Basics of Spectroscopy

Report
Day 1: Tuesday, 1 April:
Chair: Chris Lidman
11:30-12:55: Registration
12:55-13:00: Welcome (Caroline Foster)
13:00-13:30: Introduction to optical and IR facilities (Chris Tinney)
Basics of spectroscopy
13:30-14:00: Writing proposals and the TAC process (Sarah Martell)
14:00-14:30: Observing preparation and software tools (Simon O'Toole)
14:30-15:15: Gemini queue demystified, Gemini helpdesk & data archives (Richard
McDermid)
15:15-15:45: Afternoon tea
Andrew Sheinis
AAO Head of Instrumentation
Chair: Stuart Ryder
15:45-16:30: Optical and infrared detectors (Kyler Kuehn)
16:30-17:30: An introduction to data reduction (Keith Shortridge)
Day 2: Wednesday, 2 April:
Chair: Kyler Kuehn
9:00-10:00: Imaging, photometry and filters (Lee Spitler)
10:00-10:30: Morning tea
Some questions:
•
•
•
•
What are the parts of a spectrograph
Why are spectrographs so big?
What sets the sensitivity?
How do I estimate the exposure time?
Some questions:
•
•
•
•
What are the parts of a spectrograph
Why are spectrographs so big?
What sets the sensitivity?
How do I estimate the exposure time?

DTel
Spectrograph
collimator
Slit (image)
plane
Dcoll
disperser
Dcam
camera

detector
Telescope
Anamorphic factor,
r = Dcoll/ Dcam
Dispersers: Gratings, Grisms and
Prisms
•Gratings
•Reflection gratings
•Ruled vs replicated
•mosaics
•Transmission gratings
•holographic
•Prisms
Glass Dispersion ratio (9500/3500) notes
LiF
0.092335 exotic, hard to get
F_silica
0.079616 nice, easy to get
FK5
0.077572 “
“
BK7Y
0.0737
“
“
LF5
0.043
poor dispersion
ratio
•Grisms
•High dispersion Grating
•Low-dispersion prism
•Prism deflection angle chosen to
pass some central wavelegth
straight throughplus a prism
Schroeder ch 13 and 14
What causes dispersion
• Optical path difference in the interfering
beam,
• Or
• Optical time delay in the interfering beam

d
W
-
d1
n

Grating equation:
n l = d(sin(a ) + sin(b ))
Differentiate WRT :
dl d cos(b )
=
db
n
-
n
How do you get a long time delay
•
•
•
•
Long grating (echelle)
High index (immersion grating
Big beam
All of the above
What are Echelles/echellettes?
•
•
•
•
•
•
Course, precisely-ruled gratings (few grooves/mm)
Used at high-angles= high R; R= tan(b)
bis BIG, b = 63 degrees to 78 degrees
Used at high orders
N=100-600 (echelle)
N=10-100 (echellette)
Echelles/echellettes
important features
• High dispersion in compact package
• High R-value (high tanb) High throughput
• High blaze efficiency over wide wavelength
range
• Nearly free of polarization effects
Echelles/echellettes
disadvantages
•
•
•
•
Hard to manufacture
Orders overlap
Need order-blocking filters or
Cross-dispersion (becomes an advantage with
a 2-D detector)
Volume Phase Holographic Gratings
Examples of VPH grisms with tilted fringes (above, 1a), and fringes at Littrow
(below, 1b). Both gratings are 930 l/mm blazed at 600 nm. For reference, the
size of the beam, paraxial camera and focal surface are the same.
* Hill, Wolf, Tufts, Smith, 2003, SPIE, 4842,
Collimators
ESI on Keck
•Reflective parabola
•Off axis, on axis
•FOV
•Transmissive
•Catadioptric
•Schmidt
RSS on SALT
Hermes on AAT
Cameras, second to grating in
importance
•Why?
•A  is effectively larger for the camera than the collimator.
•Dispersed slit is effectively a larger field.
Anamorphism and dispersion increase “pupil” size
•Most challenging part of the optical system. Slits are big, pixels are small so we
are often demagnifying, thus cameras are faster and have a larger A .
Cameras
•Reflective
•Two Mirror correct for spherical
and coma
•Un-obscured 3-mirror an-astigmat
corrects for spherical, coma and
astigmatism, (Paul-Baker, Merseinne
Schmidt) (i.e Angel, Woolf and Epps,
1982 SPIE, 332, 134A)
•Transmissive
•Epps cameras
•Catadioptric
•Schmidt
Slits-MOS plates-IFUS
• Slits
– Separates the stuff you want
from the stuff you don’t
• Fibers
– Allow you to have a
spectrograph far from the
telescope (why would you
want this?)
• IFUS
– Reformat the filed to be
along a slit
• Mos
– Separates the lots of stuff
you want from lots of the
stuff you don’t
Detectors
•
•
•
•
•
•
•
Human eye
CCD
CMOS
MCT
InGaAs
PMT
Lots of others
Some questions:
•
•
•
•
What are the parts of a spectrograph
Why are spectrographs so big?
What sets the sensitivity?
How do I estimate the exposure time?
Three Spectrographs of similar field
and resolution
• Why do they look so different?
SDSS 2.5M
Nasmyth Focus at Keck 10M
TMT 30M
Thought experiment 1:
How Big an aperture do you need to achieve R=100,000
in the diff-limited case on a 10-meter telescope at 1 m?
a)
b)
c)
d)
2.5 meters
250 mm
25 mm
2.5 mm

