EXERCISES AND PROBLEM SETS
QUASAR ABSORPTION LINES
Volume 2, Part 5
Chapter 27
Spectrographs and Spectra
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Review Questions
Follow the light path! List the five key elements of a spectrograph in "light path order" that the light beam interacts with. For each, describe the role or purpose of the element.
What is the seeing disk and what influences its "size" on the detector? What is the "seeing" and what is it quantifying?
Why is it necessary to collimate the light beam before it interacts with the dispersing element, i.e., grating?
Consider the grating equation, Equation 27.3. For a given diffraction order, n, what is the fundamental physics governing the pattern of the constructive waveforms reflecting off the grating? As the diffraction order is increased, does the angular dispersion of the light increase or decrease?
What does it mean to "blaze" a grating? Why is it necessary to blaze a grating? What is the blaze wavelength?
Compare and contrast the grating designs for low-resolution (long slit) and high-resolution (echelle) spectrographs. (i) What is the typical facet angle (ɸ), lines per millimeter (1/d), and diffraction order (n) for a low dispersion long-slit spectrograph. What is the preferred incident angle of the collimated light (⍺)? (ii) What is the typical facet angle, lines per millimeter, diffraction order, and preferred incident angle for a high dispersion echelle spectrograph?
Consider Figure 27.7, which shows the dispersion relations and blaze functions for n = 1, 2, and 3 for a low-resolution spectrograph. Let's say you are observing the n = 2 refraction. In panel (b), it would appear that at 7500 Å there is roughly a 50% enhancement from n = 3 light at this wavelength. Describe why this is not the case at all. (Hint: examine panel (c)).
As in Problem 7, you are observing in second order using the spectrograph illustrated Figure 27.7 and you are studying the spectrum from 5000-7000 Å. But your target object is brighter in the infrared (all the way out to 20,000 Å, or 2 microns) than in the visible. Why is this a problem for you? What strategy is typically employed in order to solve this type of problem.
Why is a cross-dispersion grating required for echelle spectrographs? What are the typical grating properties for cross-dispersers (ɸ, 1/d, n, ⍺)? For the spectrograph design shown in Figure 27.8, at what dispersion angle, β, would you need to center the cross disperser in order to incercept the light refracted from the primary grating?
If one desires to increase the grating resolution for their spectrograph, what grating parameters could they change and how would they change them (make them larger, make them smaller, etc.)?
If one desires to increase the instrumental resolution (also called the resolving power) of their spectrograph, what telescope and spectrograph parameters could they change and how would they change them (make them larger, make them smaller, etc.)?
Describe why the resolving power of an echelle spectrograph is, to a rough approximation, independent of wavelength (or dispersion angle).
In your own words, what is the line spread function (LSF) and what is it accounting for in a measured spectrum? Provide a brief description of what Figure 27.10 is illustrating as resolving power is decreased/increased.
Let's consider why it is important to have a good match between the pixel size on the detector and the resolving power of the spectrograph. Based on Figure 27.11, roughly what minimum number of pixels per resolution element, p, provides an effective pixel sampling rate of narrow absorption lines (thus, preserving line shapes). Explain. On the other hand, can you provide a reason why we simply don't make p arbitrarily larger than this minimum effective number?
In words, what ratio are we measuring when we quantify the instrument "throughput"? Follow the light path and list the various efficiencies that must be considered if we are to quantitatively model the throughout.
Using CCDs, we measure "counts", i.e., the number of liberated electrons in each CCD pixel. To convert counts back into true flux values, we use the "sensitivity function" (Equation 27.61). Describe each of the terms in this expression and what role each plays in this very important conversion of counts back into flux. For example, why do we need to account for the integration time of the observation?
In practice, how do we construct a sensitivity function for our night of observations? How do we then apply it to our data?
What is integrated field spectroscopy? In general, what advantages does integrated field spectroscopy have over traditional spectroscopy? Can you think of science that requires experiments that are better suited or can only be undertaken using traditional spectroscopy?
Problems
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