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ASTR 5110, Majewski [FALL 2017]. Lecture Notes

ASTR 5110 (Majewski) Lecture Notes



  • Schroeder, Astronomical Optics, Chapters 12-15.

  • Kitchin, Astronomical Techniques, Chapter 4.

  • Lena, Observational Astrophysics, Chapter 5.

  • Howell, Handbook of CCD Astronomy, Chapter 6.

  • Birney, Observational Astronomy, Chapter 11.

  • Hecht, Optics, Sections 5.5, 5.6, 10.2.8.

  • Some of the sections of this web page were designed by Jeff Crane.

  • 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 for collimation of the diverging, post-slit beam.
    • Dispersing device (e.g., prism or diffraction grating).
    • Camera lens to focus the image of the spectrum onto the detector.
    • Detector (e.g., 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 second lens focuses that spectrum onto a detector.

      Note the two lenses and how they are positioned with respect to their focal lengths (see below for why):

    • Transmission Grating Spectrograph

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

    • Reflection Grating Spectrograph (e.g., McCormick's Spectro-Mechanics 10C spectrograph, shown below).

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

    • A schematic of the department's Model 10-C spectrograph for the LMO 26-inch telescope.

      "The tracks of a compact disc act as a diffraction grating, producing a separation of the colors of white light. The nominal track separation on a CD is 1.6 micrometers, corresponding to about 625 tracks per millimeter. This is in the range of ordinary laboratory diffraction gratings. For red light of wavelength 600 nm, this would give a first order diffraction maximum at about 22 ." Image and caption from

    • Volume Phase Holographic Gratings

      Another method for manufacturing diffraction gratings uses a photosensitive gel sandwiched between two substrates. A holographic interference pattern exposes the gel which is later developed. These gratings, called volume phase holography diffraction gratings (or VPH diffraction gratings) have no physical grooves, but instead a periodic modulation of the refractive index within the gel.

      These gratings also tend to have higher efficiencies, and allow for the inclusion of complicated patterns into a single grating.

      "A VPH grating is formed in a layer of transmissive material, usually dichromated gelatin, which is sealed between two layers of clear glass or fused silica. The phase of incident light is modulated as it passes through the optically thick film that has a periodic differential hardness or refractive index. Hence the term "Volume Phase". This is in contrast to a conventional grating, in which the depth of a surface relief pattern modulates the phase of the incident light." Caption and image from

  • The entrance slit

    • In the most basic form, when NO slit is used, 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 Sun in eclipse.
    • The above slitless spectra can be formed by simply sending the image of a source through a prism or grating 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 convolved with these effects (note how difficult it would be to get Doppler information out of the slitless spectrum of Saturn above).

    • Appreciating that a slit is a useful configuration for creating the line-shape in an image, various methods are adopted to implement "image slicing" to stuff different parts of a target into a slit:

      From Lena, Observational Astrophysics.

      Information on the MaNGA project of Sloan Digital Sky Survey IV, which will be using fibers to sample galaxies.

    • Slits or their proxies (e.g., fibers) are placed in the focal plane of the telescope.

    • In the case of slits, the slit itself is often a gap in a shiny piece of (aluminized) glass or metal, so that one can see the image plane reflecting back around the slit (as in the McCormick spectrograph, shown above).

      This is helpful for seeing where the slit is placed using a pickoff camera.

    • Generally a slit spectrograph offers different-sized slits so the user can select their desired resolution or match the slit width to the seeing.

      A focal plane mask giving the user an option of different slit widths. From thizy/dss7/dss7.htm.
      Since the width of the slit determines the actual spectral resolution, there is a trade-off of more flux versus better resolution in the case of extended sources.

      • Why in the case of point sources do we STILL need an option of different slit widths?

      One also may desire different lengths of the slit.

      The choice of different slits and/or limiting the length of the slit is usually done mechanically through a decker.

      Gemini GNIRS slit and decker mechanism. From gnirs/FabArchive.htm.

      Another slit decker plate showing various slit LENGTH options (a second metal plate with a long slit of the desired WIDTH slides over this to select the final shape in both dimensions). From 2000/2300/2321.html.

  • The collimator

    • Takes the diverging (post-slit/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, and so that different rays of the same wavelength can properly interfere with one another.

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

    • Spectrographs employ either refractive collimators (e.g., FOBOS) or reflective collimators (e.g., McCormick spectrograph).

  • 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:

      Other 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 with monochromatic light.

      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 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).
      • alternatively, with the same groove or slit spacing, increase the total number of slits the beam "sees" by increasing the size of the beam itself.
      • 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):


      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 (usually 1-5)

         = number assigned to each fringe in the diffraction pattern

    • 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.
      • The blaze can be used to set what diffraction order has maximum efficiency. This can only be defined for one particular wavelength, so it is common to state blaze wavelength the grating has been optimized for (blazed for).

      • 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.

      • Gratings are commonly blazed for the Littrow configuration , which has = β = θ. 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).

        In this case, 2d sin θ = m λ and one can use the preferred order, wavelength and line spacing to determine optimal θ.

      • From

    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, many imaging spectrographs incorporate this concept into their design, so that you can use the spectrograph to make images, not dispersed spectra, by working in 0th order.

    • Typically, higher orders will give weaker spectra -- most of the power is put into the lower orders.
    • As mentioned above, the separation of wavelengths is greater at higher orders -- resolution increases at higher orders.