DTel
Spectrograph
collimator
disperser
camera
detector
Slit (image)
plane
Dcoll

Telescope
Anamorphic factor,
r = Dcoll/ Dcam
Dcam
Fcoll
Ftelescope
Slit, s
Slit-Width resolution product
collimator
d1
f R=
2tan(q b )
Dtel
W grating
DColl
grating
Dtelescope
DCam
Telescope
camera
Bingham 1979
detector
FCam
OPD available for interference in the coherent beam !
Diff-limited
f=
l
Dtel
R=
d1
l
2tan(q b )
seeing-limited
f=
l
r0
* Not just for Littrow: n*grooves * n = OPD
r0 d1
R=
2 tan(q b )
Dtel l
•One way to think about this: Spectrograph
resolution is NOT a function of the spectrograph
or the optics!
•R ~ OPD or optical time delay available for
interference in the coherent beam (works for
prisms and other dispersing elements too)
•The job of the telescope/spectrograph/AO
system is to create as much OPD as possible then
collect that information!
Some numbers:
Consider collimator diameter for an R2 (tan=2)
spectrograph with R=50,000 at =1 micron
• 2.5-meter aperture > 150mm Dcol
• 10-meter aperture > 0.61-meter Dcol
• 30-meter aperture > 1.84-meter Dcol
• Diffraction-limited > 12.8-mm Dcol!
Some questions:
•
•
•
•
What are the parts of a spectrograph
Why are spectrographs so big?
What sets the sensitivity?
How do I estimate the exposure time?
Thought Experiment:
You observe the moon using an eyepiece attached to a 8 meter
telescope. What is the relative brightness of the image compared
to naked-eye viewing? (or will this blind you?) assume your eye has
an 8mm diameter pupil.
A) Brightness=(8e3/8)2=1,000,000 times
B) Brightness=(8e3/8)=1,000 times
C) The same, Brightness is conserved!
Spectrograph Speed
Speed=# of counts/s/Angstrom
I.
Slit-limited
II.
Intermediate
III. Image-limited
Bowen, I.S., “Spectrographs,” in Astronomical Techniques, ed. by W.A. Hiltner, (U. of Chicago
Press, 1962), pp. 34-62.
Spectrograph Speed
Schroeder 12.2e, Ira Bowen (1962)
I.
Slit-limited
Speed µD ·W
0
Tel
II.
2
grating
Intermediate
Speed µD ·W
1
Tel
1
grating
III. Image-limited
Speed µD ·W
2
Tel
Speed=# of counts/s/Angstrom, W= illuminated grating length
0
grating
Surface Brightness
• Surface brightness is the energy per unit angle per unit area
falling on (or passing through) a surface.
• Conserved for Finite size source (subtends a real angle)
• Also called
– Specific intensity
– Brightness, surface brightness
– Specific brightness
• Units: (Jy sr-1) or (W m-2 Hz-1sr -1) or (erg cm-2 Hz -1) or (m
arcsec-2)
Surface Brightness
Rybicki and Lightman,
Radiative Processes in Astrophysics (1979), Ch1
A1
A0
A2


A0 =A1  A2 

• Surface brightness is the energy per unit angle per unit area falling on (or
passing through) a surface.
• Conserved for Finite size source (subtends a real angle)
• Also called
– Specific intensity
– Brightness, surface brightness
– Specific brightness
• Units: (Jy sr-1) or (W m-2 Hz-1sr -1) or (erg cm-2 Hz -1) or (m arcsec-2)

