Charts for TPFC workshop SNR for Nulling Coronagraph and Post Coron WFS

1
Charts for TPF-C workshop SNR for Nulling
Coronagraphand Post Coron WFS

• M. Shao 9/28/06

2
Depth of Dark Hole vs Starlight Suppression

• 10-10 scattered light level _at_ 34 l/D implies
  10-7 suppression of starlight

Star image without a coronagraph
Top level error budget OPD leak 4e-8 Amp leak
3e-8 Polcolor 3e-8 Total 1e-7 Blue
means per sub aperture control 2/3 of residual
starlight is random, spread over 1000 airy spots
Star image suppressed by 107
3
Wavefront Sensing Principles

• 1) need to sense the wavefront AFTER the
  coronagraph. This reduces the accuracy needed
  from the wavefront sensor. If the E field after
  the coronagraph is measured to 10, the next
  iteration of the WFS servo can improve the null
  by 1001.
• Low accuracy in a post coronagraph WFS means more
  iterations to converge (from1e-3), but doesnt
  affect convergence.
• Low accuracy in a pre-coronagraph WFS means you
  never get to 1e-7 (1e-10/airy spot)
• Inside an optical fiber there are only 2
  quantities
• Amplitude
• Phase
• In 2 polarizations, over 20 bandpass

4
Nuller Architecture for Planet Imaging
5
Simplified Nuller/WFS

• Nulling interferometer has bright and dark output
• Dark output (star suppressed) goes through a
  fiber array.
• DM in 1 arm of nulling interferometer
• DM at a pupil
• Pupil relayed to fiber/lenslet array (input)

• Output of fiber array (new pupil) relayed to WFS
  CCD
• Wavefront sensing (amp and phase) sensed at
  pupil, corrected at pupil.
• We had looked at 3 other options

Nulling Coronagraph
DM (segmented)
Beamsplitter
Phase
-
Shifting
Mirror
Beamsplitter
C
C
D
Sampling
Beamsplitter
Beamsplitter
S
c
i
e
n
c
e

C
a
m
Spatial filter
e
r
a
Fiber/lenslet array
S
c
i
e
A
n
r
c
r
a
e
y
6
Measuring Amp, Phase

• Look at just the nuller first

Science camera At image plane
DM
shutters
Dither mirror
WFS camera at Pupil plane For now 1 pixel/fiber
7
Measuring Amp, Phase

• Look at just the nuller first

Science camera At image plane
DM
shutters
Dither mirror
WFS camera at Pupil plane For now 1 pixel/fiber
8
Measuring Amp, Phase

• Look at just the nuller first

Science camera At image plane
DM
shutters
Dither mirror
Intensity mismatch leakage (DI)2/8 lt 3x10-8 DI lt
4.9x10-4 gt N 4.2x106 photons for each of 1000
fibers
WFS camera at Pupil plane For now 1 pixel/fiber
9
Measuring Amp, Phase

• Look at just the nuller first

Science camera At image plane
DM
shutters
Dither mirror
WFS camera at Pupil plane For now 1 pixel/fiber
For l550nm Leak (Df)2/4 lt 4e-8 Df lt 4x10-4
radians 35 pm
10
OPD Dither 3 points

• In this example, dither is /- 1nm. The null is
  0.1 nm off.
• B is at 3.3x10-7 (10x too large)
• Offset (A-C)0.1nm/(P1.3x10-5)
• P is flux at peak
• Systematic errors
• Dither stroke error becomes a gain error. 1.1nm
  stroke would make a 0.1nm error signal gt 0.11nm
• Photon noise
• sx (sqrt(AC)/P)(0.1nm/1.3e-5)
• Total detected photons 4x106 gt sx 31pm

C

A
B
5 mag star gt 20 bw_at_550nm gt 2.9x109 phot/sec
into 83.5m telescope Need total of 8x109 photons
to sense amp, phi If QE, coatings are all 100,
need 3 sec. In practice 610sec?
11
Deep W.L. Null 1.5x10-9/airy spot

• Max light into single mode fiber 10nm (650nm
  20bw)
• Light attenuated (3000x) to 3 picowatts for deep
  w.l. null experiment.
• Control update could be as high as a few hz.
• Average null over 60 sec 1.5x10-9/airy spot

3 picowatts thermal whitelight bulb -gt fiber
atten by 3000x
Dark count 78 p/s
Deep WL null
12
Bright Ref Beam

• Combine in pupil
• detect in pupil
• Detect in image
• Combine ref (pupil) with image (Givon)
• Combine ref (image) with pupil

4 ways of using a bright ref beam. Purpose
(advantages) and requirements on the ref beam
13
Why Pupil / Pupil WFS?

• Combine in pupil
• detect in pupil
• Detect in image
• Combine ref (pupil) with image (Givon)
• Combine ref (image) with pupil

Speckle smearing with l. Very high dynamic range
detector needed. Complex processing to go from
image to pupil DM actuation, with unknown noise
prop.
Pupil plane interferometry
Pupil detection
Ref image with speck pupil. Very high dynamic
range detector needed. Combine flat wavefront
with converging wavefront..
Ref pupil with speckle image
Combine flat wavefront with converging wavefront.
(limited bandwidth) Speckle smearing with l.
14
Bright Reference, Heterodyne Gain

• A post coronagraph WFS is looking at the residual
  starlight after almost all the starlight has been
  removed. At this point other noise sources will
  dominate over photon noise.
• Residual starlight 1e-7 (of the star) (from which
  the servo error signal is derived)(but in 1 out
  of 1000 fibers)
• Local and Exo-zodi (into AW l2) Because the
  fiber is single mode, the local/exo-zodi per
  fiber is image plane in 1 airy spot
• Airy spot gets 1.222 more background
• CCD read noise
• CCD dark current
• If a bright ref beam is interfered with a faint
  signal the Visibility is
• Vis2sqrt(AB)/(AB)
• If A 106 B 1, the fringe signal is 2000.
• Because the fringe singal has grown, it now
  dwarfs the noise from the CCD and zodi.
• The fringe Vis of the Bright ref faint residual
  starlight is used in place of the intensity of
  the faint residual starlight.

15
Background Noise

• Residual starlight 10-10 of 5mag star 30
  mag/airy spot
• Local zodi _at_ 45deg 1.4 22 mag/sqas
• Exozodi (of a solar system clone) _at_ 45deg
  2.822mag/sqas
• Airy spot (50 lyot aperture) 1.22l/5.3m
• 4.2Zodi 27.6 mag/airy spot 10x brighter than
  residual starlight
• The bright reference is only used to improve SNR,
  the phase of the ref wavefront does not bias the
  result.
• There is no need for a high quality 0.001l, ref
  wavefront.