Techniques of Observational Astronomy AST3722C
Basic Spectroscopy

Introduction

   Some of the primary applications of spectroscopy are

·        Spectral energy distribution – effective temperature

·        Spectral classification (OBAFGKM etc.) – comparison of spectra with “standards”: determination of temperature and luminosity class

·        Radial velocity determination – need a “comparison” spectrum of a laboratory reference source (typically a hollow cathode discharge tube)

·        Spectral line formation
- Abundance analysis – from “equivalent widths”
- Line profile analysis: broadening mechanisms (thermal, collisions, rotation)
- Zeeman effect (magnetic fields)
- stellar age (Li abundance, etc.)

The Basic Spectrograph

The basic astronomical spectrograph is comprised of a slit, collimator, a dispersing element (typically a diffraction grating or prism), a camera, and a detector.

·        Slit: isolates portion of sky that is imaged in a single wavelength

·        Collimator: makes beam parallel

·        Dispersing element: disperses light as a function of wavelength

·        Camera: forms image of object (star or slit) on detector

Let , , and ,  Note:

The important design characteristics of a spectrograph are the dispersion (), which defines how widely the various wavelengths are spread out, and the resolution, which describes the minimum difference in wavelength that can be determined.

Dispersion: Let  so .  While  is properly defined as linear dispersion, astronomers frequently work with the linear reciprocal dispersion (JPO prefers the term spectral concentration), usually quoted in Å/mm.  It is not uncommon to hear linear reciprocal dispersion referred to as “dispersion”.  (Linear reciprocal) dispersions between 50 and 200 Å/mm are typically considered “low” dispersion (spectral classification), between 10 and 50 Å/mm are “medium” dispersion (radial velocities) and less than 10 Å/mm are “high” dispersion (line profiles).

Resolution: The collimator/camera optical system image the telescope focal plane on to the spectrograph detector plane.  In order to limit the spreading of light of a single wavelength in the dispersion direction, a slit is usually employed at the telescope focal plane to mask the light from the object. The ratio of image scale at the slit vs. the detector plane is.

To a first order the possible spectral resolution will be set by the width w’ (in the dispersion direction) of the image or the slit, as image in the spectrograph. Thus the wavelength resolution is given by .  (If the pixel size p of the detector is not less than w’ then the spectral resolution is set by the pixel size.) 

In reality, we must include diffraction due to the apertures in the optical train.  Typically the limiting aperture is the camera aperture a.  The minimum angle that can be resolved (recall Rayleigh’s criterion) is radians hence and . Note that when a slit is used light will be lost so there is a trade off between resolution and reaching faint magnitudes.

Dispersing Element

A reflection diffraction grating has a series of closely spaced grooves so that light reflects off of the grating surface as though there was a series of narrow parallel mirrors.  Constructive interference between the reflected beams of light at specific angles for a given wavelength and not for other wavelengths results in the creation of a spectrum.  Setting the path difference between adjacent rays equal to a multiple of whole wavelengths (thus achieving constructive interference) sets up the grating equation  and the dispersion equation.  The beam is dispersed into multiple orders.  The 0th order is not dispersed (white light). 

Note that the dispersion increases with order m, and that red light is dispersed through a greater angle than blue.  In the higher orders, the blue end of order m=1 will overlap the red end of order m.  It may be necessary to insert a colored glass filter to isolate the order of interest.  The useful spectral range (over which orders will not overlap) is approximately.

Blazed Gratings

If the grooves are properly shaped, the light reflected will be concentrated in a direction other than that of the 0th order.  Such a grating is said to be blazed.

Recent developments

Grism

Most modern spectrographs use a diffraction grating or a combination of a diffraction grating and a prism termed a grism.  Here a grating has been bonded to the surface of a prism.  The equivalent of the grating equation becomes  where n is the index of refraction of the prism glass and the grating material, which are assumed to be equal.  The deviation of the beam by the prism is compensated by the deviation of the central wavelength in the grating resulting in a spectrum centered on the system optical axis. 

Echelle

To increase the resolution of a grating on can either decrease the spacing between groove d, or increase the order m.  On version of spectrograph that adapts well to two-dimensional detectors is the echelle spectrograph.  Here a grating with a relatively coarse pattern of grooves (so large d) is used at a very high order (typically more than 50).  A weak prism is mounted with its dispersion perpendicular to the echelle dispersion, displacing the orders so that they do not overlap.

 

NSO/AURA/NSF Solar spectrum                       UV echelle spectrum

Useful References