Spectra and Spectrographs

Spectroscopy requires separating light of different wavelengths; yet in a telescope, (theoretically at least) light of all wavelengths comes to focus at the same point. Spectroscopy, therefore, requires an auxiliary optical element or instrument to disperse the light so that different wavelengths fall on different places on the detector. Such instruments are called spectroscopes when used visually and spectrographs when the spectrum is recorded on photographic film or with an electronic camera.

11.2.1 Prisms and Gratings

The key part of a spectroscope or spectrograph is its dispersing element, an optical part that splits light into its component wavelengths. The classic dispersing element is a glass prism which works because different wavelengths are refracted differently and exit the prism at slightly different angles. Although prisms are quite efficient in the sense that virtually all the light that enters a prism exits it, their dispersion is irrational; that is, the refracted angle is a strongly nonlinear function of wavelength. Light at the blue end of the spectrum is dispersed about three times more than that at the red end.

The other common dispersing element is the diffraction grating. A grating consists of fine grooves ruled very close together on a glass or metal substrate— often thousands per inch. In the wave model of light, at any given wavelength new peaks appear by constructive interference at well-defined angles from the original beam. Because at longer wavelengths the angles are larger, the diffracted light is arranged in an orderly spectrum. By carefully shaping and spacing the grooves, about 60% of the light falling on a grating can be focused into a spectrum. An important property of gratings is that the angle of dispersion is almost linear with wavelength; but a disadvantage is that they generate different spectral orders, so that if the range of wavelengths is large, gratings require auxiliary filters or prisms.

They come in two types: reflection and transmission. Reflection gratings appear mirror-like, and like a mirror, reflect the diffracted light in the direction it came from. Because of the fine grooves on their surfaces, music CDs act like diffraction gratings. Although reflection gratings are often flat, they can also be formed on a concave surface, so that a single optical element can both focus and disperse light to form a spectrum. Transmission gratings allow the bulk of the light to pass through and form a spectrum behind the grating.

The dispersing element of a spectrograph spreads a single ray of light into a spectrum. Classically, the spectrum refers to the varicolored smear of light with blue at one end and red at the other. Today, the term has evolved to mean any image, graph, or plot of flux versus wavelength. The primary task of spectroscopic image processing is to extract spectrum data from the image. Further analysis is usually required to create the spectrum from the extracted data.

In the visible part of the spectrum, the accepted unit of wavelength is the nanometer (10~9 meters). Although it's no longer officially recognized, many spec-troscopists continue to employ the angstrom (A) of 10"10 meters as a unit of wavelength. The conversion is 10 A = 1 nanometer (nm).

11.2.2 Practical Spectrographs

To be practical for an amateur astronomer, a spectrograph must be reasonably simple to construct, reasonably robust in operation, and reasonably inexpensive. Of course, "reasonable" is wide open to interpretation. It depends on the skills, finances, and available time of the individual observer. Of the enormous range of spectrographs, however, four designs stand out: objective prism, grating-prism, imaging slit, and fiber-fed.

11.2.3 The Objective Prism Spectrograph

The easiest way to create a spectrum is to place a prism in front of a telescope. The light is dispersed even before it enters the telescope, which then brings the dispersed light to focus as a spectrum. Professional astronomers use objective prisms

Objective Prism

Telescope Objective

Telescope Objective

Figure 11.1 A prism with a small apex angle spreads the light of every object in the field of view of a telescope into a spectrum. Although the resulting spectra are contaminated with the background light of the night sky, objective prisms are the easiest way to make low-dispersion spectra of stars.

to survey and catalog large numbers of stars rapidly, since with an objective prism, every star in the image appears as a spectrum.

Unfortunately, the prism must be approximately as large as the telescope objective, made of high-quality glass, and polished accurately flat on both faces. Even the glass for such a prism is expensive, and finished prisms are extremely so. However, making a prism with a 4-inch to 8-inch aperture and a 5° vertex angle is within the ability of a determined amateur optician.

Objective prisms work because the refractive index of glass varies with wavelength. Parallel rays of light of different wavelengths entering the prism will exit at different angles. To calculate the angles, use Snell's Law:

sine' n where n and n are the respective refractive indices of the glass and the surrounding air, and the angles 8 and e' are measured relative to a line perpendicular to the glass surface. Consider the following example of a spectrograph that an amateur could construct: an objective prism with a vertex angle of 5° made of high-quality but inexpensive BK 7 optical glass. For a prism 200 mm in diameter, the glass would be 10 mm thick at one side and 27 mm thick at the other. This prism would deviate a ray of green light by 2° 36', meaning that the telescope would have to be pointed this amount away from an object for it to appear in the center of the field. Rays at other wavelengths would undergo slightly different deviations (see Table 11.1), so that the angular spread between violet and deep red would be 5 minutes of arc. Although this seems like a very small difference, at the focus of a telescope

Table 11.1 Ray Paths in an Objective Prism

Wavelength (nm)

Refractive Index (BK7 glass)

Deviation Angle (degrees)

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