Spectrograph
collimator
A0
Dtelescope
grating

A1
Slit (image)
plane

camera

Telescope
Energy Collected
detector
A2
Energy Collected




Energy Collected




Do not confuse Surface Brightness
with Flux
Flux is total energy incident on some area dA from a source (resolved or not).
Flux is not conserved and falls of as R-2.
dE = fu dA du dt
dE = fu (4 pR ) du dt = Lu du dt
Lu
\ fu =
2
(4pR )
2
Some questions:
•
•
•
•
What are the parts of a spectrograph
Why are spectrographs so big?
What sets the sensitivity?
How do I estimate the exposure time?
S/N for object measured in aperture with radius r: npix=# of
pixels in the aperture= πr2
Noise from the dark
current in aperture
R*t
Signal
Noise
2ö
é
ù
æ
æ
ö
2
gain
ê R* × t + Rsky × t × npix + çç ( RN ) + ç
÷ ÷÷ × n pix + Dark × t × npix ú
è 2 ø ø
êë
úû
è
Readnoise in aperture
(R* × t) 2
Noise from sky e- in aperture
All the noise terms added in quadrature
Note: always calculate in e-
1
2
How do I calculate the number of photo
electrons/s on my detector?
• Resolved source
•
•
– We are measuring surface brightness
– E=AI
For an extended object in the IR that is easy: You just need the temperature of the
source, the system losses (absorption, QE etc), resolution and etendu of a pixel.
No telescope aperture or F/#, no slit size, no optical train!
For an extended object in the visible: You just need the surface brightness of the
source, the system losses (absorption, QE etc), resolution and etendu of a pixel.
No telescope aperture or F/#, no slit size, no optical train!
• Point source
– we are measuring flux
– E=Afdt
•
For an unresolved object, you need the source magnitude, telescope aperture,
system losses and resolution.
Ex 1: Thermal Imaging
R=5000
Pixel size= 10 microns
Final focal ratio at detector = F/3
Source temperature=5000K
Operating near 2 microns
SB from Planck=1,157,314 watts/(m2 sr micron)
D=2 microns/5000=0.0004
Solid Angle =
p /4
(F /# ) 2
Nphots = E /hn
(4.039 ×10-9 ) × (2 ×10-6 )
10
=
=
4.06
×10
6.62 ×10-34 × 3×10 8
Ex 2: Extended Object in the Visible
R=5000
Pixel size= 10 microns
Final focal ratio at detector = F/3
Moon (SB=1.81E-16 W/(m2 Sr Hz )
Operating near 1/2 micron
D=0.5 microns/5000=1 Angstrom
du=(c/2)d=1.2E11 Hz
QE = 1
Solid Angle =
p /4
(F /# )
2
Nphots = E /hn
(4.7 ×10-17 ) × (0.5 ×10-6 )
=
= 118
-34
8
6.62 ×10 × 3×10
Ex 2B: Unresolved Object in the Visible
R=5000
Pixel size= 10 microns
Final focal ratio at detector = F/3
Apparent brightness = Vmagnitude= 10
Operating near 1/2 micron
D=0.5 microns/5000=1 Angstrom
du=(c/2)d=1.2E11 Hz
QE = 1
E = fu ATel QE DnDt =
æ fu ö
m = -2.5log10 ç ÷
è f0 ø
Nphots = E / hn
Ex 3: Surface brightness of the moon
M=-12.6 (V-band apparent magnitude
Diameter=30 arcminutes
æ f1 ö
m = -2.5log10 ç ÷
è f0 ø
f1 = f 0 ×10-m / 2.5 = 3.63×10-23 ×1012.6 / 2.5
= 3.96 ×10
-18
w /m /Hz
2
A = p (15 × 60) 2 sec 2
= 2.54 ×10 sec
6
In =
2
(3.96 ×10-18 )
2.54 ×10 6
S = ml + 2.5log10 A
S=Surface brightness in magnitudes/arcsecond^2
=1.55 ×10-24 W / M 2 /Hz /sec 2
• Noise Sources:
R* × t
Þ shot noise from source
Rsky × t × p r 2
Þ shot noise from sky in aperture
RN 2 × p r 2
Þ readout noise in aperture
2
2
2
RN
+
(0.5
´
gain)
×
p
r
Þ more general RN
[
]
Dark × t × p r 2
Þ shot noise in dark current in aperture
R* = e- /sec from the source
Rsky = e- /sec/pixel from the sky
RN = read noise (as if RN 2 e- had been detected)
Dark = e _ /second/pixel
Sources of Background noise
•Relic Radiation from Big Bang
•Integrated light from unresolved extended sources
•Thermal emission from dust
•Starlight scattered from dust
•Solar light scattered from dust (ZL)
•Line emission from galactic Nebulae
•Line emission from upper atmosphere (Airglow)
•Thermal from atmosphere
•Sun/moonlight scattered by atmosphere
•Manmade light scattered into the beam
•Thermal or scatter from the telescope/dome/instrument
S/N for object measured in aperture with radius r: npix=# of
pixels in the aperture= πr2
Noise from the dark
current in aperture
R*t
Signal
Noise
2ö
é
ù
æ
æ
ö
2
gain
ê R* × t + Rsky × t × npix + çç ( RN ) + ç
÷ ÷÷ × n pix + Dark × t × npix ú
è 2 ø ø
êë
úû
è
Readnoise in aperture
(R* × t) 2
Noise from sky e- in aperture
All the noise terms added in quadrature
Note: always calculate in e-
1
2
S/N - some limiting cases. Let’s assume CCD with Dark=0,
well sampled read noise.
R* t
[R × t + R
*
sky
× t × n pix + ( RN ) × n pix
Bright Sources:
(R*t)1/2 dominates noise term
1
R*t
S/N »
= R *t µ t 2
R*t
Sky Limited
2
]
1
2
Read-noise Limited
(3 R sky t < RN) : S/N µ
R *t
( R sky t > 3 ´ RN) : S/N µ
µ t
npixR sky t
Note: seeing comes in with npix term
R*t
n pix RN
2
µt
Thankyou!

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