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2° 39'52"

with a focal length of 2000 mm, the 5-arcminute spectrum is roughly 3 mm long and spans 340 pixels on a CCD with 9-micron pixels. Thus, the very weak objective prism combined with a telescope creates an efficient and practical low-resolution instrument for stellar spectroscopy.

Images taken with an objective prism contain the spectrum of every star in the field of view. Some of the spectra run off the edges of the field, and some will undoubtedly overlap each other. The advantage of the objective prism is that no modification to the telescope is necessary except to mount the prism over the front. The telescope can be any type—refractor, reflector, or catadioptric.

The main disadvantage of this form of spectrograph is that the starlight is superimposed on the full intensity of the night sky (see Figure 11.5). An additional disadvantage is that you cannot measure wavelengths directly from the spectrum because its location, and hence the position of the spectral features in it, depends on the location of the star in the field.

11.2.4 The Grating-Prism Spectrograph

A grating or grating-prism spectrograph is perhaps the most practical way for an amateur to get into spectroscopy. A grating-prism, or grism, is a transmission grating combined with a prism. The grating or grism is placed in the beam of light converging toward focus, usually a few inches ahead of focus. The grating disperses the light into a spectrum. In a grism, the prism refracts the beam so that the spectrum is formed directly behind the grism, and in so doing, corrects some of the optical aberrations introduced by the grating.

Grating and grism spectrographs are well suited to the needs of amateur astronomers because the grism optical element is both small and relatively inexpensive (several hundred dollars). Grisms lend themselves equally well to reflectors, refractors, and catadioptric telescopes. Furthermore, it is possible to shift a grism in and out of the converging beam without making other changes to the optical configuration.

Transmission diffraction gratings consist of a thin glass substrate that supports a transparent film ruled with several hundred evenly spaced parallel grooves

Figure 11.2 Grism spectrographs disperse light by means of a small optical element, a grating or grism (a combination of a grating and a prism)., just ahead of focus. Because the dispersing element is small and close to focus, spectroscopy with gratings and grisms is relatively easy and inexpensive.

per millimeter. Light passing through the grating is dispersed into a spectrum, with the angle of deviation dependant on its wavelength. The grating equation is:

where I is the angle of the incident light, 5 is the angle of the diffracted light, m is the spectral order (which can be 0, 1, 2, or more, but usually equals 1), n is the number of grooves per millimeter, and X is the wavelength in millimeters. (The angles are measured relative to a line normal to the grating surface.) If the incident light strikes the grating perpendicularly so that I is zero, the diffracted rays are deviated by the angle 8 relative to their original paths.

The grooves in modern gratings are shaped, or "blazed," so that they diffract approximately 60% of the incident light into the first spectral order; that is, at an angle corresponding to m = 1 in the grating equation. However, some light—the zero-order spectrum—passes through the grating without being deviated. The zero-order image provides a fiducial marker for measuring wavelengths.

The distance between the grating and the detector depends on the angular dispersion of the grating, the size of the CCD, and the type of spectra you wish to obtain. From the grating equation, you can calculate the deviation angle, 8, using a grating with 200 grooves per millimeter, for deep blue light with a wavelength of 400 nm (400xl0-6 millimeters):

sinS = 1 x200x400xl0~6.

For deep blue, the first-order deviation angle is 4.6 degrees. Repeating the calculation for near-infrared light at 900 nm, the deviation is 10.3 degrees.

Figure 11.3 Throughout the twentieth century, professional astronomers have obtained spectra with slit spectrographs mounted directly on their telescopes. These instruments are ideal for making medium- to high-dispersion spectra with precisely calibrated wavelengths.

In a grism spectrograph, a prism is placed immediately in front of the grating. The vertex angle of the prism is chosen to refract light so that a wavelength in the middle of the spectrum exits the grating parallel to its original path. A prism chosen to pass light of 650 nm wavelength on a straight path gives an angular dispersion of 5.7 degrees between 400 nm and 900 nm.

We can find the length of the spectrum on the detector by multiplying the distance between the grism and the CCD chip by tan(5.7°) = 0.099 . If the distance between the grism and the CCD is 50 mm, the spectrum will be 5 mm long. The separation should be chosen so that the zero-order image and the first-order spectrum fit comfortably into the image.

