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Astronomical Observational Techniques and Instrumentation

Professor Don FigerSpectral resolution, wavelength coverage, the

atmosphere and background sources

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Aims and outline for this lecture

• describe system requirements for spectral resolution and wavelength coverage

• describe atmospheric effects on observations• summarize primary background sources and effects on

observations

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Need for Spectral Information

• “A picture is worth a thousand words.” --Barnard

• “A spectrum is worth a thousand pictures.” --an astronomer

• A spectrum is the distribution of flux versus wavelength.

• Spectra are critical for making measurements of physical properties of astronomical objects.– low resolution spectra reveals spectral energy distribution (SED)– high resolution spectra reveals emission/absorption features

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Spectrum of Arcturus

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High Resolution Spectroscopy

• High resolution spectroscopy can yield– velocity– abundances– temperature– virial mass (through integrated light)– molecular excitation– interstellar absorption– ionization state– others

• The example on the right shows high resolution infrared spectra of red supergiants.

• Note the many CO rotational-vibrational absorption lines.

• The slight translations in the wavelength axis from star to star show velocity differences.

• Weaker features to the left reflect atomic absorption and can be used for abundance analysis.

velocity difference

CO bandhead

atomic absorption

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Low Resolution Spectroscopy

• Low resolution spectroscopy can yield– emission mechanism (via spectral index)– temperature– molecular content– interstellar molecular absorption

• The example on the right shows low resolution infrared spectra of red supergiants.

• Note the CO bandhead.• The depth of the bandhead indicates that

these stars are cool. • For this application, it might be just as

well to obtain a high resolution spectrum over this waveband.

• In some cases, a low resolution spectrum can reveal curvature over a broad range of wavelengths – something difficult to detect in high resolution spectra.

CO bandhead

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Spectrograph/spectrometer

• A spectrograph/spectrometer is an instrument that can measure intensity versus wavelength.– dispersive

• prism• grating

– nondispersive• filters, circular variable filter (CVF)• Fabry-Perot

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Spectroscopy System Design Criteria

• Efficiency: amount of light directed into the spectrum

• Resolution: minimum spatial and spectral separation between resolved features

• Scattering: light directed out of the spectrum or in undesired locations in the spectrum

• Stability and calibration accuracy: ability of system to maintain or reproduce wavelength versus pixel relationship

• Background: light from all sources other than target, might be sky, telescope, optics, baffles, etc.

• Packaging: compactness of layout

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Spectrograph Cartoon

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Continuum and Emission Lines

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Absorption Lines

Equivalent Width

• Equivalent width is a measure of flux in a line.

• It is independent of instrument parameters.

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Spectroscopy System Design Form Example

• graphic shows simple layout for spectrograph

grating normal

gratingcollimator

slit

telescope

detector

lens

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Spectral Resolution

• Spectral resolution is a measure of the ability to separate nearby features in wavelength space.

features. resolved twoof separationh wavelengtminimum,

R

• Delta lambda– often set to the full-width at half-maximum of an unresolved line– can be measured in the data– depends on data analysis– can be limited by diffraction, slit width, detector sampling

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Spectral Resolution: Prism

• A prism disperses light with a transmissive optic that has chromatic index of refraction.

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Gratings: Grating Equation

• The grating equation gives the geometry for constructive interference between facets of a grating. The equation can be derived by setting the optical path difference between light scattering from two adjacent facets to an integer multiple of the wavelength.

• In more standard nomenclature,

where, m is the order number and T is the groove density.• Note that the equation reduces to the law of reflection for m=0.

mdd inout sinsindifferencepathoptical

sinsin Tm

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Gratings: Angular Resolution

• Angular resolution describes the variation in output angle versus wavelength. It can be found by differentiating the grating equation.

cosd

dmT

tan2

cos

sinsin

cos

LittrowmT

d

d

• Note that the angular resolution can be increased by increasing the output angle.

• For a fixed wavelength, angular resolution is dependent on geometry.

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Gratings: Diffraction-limited Resolution

• The diffraction-limited resolution of a grating is simply Nm, where N is the number of illuminated grooves and m is the order number.

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Gratings: Slit-limited Resolution

• The resolution, or resolving power, is usually limited by slit width. (“primed” quantity is at image plane)

)/)(/(

ddFxR

camslit

slit

R

)/(

ddR

slit

collslit FxR

/cos

sinsin

))/()(cos/(

)/()sin(sin

mTFx

mTR

camslit

cos)/)/((

sinsin

camcollcamslit FFFxR

slittele

coll

slit

collLittrow

D

D

x

FR

tan2tan2

slit

coll

x

FR

cos

)sin(sin

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Gratings: Diffraction-limited Image

• Imagine that we set the slit width to be equal to the full width at half maximum of a diffraction-limited spot. (Assume Littrow).

