# Presentation: 418874

## Charts for TPF-C workshop SNR for Nulling Coronagraphand Post Coron WFS

- M. Shao  9/28/06

## Depth of Dark Hole vs Starlight Suppression

_**10**__**-10**__** scattered light level**_ @ 3~4 /D implies ~_**10**__**-7**__** suppression**_ of starlight

- Star image without a coronagraph

- Star image suppressed by 107

- Top level error budget
- OPD leak  4e-8
- Amp leak  3e-8
- Pol&color  3e-8
- Total         1e-7
- Blue means per sub aperture control 2/3 of residual starlight is random, spread over 1000 airy spots

## 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 100:1.
- Low accuracy in a post coronagraph WFS means more iterations to converge (from1e-3), but doesn’t 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

## Nuller Architecture for Planet Imaging

## 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)

- Nulling Coronagraph

- Phase

- -

- Shifting

- Mirror

- C

- C

- D

- Beamsplitter

- Beamsplitter

- Beamsplitter

- Sampling

- Beamsplitter

- S

- c

- i

- e

- n

- c

- e

- A

- r

- r

- a

- y

- S

- c

- i

- e

- n

- c

- e

- C

- a

- m

- e

- r

- a

- Spatial filter

- Fiber/lenslet
- array

- DM (segmented)

- 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

## Measuring Amp, Phase

- Look at just the nuller first

- Science camera
- At image plane

- WFS camera at
- Pupil plane
- For now 1 pixel/fiber

- shutters

- DM

- Dither mirror

## Measuring Amp, Phase

- Look at just the nuller first

- Science camera
- At image plane

- WFS camera at
- Pupil plane
- For now 1 pixel/fiber

- shutters

- DM

- Dither mirror

## Measuring Amp, Phase

- Look at just the nuller first

- Science camera
- At image plane

- WFS camera at
- Pupil plane
- For now 1 pixel/fiber

- shutters

- DM

- Dither mirror

- Intensity mismatch leakage  (I)2/8 < 3x10-8
- I < 4.9x10-4 => N ~4.2x106 photons for each
- of 1000 fibers

## Measuring Amp, Phase

- Look at just the nuller first

- Science camera
- At image plane

- WFS camera at
- Pupil plane
- For now 1 pixel/fiber

- shutters

- DM

_**Dither mirror**_

- For =550nm
- Leak = ()2/4 < 4e-8
-  < 4x10-4 radians  ~  35 pm

## OPD Dither 3 points

- A

- C

- 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/(P*1.3x10-5)
- P is flux at peak
- Systematic errors
- Dither stroke error becomes a gain error. 1.1nm stroke would make a 0.1nm error signal => 0.11nm
- Photon noise
- x = (sqrt(A+C)/P)*(0.1nm/1.3e-5)
- Total # ‘detected’ photons = 4x106  => x = 31pm

- B

- 5 mag star => 20% bw@550nm => 2.9x109 phot/sec into 8*3.5m telescope
- Need total of 8x109 photons to sense amp, phi
- If QE, coatings are all 100%, need 3 sec.  In practice 6~10sec?

## Deep W.L. Null 1.5x10-9/airy spot

- Max light into single mode fiber ~10nm (650nm 20%bw)
- 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

- Deep WL null

- Dark count
- ~78 p/s

- 3 picowatts
- thermal whitelight
- bulb -> fiber atten
- by ~3000x

## Bright Ref Beam

- 4 ways of using a bright ref beam.
- Purpose (advantages) and requirements
- on the ref beam

- Combine in pupil
- detect in pupil
- Detect in image
- Combine ref (pupil) with image (~Giv’on)
- Combine ref (image) with pupil

## Why Pupil / Pupil WFS?

- Combine in pupil
- detect in pupil
- Detect in image
- Combine ref (pupil) with image (~Giv’on)
- Combine ref (image) with pupil

- Pupil plane
- interferometry

- Pupil
- detection

- Speckle **smearing with ******. Very **high dynamic range detector** needed.
- Complex processing to go from image to pupil DM actuation, with unknown noise prop.

- Ref pupil with speckle image

- Combine** flat** wavefront with **converging **wavefront. (limited bandwidth)
- Speckle **smearing with ******.

- Ref image with speck pupil.
- Very **high dynamic range detector** needed.
- Combine** flat** wavefront with **converging **wavefront..

## 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 A*) 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
- Vis=2*sqrt(A*B)/(A+B)
- If A =**10****6** 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.

## Background Noise

- Residual starlight 10-10 of 5mag star  30 mag/airy spot
- Local zodi @ 45deg  1.4* 22 mag/sqas
- Exozodi (of a solar system clone) @ 45deg 2.8*22mag/sqas
- Airy spot (50% lyot aperture) 1.22*/5.3m
- 4.2*Zodi ~ 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 0.001, ref wavefront.