Lyot coronagraphs with band-limited masks

Lyot coronagraphs withband-limited masks

Brian Kern (JPL)9-29-2006

(supported by all of TPF-C work to date)

Band-limited Lyot coronagraphs (Kern)

2

Overview

• Coronagraph principles• Broadband modeling• Testbed data• Masks• Wavefront Sensing / Control


3

Lyot coronagraph principles

(Sivaramakrishnan et al. 2001)


4

Band-limited mask

• Amplitude transmission mask hasfinite bandwidth (FT has finite support)

• T=0 on-axis• For uniformly illuminated pupil,

all transmitted on-axis light ends up at edges of Lyot plane– Off-axis light largely unchanged

• Lyot stop removes “all” on-axis light

(Kuchner & Traub 2002)


5

Implementation

• SpeckleCam design• No polarizing

beamsplitter• 7 reflections

beforeocculter– Includes

3rd DM (sequential)forredundancy

• Relativelysimple design

(Krist, Trauger & Moody 2006)

3rd DM


6

Throughput and IWA

• Throughput vs angle is determined by width of occulter– Throughput linearly related to occulter transmission and Lyot

area– Linear 4th-order max throughput

0.45 @ 4 /D, 0.16 @ 2 /D– Linear 8th-order (m=1, l=3) max

0.30 @ 4 /D, 0.03 @ 2 /D• Diffractive efficiency (size of

PSF) determined by Lyot stop– Smaller IWA -> narrower occulter

-> smaller Lyot stop -> bigger PSF– Bigger PSF is more sensitive

to zodiLinear sinc2

(4th order)

adjustable width


7

IWA considerations

• Stellar size limits contrast for 4th-order mask– 4th-order mask

loses 34 oftop 100 stars

• 8th-order maskcan observe all top 100 stars

(Crepp 2006)


8

Optical bandwidth – DM correction• Optical surface requirements depend on bandwidth

– For sequential DMs, amplitude-induced phase errors and 2nd-order propagation of phase and reflectivity variations set bandpass

– Requirements are linear in R = /

(Shaklan & Green 2006)

R=6.3


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Optical bandwidth - occulter

• Lyot stop size is determined by occulter width and by longest wavelength in bandpass– Shortest wavelength in bandpass would have higher throughput

if observed individually

• Occulter transmission profile, phase profile should not change with

• Nominal design has 3 bands of ~ 100 nm each– One band is “discovery” band, set for best contrast– Each band has different Lyot stop to improve throughput

• Bandwidth generally limited by wavefront correction contrast vs. surface requirements, rather than by occulter


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Aberration sensitivity: I• 8th-order masks have greatly reduced sensitivities

compared to 4th-order masks

(Shaklan & Green 2005)


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Aberration sensitivity: II

• Polarization of FB1 is a non-issue with 8th-order mask– Allows design with no beamsplitter

• With standard coatings, 4th-order FB1 with no polarization control limits contrast to ~ 10-9

– Polarization-induced aberrations are predominately low-order

(Balasubramanian et al. 2005)


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Aberration sensitivity: III

• DM cannot correctrandom occulter transmission errors over widebandpass becauseerrors are in focal plane

• Requirements areconsistent with superpolished surfaces

• Linear occulter can betranslated to avoid“bad spots”

(Duparre & Jakobs 1996)

(Lay et al. 2005)


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RequirementsPerturbation Contributor Nature Contrast FractionStructural Defomation Beam Walk Thermal 8.29E-13 16.12%

Jitter 6.33E-13 12.31%Aberrations Thermal 3.28E-14 0.64%

Jitter 4.43E-17 0.00%Bending of Optics Aberrations Thermal 8.60E-13 16.72%

Jitter 8.60E-13 16.72%Pointing Beam Walk 1.29E-12 25.10%

Image Motion 9.04E-14 1.76%Mask Error 5.46E-13 10.63%

SUM 5.14E-12

Perturbation Contributor Nature Contrast FractionStructural Defomation Beam Walk Thermal 8.29E-13 16.12%

Jitter 6.33E-13 12.31%Aberrations Thermal 3.28E-14 0.64%

Jitter 4.43E-17 0.00%Bending of Optics Aberrations Thermal 8.60E-13 16.72%

Jitter 8.60E-13 16.72%Pointing Beam Walk 1.29E-12 25.10%

Image Motion 9.04E-14 1.76%Mask Error 5.46E-13 10.63%

SUM 5.14E-12(STDT 2006)

(Shaklan STDT 2005)

• Dynamic errorbudget dominatedby pointing error

• Reminder ofrelaxation allowedby 8th-order mask

8th order


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Broadband modeling

• 3 independent packages for detailed modeling of full Fresnel propagation effects over finite bandwidths– PROPER (Krist)– MACOS + Matlab proprietary code (Sidick)– Python proprietary code (Moody)– Monochromatic binary mask modeling (Hoppe)

• Avoids limitations of semi-analytic approximations– E.g., analysis for surface requirements uses 2nd-order Taylor

expansions

• Models point to specific problems, mitigations– E.g., effects of nonideal (complex) mask transmission, variations

in Lyot stop size, speckle nulling algorithms


15

Broadband modeling guidance

• Requirements on systematic occulting mask errors are difficult to quantify analytically– Band-limited portion of mask errors are filtered by Lyot stop– More restrictive Lyot stops relax mask requirements

