Previous Topic: Intro to Spectroscopy Lecture Index Next Topic: Coordinate Changes

ASTR 3130, Majewski [SPRING 2015]. Lecture Notes

ASTR 3130 (Majewski) Lecture Notes



  • Birney et al., Chapters 12, 13.

  • Roy & Clarke, Chapters 4, 15, 19.9.

  • Howell, Chapter 6.

A spectrograph is an instrument used to form a spectrum of an object.

  • Uses dispersion: the spreading of light into an ordered sequence of wavelengths.
  • A typical spectrograph has the following parts:
    • Entrance aperture, typically slit-shaped.
    • Optical system to collimate diverging light; make rays parallel so that all rays approach dispersing device at same angle.
    • Dispersing device (e.g., prism or diffraction grating).
    • Camera to focus the image of the dispersed light onto a detector (photographic plate, CCD).

  • Spectrograph types are based on what kind of dispersing device is used:
    • Prism spectrograph
    • Uses a prism to to break up the light from an object into a spectrum. The lenses focus that spectrum onto a detector.

    • Transmission grating spectrograph

      Transmission grating is a piece of transparent glass with etched grooves in it.

    • Reflection grating spectrograph (e.g., McCormick spectrograph)

      Reflection grating is a reflecting surface with etched grooves in it.

  • The entrance slit

    • In the most basic form, a spectrograph produces a continuous set of images of the source, ordered by wavelengths:

      (Left) An image of Saturn in the K band (2.2 microns). The planet appears dark because of methane absorption in the Saturn atmosphere, while the rings are icy and bright (and saturated). (Right) A slitless spectrum of Saturn at infrared wavelengths. One can see that the peak emission wavelength for the ring and the planet are different by the changing relative brightnesses of the two parts of the image with wavelength. The two Saturn images here were reduced by R. Pogge (OSU) from data obtained UT 1996 Sept 22 with the NOAO 2.1-m telescope, and shown at

      A slitless spectrum of the corona of the Sun.
    • The above slitless spectra can be formed by simply sending the image of a source through a prism and taking a picture of the result.

    • A slit-shaped entrance aperture is often used to narrow the contribution of the image at each wavelength to a "line-shape" in the spectrum.

      This allows us to assess most easily the profile/shape of the line due to the various effects (Doppler broadening, Zeeman splitting, etc.) discussed before, without having the finite shape of the source convolve with these effects (note how difficult it would be to get Doppler information out of the slitless spectrum of Saturn above).

  • The collimator

    • Takes the diverging (past telescope focal plane) rays from the source and makes them parallel. Need to do so that any differential angles of rays coming out of spectrograph is entirely due to wavelength dispersion only.

    • Have to make sure to make big enough to capture all rays coming out of telescope.

  • Dispersing element: grating example (most commonly used in astronomy).

    • Based on the theory of diffraction.

    • Recall diffraction pattern (single slit aperture):

      Destructive interference from middle to edge of slit when path from each is at half integer multiples of wavelength:

      So that minima occur at:

      Constructive interference from middle to edge of slit when path from each is at full integer multiples, n, of the wavelength -- thus get multiple peaks at 2λ/a, 4λ/a, 6λ/a, etc.

      Go to this website to see how this equation works as a function of wavelength. Note how the positions of the peaks change as a function of wavelength. This is the basis of the grating, described below.

    • We discussed this earlier in the context of diffraction from a circular aperture of diameter D (i.e., a telescope aperture).

      Intensity of light I decreases as m increases

      In this more complicated, two-dimensional case, first minimum occurs at:

      radius (radians) = 1.22 λ/D

      r = 2.52x105 λ/D (arcsec)

      2r = "Airy disk", and this is surrounded by multiple rings.

    Diffraction Gratings

    • Based on the concept of diffraction with multiple slits.

      Recall what happens when you add two slits to the beam.

      Due to multiple possible interferences, we increase the number of peaks, but the heights of these peaks is still modulated under the envelope of the pattern delivered by a single slit.

