I want to match the image scale with my DSLR or CCD camera to my scope’s focal length. Why should I do that? How do I increase or reduce my focal length or f/ratio to do that?
October 7, 2009
The basic imaging element of today’s electronic camera is the pixel. It can be thought of as the individual cell or unit on the chip (picture element) that actually captures the light from the sky. The analogy to film imaging is the grain size of the photographic emulsion.
Pixel sizes (or more accurately, spacing on the chip) range from about 2 microns to about 30 microns for cameras used for astroimaging.
In a camera attached to a telescope, these small pixels are located at the focal plane of the telescope, Just like film grain is important to how small detail can be resolved, so is pixel size for digital cameras.
The goal is to match this size with the resolving power of your telescope. This yields sharp stellar images in your pictures. You don't want to blow up seeing blurs and diffraction patterns, or unintentionally lose details that you could be imaging.
This concept is called the image scale and is measured in seconds of arc per pixel.
The resolution of a telescope is higher for larger aperture scopes. A basic approximate formula for resolution is to divide 4 by the aperture of the scope in inches to get resolution in arc-seconds. For example, an 11-inch scope would have 4/11 or a resolution of 0.36” or approximately 4/10ths arc-second. This angle is the size of the diffraction disk produced by the scope’s optics.
Taking into account both this so-called diffraction limit and more importantly, effects from the atmosphere, there are practical limits that mean you will not capture images at the resolution from the formula above. Instead, you will be imaging the seeing disk or blurred light. On average nights your resolution limit might be 5 arc-seconds or 5”. On good nights the limit can be 2” for deep-sky objects.
The size of a given angular resolution in microns at the focal plane depends on your scope’s focal length. This disk size is the angle in arc-seconds times the focal length of the telescope in millimeters divided by 206. For example, a 2 arc-second seeing disk imaged with a C-8 Schmidt-Cassegrain telescope with a 2032 mm focal length is 20 microns across (2x2032 = 4064 divided by 206 is 20).
If a scope’s resolution in microns is much bigger than the pixel size, then the camera’s resolving ability is wasted. It is only recording the seeing blur, not additional details in the object. If the scope’s resolution is much smaller than the pixel size, then the scope’s resolving power is wasted. While these situations have their places in the real world of astroimaging, often you’ll strive for a near match in your setup. Figure out the image scale with the camera and basic optical setup. Then change it to match the image scale to your task by adding projection lenses to increase or focal reducers or even Fastar lenses to decrease the effective focal length of your scope.
To match the numbers, first calculate the image scale for your setup by dividing the pixel size of your camera in microns by your scope’s aperture in millimeters, then multiplying the result by 206. Example: a camera has 6.4 micron pixels and is used with a C-8, 2032mm focal length. 6.4/2032 = 0.00315. 206 x 0.00315 = 0.65 arc-seconds per pixel.
This image scale of around 0.5” per pixel is a reasonable match for planetary imaging, where short exposures can be stacked in an attempt to “beat” seeing. Use negative lens (Barlow) or eyepiece projection techniques to further increase the image scale if desired.
For deep-sky work with larger seeing disks, the camera’s smaller pixels might be better used for a wider field of view rather than magnifying the blur. To do this, change the f/ratio of your scope by using a focal reducer, a positive lens screwed onto the baffle threads that will shorten the focal length and reduce the f/number of the scope.
Using an f/6.3 reducer such as Celestron #94175 shortens the example scope’s focal length to only 1280mm, changing the image scale to a more useful 1” per pixel and increasing sky coverage by 250 percent.
Using a Fastar lens at f/2 makes for an even smaller image scale of 3.3” per pixel and increases sky coverage by 25 times.