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where X is the effective wavelength, A is the aperture of the telescope, F is the focal length, and N is the focal ratio, F/A. At the wavelength of peak sensitivity for many digital cameras and astronomical CCDs (550 nanometers), the diameter of the diffraction disk at the focus of an/76 telescope is 3.4 microns.

Compare this figure to the 7- to 12-micron dimensions of pixels in a typical astronomical CCD camera: because the diffraction disk is considerably smaller than the pixel size, diffraction-disk-size detail cannot possibly be captured.

For critical sampling of image detail, the bright central region of the diffraction disk should meet the Nyquist criterion—it should be at least twice as large as the pixels that sample the image. For a sensor with 10-micron pixels, the diffraction disk should be enlarged to twice their size, or 20 microns. At an effective wavelength of 550 nanometers, this corresponds to a focal ratio of/736.

Airy Disk Pixel Array

Figure 5.14 Theory says that to capture all of the information present in a telescope image, the bright inner portion of the Airy disk should span a minimum of two pixels on the detector. As a practical matter, however, the seeing blur rather than the Airy disk often limits the information content of telescopic images.

For a variety of reasons, it is usually expedient to use a less extreme focal ratio than the Nyquist focal ratio for the diffraction disk. First, atmospheric turbulence enlarges the star image into a blur that is bigger than the bright core of the ideal diffraction disk. Second, there's a trade-off between exposure time and atmospheric stability. At the Nyquist focal ratio, the image may blur during the integration; but at lower focal ratios, the integration time necessary becomes shorter, and you can "freeze" moments of good seeing.

In the end, use the Nyquist focal ratio as a starting point and let your imaging results be your guide. A practical starting point for planetary and lunar imaging with an astronomical CCD having 10 micron pixels is//25. For a digital camera with 7 micron pixels, a reasonable starting point is/718.

The two classic techniques for enlarging the image are projection from an eyepiece and projection with a Barlow lens. Astrophotographers have long used eyepiece projection to increase the scale of their lunar and planetary images.

Eyepiece Projection. In this method an eyepiece is placed slightly farther from focus than it normally is for viewing, so that instead of emitting parallel rays, it emits a converging beam that forms a real image at some distance (called the projection distance) behind it. Solar observers use eyepiece projection to view an image projected safely onto a sheet of white cardboard. For digital imaging, instead of the cardboard, the image falls on a CCD.

To set up for eyepiece projection, you must first figure out how much image enlargement you need and then calculate the eyepiece-to-CCD distance. For example, to convert an//6 Newtonian to//36, you need to increase the focal length by a factor of 36/6, or 6 times:


Projection Distance, P

Figure 5.15 The geometry of eyepiece projection is simple: to enlarge the image by a factor of E, add 1 to E and multiply by the focal length of the eyepiece. The resulting value is the projection distance, P. To avoid scattered light with eyepiece projection, place a small stop at the focal plane of the eyepiece.

where P is the projection distance; E is the desired enlargement; and Fe iece the focal length of the projection eyepiece. To boost your//6 focal ratio to//36 with a 12-millimeter eyepiece, the projection distance is (6+1) x 12, or 84 millimeters. You can set this distance with a ruler when you assemble the eyepiece projection system.

Barlow Lens Projection. Barlow lenses are negative (i.e., diverging) lenses placed in front of an eyepiece to increase the focal length of the telescope. Modern high-performance systems such as the TeleVue Powermate series increase the focal length of a telescope by factors from 2x to 5x, converting an//6 system to focal ratios from//12 to/730. On an//10 telescope, a 2x Barlow increases the focal ratio to//20, which is about right for a digital SLR with 7-micron pixels.

The distance from the focal plane to a standard Barlow lens must be set correctly to produce the design magnification. The Powermate systems were designed to produce the desired image enlargement over a much wider range of lens-to-focal-plane distances than conventional Barlows. Field of View

At long focal lengths and long focal ratios, the field of view becomes extremely small. The formula for the field of view in arcseconds is:

dec n

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