Spectroscopy in the Laboratory

Astronomical Laboratory 29:137, Fall 2013
by Philip Kaaret and Steven Spangler

Reading

Sections 6.1-6.5 in Handbook of CCD Astronomy, second edition, by Steve B. Howell.
SBIG DSS-7 Spectrograph manual
Santa Barbara Instruments Group ST-402ME CCD camera
SBIG CCDOps manual

Introduction

Spectroscopy is crucial to astronomy. It is the principal diagnostic for determining the temperature and chemical composition of stars, nebulae, and galaxies. Spectroscopy is of equal importance to physics. No experimental evidence was of more importance to the emergence of modern physics than the existence of spectral lines of different atoms and molecules. Today, spectroscopy continues to be one of the most important experimental or observational measurement in both astronomy and physics.

In this class, we will have the pleasure of measuring and analysing spectra. We will use the same ST-402XME camera used in the previous exercises as the detector of our spectrograph. The equipment which actually makes up the spectrograph (slit, internal optics, and most importantly, diffraction grating) is provided by a unit which connects to the front of the ST-402XME. The instrument is called the Deep Space Spectrograph DSS-7. This unit is also manufactured by the Santa Barbara Instrumentation Group (SBIG). The SBIG company designed this spectrograph to be mounted on a telescope.

Today, we will set up the DSS-7 with the ST-402 in the laboratory and get it working. We will then calibrate it by taking spectra of gas discharges of hydrogen, helium, etc.

This exercise will be much more meaningful if you know what is going on. Be sure to read sections 6.1-6.5 in Handbook of CCD Astronomy before coming to class. Also, the manual for the DSS-7 spectrograph has much worthwhile tutorial material as well as indispensible material on the construction and operation of the DSS-7. You should particularly look at Figures 1, 5, and 7 of the DSS-7 manual. An important characteristic of the DSS-7 is its wavelength range. As stated in the manual, it is nominally 400-800 nanometers (or 4000-8000 Angstroms, in a unit more traditionally used in astronomy).

Equipment

SBIG ST-402XME camera, with power adapter and USB cable
Computer running the CCDOps software package and DS9 for image analysis
DSS-7 Deep Space Spectrograph
7 inch phone cable to connect the spectrograph and camera
Adapter ring to connect the DSS-7 and ST-402XME
Set of Allen wrenches, including little ones
Gas discharge tubes of hydrogen and helium (other elements would be good, too) plus associated power supplies.

System Setup

Physically connect the spectrograph to the camera, as described in step 2 in the section "Attaching the DSS-7 to the camera" in the DSS-7 manual. There is an adapter ring, properly threaded, which connects the DSS-7 and the ST-402XME. Figure 12 of the manual shows what the properly assembled system should look like.
Remove the side panel of the spectrograph with the Allen wrench. Looking inside will give you a very clear idea of how the spectrograph works. Be sure and compare what you see with Figures 1, 5, and 7.
Connect the phone line between the two units so the ST-402XME can talk to the DSS-7. Turn on the DSS-7 with its on-off switch. The red light in the switch should glow (dimly). If it doesn't change the 9V battery in the DSS-7. Connect the USB cable from the ST-402XME to the workstation, and connect power to the ST-402XME. Bring up CCDOps, connect to the camera, and listen for the contented clicking sounds.
Now we wil check that the mechanisms inside the DSS-7 move correctly. Start by disabling the DSS, in CCDOps do DSS/DSS Mode and make sure that the "Enable DSS" box is not checked. Now run through the commands that move the slit in and out of the light path and rotate the diffraction grating. This procedure is done as described in the section "Aligning the DSS-7 to the camera:" of the DSS-7 manual, starting on page 11. One will use the Track/Move Telescope and then run through the movements.
When you have checked that all of the mechanisms move properly, close the side panel on the DSS-7.

Centering and Focusing on the Slit

The goal is to make sure that the internal optics of the spectrograph are focused on the slit and that the slit images are falling in the middle of the CCD chip (instead of off to the side).