• Nulling algorithms may be tested and optimized– “Full knowledge” about complex electric fields are available to

models


16

Model validation testbed

• High Contrast Imaging Testbed (HCIT) provides experimental validation and guidance to models

occulter

Lyot

DM


17

Testbed layout

• Testbed is classical Lyotarrangement– 32x32 DM

• Optics ready for 64x64 DM– Re-imaging back end for

adequate sampling on CCD

• Monochromatic and broadband light sources– Broadband light generated

with supercontinuum laser– Select bandpass using

filters• 2%, 10%


18

Testbed results

• Monochromatic contrast to < 10-9

• Explore variations in contrast with bandwidth– Null at 785 nm with 2% bandwidth– Measure contrast at 10%

bandwidth without changing DM

• Agreement with model ~ 20%• Modeling shows path

for improvement– Performance limited by systematic mask errors (dispersion)– Optimal Lyot stop improves by ~ 2x


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Occulting mask technology

• Ideal occulting mask transmission is real-valued and independent of wavelength– No spatial variations in transmitted phase– No spatial variations in dispersion– No spatial variations in absorption spectrum

• Occulting profile smooth on f/D scale– Profiles can be grayscale or binary on smaller scales

(Balasubramanian et al. 2005)


20

Occulting mask materials

• Metal evaporation for binary occulters– Si substrate, etched to leave “windows” for transmission– Variable duty-cycle approach leads to “waveguiding” polarization

effects

• High Energy Beam Sensitive (HEBS) glass– Glass becomes absorbing with e--beam dose– Excellent grayscale control, good absorption (108), good spatial

resolution– Different exposure levels show different absorptive spectra,

exposure changes index of refraction (dispersion also changes)


21

Occulting mask experiments - I

• Binary mask polarization models validated on HCIT– Prediction was that

orthogonal linear polarizations seedifferent occultingmask phase

– Resulting contrastshould be differentin two polarizations

Data Models

Nulledpolarization

Orthogonalpolarization

> 10-7

< 10-8

(Hoppe 2006)


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Occulting mask experiments - II• HEBS transmission is non-

ideal in phase and modulus– Spectrometer measures

intensity transmission in lab– Interferometer measures

transmitted phase in lab• Phase dispersion in particular

limits broadband performance– Anomalous dispersion,

consistent with resonant absorber model

• All HEBS formulations to date show similar dispersion

• Model of broadband contrast limits matches testbed data

(Halverson et al. 2005)


23

Occulting mask development

• Current HEBS and binary masks don’t reach 10-10 contrast over 10% bands (in both polarizations)

• Modeling has begun on combined metallic – dielectric occulters– Occulter transmission modulus of candidate formulations

maintain systematic errors for contrast < 10-10

– Control of transmitted phase should be feasible with multi-layer dielectrics


24

Nulling algorithms

• Wavefront sensing performed on same light that heads to science camera– Avoid non-common path sensing

• Image-plane vs. Lyot-plane nulling– Aberrations in pupil plane cause speckles from on-axis source to

scale radially with wavelength when viewed in image plane– Speckle in image plane (smeared radially) can be nulled by

sinusoidal phase in pupil plane• Uses all actuators on pupil-plane DM

– Speckle in Lyot plane (not smeared) can be nulled using a small number of neighboring actuators in pupil plane

• Uses actuators in “band-limited” neighborhood of speckle, projected onto pupil-plane DM


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Sensing for null - I

• Must determine complex correction from intensity images• Image-plane “Speckle nulling” applies

discrete spatial frequencies to DM and minimizes image-plane intensities– Sparse nature of image-plane observations is tolerant of noise– Must iterate to correct continuous distribution of errors

• Lyot-plane speckle nulling actuates noncontiguous actuators at DM and minimizes Lyot-plane intensities– Simplest technique ignores

structure of occulter transform– Does not discriminate speckle

image-plane position

DM image

DM Lyotocculter FT


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Sensing for null - II

• Bordé-Traub algorithm senses entire correction at pupil using complicated “test pattern”– Uses linear-phase approximation (ei = 1 + i)– Applies to image plane or Lyot plane– Complexity of “test pattern” (number of degrees of freedom)

determines sensitivity to noise

• Detailed behavior in presence of noise not yet known– Spectral smearing in image plane sensing may require more

iterations– Lyot plane nulling may lead to undesirable distribution of

speckles in the dark hole– Could consider information from both Lyot and image plane


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Model of nulling algorithm

• MonochromaticBordé-Traub nulling algorithm

• Start from “blank”DM setting

• 20 iterations to10-9, 30 to 6x10-10

• Includes opticaleffects not presentin linear-phaseanalysis

(Krist & Bordé / PROPER)


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Summary

• Con: Band-limited masks have lower throughput, larger PSF than some coronagraph designs

• Pro: 8th-order mask offers excellent rejection of low-order aberrations– Allows relaxed requirements / no polarization control

• Pro: Low optical complexity• Pro: Lower risk (well validated models)

Lyot coronagraphs with band-limited masks

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