The High Contrast Performance Of An Optical Vortex Coronagraph By Dr. David M. Palacios Jet Propulsion Laboratory California Institute of Technology

Stuart Shaklan Jet Propulsion Laboratory G.A. Swartzlander Jr. University of Arizona Dimitri Mawet University of Acknowledgements

1.) What is an Optical Vortex? 2.) Optical Vortex Mask Design 3.) Lyot Optimization 4.) Planet Light Throughput Efficiency 5.) Conclusions Outline

E(r, ,z;t)  A(r,z)exp(im  )exp[i(  t  kz)] The Complex Field AmplitudePhase What is an Optical Vortex?

Optical Vortices in Speckle

Astigmatic Mode Converter

Optical Vortex Holograms

The Optical Vortex Mask Mask Thickness

Coronagraph Architecture Final Image Plane Incident Light Pupil L1L1 OVMLyot Stop L2L2 L3L3 FP 0 2m2m

The Optical Vortex Mask Mask Thickness

dd  dd   n1n1 n0n0 dz tt Ray Trace Analysis of the Vortex Mask

dd  dd   n1n1 n0n0 dz The Vortex Core When  c E Transmitted = 0

Output Amplitude Profile Transmitted amplitude for the E  Polarization Transmitted amplitude for the E r Polarization

A Discrete Representation of an OVM 0 88 Phase profile of an m=4 OVM dz dd dd

Coronagraph Leakage! Ideal OVC6 PupilDiscretized OVC6 Pupil OVC Discretization Leakage

Numerical Simulations Array Size Pupil Size f # Mask Pixel Size n 1   4096 x 4096 pixels 100 pixels in diameter 600 nm microns 1.5 1

m=2m=4m=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 Contrast Between 2-3 /D Contrast m=6 r ( /D)

Contrast m=6 Average Contrast Between 2-8 /D Average Radial Contrast r ( /D)

Contrast m=6 Average Radial Contrast Average Contrast Between 4-5 /D r ( /D)

Contrast m=6 Average Radial Contrast Average Contrast Between 4-10 /D r ( /D)

Contrast m=2 m=4 m=6 Lyot Size (r/R p ) Contrast vs. Lyot Size Average Contrast Between 2-3 /D

Contrast m=2 m=4 m=6 Lyot Size (r/R p ) Contrast vs. Lyot Size Average Contrast Between 2-8 /D

Contrast m=2 m=4 m=6 Lyot Size (r/R p ) Contrast vs. Lyot Size Average Contrast Between 4-5 /D

Contrast m=2 m=4 m=6 Lyot Size (r/R p ) Contrast vs. Lyot Size Average Contrast Between 4-10 /D

Optimized Contrast Lyot Stop Radius = 0.8P r Average Contrast 2-3 /D2-8 /D 4-5 /D 4-10 /D 5.3x x x x m = 2 m = 4 m = 6 1.2x x x x x x x x10 -11

Throughput Lyot Size (r/R p ) m=2 m=4 m=6 m=0 Throughput Efficiency vs. Lyot Size Planet Located at 2 /D

Throughput Lyot Size (r/R p ) m=2 m=4 m=6 m=0 Throughput Efficiency vs. Lyot Size Planet Located at 4 /D

m=6m=4m=2m=0 2 /D 4 /D Optimized Planet Light Throughput Lyot Stop Radius = 0.8P r

Is an Achromatic OVC Possible? C m m must be maintained to ~5x10 -4 across the bandpass!

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%) 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 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 = 0.8P r 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 sinc 2 masks best demonstrated contrast 8th order masks presently being explored Vortex masks possess a 2m th 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 r m dependence vanish! The Intensity has a 2 mth aberration sensitivity! For the m=5 case: 10 th order sensitivity predicted!

Low Order Zernike Modes Z=4 Z=5 Z=6Z=7 Z=8Z=9Z=10Z=11

Numerical Simulations Aberration size (waves peak to valley) C

Coronagraph Comparisons m=5 vortex8th Order Zernike # Improvement

PupilVortex MaskLyot Stop Lyot PlaneFocal Plane  /D The Lyot and Focal Plane Profiles

Amplitude Occulting Spots E(x,y) = A(x,y)exp[i  (x,y)] Sinc 2 (r) Hard Stop

The Lyot Stop Hard Stop Cat’s Eye Stop

The Final Image Before After

R/R diff An Optical Limiting Technique Amplitude

Contrast Simulations Contrast Image Compute the Radial Average Contrast