To obtain the best images, it is very important to match your camera to your optical system.
Resolution depends on both the focal length of the telescope, and the size of the pixels in the camera sensor. Long focal lengths and small pixels result in higher resolution. Too much resolution and the images will be fuzzy. Too low resolution and you will not be achieving the full potential of the instrument – you may even end up with small square-looking stars.
Often the matching can be adjusted by using auxiliary optics (reducers and barlows) or binning. The key to good performance is achieving proper Nyquist sampling.
The Nyquist Sampling Theorem sets the fundamental limits on any system that digitizes signals, whether it be a CD player, a telecommunications system, or a digital camera. The theorem tells you how fine sampling is required to produce a ”perfect” representation with no loss in quality.
The American physicist and electrical engineer Harry Nyquist proved that if the sampling is at least twice the highest spatial frequency component in the image, no distortion will occur and you can reconstruct an exact replica of the original image. The theorem really requires the image to be filtered (smoothed) to remove any higher frequency components; but in practice, the limitations of the optics and seeing take care of this for you.
For that reason, for optimum performance, you need to have at least two pixels across the core of a star image. By ”core” we mean the Full-Width Half Maximum (FWHM); i.e. the diameter at which the star intensity falls to one-half its peak value. For practical purposes, the sampling really needs to be 2.5 to 3 pixels across the FWHM. For high performance applications, such as profile-fitting photometry, even higher sampling is required to represent the exact shape of the star image.
There is a second part to the Nyquist Sampling Theorem – the image you capture isn’t a perfect representation of the original image; it just contains all the information necessary to reconstruct it. To properly view the image, you need to pass it through a reconstruction filter. In a digital system, this can be done only by resampling the image to a higher resolution and then low-pass filtering it. MaxIm DL can do this with the Double Size command.
For small optics (microscopes, telescopes under 10 cm or 4 inches), the focal ratio is the important factor. The pixel size needs to match the spot size, which for a perfect optical system is the diameter of the Airy disk, the image created by a perfect point source such as a star. The spot size can be calculated with the following formula (assuming a wavelength of 550 nm):
spot size (microns) = 1.38 * f/ratio
If you adjust the focal ratio so that the spot size is at least twice the pixel size, you will have adequate sampling.
The effects of seeing, the random star motion caused by atmospheric turbulence, increases the practical spot size for larger instruments. In this case, the seeing disk in arc-seconds and the focal length are the important parameters. You can calculate the size of a pixel in arc-seconds using the following formula:
pixel size (arc seconds) = 206 * pixel size (microns) / focal length (mm)
(The result can be quickly estimated by rounding off the constant in the equation to 200. For example, suppose a camera that has a pixel size of 9 microns is attached to a telescope with a focal length of 2000 mm. The pixel size is 9 * 200 / 2000 = 0.9 arc seconds.)
Seeing can vary quite dramatically from night to night, and even during a single night. At a typical low-altitude observing site, the seeing disk typically varies from 2.5 arc-seconds to 4 arc-seconds. You may see the occasional night that is even better, or much worse! A premium site may have seeing as good as 1 arc-second and sometimes even better.
Under reasonably good conditions (2.0 to 2.5 arc-seconds), you need a resolution of 0.6 to 0.8 arc-seconds to adequately sample the images.
At a prime location with excellent seeing, you may need a resolution of 0.5 arc-seconds or better. Higher resolution is also helpful if you plan to use deconvolution to sharpen your images. Imaging at this level requires excellent optical quality and a very stable mounting or a high-speed tip/tilt "AO" guider.
You should also consider how much sky area you wish to cover. If you have a small sensor, you may wish to reduce resolution to as much as 2 arc-seconds per pixel. Acceptable imaging is possible at 4 arc-seconds per pixel, but you will be sacrificing resolution. Beyond this point, your stars begin looking like little squares.
The short exposures used during planetary imaging can ”freeze” the seeing and allow full-resolution imaging even with very large instruments (assuming good optics). For planetary imaging with short exposures, start with an image scale of 0.25 arc seconds per pixel; use trial-and-error to determine the best image scale for your equipment, conditions, and the planet being imaged.
Since seeing is highly variable, it is recommended to take many exposures and keep only the best. For this reason, video capture is often used on planets. MaxIm DL supports video file ("AVI") capture when using video devices through the Video DirectShow driver. Tools are also provided to split individual frames from the video stream.