    • By increasing the number of equal slits (in spacing and width) into the beam, we narrow the width of the individual peaks.

      Go to this website to click through the various slit numbers shown here. (This website -- -- is also the source for the images shown here.)

    • Obviously, as the number of slits is increased to large numbers, we can make the peaks arbitrarily narrow.

      Thus, by increasing the number of slits we can arbitrarily set the resolution, or the narrowness of the lines.

    • When you couple the above with the fact that the locations of the sets of peaks shift as a function of wavelength, you can see that the ability to discriminate or resolve different wavelengths directly depends on the number of slits, and the interference order, m.

    • Portion of the image structure for a single bichromatic point source viewed through several slits. From Kitchin's Astrophysical Techniques.
    • Thus, one can increase the wavelength resolution by:

      • increasing the number of slits the beam "sees" (i.e., decreasing the groove or slit spacing, d, which is the same as increasing the number of grooves or slits per inch).
      • increasing the interference order, m, that you choose to observe.
    • A grating is a set of finely placed wires, or a transparent piece of glass or mirror scored with many fine, parallel, closely spaced grooves or slits (~ several x 103 or more per inch) that act to make multislit diffraction patterns like that shown -- one diffraction pattern corresponding to each wavelength.
      • Transparent sheet or wires -- transmission grating

        light can pass through only between grooves (wires).
      • Reflective sheet (mirror) -- reflection grating

        light reflected only between the grooves.

    • Grating equation:

      Same as diffraction/interference equation above, except now have to consider two pathlengths, the incoming and outgoing rays, which together must have a combined pathlength difference that is an integer multiple of the wavelength in order to create a maximum (and a half-integer multiple for a minimum):

      Figure from by Karen B. Kwitter. The pathlength dsinα is the extra path length difference of the two incident rays, and dsinβ is the path length different of the two diffracted, exiting rays at angle β.


      d = space between adjacent grooves or slits

      = angle of incidence of collimated beam to grating.

      β = angle of emergence of a ray of certain wavelength from the grating.

      λ = wavelength

      m = order of interference (most commonly a small number)

         = number assigned to each fringe in the diffraction pattern

      The grating equation as satisfied by multiple orders with a monochromatic incident beam. From .

      The grating equation as satisfied by multiple orders with polychromatic light diffracted from a grating. Only the negative orders are shown for clarity. This situation is discussed more below. From .

    • Blaze the grating to different angles to change the wavelength coverage:
    • θ = blaze angle - determines portion of spectrum you want coming out at a given β for a fixed λ and sin

      • Find that θ = ( + β)/2

      • From echelle/fig_angl.html.
      • is typically set in a given spectrograph, and the range of β is sometimes limited, so you can tune what wavelengths are optimized by changing gratings with different θ.

      • Often spectrographs are built to work in the Littrow condition, which has = β = θ (i.e., all angles on the same side of the grating normal).

        In this case, the incoming and outgoing rays travel along the same axis, and directly normal to the face of the groove (not the normal to the grating).

      • From .
        In the Littrow arrangement (or autocollimating spectroscope), a single lens or mirror acts as both the collimator and the imaging camera objective to save on both cost and the size of the system.

      From Kitchin, Optical Astronomical Spectroscopy.

    Effect of orders of interference (m) on spectrum

    • When we use a grating, we get multiple individual spectra produced, one for each order of interference. We also call these individual spectra orders.

      Portion of the image structure for a single bichromatic point source viewed through several slits. From Kitchin's Astrophysical Techniques.
    • For m = 0, all wavelengths fall in the same place, and the grating acts as a simple mirror. (In fact, often spectrographs are used as simple imagers when the grating is turned to have zero order go to the camera. Thus, get imager and spectrograph in the same instrument.)
    • Typically, higher orders will give weaker spectra -- most of the power is put into the lower orders (as shown by the relative heights of the peaks shown in the different orders as shown in the figure above -- a function of the envelope set by the single slit diffraction pattern).
    • As mentioned above, the separation of wavelengths is greater at higher orders -- resolution of different wavelengths increases at higher orders.

