Properties of Spectrum Images

Spectra come in a great variety of lengths, widths, and resolutions. The splash of color thrown on the classroom wall from a prism is an extremely low-resolution spectrum, spreading the light only enough to show broad bands of color. To carry out spectroscopy, you must understand the range of wavelengths you need to examine, how the wavelengths should be spread, and how clearly separated the wavelengths need to be. In the jargon of spectroscopy, the key properties of spectra are:

• the free spectral range,

• the spectral resolution.

These properties depend on the dispersing element, the optical design of the spec-

Prism Astronomy Image Processing

Sky Image Objective Prism Spectrum Image

Figure 11.5 The image seen with a telescope equipped with an objective prism consists of every object in the field of view converted into a spectrum. Because objective prism spectra are superimposed on the night sky background, obtaining spectra of faint objects may be difficult.

Sky Image Objective Prism Spectrum Image

Figure 11.5 The image seen with a telescope equipped with an objective prism consists of every object in the field of view converted into a spectrum. Because objective prism spectra are superimposed on the night sky background, obtaining spectra of faint objects may be difficult.

trograph, and the width of the slit, star image, or fiber tip.

The free spectral range is simply the range of wavelengths in the spectrum. In an objective prism spectrograph, the spectrum may run from the short-wavelength cutoff of the atmosphere at -360 nm in the near ultraviolet to the CCD's long-wavelength cutoff around 1100 nm in the near infrared, yielding a free spectral range of 740 nm. More typically, however, stellar spectra are studied with higher dispersion over a free spectral range of 150 nm.

Dispersion is the rate of change of wavelength with unit distance in the spectrum. In the days of photography, the dispersion was expressed in angstroms per millimeter; but in CCD spectroscopy, dispersion is usually given in nanometers per pixel. For a grating spectrograph, the dispersion is easy to calculate because it is nearly constant along the spectrum:

Number of pixels

For example, consider a spectrum image with a free spectral range of 150 nm on a CCD image 512 pixels wide; the dispersion would be 0.293 nm per pixel.

Spectral resolution is the instrument's ability to separate lines of nearly the same wavelength. The resolution achieved by a spectrograph is a rather complex mix of factors, including:

• the reimaged width of the slit,

• the dispersion of the prism or grating, and

Spectrum of the Ring Nebula (M57)

Figure 11.6 An objective prism spectrum of M57 reveals three strong spectral lines and more than a dozen weak ones. Planetary nebulae and HII regions emit light at discrete wavelengths, so their spectra show multiple images of the object. The strongest lines are due to hydrogen, oxygen, and neon.

• the optical quality of the spectrograph optics.

Assuming good optics and a reimaged slit smaller than a pixel width, the resolution in nanometers is roughly twice the dispersion. The resolving power of a spectrograph, R, is expressed as the ratio between the wavelength and the resolution at that wavelength:

^ _ wavelength resolution

A spectrograph that can just resolve the two lines of the sodium doublet (at wavelengths of 589.0 and 589.6 nm) has a resolution of 0.6 nm and a resolving power of about 1000. Classification of star types can be done with resolving powers between 150 and 1000. The spectrographs that professional astronomers use to study the profiles of lines in stellar spectra have resolving powers in excess of 100,000.

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