Optical/NIR Spectroscopy
A3130
John Wilson
Univ of Virginia
Topics:
•
Photometry is low‐resolution spectroscopy
•
Uses of spectroscopy in astronomy
•
Data cubes and dimensionality challenge
•
Spectrograph design basics
• Slit
• Collimation
• Dispersion
• Camera
• Detector
•
Characterization of spectrographs (wavelength range, resolving power, Efficiency, number of objects)
•
Specific elements:
• Prisms
• Plane Reflections Gratings
• Grisms
• Volume Phase Holographic Gratings
• Fabry‐Perot Interferometry
•
Spectral calibration
Spectrograph Design Basics
Telescope Focal Plane
A = d/d
Light from Telescope dl = fcam d
Types of Dispersers: Prisms
Generally used in minimum deviation mode – no astigmatism.
Can be used across more than one octave (factor of 2 in wavelength), so great for cross‐dispersers.
Schroeder, Ch. 3
Poor choice for UV (few glasses transmit well in the UV)
Types of Dispersers: Prisms
Angular Dispersion using Fermat’s Principle of Least Time ‐‐‐ travel time (optical path difference) is equal for closely adjacent paths
Path Length Difference (index of refraction x distance) between top ray and bottom ray:
1
nprism t = nair 2L cos ()
Differentiate with respect to wavelength:
t dn/d = ‐ 2L sin () (d/d)
t dn/d = ‐ 2L sin () (d/d) (d/d)
Schroeder, Ch. 3
Can simplify to based on geometry and differentiation to:
A = (d/d) = (t/a) (dn/d)
Most materials have a dispersion curve (variation of index with wavelength) that conform to:
n() = A + B/2
Differentiating:
dn/d = ‐2B/ 3
So finally:
A = (d/d) = ‐(2t/a)(B/ 3)
Negative sign:  decreases as  increases … blue light is deviated more
FIRE: “Folded‐port InfraRed Echelette” on Magellan Telescope
FIRE
Magellan Telesceope
Continuous spectrum
2.5 um
0.8
mirror
R~250 spectrum of (J=16.7) T‐dwarf with FIRE (Magellan) in prism dispersed mode. (subtraction of two 150 sec exposures)
http://web.mit.edu/~rsimcoe/www/FIRE/index.html
http://nebulium.wordpress.com/2010/04/30/fire‐
on‐the‐sky‐report‐from‐fires‐commissioning‐run/
Types of Dispersers: Diffraction Gratings
• ‘Diffraction Gratings’ are poorly named ‐‐‐ they operate based on constructive and destructive interference of light.
TripleSpec (APO) plane reflection grating
• Diffraction Gratings, particularly ‘plane reflection gratings’, are the work‐horse dispersing optic for moderate – high resolution spectrographs in astronomy
Types of Dispersers: Diffraction Gratings
Single Slit Diffraction
Destructive interference when
b/2 sin(m) = m * /2
sin(m) = m /b
Intensity Pattern I() = I(0) sinc2 () = Io [(sin )/]2
Where  = (2/)(b/2)sin
Figures from Hecht, Optics, Ch. 10
Types of Dispersers: Diffraction Gratings
Double Slit Diffraction
Constructive interference when
a sin() = m 
Notice:
a
• As a gets smaller,  gets larger
a
http://webpages.ursinus.edu/lriley/courses
/p212/lectures/node30.html
• As m, the order, gets larger,  gets smaller
• This assumes parallel light is incident normal to the slits
Single slit intensity envelope based on single slit width b
Fringes created by double slit based on slit separation a
Figure from Hecht, Optics, Ch. 10
Multiple Slit Intensity Pattern I() = I(0) (sin ()/)2 (sin (N)/sin )2
Where  = (2/)(b/2)sin
 = (2/)(a/2)sin
Figure from Hecht, Optics, Ch. 10
Types of Dispersers: Diffraction Gratings
Finally we can simply write down the more general grating equation based on path length differences when parallel light is incident on the grating at some arbitrary angle :
m/ = sin  + sin 
Angular Dispersion for a grating from differentiation:
A = d/d = m/( cos )
Chromey Ch. 11
Types of Dispersers: Diffraction Gratings
Ruling engines ‘burnish’ (scrape) material away in a highly controlled manner
MIT ‘B’ Ruling Engine
Richardson Grating Labs
Types of Dispersers: Diffraction Gratings
We purchase ‘replicas’ of gratings:
• Inverse shape of a ‘submaster’, which ultimately derives from a ‘master’, recorded into resin
• A custom coating is applied to the resin to make it reflective
Diffraction Grating Handbook