    • The dispersion (i.e., wavelength range per set range of output angle) is commensurately smaller (fewer angstroms per angle) as the orders go up. See more on this below.

    • Orders can overlap. For example, for a given mλ=constant, and a fixed d, sin, and sinβ, you have all of these coming out at the same place (same β angle):

        λ of the m=1 order

        λ/2 of the m=2 order

        λ/3 of the m=3 order

        ... etc.

      Overlapping of spectral orders. The light for wavelengths 100, 200 and 300 nm in the second order is diffracted in the same direction as the light for wavelengths 200, 400 and 600 nm in the first order. Figure and caption from the Diffraction Grating Handbook, by Christopher Palmer & Erwin Loewen, Newport Corporation.
      Another image showing order overlap and the relation between order and dispersion. In the case of the instrument being discussed here, the positions of wavelengths less than 190 nm are marked, but these wavelengths are absorbed by the air and so are not expected to get to the instrument (and so are indicated with parentheses). From

      In general we do not need to worry about most of these overlaps, e.g., if our detector is not sensitive to the wavelengths of the overlapping parts of the overlapping orders.

      • For example, in the example above the wavelengths < 190 nm are absorbed by air, so will be "filtered out" by air.

      But in many cases there are problems:

      • Visible range:
      • m λ(Å) for a given m λ = constant
        1 3,000
        2* 1,500
        3** 1,000
        * partially overlaps m=1 spectrum
        ** partially overlaps m=1 and m=2 spectra

        Thus, if we want to observe the m=1 spectrum from 4000 to 8000 Å, we need to put in a filter to block wavelengths less than 4000 Å:

        • If we do not put in such a filter, then we will also have the m=2 spectrum from 2000-4000 Å landing on top of our m=1 spectrum from 4000-8000 Å.

        • Now, for work on astronomical objects from the ground, we know that the atmosphere doesn't allow light through that is bluer than about 3000 Å, so we don't need to worry about the overlap of the 2000-3000 Å piece of the m=2 spectrum (which will overlap the 4000-6000 Å piece of the m=1 spectrum).

        • But we DO still have a problem with the m=2 optical spectrum from 3000-4000 Å, which is overlapping the m=1 order spectrum from 6000-8000 Å.

          But we can remove this part of the m=2 spectrum by inserting into the spectrograph (or telescope) a filter that blocks wavelengths bluer than 4000 Å, and this filter doesn't do anything to the part of the m=1 spectrum we care about.

        • Such filters are called order blocking filters.

        • Note also that for the same m λ range, the higher orders span a smaller range of λ, but this higher order has its light more spread out, so better resolution.

      • Infrared range:
      • Here is an example of spectral order overlap in the infrared, where we are observing from 7,000-100,000 Å:

        m λ(Å) for a given m λ = constant
        1 7,000
        2* 3,500
        * overlaps m=1 spectrum

        Think about how you would avoid order mixing in this case.

      • Ultraviolet range:
      • And here is an example of spectral order overlap in the ultraviolet, where we are observing from 100-4000 Å:

        m λ(Å) for a given m λ = constant
        1 100
        2* 50
        * overlaps m=1 spectrum

      Think about how you would avoid order mixing in this case.

  • Camera

    Purpose is to refocus the dispersed light from the grating/prism onto a focal plane for recording the information on film or a CCD.

  • Characterizing the Power of a (Grating) Spectrograph

    • Resolving power -- defined as
    • where:

      N = # of grooves

      m = order of interference

      • As described above, increase resolution by increasing N or m.
      • Approximately:

        • Low resolution: R <~ few 1,000

        • Medium resolution: R ~ few 1,000 to ~ 10,000 or so

        • High resolution: R ~ 10,000+ (into the 100,000s)

      • Note that by the definition of redshift, we have that v / c = 1 / R.

