AST Senior Review Major Recommendations

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Instrumentation ConceptsGround-based Optical
Telescopes
Keith Taylor (IAG/USP)? Aug-Nov, 2008
Aug-Sep, 2008
IAG-USP (Keith Taylor)?
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The Fabry-Perot(French translation Perot-Fabry)

• Fabry-Perot etalon works by constructive
  interference of light from multiple reflections
  between two exactly parallel surfaces
• Usually a gap between two precisely manufactured
  plates of some material
• glass for an optical FP
• sapphire for infra-red FP
• The gap is usually air (or vacuum)
• Interference Filters (IFs) have high refractive
  index materials.
• Inner surfaces are coated with a reflective
  surface.

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Fabry-Perot

• Light enters etalon and is subjected to multiple
  reflections
• Transmission spectrum has numerous narrow peaks
  at wavelengths where path difference results in
  constructive interference
• need blocking filters to use as narrow band
  filter
• Width and depth of peaks depends on reflectivity
  of etalon surfaces finesse

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FP notation

• ? refractive index of air
• a amplitude of incident ray
• r fraction of amplitude reflected light at
  air/glass interface
• r fraction of amplitude of reflected light at
  glass/air interface
• t fraction of amplitude transmitted light at
  air/glass interface
• t fraction of amplitude transmitted light at
  air/glass interface
• l gap between reflective surfaces
• ? angle of incidence
• m order of interference
• ? wavelength of radiation k wave number
  (2?c/?)
• ? phase difference between successive
  reflective rays

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Stokes' treatment of reflectionat a surface

• The principal of reversibility states that if you
  reverse the direction of all rays at a surface,
  the amplitudes will remain the same.

Reversibility implies att arr a art
art 0
Therefore r ?r tt (1 ? r2)
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Reflectivity r Transmissivity t (1
? r)
atr8t
atr6t
atr4t
atr2t
att
By inspection, the reflective rays obey ARei?
a(r (1 ? r2)rei? r3e2i? r5e3i?
?
l
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Convert from amplitudesto intensities
To get the transmitted intensity (IT) multiply
Aei? by its complex conjugate
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from which we can derivethe Airy Function
and the reflected intensity R r2
The FP Airy Function
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FP in reflection and transmission

• IT is a maximum when sin(?/2) 0
• ie when 2?l.cos? m?
• Constructive interference
• This is also the condition for when
• IR is a minimum
• Destructive interference

NB For zero reflection all beams after the first
reflection are destructive of this first
reflection.
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Free Spectral Range (FSR ??) Finesse (N)
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More games with Finesse
This reduces to the familiar expression R
mNR the product of the (order of recombining
beams) In turn this means that we can identify
the finesse N with the of recombining beams (or
the e-fold decay of that quantity).
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Problems with absorptionin the coatings

• For the maximum transmitted intensity the
  important quantity is (A/T).  Even though A may
  be very small, if T is also small (hence R
  large), (A/T) may become large and the Tmax will
  may be very low. Eg
• Let R 99.7 and A 0.2 ? T 0.1
• Max. Intensity 11
• Let R 99.7 and A 0.29 ? T 0.01
•  Max. Intensity 0.11

What is happening physically is that while for
each reflection there is very little loss, the
reflectivity is so high that there are many
effective reflections and the total loss becomes
large.
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FPs are dirty OK for emission-lines (HII
regions) (Spirals) (PNe) Not OK
for absorption-lines (Stars) (E-galaxies)
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FPs in practice

• Fabry-Perots are generally used in high order m
  to give high resolving power, the free spectral
  range (FSR ?/m) is therefore small.
• Large gap (d) gives
• Large order (m 2?d.cos?/?)
• Large resolution (R mN)
• Small free spectral range (FSR ?/m)

• Small gap (d) gives
• Problems as d ? 0

• LIGO FPs
• d ? 1 km

FP
IF
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FP interference fringes
Recall Constructive (transmission)
interference, or Destructive
(reflection) interference when 2?d.cos? m?
Note cylindrical symmetry of fringes - cos? term -
White high intensity Black low intensity
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What you see with your eye
Emission-line lab source (Ne, perhaps) note the
yellow fringes

• Orders
• m
• (m-1)
• (m-2)
• (m-3)

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FP applications (traditional)
This converts easily to R ?/??
8/?J2 or in other words, R? 2?