22.1

tan2

)/22.1(

tan2

)/22.1(

tan2 coll

teletele

collcoll

teletele

coll D

DF

fD

DF

FR

• Note that the resolution can be increased by increasing the size of the collimated beam (and size of grating), increasing the output angle, or decreasing the wavelength (assuming that the decrease in wavelength is accommodated by a decrease in the spot size and decrease in slit width).

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Gratings: Increasing Resolution

• From the previous equations, it appears that resolution can be increased by:– decreasing the slit width (which might decrease the transmitted flux)– increase the collimator focal length (which will increase the beam size and

required size of the grating) – increase the output angle (which will increase the required size of the grating)

• There is another possibility that is not apparent from the grating equation, given that its derivation assumed that the index of refraction of the material surrounding the grating was one.

• A more general derivation would show that the realized angular dispersion is multiplied by n. – This effect is used in an immersion grating– Silicon is a particularly useful material for this purpose because it has a high

index (n~4), although it is only transmissive in the infrared.

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Gratings: Immersion Grating Resolution

• The resolution can be increased by immersing the grating surface in a high index material.

)sin(sin nTm

tan2

cos

sinsin

cosnn

n

mTn

d

dn

d

d Littrow• Note that angular dispersion is n times greater than for case without immersion.

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Gratings: Echelle Grating

• Angular dispersion is dramatically increased when using an “echelle” grating.

• In this case, the output angle is typically >60 degrees.

• Because an echelle is used at a large angle, it must be rectangular.

• The grating facets must be ruled at a large angle, because:– In order to maintain high efficiency, the input and output angles should

be the same (“Littrow condition”).– In order to provide high resolution, the output angle must be large.

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Gratings: Echellogram

HIRES order format showing the solar spectrum(note that color was artificially added for illustrative purposes)

+

+

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Gratings: Immersion Grating

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Fabry-Perot Etalon

• A Fabry-Perot etalon is a filter that selectively transmits a narrow range of wavelengths.

• Like a thin film, it transmits the most flux at wavelengths that satisfy the thin film condition.

• Finesse is a function of reflectivity.

thickness. tandnumber order m ,refraction ofindex n where,

,2

max

m

nt

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Wavelength Coverage: Free Spectral Range

• Multiple orders of the same wavelength range are dispersed to either side of the order of interest.

• The non-overlapping wavelength region in the order of interest is defined as the “free spectral range.” Outside of this range, light of different wavelengths in multiple orders overlap.

m m+1m-1

order=m

1 2

1 2

FSR

overlap overlap

• FSR=/m

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Atmospheric effects

• Absorption– reduced flux from source– difficult calibrations

• Emission– increased background noise– reduced integration times– difficult calibrations (subtracting time-varying components)

• Turbulence– increased object size (“seeing”)

• All effects vary with wavelength, time, altitude, line-of-sight

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Atmospheric absorption

• Molecules are the dominant absorbers (H2O, CO2, Ox)

• Strong function of:– wavelength, atmospheric wavebands– time, frequent calibration (hour timescales)– altitude, mountain-top observing sites– line-of-sight, limited target access and frequent calibration

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Atmospheric absorption versus

• Sharp cutoffs – defined primarily by H2O– shape wavebands

• Higher transmission between lines with higher resolution

• Can introduce large calibration errors for low resolution observations (MNRAS, 1994, 266, 497)

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Wavelength Regimes: near/mid-infrared: Atmospheric Transmission

Atmospheric Transmission: near/mid-infrared

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 5 10 15 20 25 30 35

Wavelength (microns)

Tra

nsm

issio

n

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Wavelength Regimes: near-infrared: Atmospheric Transmission

Atmospheric Transmission: near-infrared

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

Wavelength (microns)

Tra

nsm

issio

n J H K L M

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Atmospheric absorption versus - high res

Array defects

CO2 absorption lines

Keck II 10-m

+

+

R =

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• Particle number densities (n) for most absorbers fall off rapidly with increasing altitude.

• Density of atmospheric constituents modeled as exponential.

• x0,H20 km, x0,CO2 km, x0,O3

km

• So, 95% of atmospheric water vapor is below the altitude of Mauna Kea.

