# Presentation: 947208

## The High Contrast Performance 

- The High Contrast Performance
- Of An Optical Vortex Coronagraph

- By
- Dr. David M. Palacios
*Jet Propulsion Laboratory*
*California Institute of Technology*

## Acknowledgements

*Jet Propulsion Laboratory*
- G.A. Swartzlander Jr.
*University of Arizona*
- Dimitri Mawet
*University of*

**Acknowledgements**

## Outline

- 2.) Optical Vortex Mask Design
- 3.) Lyot Optimization
- 4.) Planet Light Throughput Efficiency
- 5.) Conclusions

**Outline**

## What is an Optical Vortex?

- The Complex Field

- Amplitude

- Phase

**What is an Optical Vortex?**

## Optical Vortices in Speckle

**Optical Vortices in Speckle**

## Astigmatic Mode Converter

**Astigmatic Mode Converter**

## Optical Vortex Holograms

**Optical Vortex Holograms**

## The Optical Vortex Mask

**The Optical Vortex Mask**

- Mask Thickness

## Coronagraph Architecture

- Final Image Plane

- Incident Light

- Pupil

- L1

- OVM

- Lyot Stop

- L2

- L3

- FP

- 0

- 2m

## The Optical Vortex Mask

**The Optical Vortex Mask**

- Mask Thickness

## Ray Trace Analysis of the Vortex Mask

- d

- 

- d

- 

- 

- n1

- n0

- dz

- t

**Ray Trace Analysis of the Vortex Mask**

## The Vortex Core

- d

- 

- d

- 

- 

- n1

- n0

- dz

**The Vortex Core**

- When c              E Transmitted = 0

## Output Amplitude Profile

- Transmitted amplitude for the E Polarization

- Transmitted amplitude for the Er Polarization

## A Discrete Representation of an OVM

- 0

- 8

- Phase profile of an m=4 OVM

- dz

- d

- dz

- d

## OVC Discretization Leakage

- Coronagraph Leakage!

- Ideal OVC6 Pupil

- Discretized OVC6 Pupil

**OVC Discretization Leakage**

## 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

## The Lyot Plane for Even Values of m 

- m=2

- m=4

- m=6

- Even charged OVMs theoretically
- cancel the entire pupil!

**The Lyot Plane for Even Values of m **

## System Performance

- Contrast

*I(x,y) = *Intensity with the occulter in place

*I**open**(x,y) = *Intensity with the occulter removed

*o(x,y) = *Occulter transmission function

## Average Radial Contrast 

**Average Radial Contrast **

- Average Contrast Between 2-3 /D

- Contrast

- m=6

- r (/D)

## Average Radial Contrast 

- Contrast

- m=6

- Average Contrast Between 2-8 /D

**Average Radial Contrast **

- r (/D)

## Average Radial Contrast 

- Contrast

- m=6

**Average Radial Contrast **

- Average Contrast Between 4-5 /D

- r (/D)

## Average Radial Contrast 

- Contrast

- m=6

**Average Radial Contrast **

- Average Contrast Between 4-10 /D

- r (/D)

## Contrast vs. Lyot Size

- Contrast

- m=2

- m=4

- m=6

- Lyot Size (r/Rp)

**Contrast vs. Lyot Size**

- Average Contrast Between 2-3 /D

## Contrast vs. Lyot Size

- Contrast

- m=2

- m=4

- m=6

- Lyot Size (r/Rp)

**Contrast vs. Lyot Size**

- Average Contrast Between 2-8 /D

## Contrast vs. Lyot Size

- Contrast

- m=2

- m=4

- m=6

- Lyot Size (r/Rp)

**Contrast vs. Lyot Size**

- Average Contrast Between 4-5 /D

## Contrast vs. Lyot Size

- Contrast

- m=2

- m=4

- m=6

- Lyot Size (r/Rp)

**Contrast vs. Lyot Size**

- Average Contrast Between 4-10 /D

## Optimized Contrast

- Lyot Stop Radius = 0.8Pr

- Average Contrast

- 2-3 /D

- 2-8 /D

- 4-5 /D

- 4-10 /D

- 5.3x10-11

- 2.9x10-11

- 2.5x10-11

- 2.0x10-11

- m = 2

- m = 4

- m = 6

- 1.2x10-10

- 5.1x10-11

- 4.1x10-11

- 2.5x10-11

- 2.8x10-10

- 9.3x10-11

- 6.4x10-11

- 3.5x10-11

## Throughput Efficiency vs. Lyot Size

- Throughput

- Lyot Size (r/Rp)

- m=2

- m=4

- m=6

- m=0

**Throughput Efficiency vs. Lyot Size**

- Planet Located at 2/D

## Throughput Efficiency vs. Lyot Size

- Throughput

- Lyot Size (r/Rp)

- m=2

- m=4

- m=6

- m=0

**Throughput Efficiency vs. Lyot Size**

- Planet Located at 4/D

## Optimized Planet Light Throughput

- m=4

- m=2

- m=0

- 2/D

- 4/D

- 0.64

- 0.64

- 0.64

- 0.62

- 0.58

- 0.62

- 0.53

- 0.43

**Optimized Planet Light Throughput**

- Lyot Stop Radius = 0.8Pr

## Is an Achromatic OVC Possible?

- C

- m

- 6

- 6.001

- 5.999

- m must be maintained to ~5x10-4 across the bandpass!

## Achromatic Holographic 

- f/30 beam

- Holographic Vortex

- Direction-compensating Grating

- Zero-order blocker

- Lyot Stop

**Achromatic Holographic **
**Vortex Coronagraph**

## System advantages

- Small inner working angle ~ 2/D
- High throughput (theoretically 100%)_x0010__x0010__x0010__x0010__x0010_
-  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

## 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.

## Conclusions

- An m=6 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%

## 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

## The Aberration Sensitivity

- Mask Amplitude Transmission Function

- The Entrance Pupil

- Assuming ***(r,****)* <<1,

## More Math...

- The Exit Pupil

- Using the identity:

- The Approximate Exit Pupil

## The Approximate Solution

- The first term in the expansion k=m

- All terms with less than an rm dependence vanish!

- The Intensity has a 2mth aberration sensitivity!

- For the m=5 case:

- 10th order sensitivity predicted!

## Low Order Zernike Modes

- Z=4

- Z=5

- Z=6

- Z=7

- Z=8

- Z=9

- Z=10

- Z=11

## Numerical Simulations

**Numerical Simulations**

- Aberration size (waves peak to valley)

- C

## Coronagraph Comparisons

- m=5 vortex

- 8th Order

- Zernike #

- 2

- 3

- 4

- 5

- 6

- 7

- 8

- 9

- 10

- 11

- 12

- 8

- 8

- 4

- 4

- 4

- 4

- 4

- 4

- 4

- 2

- 2

- 9

- 9

- --

- 6

- 6

- 4

- 4

- 5

- 5

- 5

- 5

- Improvement

## The Lyot and Focal Plane Profiles

- Pupil

- Vortex Mask

- Lyot Stop

- Lyot Plane

- Focal Plane

- /D

**The Lyot and Focal Plane Profiles**

## Amplitude Occulting Spots

- E(x,y) = A(x,y)exp[i(x,y)]

- Sinc2(r)

- Hard Stop

## The Lyot Stop

- Hard Stop

- Cat’s Eye Stop

## The Final Image

- Before

- After

## An Optical Limiting Technique

- R/R*diff*

**An Optical Limiting Technique**

- Amplitude

## Contrast Simulations

- Contrast Image

- Compute the Radial Average Contrast