• Lets do some typical numbers
• Say DT 4m d 50mm, then for R 20,000 ?J
  50 arcsec
• cf Grating in Littrow condition R
  2d.tan?/?DT
• With the same parameters, taking ? 30º Slit
  width ? 0.15 arcsec
• This is known (in some quarters) as the Jacquinot
  Advantage
• but why stop there?

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FP with Area Detectors

• FP interferograms
• Confocal with sky image
• Originally with photographic plates
• Good for line emission typically H?
• Fringe distortions due to changes in wavelength
• Used to map velocity fields in late-type
  galaxies

• Fundamental ambiguity
• Is fringe distortion due to
• Velocity field perturbation?
• Flux enhancement?
• or both?

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Partial solution Change the gap and repeat
interferogram
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Why only take 2 interferograms?Why not take 2N?
The birth of the TAURUS concept

• Note A single interferogram only contains
  (1/N)th of in spatial information
• Scanning the FP across a full FSR is a natural
  way to
• Recover ALL of the spatial information
• Resolve the fundamental ambiguity in the
  individual interferograms
• Scanning can be achieved in 3 ways
• Changing ? - by tilting the FP or by moving the
  image across the fringes
• as in photographic interferograms (to
  partially resolve ambiguity)
• Changing ? - by changing the pressure of a gas
  in the FP gap
• as in 0th dimensional scanning with eg
  propane
• Scanning d - by changing the physical gap
  between the plates
• very difficult since need to maintain
  parallelism to ?/2N, at least

TAURUS QI etalons IPCS c1980
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Queensgate Instruments (ET70)
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Queensgate Instruments (Capacitance Micrometry)
FP etalons

• Construction
• Super-flat ?/200 base
• Centre piece (optical contact)
• Top plate

• Capacitors
• X-bridge
• Y-bridge
• Z-bridge ( stonehenge)

Scanning d over 1FSR m ? (m-1) d ? d (?/2)
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Alec Boksenberg and theImage Photon Counting
System (IPCS)
Perfect synthesis
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How big a field?

• From before, Jacquinot central spot given by
• R? 2?
• or R 8?2/?2 8?2(d/DT)2/?J2,
• where ?J is the angle on the sky.

However, given an array detector, we can work
off-axis So, how far? Answer Until the rings
get narrower than ? 2 pixels (the seeing disk)
Now, from the Airy Function we obtain d?/d?
-1/?0.sin(?) The full TAURUS field, ?F is
then ?F 2?2(d/DT)2/R?
?F/?J 20, typically or 400 in ?
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TAURUS Datacube

• Recalling the phase delay equn
• m? 2?l.cos?
• For small values of ?
• ? goes as 1 (?2/2)
• where ? ? tan-1(y-y0/x-x0)
• and (x0,y0) centre of FP fringes
• ?(x1,y1) is shifted in z-dirn
• w.r.t. ?(x0,y0)
• and this ?-shift is thus
• parabolic in ?
• It is also periodic in m. We thus refer to
  this shift as a
• Phase-correction
• So the surface of constant ? is a

