bright stars in this image are about magnitude 7.5- the viewfinder appears black as these stars are too faint to be seen by eye. I ‘sight’ the image off nearby ρ Vir, a magnitude 4.9 star. This image tells us a few things. First, the stars image with a FWHM of 4 pixels- this should be compared with the diffraction-limited Airy disk, which corresponds to 3.5 pixels. The image is (spatially) pretty good. However, dim objects can’t readily be seen- here’s what I mean.

The image is an 8-bit greyscale image- the brightest stars are at a grey value of 255. The noise in this image has a grey value of about 22: the ‘dynamic range’ of this image, in terms of stellar magnitudes, is 2.5[log(255/22)] = 2.66. This means, if the brightest object in the frame is magnitude 7.5, the dimmest object is only magnitude 10. Given the limit of a 6″ telescope is magnitude 13, there’s *lots* of room for improvement. ‘Image stacking’ is a way to increase the signal-to-noise ratio, by distinguishing between background noise (which scales as the square root of exposure time) and signal (which scales linearly). The way we do this is to acquire a *lot* of images- like 6000. These are split into groups of about 700 (batches), and each batch is stacked over the weekend. After a few days, we have reduced (say) 6000 8-bit images to 8 16-bit images. We subtract the background from each of these intermediate images, and then stack those to produce a the final image:

This doesn’t look much better. BUT, the bright stars (in this case) have a grey value of 59000 and the background noise has a level of 50, for a dynamic range of 7.7 stellar magnitudes. So, we should be able to find objects as faint as magnitude 14.7- easily beating the ‘limit’. But there’s still a problem- the display only shows 8 bits of greyscale, so somehow we have to compress the dynamic range. This process is much more ‘bespoke’ and requires a lot of trial-and-error tweaking, but generally involves changing ‘gamma’ (a nonlinear contrast enhancement similar to midtone adjustments) and unsharp masking combined with denoising to clean up the compressed image. The reason the final image has concentric circles is an artifact of all this post-processing, and decreases as the number of images increases (remember, the background increases *slower* than the signal). So let’s see what we can find- here’s the image again with some ‘goodies’ circled:

“Obvious” galaxies are circled (blue are Messier objects, yellow are New General Catalogue (NGC)- some of these are magnitude 13, so a more careful search will likely find more. There are about 100 in this section of sky, most of them magnitude 15 or brighter, so there’s a chance we can find a *lot* more. Stay tuned!

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