Begin by picking DSS in the CCDOPS menu, and now checking the ENABLE DSS box. This means the spectroscopic commands to the computer will move the slit and diffraction grating. The following commands are also in the DSS-7 manual in the section "Aligning the DSS-7...".
Choose VIEW SLIT from the DSS menu, and choose an exposure time of 1 second. This runs the camera and spectrograph in normal camera mode, except you are taking a picture of the slit. You should see an image of the slit (see Figure 2 in the manual), which is blurry (out of focus), offset from the center, and rotated with respect to the horizontal. We need to correct all three of these. The slit actually consists of 5 slits of different widths. The larger the width of the slit, the poorer the spectral resolution, but the higher the signal-to-noise ratio because more light is admitted. This instrument lets you confront the trade-off, always present in astronomical spectroscopy, between high spectral resolution and high signal-to-noise ratio. For the experiment in the lab, we will use the narrowest slit with the highest spectral resolution.
If necessary, focus the internal optics on the slit. Be sure and read the section in the manual entitled "Aligning the DSS-7 to the camera" for guidance on how to do this. Look at Figure 13 in the manual for an idea of what we have to do. On the side of the spectrometer opposite of the side panel that you just removed and replace, there is a pair of screws with Allen heads. Loosen the two screws on the little plate. Do not touch the other two screws. Once you have loosened them, move the little plate back and forth. This moves one of the focusing lenses in the instrument. Run the camera in focus mode. Continue adjusting the position of the sliding plate until the images of the slits are as small as possible, and the edges are crisp. Then re-tighten the screws on the slider. Tightening the screws often shifts the focus, which can make getting a really focus a bit frustrating.
Finally, put the narrowest slit in the middle of the CCD chip, and align it so it is parallel to the vertical direction as seen on the workstation screen (i.e., the way a spectrograph slit should be). The spectrograph can be moved relative to the camera by loosening the brass thumbscrews and moving the spectrograph around. You will need to both rotate and translate the spectrograph. In the end, the image on the workstation screen should look like Figure 2 (copied below) in the manual with the narrowest slit centered and vertical in the image.

Let's take a moment to discuss the spectrum images. The image of the spectrum of a hydrogen lamp is shown below. The horizontal axis in the image below is the 'dispersion axis', i.e. the axis along which the photons are dispersed by the grating according to their wavelength. Thus, position along the horizontal axis is a measure of wavelength (which we will calibrate in detail below).

The vertical axis is un-dispersed. The grating essentially acts like a mirror for reflection in this axis. Thus, the vertical axis is actually a spatial axis. A vertical slice across the spectral image through a bright spectral line will give a one-dimensional image of the source along an axis aligned with the slit. For the hydrogen lamp, the light source fills the whole slit, so one sees the whole outline of the slit in the bright lines. In contrast, a star will fill only a few pixels of the vertical extent of the slit.

Sometimes spectra images are binned along the vertical direction. Typically one integrates a stellar spectrum across the whole width of the stellar image, usually several pixels. When acquiring spectra, CCDOps has an option to do this binning for you. Setting 'Vertical Binning' to a value greater than one, simply combines that number of adjacent vertical pixels. To set the vertical binning for dark frames, do Camera/Setup and look at the 'CCD Setup' part of the dialog box. It should be fine to set 'Vertical Binning' to a small whole number to combine vertical sets of pixels and allow shorter exposures times. However, it seems that CCDOps ignores 'Vertical Binning' when taking dark frames, so keep 'Vertical Binning' set to 1. It is important to have a set of dark frames that can be directly subtracted from the spectrum images; the dark frames should have the same vertical binning and exposure time.

To acquire a spectrum, do DSS/DSS Mode then check the boxes for 'Grab Spectra' and 'Enable DSS', set 'Vertical Binning' to your preferred value, adjust the exposure time, and then click 'OK'.

The 'Grab Spectra' command does not do dark frames, so you'll need dark frames for all the exposure times that you use for your final set of spectra. Note that the exposures needed for the spectra can be long, so you might want to cool the CCD. Be sure that your spectra and darks are taken at the same temperature and with the same vertical binning.

We are now ready to take data.

Data Taking and Measurements

The main goal of this lab exercise is to calibrate the spectrograph. You will now take spectra of hydrogen, helium, and neon lamps and blue and red LEDs for calibration purposes. We will need to have the lights off in the lab for this part.