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Wavelength Calibration(converting z to ?)
As shown, surfaces of constant ?, as seen in an
(x,z)-slice are defined by a set of nested
parabolæ, equally spaced in z. Any (x,y)-slice
within the cube cuts through these nested
paraboloids to give the familiar FP fringes
(rings).
Now ?-calibration requires transforming z ? ?
where l(z) l(0) az a is a constant of
proportionality.
Constructive interference on axis (x0,y0)
gives az0 m?0/2? - l(0) but an off-axis
(x,y) point transmits the same ?0 at (z0 pxy)
where apxy l(z0).(sec?xy 1)
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Phase Correction
The 2D phase-map, p(x,y), can be defined such
that p(x,y) m?z0(sec? 1) The phase-map,
p(x,y), can be obtained from a ?-calibration
data-cube by illuminating the FP with a diffuse
monochromatic source of wavelength, ?.
Note Phase-map is discontinuous at each ?z
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The Phase-Map
The phase-map is so called since it can be used
to transform the raw TAURUS cube, with its
strange multi-paraboloidal iso-wavelength
contours into a well-tempered data cube where all
(x,y)-slices are now at constant wavelengths.
The process is called phase-correction since it
represents a periodic function of period, ?z. ie
If the z-value (z) of a phase-shifted pixel
exceeds the z-dimensions of the data-cube, then
the spectra is simply folded back by one FSR to
(z - ?z).
It will be noted that the phase-map (as defined
previously) is independent of ? and hence in
principle any calibration wavelength, ?cal, can
be used to phase-correct a observation data-cube
at an arbitary ?obs, remembering that ?? ? ?2
?z ?/2
But also, the phase-map can be expressed in
?-space as ??xy ?0(1 - cos?) and hence is
also independent of gap, l, and thus applicable
to all FPs at all ?.
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Order (m) and gap (l) determination
The periodicity of the FP interference fringes
makes ?-calibration non-trivial. The
paraboloidal mapping from z ? ? doesnt exactly
help, either!
Nevertheless, using 2 calibration
wavelengths Say ?1 and ?2, peak on-axis at z1
and z2 The trick is to find m1 (and hence m2),
the order of interference. From m we can infer
the gap, l , and hence obtain a ?-calibration
where az0 m?0/2? - l(0) Then
If m1 can be estimated (from manufacturers specs
or absolute capacitance measures) then we can
search for a solution where m2 is an integer.
This can be an iterative process with several
wavelength pairs. Clearly the further ?1 and ?2
are apart, the more accuracy is achieved.
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Wavelength Calibration
If m1 can be estimated (from manufacturers specs
or absolute capacitance measures) then we can
search for a solution where m2 is an integer.
This can be an iterative process with several
wavelength pairs. Clearly the further ?1 and ?2
are apart, the more accuracy is achieved.
Once the interference order, m1, for a known
wavelength, ?1, has been identified then
wavelength calibration is given by
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FPP in collimated beam

• Interference fringes formed at infinity
• Sky and FP fringes are con-focal
• Detector sees FP fringes superimposed on sky
  image

FP
IF
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FPI in image plane

• Interference fringes formed at infinity
• Sky and FP fringes are not con-focal
• Detector sees FP plates superimposed on sky
  image
• ie No FP fringes seen on detector
• FP is not perfectly centred on image plane (out
  of focus) to avoid detector seeing dust particles
  on plates.

FP
IF
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FP (or Interference Filter)in image plane
The FP still acts as a periodic monochromator but
the angles into the FP (or IF) must not exceed
the Jacquinot criteria, which states that
?2 At f/8 ? 2.tan-1(1/16) 7.2º, so R 500 At f/16 ? 2.tan-1(1/32) 3.6º, so R 2,000
Note the FoV is determined not by the width of
the fringes but by the diameter of the FP.
Also, an IF is simply a solid FP (? 2.1) with
very narrow gap.
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FB observations of NGC 7793 on the 3.60 m. Top
left DSS Blue Band image. Top right Spitzer
infrared array camera (IRAC) 3.6 µm image. Middle
left Ha monochromatic image. Middle right Ha
velocity field. Bottom position-velocity (PV)
diagram.
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FB observations of NGC 7793 on the 36 cm. Top
left DSS Blue Band image. Top right Spitzer
IRAC 3.6 µm image. Middle left Ha monochromatic
image. Middle right Ha velocity field. Bottom
PV diagram.
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ADHOC screen shot (Henri)
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ADHOC screen shot (Henri)