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As with all aspects of AstroPhotography what is offered here is very much an 'idiots' guide, intended as an introduction for those who have little of no knowledge of the subject. So apologies to all expert photographers for all errors and omissions! But comments welcome.
A webcam offers an affordable way into AstroPhotography, at least as far as the Moon, planets and brighter objects are concerned. The idea is simple. You capture a video, as short or as long as conditions and your scope will allow, then use computer software to select the best images to produce something like the brilliant astronomical photos that adorn the the magazines - well, eventually, with lots of practice and lots of luck.
One popular webcam is the Phillips SPC900NC and variants of that such as the 880SPC flashed to 900. These relatively cheap webcams are now only available second-hand. Telescope House say that their Orion StarShoot Solar System Colour Imager IV is a worthy successor to it. This costs around £85. There are also other Logitech models which can be modified as well as the Xbox, but that is outside the scope of this site - see forums such as the Stargazers Lounge for more information on this kind of thing.
More recently the Chinese manufacturer ZWO had produced a range of webcam which, as well having sensitive chips, offer much higher frame rates. I have the ZWO ASI120MC-S with which I can easily capture 5000 Lunar frames in about 1 minute. For this camera I use Sharpcap (mainly for the Moon) and Firecapture for the planets
As well as the webcam you also need to download software, including the webcam drivers. The program Phillips offer for video capture is called VLounge but wxAstroCapture is much better as it was optimised for this particular webcam. You also need programs for aligning and stacking the software of which the best is undoubtedly AutoStakkert!2 and for futher processing such as Registax - and later on something like PhotoShop - I use the cheaper Elements 11 which seems to do all the things that PS does as far as I am concerned.
With wxAstroCapture you need to join their forum - it's free. - in order to get the manual. Then, once you downloaded and installed the program it is a very good idea to connect up the camera and get used to the program before you even consider using it for astronomy. In particular look at the Properties and note the Colour option and the Exposure where you can see the settings for Brightness, Gamma and Gain. For the ZWO cameras the options include Sharpcap, which I mainly use for the Moon, and Firecapture which I use for the other planets.
Your first problem is actually finding your object. The procedure sounds simple. Power up your computer with the webcam attached, load WxAstroCapture, then put a low resolution eyepiece in your scope, center the planet nicely, then switch to a high power one - say 10mm - do the same with that. But far better still is to use a Reticule Eyepiece such as the Skywatcher 12.5m illuminated eyepiece rather than the 10mm. That will give you much more accurate centering.
Once you have centered your object take out the eyepiece and put in the webcam. Now select your camera from one of the options there and with luck you will see some sort of image in the black box on your screen. If you do then all you have to do is focus and center it as best you can and adjust the properties - see below. The Moon is big and bright and even if you want to image something else, it's a good first target to practice on and finding it will enable you to get the focus right and make it easier to find other targets.
However, if your are looking for something other than the Moon seeing something on your computer screen can be quite a challenge at first. And even if you have carefully centered the object, if the focus and/or brightness aren't correct you may not see anything anyway. So first try adjusting the properties - turn up the brightness and gain. Then try adjusting the focus. If you still can't find it and you are sure that the focus has been adjusted for the webcam, then start again - use a low power eyepiece and then defocus it so that it is quite a large circle - much easier to see if it is actually central. Then put in a high power one and center it. If you can't see it start again. Once you have it wait to see if it remains centrally in the eypiece. If it does, then carefully remove the eyepiece and put in the webcam.
Fo a bigger, more magnified image you would start off with something like a 2x Barlow and a low power eyepiece and then proceed as above. However, if the viewing is not good you will get better results without the Barlow. With my latest Celestron 235mm SCT AVX scope I find that although the Barlow works with Jupiter, with the Moon the results are just too fuzzy.
Once you have found your target adjust the Brightness. Too high values will give you over-exposed images and it is better to be on the dim side of things. And remember that what you see on the computer screen may not correspond with the image that the webcam sees. Adjusting the Gain may help but too high values can result in a grainy image. The Gamma option can sometimes be used to bring out the detail but should be used sparingly. If you are imaging a planet then make sure the Colour option is chosen. The Saturation and Hue can all be altered to change the colour and intensity of the image and it will be a question of experimenting and see what best suits your equipment and the object you are imaging.
With all the above getting the focus right is crucial. However, adjusting the focus will certainly cause the image to wobble for a few seconds - be patient and do as small adjustments as possible until the image is as sharp as possible - it will, of course be nowhere near as good as the end result - hopefully!
For all the properties, Brightness, Gain and Saturation the best values for any object will depend on viewing conditions and can vary considerably from night to night. Other factors that are important are the shutter speed, the frames per second and the number of frames captured. With something like the Phillips webcam and Jupiter start with 1/25 sec and 10 fps. The number of frames captured will depend on the subject and tracking ability of your scope.
With Jupiter you should limit the number of frames to around whatever you can get in 2.5 minutes. In the case of the Phillips webcam this limits you to around 1500 but with the ZWO I can get nearer 3000. The reason for this limit is because Jupiter rotates so fast. And with most of the smaller, cheaper scopes, the tracking ability will be less than perfect and the object may wander across the screen, thus limiting the length of the video you are capturing. This shouldn't matter too much and if you know in which direction the wandering will occur you can offset it to start with. Once you have everything set up simply Capture and away you go. If you have already decided on the number of frames - the default in WxAstrocapture is 2000 - then it is simply a matter of waiting until this is reached. If not then press Stop when you think you have enough. All you have to do then is process the resulting video. Best done indoors in the warmth with a nice cup of something hot!