Rob’s recent post on his new scope led me to reflect (!) on my own experiences. My main interest is deep-sky objects, or “faint fuzzies”. I have a rule of thumb that says that to see any appreciable difference in object brightness, you have to go up 2 stops in focal ratio (f-numbers). This translates to a doubling in aperture (doubling the aperture increases the light grasp by 4X). So when I upgraded from my old 4”, I went to 8”. Doing the same again would suggest a 16” would be needed. For me, a 16” would be unmanageable, so I went to a 12”. This is only 1 stop advantage to the 8”, and visual results were a bit disappointing. This more-or-less coincided with getting the PD camera, and even using this “live” as an electronic eyepiece gave views so superior to the 12” that the 12” virtually never got used.
So I wondered why this was, so here is a bit of basic physics.
Firstly, the eyeball. This iris opens to about 7mm when fully adapted to the dark. Or maybe 5mm in an old fogey like me. Given the size of the eyeball this is around f/3. See http://www.faculty.virginia.edu/rwoclass/astr1230/human-eye.html
To get the brightest image from a scope, the magnification from the scope must produce an exit pupil (the beam width leaving the eyepiece) pupil less than 5-7 mm. Otherwise some of the light leaving the scope doesn’t enter the eye and is wasted. This defines the minimum magnification you can use for a given aperture. For example with the 8” and a 5mm exit pupil, this minimum magnification is 200/5 = X40. (The SCT has a focal length of 2000mm, so this is an eyepiece of 50mm FL). A lower magnification than this is not harmful, it is just that you are then not making use of all the available aperture. 7X50 binoculars are known as “night glasses” for exactly this reason – their exit pupil is 7mm, making the best use of all night-time light. Therefore, going up in aperture does not necessarily make the view brighter, but rather allows you to us a higher magnification for the same brightness. This might be a huge advantage for small objects like planetary nebulae, but less so for extended objects. Bigger aperture also improves resolution, allowing you to split closer binaries, but this is usually not the critical issue for faint fuzzies. The other issues affecting brightness are the eye sensitivity (more of this later) and its “integration time”, or the time period over which the eye sums the image it sees. This is its “shutter speed” and there is some literature that suggests in the dark, this is about 0.2 seconds. Again. see http://www.faculty.virginia.edu/rwoclass/astr1230/human-eye.html
Now, from here, I have NEVER conclusively seen any galactic spiral arms visually, although sometimes I have persuaded myself I can. So when I first coupled up the PD camera to the 8”, and turned it on M51, this is what I saw, live, with no processing at all:
Bingo! Spiral arms!
So if we are now talking about imaging, rather than the eyeball, what comes into play for image brightness?
- Focal ratio (not aperture)
- Integration time. The PD single image is 1/50 second. Its “senseup” parameter allows it to internally stack up to 1024 single images, giving an integration time of about 20 seconds, or about 100 times the eyeball.
- If the CCD had the same sensitivity as the eye, the brightness of the CCD image would be the same as the eye if a senseup of 4 were used. An experiment is called for!. I attached a lens to the camera, set it to around f/3 (similar to the eye), then in a darkened room compared the image from it to that I could see with my eye for various senseups. Although this is a very crude experiment, I reckoned that about senseup=2 was about right-not miles away from the predicted value. So a senseup of 1024 suggests a sensitivity about 8 stops faster than the eyeball.
There is also another factor involved, and that is contrast. This is the brightness of the faint fuzzy compared to the sky “background”, and I have found that with our local skies, that is the controlling factor. You can improve this visually using filters (UHC or OIII for example). These tend to dim the whole view, but the right one can improve contrast. Light pollution filters used to be good in the days of low-pressure sodium street lighting but are not much use with LED lights. On the other hand, the camera has a “gamma” setting that allows you to “stretch” the contrast, live, or if you post-process, the sky is the limit, as they say! For example, stacked 11 of the basic frames of M51 (11264 frames in total), processed it with GIMP, and here is the result. It is flipped vertically to get the orientation right (See http://www.thornett.net/Rosliston/Astrophotography/DSO.pdf for the details). Stacking 11 frames with a senseup of 1024 gives another 3 ½ stops faster than the eyeball or 11 or so altogether.
Interesting as all this might be, let’s remember that this is a hobby – and you do whatever you enjoy!
As a final thought, Lord Rosse used a 72″ aperture reflector to first identify the spiral nature of M51!