The High Contrast Performance

1
The High Contrast Performance Of An Optical
Vortex Coronagraph
By Dr. David M. Palacios Jet Propulsion
Laboratory California Institute of Technology
2
Acknowledgements
Stuart Shaklan Jet Propulsion Laboratory G.A.
Swartzlander Jr. University of Arizona Dimitri
Mawet University of
3
Outline
1.) What is an Optical Vortex? 2.) Optical
Vortex Mask Design 3.) Lyot Optimization 4.)
Planet Light Throughput Efficiency 5.)
Conclusions
4
What is an Optical Vortex?
The Complex Field
E(r,f,zt)A(r,z)exp(imf)expi(wt-kz)
Amplitude
Phase
5
Optical Vortices in Speckle
6
Astigmatic Mode Converter
7
Optical Vortex Holograms
8
The Optical Vortex Mask
Mask Thickness
9
Coronagraph Architecture
Pupil
OVM
Lyot Stop
FP
L1
L2
L3
0
2?m
Incident Light
Final Image Plane
10
The Optical Vortex Mask
Mask Thickness
11
Ray Trace Analysis of the Vortex Mask
n0
?t
dz
??
d?
n1
?
??
?d?
12
The Vortex Core
n0
dz
??
d?
n1
?
??
?d?
When ?????c E Transmitted 0
13
Output Amplitude Profile
Transmitted amplitude for the E? Polarization
Transmitted amplitude for the Er Polarization
14
A Discrete Representation of an OVM
Phase profile of an m4 OVM
dz
dz
?d?
?d?
0
8?
15
OVC Discretization Leakage
Ideal OVC6 Pupil
Discretized OVC6 Pupil
Coronagraph Leakage!
16
Numerical Simulations
Array Size Pupil Size ? f Mask Pixel
Size n1 ??
4096 x 4096 pixels 100 pixels in diameter 600
nm 27 0.2 microns 1.5 1
17
The Lyot Plane for Even Values of m
m2
m4
m6
Even charged OVMs theoretically cancel the
entire pupil!
18
System Performance
Contrast
I(x,y) Intensity with the occulter in place
Iopen(x,y) Intensity with the occulter removed
o(x,y) Occulter transmission function
19
Average Radial Contrast
Average Contrast Between 2-3 ?/D
m6
Contrast
r (?/D)
20
Average Radial Contrast
Average Contrast Between 2-8 ?/D
m6
Contrast
r (?/D)
21
Average Radial Contrast
Average Contrast Between 4-5 ?/D
m6
Contrast
r (?/D)
22
Average Radial Contrast
Average Contrast Between 4-10 ?/D
m6
Contrast
r (?/D)
23
Contrast vs. Lyot Size
Average Contrast Between 2-3 ?/D
Contrast
m2
m4
m6
Lyot Size (r/Rp)
24
Contrast vs. Lyot Size
Average Contrast Between 2-8 ?/D
Contrast
m2
m4
m6
Lyot Size (r/Rp)
25
Contrast vs. Lyot Size
Average Contrast Between 4-5 ?/D
Contrast
m2
m4
m6
Lyot Size (r/Rp)
26
Contrast vs. Lyot Size
Average Contrast Between 4-10 ?/D
Contrast
m2
m4
m6
Lyot Size (r/Rp)
27
Optimized Contrast
Lyot Stop Radius 0.8Pr
Average Contrast
2-3 ?/D
2-8 ?/D
4-10 ?/D
4-5 ?/D
m 2
9.3x10-11
6.4x10-11
3.5x10-11
2.8x10-10
m 4
5.1x10-11
4.1x10-11
2.5x10-11
1.2x10-10
2.9x10-11
2.5x10-11
2.0x10-11
m 6
5.3x10-11
28
Throughput Efficiency vs. Lyot Size
Planet Located at 2?/D
Throughput
m0
m2
m4
m6
Lyot Size (r/Rp)
29
Throughput Efficiency vs. Lyot Size
Planet Located at 4?/D
Throughput
m0
m2
m4
m6
Lyot Size (r/Rp)
30
Optimized Planet Light Throughput
Lyot Stop Radius 0.8Pr
m6
m4
m2
m0
0.64
0.62
0.53
2?/D
0.43
4?/D
0.62
0.58
0.64
0.64
31
Is an Achromatic OVC Possible?
C
6
6.001
5.999
m
m must be maintained to 5x10-4 across the
bandpass!
32
Achromatic Holographic Vortex Coronagraph
Lyot Stop
Direction-compensating Grating
f/30 beam
Zero-order blocker
Holographic Vortex
33
System advantages

• Small inner working angle 2?/D
• High throughput (theoretically 100)
• Same WFC architecture as other Lyot type
  coronagraphs
• Small polarization effects (dependent on creation
  method)
• Low aberration sensitivity to low-order Zernikes
• Large search area (radially symmetric)
• System can be chained in series

34
System Disadvantages

• Broadband operation requires further research on
  new OV
• creation techniques
• Issues with mask Fabrication or hologram
  fabrication are just
• beginning to be explored.
• The Useful throughput decreases with stellar size
  making
• operation at 2?/D difficult on 0.1?/D sized
  stars.

35
Conclusions

• An m6 vortex coronagraph meets TPF contrast
  requirements
• Simulated 10-11 contrast at 2?/D with a
  discretized OVM
• OVM discretized with 0.2 micron pixels
• Even charged OVMs theoretically cancel over the
  entire pupil
• With discretization errors the Lyot stop radius
  0.8Pr
• 53 throughput efficiency at 2?/D
• 62 throughput efficiency at 4?/D near optimal of
  64

36
Aberration Sensitivity
? is the order of the aberration sensitivity
4th order linear sinc2 masks best demonstrated
contrast
8th order masks presently being explored
Vortex masks possess a 2mth order aberration
sensitivity
37
The Aberration Sensitivity
The Entrance Pupil
Assuming ?(r,q) ltlt1,
Mask Amplitude Transmission Function
38
More Math
The Exit Pupil
Using the identity
The Approximate Exit Pupil
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The Approximate Solution
The first term in the expansion km
All terms with less than an rm dependence vanish!
The Intensity has a 2mth aberration sensitivity!
For the m5 case
10th order sensitivity predicted!
40
Low Order Zernike Modes
Z4
Z6
Z7
Z5
Z8
Z9
Z10
Z11
41
Numerical Simulations
C
Aberration size (waves peak to valley)
42
Coronagraph Comparisons
m5 vortex
8th Order
Zernike
Improvement
2
8
9
3
8
9
4
4
--
5
4
6
6
4
6
7
4
4
8
4
4
9
4
5
10
4
5
11
2
5
12
2
5
43
The Lyot and Focal Plane Profiles
Pupil
Vortex Mask
Lyot Stop
Lyot Plane
Focal Plane
??/D
44
Amplitude Occulting Spots
E(x,y) A(x,y)expiF(x,y)
Hard Stop
Sinc2(r)
45
The Lyot Stop
Hard Stop
Cats Eye Stop
46
The Final Image
After
Before
47
An Optical Limiting Technique
Amplitude
R/Rdiff
48
Contrast Simulations
Contrast Image
Compute the Radial Average Contrast