Why match telescope focal length to CCD pixel size – by Albert Lim

Matching a telescope’s focal length to a CCD’s pixel size is important for achieving maximum performance. Telescopes with different focal lengths produce different image scales while different CCD’s have different number of pixels and different pixel sizes. Star images and other point sources on too large an image scale on any particular CCD will cover multiple pixels and lower the CCD’s optimal detectability. The light from a star or point source would illuminate many different pixels and become dimmer because of the spread and no single pixel would receive a large fraction of the total light from that star. This does not produce more information than if the star were recorded via one or two pixels because of lower signal to noise ratio. Too small an image scale on the other hand will see more background sky but introduce an increase in noise which is undesirable. Nyquist sampling criterion sets a frequency limit called the Nyquist frequency which is equal to 1/(2 x Δt), where beyond this limit, the spectrum is reproduced symmetrically. This implies that a minimum of 2 pixels are required to properly detect and record a point image source such as a star on a CCD. Optimal sampling depends not only on observing conditions but are also affected by factors such as telescope vibration and tracking accuracies. In general, a telescope’s focal length need to be match to the  pixel size of the CCD whereby each pixel covers 2 - 3 arcseconds for typical observing sites. It should be noted that 0.3 arcsecond per pixel coverage is usually employed at superior professional observatory sites for deep sky work to fully exploit the CCD to attain superior resolution attainable at these sites because of their superb conditions by spatially over-sampling the stellar image. While we can calculate the star size based on the diffraction theory of light and the parameters of the optical system, it should be noted that star images are often larger than what theory predicts. This is caused mainly by deterioration of the stellar image by atmospheric seeing. Telescopes with longer focal lengths in 2 to 3 m range should generally be match with CCDs with larger pixel sizes of about 20 mm to achieve the required optimal image scale. Today’s popular CCDs such as Kodak’s for example may however only have 9 mm pixels. Software binning ( called 2 x 2 binning in this case ) may then be used to combine 4 pixels of 9 mm into an 18 mm pixel. Other methods involve reducing or increasing the focal length of the telescopes via the use of reducers and barlows to achieve the correct match image scale to the known pixel size of the CCD.