Richardson Grating Lab
• The substrate can be the user’s choice, e.g. aluminum or fused silica
Types of Dispersers: Diffraction Gratings
‘Blazed’ Gratings
• Steer the single slit diffraction peak at zero’th order to a more useful order
• Variety of blaze angles, groove frequencies available
• Grating equation becomes
Chromey Ch. 11
sin ( + ) + sin ( ‐ ) = m/
“Littrow mode”: incident and exit beams orthogonal to facet for highest effieciency
110 l/mm groove frequency Blaze angle 22 deg
Blaze wavelength 6.2 micron
TripleSpec (APO) plane reflection grating
Triplespec Grating Efficiency
2nd Retest v. 1st Retest
order
Blaze
wavelenth
1
6.2
2
6.2/2 = 3.1
3
6.2/3 = 2.07
4
6.2/4 = 1.55
1
0.9
Mauna Kea Atm Trans
UVA Order 3 Unpol 1st Retest
0.8
UVA Order 4 Unpol 1st Retest
UVA Order 5 Unpol 1st Retest
Transmission / Efficiency
0.7
Cornell Order 3 Unpol 1st Retest
Cornell Order 4 Unpol 1st Retest
0.6
Cornell Order 5 Unpol 1st Retest
UVA Order 3 Unpol 2nd Retest
UVA Order 4 Unpol 2nd Retest
0.5
UVA Order 5 Unpol 2nd Retest
UVA Order 6 Unpol 2nd Retest
0.4
UVA Order 7 Unpol 2nd Retest
Cornell Order 3 Unpol 2nd Retest
0.3
Cornell Order 4 Unpol 2nd Retest
Cornell Order 5 Unpol 2nd Retest
0.2
Cornell Order 6 Unpol 2nd Retest
Cornell Order 7 Unpol 2nd Retest
0.1
0
700
900
1100
1300
1500
1700
Wavelength (nm)
1900
2100
2300
2500
Etc.
Types of Dispersers: Diffraction Gratings
‘Echelle’ Gratings
• Operate in high order and steep incidence angle to generate high angular dispersion and thus high resolution
A = d/d = m/( cos )
Chromey Ch. 11
HARPS at ESO 3.6‐m Telescope
R ~ 115,000 with mosaic echelle grating
Types of Dispersers: Diffraction Gratings
Problem of order overlap
mm = (m + 1)  (m + 1)
There will be a ‘free spectral range’ in each order where there is no overlap with adjacent orders.
Chromey Ch. 11
Types of Dispersers: Cross‐Dispersed
• Use a second dispersing optic in the opposite dimension to disentangle overlapping orders of a grating
• Often use a prism
Chromey Ch. 11
• One can use another grating but be careful not to exceed a factor of 2 (octave) in wavelength
Continuous spectrum
2.5 um
0.8
mirror
R~250 spectrum of (J=16.7) T‐dwarf with FIRE (Magellan) in prism dispersed mode. (subtraction of two 150 sec exposures)
http://web.mit.edu/~rsimcoe/www/FIRE/index.html
http://nebulium.wordpress.com/2010/04/30/fire‐
on‐the‐sky‐report‐from‐fires‐commissioning‐run/
Echelle Mode
2.5 um
grating
0.8
R~6000 spectrum of (J=20) quasar with FIRE (Magellan) in echelle mode. (subtraction of two 900 sec exposures)
http://nebulium.wordpress.com/2010/04/
30/fire‐on‐the‐sky‐report‐from‐fires‐
commissioning‐run/
Types of Dispersers: Grism
‘Grism’: Grating + Prism
• Uses a prism to allow center wavelength of a diffracted order to go ‘straight through’
Richardson Grating Lab
• Very useful for providing moderate resolution spectroscopy in a traditional camera layout
LMIRCam 3 – 5 micron imager at LBT
Grisms used here at pupil conjugate immediately before final focus at detector
Efficiency (unpolarized)
Grism 1 (40.0 l/mm)
1
0.8
0.6
L‐band
0.4
0.2
0
2
2.5
3
3.5
4
Wavelength (um)
Order 1
Atm Transmission
4.5
5
Order sorting for Grism 2 done with K and M‐band filters.
Efficiency (unpolarized)
Grism 2 (32.0 l/mm)
1
0.8
0.6
0.4
M‐band
K‐band
0.2
0
2
2.5
3
3.5
4
Wavelength (um)
Order 1
Order 2
Atm Trans
4.5
5
Figure 9. Photo taken during the machining process shows the tip of the diamond tool extending from a holder on the rotating spindle. A spray of light mineral oil from the right acts as a coolant and cutting fluid as well as clearing chips from the workpiece.
Zygo interferometer measurement on grism #6 shows surface error in grooves to be 0.10 waves peak to valley at 633 nm over the full 14 x 14 mm aperture of the grism ‐‐‐ 0.10 waves is 63 nm.
SEM photos of grism #3 (40 lines/mm). On the left are details of several grooves showing the very flat and smooth blazed surfaces. On the right is a magnified view of a single groove showing the very sharp groove angle.