Atmospheric absorption versus altitude

.

depth, optical is τwhere,

0/

λ,0

dxendx

eII

xx

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Atmospheric absorption versus airmass

• The amount of absorbed radiation depends upon the number of absorbers along the line of sight

Atmosphere

t.coefficien extinction atm. is χ where

,,10 5.2/,0 AMmagII mag

AM=1AM=2

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Atmospheric emission

• Blackbody (thermal)

• Molecular (OH)

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Thermal emission

spectral radiance, brightness, specific intensity:I = cos B(T) W m-2 Hz-1 sr-1

B(T) = 2h3 1 c2 exp(h/kT) - 1

Planck (blackbody) function:

emissivity (dimensionless)

max(m) = 3674 K T

Peak in B or B:

B(T) = 2hc2 1 5 exp(hc/kT) - 1

max~10 m for room temp.

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Total power onto a detector: P = AskyB(Tsky)

: transmission of all optics x Q.E.sky: emissivity of skyA: telescope area: solid angle subtended by focal plane aperture: bandwidthB(Tsky): Planck function

At 10 m, typically: ~ 0.2, ~ 0.1, A~ 3x10-10 m2 Sr ~ 1.5 x 1013 Hz (10 m filter), T ~ 270 K

P ~ 10-9 W or ~ 4 x 1010 s-1

Atmospheric emission: Blackbody

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Atmospheric emission: A Note on Solid Angle

• Background from the sky can be calculated by multiplying the blackbody equation by the area of the sky seen by the detector and the solid angle subtended by the telescope aperture.

).(TB A Flux skyskytelescopesky

• The A product is invariant in a system.

.AA skytelescopetelescopesky

.2

)2/(~)cos1(2

sinˆA

2

2

22

2

2

02

2

2

0

22

0 02

22

2

2

telescopesky

0

F

xD

d

Dx

F

dx

F

dx

F

d

d

dddx

F

d

d

Adnx

F

d

.

2

2/2

2A

2

2

222

12

2

21

2

skytelescope

F

xD

F

xDD

d

dD

AtelescopeAsky

detector

D

xd

F

• It is easier to use area of telescope and solid angle of sky.

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Atmospheric emission: OH lines

OH linesPh

oton

s s-1

m-2 a

sec-2

m

-1

Wavelength {m}

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Array defects OH lines

+

+

R =

Atmospheric emission: Molecular lines

Array defects

Keck II 10-m

+

+

R =

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Atmospheric emission versus time

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Atmospheric Turbulence

• Static atmosphere bends light (n=1.000273 at 2 m)

• Dynamic atmosphere distorts the wavefront

Data from the William Herschel 4.2 metre Telescope in La Palma. Wavelength 689.3nm, Exposure time 30ms per frame. The data were taken with a simple Speckle Camera situated on the GHRIL platform of the telescope. The data sets were taken with the Speckle Imaging group at Cardiff University.

Orionis (“Betelguese”)

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Atmospheric Turbulence

• A diffraction-limited point spread function (PSF) has a full-width at half-maximum (FWHM) of:

• In reality, atmospheric turbulence smears the image:

• At Mauna Kea, r0=0.2 m at 0.5 m.

• “Isoplanatic patch” is area on sky over which phase is relatively constant.

}.{" }{

}{25.0{radians}

}{

}{2.1

mD

m

mD

mFWHM

. where},{" }{

}{25.0 5/6

00

rmr

mFWHM

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Lick 3-m (1994)

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Keck 10-m (1997)

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HST/NICMOS (1997)

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VLT/AO (2002)

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Keck/LGSAO (2006)

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• Atmosphere– thermal– molecular

• Telescope– thermal– scattering

• Zodiacal light• Astronomical sources

Background - sources

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• Thermal

• OH– The average OH line intensity is approximately 25,000 s-

1 m-2 asec-2 m-1. See Maihara et al. 1993.– The continuum between lines is about 50 times lower than

this value (in the H band).

}{ )( 1,

seQETB

hAC skyskyteleinstrthermalsky

Background - sources: Atmosphere

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• Mirrors

• Baffle edges and walls• Secondary support

surface.perfectafrom

deviationRMSisswhere,2

s

I scattered

Background - sources: Telescope - scattering

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Background - sources: Astronomical

• Astronomical objects can be objects of interest or noise contributors, depending on the project.– Sunlight, moonlight– Light scattered by solar system dust (“zodiacal”)– Light emitted (thermal) by solar system dust (“zodiacal”)– Stars (especially in a crowded field)– Light emitted by interstellar dust (“cirrus”)

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Background - sources: Astronomical

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Background - sources: COBE data

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• Background noise is the quadrature sum of shot noise for each background source.

.2

iiN

S

N

S

2222backsourcedarkreadtotal NNNNN

Background and Signal-to-Noise Ratio

• Recall the expression for SNR.

• The noise is the quadrature sum of uncorrelated noise sources.

.222,

2,

2,

2otherzodithermaltelethermalskyOHskyback NNNNNN