        What this means is we can define the resolution of the spectrograph in terms of the relative Doppler shifts (in km/s) that the spectrograph can resolve.

      • Can achieve higher resolution with gratings:

        Rgrating ~ 10 x Rprism

    • Dispersion
    • A measurement of the angular separation of different wavelengths of light.

      Over what range of output angles, dβ, is dispersed the range of wavelength dλ?

      where W = width of grating (N/W gives the groove density)

Special Spectrographs

  • Multislit spectrograph -- instead of a single long slit, cover the focal plane with opaque sheet having precision-milled slits for many stars in the field.

    Example of a "slitmask" for multiple object spectroscopy. From
    Example of a field with a multislit mask being designed to cover many targets (left). (Right) the resulting spectroscopic image with multiple spectra, one per slit. The large relative shifts of the emission lines in the spectra are primarily due to the lateral displacement of the individual slits with respect to one another on the mask. From

    • Why must these slits not overlap?

  • Fiber-Fed Spectrographs -- multiplexing capabilities

    Instead of a slit, use fiber optic cables to deliver light from telescope focal plane to spectrograph.


    • Spectrograph stability - use for minimizing flexure
      • Flexure is bending of metal from gravity; can, e.g. cause slight shifts of spectra in the detector focal plane and create false shifts in Doppler velocities, increase errors. Flexure/errors change as move telescope around.
      • Mount spectrograph on fixed, rigid surface in environmentally controlled and stable environment - e.g. Fan Mountain Spectrograph.
    • Large spectrographs cannot be mounted easily on telescope -- mount off telescope and pipe light to them.
    • Multi-aperture spectroscopy - not restricted to slit configuration; can take light from anywhere and redirect to slit.

      Two ways to use:
      • Multi-object fiber spectroscopy -- spectra of many individual sources obtained simultaneously with one spectrograph fed with light through multiple fiber optics.
      • - Examples:

        • Two Degree Field system (2dF) on the Anglo-Australian Telescope (AAT).
        • Hydra spectrographs on NOAO telescopes.
        • Sloan Digital Sky Survey spectrographs (e.g., APOGEE, BOSS surveys).
        • Hectospec on the MMT telescope.

        On the telescope end of the fibers, need to place the fibers accurately in the focal plane to match the positions of targets in a field (requiring accurate astrometry beforehand).

        Several ways to work with fibers on the telescope end:

        Manual plugging into a precision-milled metal plate:

        - Method originally used, but still very much in use, e.g., in Sloan Digital Sky Survey:

        BOSS is capturing accurate spectra for millions of astronomical objects by using 2,000 plug plates that are placed at the Sloan Foundation Telescope's focal plane. Each of the 1,000 holes drilled in a single plug plate captures the light from a specific galaxy, quasar, or other target, and conveys its light to a sensitive spectrograph through an optical fiber. The plates are marked to indicate which holes belong to which bundles of the thousand optical fibers that carry the object's light. (Click on image for better resolution.). Photo from the Sloan Digital Sky Survey.
        - With this method, plugging of the fibers can be done in the night, but this wastes a lot of time when you are not observing sky because you are replugging fibers.

        - Alternatively (SDSS method), can have many fiber units (in "cartridges") and plug many plate cartridges in the daytime.

        The hang plugging method is human intensive, but, in the end, can still be more cost effective than expensive robotic method and it saves telescope time during the night.

        Click here to see a time lapse video of the plugging of an SDSS plugplate for the BOSS survey. Two "pluggers" working together can plug a 1,000+ fiber plate like this in 30 minutes.

        Robotic Placement of Movable Fibers:

        - Build a computer driven robot that can actively move fibers to specific positions.

        - No plates to drill, but complicated, computerized ballet to get the fibers placed and without tangling.

        - For example, hundreds of fibers as "fishing poles" attached to upward looking prisms with magnetic grip to a metal plate at the telescope focal plane.

        2dF fiber system on the AAT.

        - Use of robotic arm (gripper) to place fiber ends precisely.