The "Spectrum Tube Carousel" has several different gas discharge tubes. Make sure the power supply is off while rotating the carousel.
Select the Helium tube in the carousel and turn it on. Don a pair of diffraction grating glasses and admire the spectrum of lines produced by hydrogen. Remove the glasses.
Set up a white piece of paper (that we'll call the screen) and adjust the tube carousel so that the Helium tube illuminates the screen. Adjust the DDS-7 so that it views the tube.
Acquire a spectrum (DSS/DSS Mode/Grab Spectrum or Grab). Adjust the exposure time so that the brightest pixels in the image of the narrowest slit are have values of at least several 1000 counts but are not saturated. Save the spectrum with a filename containing 'helium'. You should also get into the habit of specifying the object (in this case 'helium lamp') while saving so that it is written to the FITS header.
Repeat the this procedure for the hydrogen tube and the neon tube. You might need to adjust the position of the carousel, screen, and DSS-7 for each lamp. Save the hydrogen and neon spectra.
Now replace the tube carousel with one of the LED boxes. To turn on the LED box, press the button on top. Repeatedly pressing the button cycles through the various LEDs with two brightness settings for each. Set the box so the red LED is on at the brighter level. Position the LED box so that it illuminates the screen and the DSS-7 so that it views the illuminated portion of the screen. Acquire and save a spectrum of the red LED.
Repeat this procedure for the blue LED and acquire and save a spectrum of the red LED.
Check that you have a full set of spectra (helium, hydrogen, neon, red LED, blue LED) and that the brightest pixels in the image of the narrow slit for each spectrum has a decent signal but are not saturated. Go back and re-acquire any spectra that are bad or dodgy. Now take and save dark frames for every exposure time that you used for your set of final spectra. Be sure that each dark is at the same temperature as the corresponding spectrum.
When you are finished, shut down the system. Turn off the DSS-7 and shut down the ST-402.

Gratings

When light is normally incident on a grating, the diffracted light will have maxima at angles θ_m given by:

$d \ \sin{\theta_m} = m \lambda$

where d is the spacing of the rulings on the grating, m is the order number and can be any integer, λ is the wavelength of the light. This is the so-called 'grating equation'. From inspection of Figure 1 in the DSS-7 manual (or inspection of the DSS-7 itself with the panel removed), one can see that the DSS-7 is designed so that the light is normally incident on the grating (when used in spectroscopic mode). The DSS-7 grating operates in first order when used in spectroscopic mode. Thus m = 1.

Calibrating the Spectrograph

In principle, one could measure the d and then trace the path of rays through the DSS-7 and ST-402 to find the angle θ corresponding to each pixel in an image. In practice, this is too difficult and fraught with error, so one, instead, observes a light source, usually a gas discharge lamp, that produces several emission lines of known wavelength and uses those to determine the relationship between pixel number and wavelength of spectral lines for the spectrograph. This is called 'calibrating the spectrograph'.

To do this, one must first identify the various lines in each spectrum.

Load the spectra for hydrogen, the red LED, and the blue LED into ds9. You will want to look at all three spectra simultaneously, so after you load the first spectrum, do Frame/New Frame before loading each of the other spectra. Then after all three spectra are loaded, do Frame/Tile Frames and Frame/Frame Parameters/Tile/Rows. You should see your three spectra in three rows.
You may want to play with the scale settings for each image in ds9 in order to get the lines (more like bands for the LEDs) visible. People often look at spectra using an inverted colormap (Color/Invert Colormap) when examining spectra (it saves on toner when printing).
After you are done adjusting your images, do Frame/Match/Frame/Image to make sure that all of the images are lined up in ds9. This allows you to directly compare pixel number between the images.
Print out the three images (together) and paste into your notebook. Mark which image is which in your notebook.
The dominant lines in the hydrogen spectrum should be H-alpha at 656.285 nm and H-beta at 486.133 nm (see Appendix A of the DSS-7 manual). Figure out which is which by comparing with the blue and red LED spectra. Write down the image x coordinate of the center (vertically and horizontally) of the H-alpha and H-beta lines. These are your first approximation to the calibration of the spectrograph. Estimate the width of the line (in terms of number of pixels).
Write down the image y coordinates of the center of the lines for use later. These should be the same or very close to the same. Determine the width of the line image in y.

You will now calibrate your spectrograph using Python and your hydrogen spectrum with its newly identified lines.

In general, there can be a complex relation between pixel number p and diffraction angle θ that depends on the optical properties of the spectrograph. If the diffraction angles are small, θ << 1, then the relation between pixel number p and diffraction angle θ can be approximated as p = aθ + b. We will use a linear relationship. Note that since there are only two strong lines in the hydrogen spectrum, we don't actually have enough information to derive a more complex calibration curve. In astronomical research, much larger line sets, often 20 to 40 lines or more, are used to correct for non-linearities in the pixel number versus wavelength relation. The software that comes with the DSS-7 also only uses two lines and the manual states that the calibration is good to 0.1 pixels.

