Image scale, not pixel size, controls the resolution of digital images. To illustrate this point, the author made these pairs of 3-minute exposures of the edge-on spiral galaxy NGC 981 in Andromeda with a Meade 16-inch LX200 Schmidt-Cassegrain telescope and SBIG ST-7 camera equipped with a KAF-0400 CCD. By changing focal reducers and binning pixels, roughly similar pixel scales were obtained at focal lengths of 1,303 and 2,365 millimeters (f/3.21 and f/5.85, respectively). Note that the resolution at a given scale is independent of pixel size. The shorter focal length covered about four times more sky than the longer one. Insets: A 5x enlargement of the double star to the lower right (southwest) of the galaxy’s nucleus. The magnitude-161/2 components are separated by 5.8'.
Sky & Telescope / Dennis di Cicco
Pixel Binning
You might think that these parameters would be fixed for a given telescope and CCD camera. However, it is usually possible to vary both the focal length and pixel size within some limits.
Most cameras sold today offer what are called binning modes -- the ability to electronically combine the signal collected by several adjacent pixels such that it appears to come from a single, larger pixel. There are several advantages of binning, including faster image readout, smaller file sizes, and greater CCD sensitivity for a given optical system. This technique is often used with long-focal-length systems, which deliver generous images scales. Unfortunately, binning also reduces a CCD’s effective number of pixels.
Roger W. Sinnott developed this nomogram to show the relationship between image scale, effective focal length, and pixel size. A straight line connecting any two values passes through the third. For example, in order to have a 9- micron pixel cover 11/2' of sky requires a focal length of about 50 inches. While experience ultimately dictates the best image scale for given conditions, conventional wisdom suggests that scales of 11/2' to 2' are good for general deep-sky imaging, while lunar and planetary work can benefit from scales as small as 1/2' with apertures large enough to allow short exposures that "freeze" the astronomical seeing.
Sky & Telescope diagram.
Consider the example of 3x3 binning with the KAF-1600. The resulting 27-micron-square pixels are similar in size to those of the KAF-1000, and both chips will provide similar resolution when coupled to the same telescope. This binning, however, reduces the KAF-1600’s effective number of pixels from 1.6 million to about 178,000, which is roughly one-fifth the number available with the KAF-1000 chip. In this situation the sky coverage of the KAF-1600 will be about one-fifth that of the KAF-1000, which is exactly what common sense tells us. When placed on the same telescope, the KAF-1000 covers about five times more sky than the KAF-1600 since physically it has about five times more area. Changing the binning mode of the KAF-1600 will change the resolution but not the total sky coverage.
If we want the greatest sky coverage from a given CCD, we should operate the chip in its full-resolution (unbinned) mode and select a focal length to produce the desired image scale. As mentioned earlier, for 9-micron pixels, a scale of 2" requires an effective focal length of about 37 inches. Traditionally such short focal lengths have been the domain of small apertures. While CCDs can deliver remarkably big performance with small telescopes, it’s still desirable to use large apertures for deep-sky imaging. Besides, you probably want to work with your existing telescope. So from a practical standpoint the question becomes, what can be done to adjust its focal length? Fortunately, you can do a lot.
