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Grism Spectrum Image
Figure 11.7 Spectra formed by gratings and grisms have a zero-order image of every celestial object in the field as well as a spectrum of each object. However, the distance between the zero-order image and features in the spectrum is constant, making it easy to calibrate the wavelength scale.
gon glow lamps. Flux calibrations are done by taking spectra of a source, such as a tungsten filament, with a known spectrum.
Recall that the spectrum is a graph, plot, or image of the flux versus wavelength. In the raw image from a spectrograph, the spectrum is widened by several pixels in height and contaminated by the background sky light. To extract the spectrum from an image, the background light must be removed and the spectrum summed over its height. The extracted spectrum consists of a plot of the extracted signal versus a pixel coordinate.
• Tip: AIP4Win provides a Spectroscopy tool for extracting spectrum data from CCD images. To create wavelength—and intensity— calibrated spectra, transfer the extracted data to spreadsheet software to perform the analysis that your observations require.
Spectrum images from telescopes equipped with an objective prism consist of spectra superimposed on the light of the night sky. Because the locations of the spectra depend on the locations of the stars in the sky and the orientation of the objective prism, partial spectra enter and exit the images; and complete spectra in the center of the image may overlap one another.
Assuming that the spectrum you wish to extract does not overlap other spectra, and is oriented with the direction of dispersion along the sample axis (i.e., the jt-axis) of the CCD chip, extracting the spectrum is straightforward. (If the spectrum is not properly aligned, the image should be rotated and enlarged before extracting it.) Extracting the data consists of identifying the range of lines contained
Figure 11.8 This spectrum of the Eskimo Nebula, NGC2392, was made with a diffraction grating placed ahead of focus. Zero-order spectra appear to the left of the spectrum for each object. The zero-order images simplify calibrating the wavelength scale of the spectra. Image by Tim Puckett.
in the spectrum, and two ranges of lines containing regions of blank sky above and below it. The formula for the spectrum is:
where S(x) is the spectrum at pixel x, P is the pixel value of pixel (x, y), and a is a coefficient that matches the measured brightness of the background sky to the sky brightness contaminating the spectrum. Assuming a uniform sky background, you would compute a from:
Lines of sky background Lines of star spectrum
For example, if the range of lines containing the spectrum included six lines, and you included four lines of sky above the spectrum and five lines of sky below it— a total of nine sky lines—then a would be 0.6667.
Figure 11.9 In this objective prism spectrum, the region containing the star image-superimposed on the light of the background sky—lies between two sky background regions. Measuring the sky background and removing it from the spectrum curve yielded the spectrum in Figure 11.10.
• Tip: A!P4Win does not assume that the sky background is uniform. Instead, it saves a table of Sstar+sky(x) and Ssky(x), leaving the determination of the optimum sky subtraction to the observer.
Images from slit spectrographs consist of a slice of sky spread into a spectrum. If the CCD has been aligned correctly, its long axis coincides with the long axis of the spectrum. In the days of photographic spectroscopy, the normal practice was to broaden the stellar spectra by trailing the star back and forth along the slit—a practice made necessary by the limited storage capacity of the photographic emulsion and made desirable by the greater ease of "reading" widened spectra. With CCDs, widening the spectrum is necessary only in the case of extremely bright stars to prevent saturation.
The spectrum of the object of interest thus appears as a streak against a broad spectrum of the night sky. Its width can be as little as three or four pixels for a well-guided spectrum of a dim star, or as much as half the height of the slit for an extended source such as a nebula or galaxy. For extended objects that fill the slit height, it is necessary to make additional sky spectrum exposures well away from the object under study. In spectrographs designed for measuring precise wave-
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CCD Column (Pixels)
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