Load hydrogen.py into your preferred text editor. Edit the lines that read in the spectrum files to match the names of your files. Edit the variable y0 to match the value that you found using ds9 for the (vertical) line center and the variable dy to be half of the width of the line (or a bit smaller).
Run the program. You should see a 2d image of the spectrum, similar to what you saw in ds9 (you many want to edit the values for vmin and vmax in the plt.imshow command if the lines don't show up well) and a line plot of a 1d spectrum. Adjust y0, dy, vmin, and vmax until you are happy with the plots.
Now edit the values in the arrays linec and lined to match the line centroids and half the line widths that you estimated from ds9. Note that these values must be integers. Make sure that the centroids correspond to the right wavelength in the array linew.
Run the program again. Inspect the vertical lines overdrawn on the 1d spectrum plot. Each pair of dashed lines marks the interval used to calculate the centroid of a spectral line. The solid line between them marks that centroid. Check your intervals and centroids and adjust them so they look reasonable. The ipython plot windows are interactive, so you can zoom in on your lines. Click on the cross with arrows, then left click in the plot window to pan and right click to zoom. Clicking on the house will restore the plot to its original settings.
When everything is good, run the program again print out the 1d spectrum (versus pixel number) plot and put it in your lab notebook.
After calculating the centroids, the program does a linear fit to the pixel versus wavelength relation (which is trivial when only using two points). Rather than using just two parameters as needed to specify a line, the program prints out three parameters which are the average pixel number of the lines used in the calibration, the corresponding wavelength, and the slope of the relation. Record these.
The last part of the program applies the calibration, makes a spectrum plot versus wavelength, and calculates centroids in terms of wavelength given a line list in terms of wavelength. Inspect that plot. Adjust the values of lined in the 'Line centroids in wavelength' part. Print out the plot when you are satisfied. Note that with only two points for the calibration, the calculated wavelengths should match the known values exactly. Once you have a calibration, specifying lines of interest in terms of wavelength is much more convenient since the wavelengths are known before hand.

Having now calibrated our spectrograph, we can test the accuracy of the calibration.

Save a copy of hydrogen.py as spectra.py. Delete the stuff about plotting the spectrum versus pixel number and finding line centroids in pixels (since we will now be working in wavelength). You can also delete the stuff about plotting the difference image if you like (or leave if it you like to double check you have the right spectrum image). Replace the lines where the calibration is calculated with statements that assign your calculated values to centralp, centralw, and slope.
Run the program and checks that it work on the hydrogen spectrum and finds the appropriate centroids.
Now look at the helium spectrum. Edit the file name (and dark file if needed) to load the helium spectrum. Find at least five lines. You might want to change to a log scale on the vertical axis to see weak lines. It is good to peak narrow lines, since the broad features are often combinations of multiple lines and it is harder to accurately calculate the centroid of a broad line.
You can get an estimate of the wavelength of by moving your cursor over it and the x position at the bottom, right of the plot window. Find your lines in the Tables at http://physics.nist.gov/PhysRefData/Handbook/Tables/heliumtable2.htm If there are multiple lines close to your estimated wavelength, pick the one with the highest intensity in the table. Edit the values for linew and lined.
Note that you really need to inspect each line. The centroiding code will always find a centroid, even if there is no line present. Indeed, if you draw on interval on a region with no line, the centroid will be very close the center of the region, so it is easy to get spurious good agreement between input wavelengths and centroids.
After you have found at least five lines and calculated their centroids, print out a plot of your spectrum with all of the centroid overplotted.
Take your centroids and calculate the difference (centroid - known wavelength) and then the standard deviation of those differences. The standard deviation is a measure of the accuracy of your calibration of the spectrograph. Calculate it in wavelength units and also convert that number into pixels using the slope of your calibration. Record your calculations and thoughts in your lab notebook.

For extra credit, you can repeat this exercise for your neon spectrum. A list line for neon is available here: http://physics.nist.gov/PhysRefData/Handbook/Tables/neontable2.htm (not just any line list, the official US line list). If you are planning on using the DSS-7 for your research project, you should think about how you can use the whole set of line spectra to improve the calibration.