Because of aberrations introduced by the grating, the zero-order image and the spectrum do not lie at exactly the same focus. If you make grating or grism spectra, be sure to focus on the spectrum rather than on the zero-order image.

11.2.5 The Slit Spectrograph

The slit spectrograph is an optical instrument designed to isolate a narrow strip of light from the focus of a telescope by means of a slit, pass it from the slit through a dispersing element, and reimage a wavelength-dispersed image of the slit onto a detector. The two-dimensional spectrum recorded by the detector consists of a thin slice of sky in one axis and a sequence of images of the slit at different wavelengths spread along the other axis.

Textbook illustrations necessarily present a simple picture of spectrograph optics; the reality is that they require sophisticated design. In addition to the basic function of dispersing light, the spectrograph must form sharp images of the slit at

Figure 11.4 The fiber-fed spectrograph makes spectroscopy practical for amateur astronomers because starlight is carried from the focus to the spectrograph through a fiber-optic bundle, so the telescope does not have to support the weight of a spectrograph.

different wavelengths over a fairly wide range of angles with little or no vignetting. To avoid incurring significant aberration by dispersing a converging or diverging beam, rays passing through the dispersing element should be parallel. The basic elements are therefore a slit to isolate a thin strip of the light from the focal plane, a collimator to render the beam parallel, the dispersing element, and camera optics to reimage the slit in monochromatic light.

To avoid vignetting, it may be necessary to place a field lens behind the slit to reimage the telescope objective on the collimator, which must be able to colli-mate light over the full height of the slit. The dispersing element—whether a prism, grating, or grism—must be sized and placed to intercept all of the diverging parallel bundles from the collimator. The reimaging camera optics must be large enough to intercept ray bundles diverging along the height of the slit as well as along the axis of dispersion, and capable of forming good images over those two dimensions. The CCD is located at the focal plane of the camera optics to record the image that the spectrograph optics produce.

Finally, the assembled spectrograph optics must be mounted solidly at the focus of a telescope, with adequate provision for focusing, viewing the location of the slit, and guiding. Despite these challenges, amateur astronomers have designed and constructed slit spectrographs.

11.2.6 The Fiber-Fed Spectrograph

Because high-resolution slit spectrographs are bulky to mount at the focus of even a large telescope, in the late 1980s and early 1990s professional astronomers began experimenting with thin optical glass fibers to carry light from the focus of the telescope to the slit of the spectrograph. Moving the heavy instrument off the telescope so improved the accuracy and stability of spectrographs that a wave of exo-planet discoveries (using radial velocity measurements to detect the effect of the orbiting planets on a parent star) soon followed. In addition, by placing hundreds of fibers at the focus of a telescope, observational cosmologists could record the spectra of a hundred distant galaxies per integration, making massive surveys of galaxy redshifts feasible.

For amateurs, fiber-fed designs move the spectrograph and CCD camera system to a convenient position beside the telescope. At the focus of the telescope is a "light pipe" to pick up starlight. The light pipe consists of a bundle of tiny optical fibers that convey the starlight several meters from the telescope to the spectrograph. At the pickup end, the fibers are bundled into a circular region to capture the whole star image; but at the output end, they are lined up side by side to form a narrow slit pattern.

The optical arrangement of this design parallels that of a slit spectrograph, but the properties of the fiber bundle dictate the design. Although starlight may enter a fiber bundle in an//10 cone, after transversing and exiting it, the light spreads into a conical distribution requiring a much faster lens to collimate. As an alternative to using a collimator, grating, and camera lens, the spectrograph can employ a concave reflection grating to collimate, disperse, and focus the spectrum with just one optical element. The CCD is placed to receive the spectrum at the focus of such a grating.

Although fiber-fed spectrographs are compact and convenient, the light pipe scrambles all of the light that enters it, mixing starlight and background sky light into an image that is effectively a single spectrum. Unless the source is so bright that the sky background can be ignored—fairly often the case with stars—it is necessary to point the telescope at a nearby patch of sky and make a separate exposure to capture the spectrum of the night sky. Since the spectrum is captured digitally, the background sky light can be subtracted later.

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