HD 82198
L‐band Grism
Chromey Ch. 11
Types of Dispersers: Volume Phase Holographic (VPH) Grating
Chromey Ch. 11
•
Volume
– 3‐dimensional: thickness few – 100’s of m
– ‘film’ capable of recording ‘fringes’
•
Phase
– Diffractive element works as a ‘phase grating’, not a ‘surface relief’ grating
– Optical phase = n*d
•
Holographic
– ‘fringes’ in the grating are recorded through holography, not mechanical means such as ‘ruling’
Types of Dispersers: Volume Phase Holographic (VPH) Grating
Historical Uses
•
•
•
Aircraft Heads‐up Displays
Telecom Industry
Laser Pulse Compression
Types of Dispersers: Volume Phase Holographic (VPH) Grating
Advantages:
•
•
•
•
•
High theoretical (and realized) efficiency
Low scatter Once ‘capped’, environmentally stable and ‘cleanable’
Transmissive optic – very helpful in designing spectrographs
Can record a broad range of fringe frequency
Types of Dispersers: Volume Phase Holographic (VPH) Grating
Disadvantages:
•
•
•
•
Few vendors available to make good VPH’s
– Art and science
Depending on design, may not get as broad an efficiency envelope as a ruled grating.
Edges of efficiency envelope ‘droop’
Hard to get higher orders
Dichromated Gelatin
• Gelatin:
– Gelatin is a mixture of peptides and proteins produced by partial hydrolysis of collagen extracted from the skin, boiled crushed bones, connective tissues, organs and some intestines of animals such as domesticated cattle, chicken, and pigs. The natural molecular bonds between individual collagen strands are broken down into a form that rearranges more easily. ‐‐‐ Wikipedia
– No artificial source has been found to have better properties.
• Dichromated:
– Dichromate, together with UV or blue light, cross‐links gelatin. Cross‐
linked gelatin is insoluble in water. Processing in water bath (swelling), followed by rapid dehydration in alcohol bath (collapse), produces periodic density variation (index of refraction) variation in gelatin. –
Barden et al. 2000, PASP; “Optical Holography”
Forming an Interference Pattern
Light from a
Coherent Source
Laser wavelength and relative beam angle determines interference fringe spacing
Beam
Splitter Steering Mirror (x4)
Put the film here!
Recording a Volume Phase Transmission Grating
Fringe planes recorded perpendicular to the film surface result in a transmission grating.
Reconstruction of a VPH
Transmission Grating
Single wavelength in…
Single wavelength out
Multiple wavelengths in…
Single wavelength out at it’s unique angle
Volume Phase Holographic Grating Physical Construction
Anti‐reflection
Coated Surface
(optional)
Optical Adhesive
Glass cover
Glass substrate
Thin film with
recorded grating
Anti‐reflection
Coated Surface
(optional)
Gratings: Anamorphic Magnification
Anamorphic Magnification = Different plate scales in the slit width and slit length directions
f = f/# D so focal length for a given camera (f/#) will be different for each direction
Schroeder, ‘Astronomical Optics’
Gratings: Anamorphic Magnification
Both ‘normal‐to‐camera’ or ‘normal‐to‐collimator’ orientation satisfy grating equation. But choice influences efficiency, order format, resolution and scattered light
Shadowing by this ‘ledge’
Reflection back towards collimator because of this ‘ledge’
Allington‐Smith 2002
Gratings: Anamorphic Magnification
Peak Efficiency drops, 
decreases when go off littrow in normal to camera case (
> )
Schroeder, ‘Astronomical Optics’
Gratings: Anamorphic Magnification
Example: Triplespec
d1
d1
d2
d2
r = d1 / d2 = 71.81 / 91.13 = 0.79
Gratings: Anamorphic Magnification
Example: Triplespec
Slit Width (dispersion direction)
2.8 pix / arcsec
Slit Length (x‐dispersion direction)
3.5 pix / arcsec
r = 2.8 / 3.5 = 0.8
Final Resolution equation: read Chromey section 10.4
Ways to increase R:
Higher order, higher exit angle, smaller seeing
As work at larger telescopes need larger collimators (spectrographs)
Chromey Ch 11
Wavelength Calibration
• How do we convert from pixel position (x,y) on detector to  ?
– Use a calibration source with known spectral lines
– Empirically derive a ‘solution’ (f(x,y) = ) using mathematical fitting routines
Wavelength Calibration
• Why isn’t the wavelength proportional to pixel position, I.e. linear?
– Optics of Prism & Gratings, our primary dispersion elements have non‐
linear angular dispersions
• A  dn/d (prism)
• A  m/cos (grating)
Wavelength Calibration
Spectral Source
 Regime
Resolution
Arc Lamp
UV-NIR
all, but watch for
blended lines
OH lines
NIR
R > 600 to resolve
blends
Planetary
Nebulae
VIS-MIR
low (insufficient
lines for high res)
(e.g. Argon, Neon, etc.)
(H/He emission lines)
Wavelength Calibration
• How often must one observe a calibration source?
– As often as required to be certain the ‘solution’ has not changed.
– Depends on instrument mechanics, resolution, and observation program
• Why would the solution change?
– Movement of the orders on the detector
• Mechanical Flexure of Instrument Optics
• Changing thermal conditions inside instrument