Astronomical SpectroscopyAstronomical Spectroscopy

• Basic Spectrograph Optics • Objective Prism Spectrographs• Slit Spectrographs• Real Spectrographs

• Grating Spectrographs• IR Spectrographs• Echelle Spectrographs• Fiber & Multi-Object Spectrographs

SpectrographSpectrometerSpectroscopeSpectrogramSpectrum

Vocabulary

• Spectral resolution, Resolving Power: R = /– is the wavelength of interest– is the smallest wavelength interval that

can be resolved– “low” resolution 10<R<1000– “moderate” resolution 1000<R<10,000– “high” resolution R>10,000, R>100,000

• Dispersion – /pixel or /Å (informal)

Refraction

• The speed of light in a dense medium (air, glass…) is (usually) slower than in a vacuum

• Index of refraction (ratio of speed of light in a vacuum to the speed in the medium)– air: n = 1.0003– water: n= 1.33– fused quartz: n=1.46– salt: n=1.53

• The speed of light in a material depends on wavelength – “dispersion” (another use of that word)

Diamond

Prisms• Prisms disperse light by

refraction• When a beam of white light

passes from one medium into another at an angle, the direction of the beam changes due to refraction

• Different colors of light are bent at different angles

• Generally, red light is bent less, blue light is bent more

air

glass

A

C

A’

C’

Objective Prism Spectroscopy

• Prism installed at the top of the telescope

• 24” diameter, about 10 degree wedge

• Each point source produces a spectrum

• Low resolution, useful for surveys

KISS Images/Burrell Schmidt

Diffraction Gratings

• Multi-slit diffraction• reflection gratings and

transmission gratings• most astronomical

gratings are reflection gratings

Reflection Gratings

• light reflecting from grooves A and B will interfere constructively if the difference in path length is an integer number of wavelengths.

• The path difference is dsin + dsinwhere d is the distance between facets on the grating), so

d (sin + sin) = n (the grating equation)

• n is the “spectral order” and quantifies how many wavelengths of path difference are introduced between successive facets or grooves on the grating)

The Grating Equation

• The groove spacing d is a feature of the grating• The angle of incidence, , is the same for all

wavelengths• The angle of diffraction, , must then be a

function of wavelength

sin = n/d – sin

d (sin + sin) = n

Sample Problem

• You are working with a grating with 1000 grooves per millimeter.

• The angle of incident light () is 15º

• At what angle will light of 400 nm be diffracted in 1st order (n=1)?

• 500 nm? 600 nm?

• Careful: express wavelength and groove spacing in similar units

sin = n/d – sin

Multiple Grating Orders

• multiple spectra are produced by a diffraction grating, corresponding to different orders (n=1,2,3…)

• For a grating of 1000 grooves/mm and 15º incident angle, what wavelength of light will be diffracted to an angle of 14º in second order?

sin = n/d – sin

(for this figure, m=n)

Slit Spectrographs

Image from CSIRO

• Entrance Aperture: A slit, usually smaller than that of the seeing disk

• Collimator: converts a diverging beam to a parallel beam

• Dispersing Element: sends light of different colors into different directions

• Camera: converts a parallel beam into a converging beam

• Detector: CCD, IR array, photographic plate, etc.

Why use a slit?• to increase resolution

– by narrowing the slit– also decreases throughput

• blocks unwanted light– from the sky– other nearby sources

• sets a reference point

A decker offers a range of slit widths

Collimator

• The focal ratio of the collimator must be matched to the effective focal ratio of the telescope

• The diameter of the collimator determines the diameter of the light beam in the spectrograph

• The size of the collimator affects the size of the “slit image” on the detector

• Bigger, longer focal length cameras reduce the size of the slit image, and increase the resolution of the spectrograph

The collimator converts the diverging beam of white

light from the slit to a parallel beam

Reflection Grating Efficiency• Problem: A grating diffracts

light into many orders; one order contains only a fraction of the light

• Fix: rule the grating facets so that the direction of reflection off the facet coincides with the desired order of diffraction

• Up to 90% of the light can be concentrated into the desired spectral order

• Most spectrographs use reflection gratings

– easier to produce – easier to blaze

C. R. Kitchin, Optical Astronomical Spectroscopy

“Blaze” a grating

Camera Types• reflecting camera

(schmidt camera)– broad wavelength

coverage– on- of off-axis (central

obstruction?)

• transmission camera– lenses– generally on-axis, no central

obstruction– broad wavelength coverage requires

multiple elements

Spectrograph Math

• based on the grating equation

d (sin + sin ) = n• “” is the angle from the slit to the grating

normal and “” is the angle from the grating normal to the camera. is usually fixed.

• The “angular dispersion” of a spectrograph is given by /:

d

n

cos

1sin

/sin

1sin

sin

The Math (cont’d):

• The resolution varies as– the order number (higher=more resolution)– the grating spacing (more rulings = smaller spacing =

more resolution)– the camera-collimator angle (as increases, cos

gets smaller and resolution increases)• The effective resolution of a spectrograph is a

function of– the grating resolution– the size of the slit image (collimator and camera focal

lengths: (slit size x fcam/fcol)– the pixel size

d

n

cos

1

Throughput Matters• The higher the throughput, the better• Limitations:

– slit width (get a bigger collimator or better seeing)

– efficiency of • mirror coatings• grating• lens transmission• detector

(typical)

GoldCam Spectrograph, KPNO 2.1m Telescope

Coude light path KPNO 2.1m Telescope

coude = elbowlarge, fixed spectrographhigh resolution spectroscopy

2.1-m Coude Spectrograph

IR spectrometers•IR array detectors, 1-5 microns•spectrograph must be cooled to reduce thermal background

Now onGemini South

Phoenix

Limitations for High Dispersion

• Problem: detector size, shape– generally square or 1x2 format– a conventional grating spectrograph produces a very

LONG high dispersion spectrum that won’t fit on a CCD

• Solution: the echelle grating– works in high orders (n=100)– a second dispersing element spreads the light in a

perpendicular direction

KPNO 4-m Echelle

Spectrograph

•Compact Cassegrain instrument•Resolution ~ 4 x 104•Originally designed for photographic plates, image tubes, now used with CCDs

Echelle Gratings

• To increase spectral resolution, increase the order at which a grating is used

• For high orders, must increase and in the grating equation (to ~50-75o)

• The spectral range for each order is small so the orders overlap

• Separate the orders with a second disperser (cross disperser) acting in a perpendicular direction.

C. R. Kitchin, Optical Astronomical Spectroscopy

WIYN’s Hydra MOS

• ~85 fibers• Full degree FOV• Wonderful for star

clusters, globular and galactic!

• blue and red fibers• R from a few x 102 to 2

x 104

Solar Spectrum