    • Orders can overlap. For example, for a given m λ = 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




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

      A diagram for visualizing how orders work and potentially overlap. In the figure, each sector for each order is showing the same spectral range. Note how for the same wavelength range, higher orders are spread out over a larger angular spread (think about why this is). From
      But in many cases there are problems:

      • Consider the visible range of the spectrum observed in first order.
      • At the same points of the first order spectrum in the focal plane we have the following contributions from higher orders:

        m m λ(Å) λ(Å)
        1 3,000
        2* 3,000
        3** 3,000
        * partially overlaps m = 1 spectrum
        ** partially overlaps m = 1 and m = 2 spectra

      • Thus, in some cases we are forced to isolate which order spectrum we want by use of order blocking filters.

        • For example, 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, or else we will see the m = 2 optical spectrum from 3000-4000 Å overlapping the m = 1 order spectrum from 6000-8000 Å.

      • The free spectral range of a grating is the largest wavelength interval in a given order that doesn't overlap the same interval in an adjacent order.

        • If λ1 is the shortest wavelength and λ2 is the longest wavelength in the wavelength interval, then you can show (derive this!) that the free spectral range of order m is given by

          λ2 - λ1 = λ2 / (|m | + 1).

        • Obviously, the FSR is reduced at higher orders.

          For example (show that!):

          • ... in 1st order, the grating can be used unblocked from λ1 to 2 λ1.

          • ... in 2nd order, the grating can be used unblocked from λ1 to (3/2) λ1.

          • ... in 3rd order, the grating can be used unblocked from λ1 to (4/3) λ1.

          • ...etc.


    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

    The resolution of a grating -- its line spread function or instrumental spectral width -- determines how clearly one can see that true line shape from a source.

    From Lena, Observational Astrophysics.

    • 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 ~ 102-3.5

        • Medium resolution: R ~ 103.5-4

        • High resolution: R ~ 104+

      • Typically can achieve higher resolution with gratings:

        Rgrating ~ 10 x Rprism

    • Dispersion
    • Over what range of dβ is dispersed the range of wavelength dλ?

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

      Typically we are more interested in the linear dispersion, which is how the above gets translated onto a linear plane (the detector) and given in Å/mm or Å/pixel.

      • Recall that with Nyquist sampling, we want to be able to sample the intrinsic resolution of the optics.

      • So typically, we want to have at least two detector pixels per resolution element, the narrowest resolved feature possible in the spectrum.

      • This requires matching the detector pixels, and the pixel binning to achieve Nyquist sampling of the resolution.

    Special Spectrographs

    • Multi-slit Spectrographs -- multiplexing capability with slitmasks

      In principle, can use more than one slit in the focal plane of the telescope to obtain spectra of multiple objects.

      The Gemini Multi-Object Spectrograph (GMOS). From

      A slitmask is generally either a precision-milled steel plate or a (mostly dark) photographic film with clear parts for slits.

      Top: Designing a mask for the Keck DEIMOS multislit spectrograph. Bottom: Precision milling a DEIMOS mask. From

      • Must undertake careful astrometric measure of the relative positions of the objects of interest.

      • Must be concerned with spectral overlap -- balance density of slits with area of detector, length of expected spectra and length of slits.

      • To avoid "collisions" have to make prioritized lists of objects; computer algorithms are generally designed to optimize the number of highest priority objects that can be placed.

      From Lena, Observational Astrophysics.

    • Fiber-Fed Spectrographs -- multiplexing capability with fibers

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

      From Lena, Observational Astrophysics.


      • 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.
      • Multiplexing capability through multi-aperture spectroscopy - not restricted to slit configuration; can take light from anywhere and redirect to slit

        Two ways to use:
        • Multi-object spectroscopy -- spectra of many individual sources obtained simultaneously with one spectrograph
        • - Examples: The Two Degree Field system (2dF) on the Anglo-Australian Telescope (AAT) and the Hydra spectrographs on NOAO telescopes.

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

          From Lena, Observational Astrophysics.

          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.

          All fibers from random directions put onto a single slit to create a multiobject spectrum:

          Spectra of about 100 stars using multiple fibers to pipe light to a single slit.

        • 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.

      • Trade off with fibers - multiplexing capability versus the problem of fiber losses - fibers lots of light (say 80%).

        So, e.g., 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 -- 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 dwarf stars (for the 26-inch parallax program) at McCormick doghouse with the 10-inch astrograph.

        • Today the technique 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.
      • From

        • 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
        Direct and slitless grism spectroscopy images of a field of galaxies using the HST Advanced Camera System. Note three emission line galaxies appearing in the right image. From

      • Often used with a Schmidt telescope (at < 1 m) or astrograph to cover large fields of view, many targets at once.

      Objective prism spectrum image of the star field including the M57 Ring Nebula. From snspec.htm.

      Question: Which of the above two images was made with an objective prism and which was made with an transmission grating?

      Of course, 1-D spectra can be extracted from slitless surveys:

      From Howell, Handbook of CCD Astronomy.
      • Gives nature of source.

      • Doppler shifts measurable, but only if you have zero order spectral image to serve as zero point, or you have a direct image to determine the proper relative positions of the spectra to serve as a velocity zero point.

    • Echelle Spectrograph -- high dispersion and high resolution

      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 high orders, as high as m = 100 or more.

      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.

        Note that TripleSpec, although not an echelle spectrograph, uses the cross-dispersion concept to access different orders covering different parts of the near-infrared.

        An image of the TripleSpec focal plane, showing the different orders and their relative wavelengths. From Remy Indebetouw & Mike Skrutskie.

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    AAO photographs from All other material copyright © 2002, 2005,2007,2009,2013,2017 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 5110 at the University of Virginia.