        - Fibers typically 2 arcsec or so in diameter, need to be placed to few tenths of an arcsecond to maximize light throughput from each source.

        - Accurate astrometry to get precise coordinates in advance.

        - Intricate software to program robot arm, plan positions to prevent tangles and collisions.

        Example of Hydra setup on stars in the Pyxis globular cluster by Majewski research group. Two yellow fibers do not go to spectrograph but are used to check the telescope guiding by monitoring flux from two bright stars in the field.

        - Typically takes 20-40 minutes to place 100-400 fibers automatically -- "lost" observing time.

        - AAO 2dF system has two systems so that one can be observing while the other configures:

        The AAT with 2dF spectrograph system.

      • At the spectrograph end, the fiber optics are brought together into a slit-like pattern:

        Multiple fibers channeling the light from different sources are put into a single slit-like pattern to create a multiobject spectrum.

        Image of the spectrograph end of the 300 fibers used in the SDSS3/APOGEE system. Photograph by Steven Majewski, Univ. of Virginia.
        The resulting appearance of the data is shown in the next picture.

        Portion of a raw image from the APOGEE infrared detectors showing sections of spectra for some of 300 stars in a field in the bulge of the Milky Way. Note the emission lines from airglow and some absorption lines from molecules in the Earth's atmosphere (neither which show Doppler shifts from fiber to fiber) and lines from the stars themselves (which show different Doppler shifts from star to star, and different lines depending on the temperature and metal content of the stars). Image by Steven Majewski, APOGEE project.

        This "first-light" field of stars observed by APOGEE keys in on a large region in the disk of our galaxy towards the constellation Cygnus (the Swan, or Northern Cross), which is filled with Milky Way stars, star clusters and dust (seen as colored, glowing clouds in this image from NASA's WISE infrared observatory). The large white circle is the field of view of APOGEE, with a width spanning six moon diameters. The green circles indicate known or suspected young star clusters. The small red circles indicate the position of each faint star targeted with APOGEE's fiber optic system. The inset shows pieces of the APOGEE spectra for stars determined by APOGEE to be members of two of the clusters shown. These members were identified by the near identical motions through the galaxy shared by each clusters' stars. The motions are detected as shifts of the spectral features caused by the Doppler effect. These dark line features are caused by absorption of specific colors of light by the atoms of the different chemical elements in each star. Image Credit: P. Frinchaboy (Texas Christian University), J. Holtzman (New Mexico State University), M. Skrutskie (University of Virginia), G. Zasowski (University of Virginia), NASA, JPL-Caltech and the WISE Team.

        Spectra of about 100 stars using multiple fibers to pipe light to a single slit from the Hydra optical wavelength spectrograph. The resolution of these spectra is lower, so it is difficult to see many absorption lines, and the relative Doppler shifts are difficult to discern.

      • Integrated field spectroscopy -- essentially reshape "slit" to sample points of light in random places of single, extended source.
      • Pattern of fibers sampling the sky in the SparsePak system built by Matthew Bershady and collaborators (including former UVa undergrads) at the University of Wisconsin for the WIYN telescope at Kitt Peak. From sparsepak/description.html.

    • There is a trade off with fibers -- they provide a multiplexing capability but do have the problem of light lost through the fibers.

      So, e.g., if the losses are 80%, only pays to do multiaperture if N >= 5.

    Aside: Details on the Fan Mountain Observatory Bench Spectrograph (FMOBS)

    (for interested readers)

    Single science fiber and six sky fibers.

    Mainly for rigidity for precision velocity work.

    Spectroscopy in General

    Spectrograph Mechanics

    The Telescope

    The Entrance Slit

    The Collimator

    Dispersing Element

    Camera (focusing) Optics

    Fiber-fed Spectrographs

    Integral Field Spectroscopy

    Difficulties of Fiber-fed Systems


    Focal Plane Module

    Fiber Train

    Bench Spectrograph

  • Objective Prism Spectrograph -- a way to get multiplexing capabilities in a simple way

    • Full-field, slitless spectroscopy -- generally for survey work.
      • Use to classify stars and measure low quality radial velocities of many stars at once.
      • For example, Vyssotsky and Williams survey to find M stars in the McCormick doghouse with the astrograph (now at Fan Mountain Observatory).

      • Today often used to find emission line objects, like quasars, AGN, planetary nebulae.

    • Typically place prism or transmission grating over top of telescope or intercept full telescope beam downstream.
      • Small apex angle prism (<= 10o) --> low resolution.
      • Net reciprocal dispersion ~ 100-300 Å/mm in the camera focal plane.
      • Combination system (for at > 1 m)
        • grism = grating + prism
        • grens = grating + lens
        • dispersion ~ 150 Å/mm
    • Often used with a Schmidt telescope (at < 1 m) to cover large fields of view, many targets at once.
    A beautiful objective prism image of the Hyades star cluster taken by Melinda & Dean Ketelsen. Note the obvious absorption lines in these spectra. See their description of taking this image here.

    Objective prism spectrum image of the star field including the M57 Ring Nebula. The image shows both the an m=0 order ("real image") and m=1 order (wavelength-dispersed) image for each object in the image. From snspec.htm.

    Question: How can you tell that the first two slitless spectroscopy images shown just above were made with an objective prism while the third was made with a transmission grating?

  • Echelle Spectrograph -- A special design that can be used to deliver high dispersion, high resolution, and large spectral ranges all at the same time.

    (With normal spectrographs, often have to decide between high resolution over small λ range, or, forced to go to low resolution -- cram the wavelengths together -- to get large λ range.)

    Recall that as we work at higher orders of spectrograph, we get higher dispersion and higher resolution. So, one way to get to high resolution is to work in high orders.

    mλ/d = sin ± sinβ

    Echelle spectrographs: Instead of decreasing groove spacing, d, to achieve high resolution, work with modest groove spacing (80 grooves/mm) but at very high m (as high as m = 100's).

    Net reciprocal dispersion ~ 1-2 Å/mm in the focal plane.
  • Brings up two problems:

    • Groove Shadowing

      Because m is large, then sin + sinβ large:

      High orders are at very large β angles with respect to grating normal -- soon you get groove shadowing -- blocking of the reflection by one groove by the next groove over.

      Solution: Make blaze angle very large in echelle and illuminate at large angles to normal surface ( ~ 90o.

      From Kitchin's Optical Astronomical Spectroscopy

    • Severe Order Overlap

      Because m is very large, have severe overlap of many adjacent orders (e.g., m=101, 102, 103, 104, 105, .... all overlap at almost similar wavelengths).

      Solution: Use two elements to disperse light in two dimensions.

      Second dispersing element is used to separate the orders in a second dimension.

      From Kitchin's Optical Astronomical Spectroscopy

    • Results in many separated spectra of similar spectral ranges sloping diagonally in camera focal plane.

      Echelle spectrum from the FOCES instrument at Calar Alto Observatory. Image from gehren/foces.html.
      Echelle spectrum of the Sun from Nigel Sharp of NSO/KPNO.

    Another cross-dispersed spectrograph is the TripleSpec near-infrared system built at UVa for Apache Point Observatory.

    Though not an echelle spectrograph, the system does use cross-dispersion in order to separate the first few orders of the grating and therefore get simultaneous spectra of all parts of the near-infrared wavelength range:

    Figure by Remy Indebetouw and Jarron Leisenring showing the TripleSpec focal plane and five of its cross-dispersed orders (orders 3-7). Wavelengths for some lines are marked (in Angstroms). Note that the orders have overlapping wavelengths that are now visible, rather than blending together in one spectrum.

Previous Topic: Comets & Meteor Showers Lecture Index Next Topic: Coordinate Changes

AAO photographs from All other material copyright © 2002,2006,2008,2012,2015 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 313 and Asronomy 3130 at the University of Virginia.