1. Lyot coronagraphs with band-limited masks Brian Kern (JPL) 9-29-2006 (supported by all of TPF-C work to date)

2. Band-limited Lyot coronagraphs (Kern) 2 Overview Coronagraph principles Broadband modeling Testbed data Masks Wavefront Sensing / Control

3. Band-limited Lyot coronagraphs (Kern) 3 Lyot coronagraph principles (Sivaramakrishnan et al. 2001)

4. Band-limited Lyot coronagraphs (Kern) 4 Band-limited mask Amplitude transmission mask has finite 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. Band-limited Lyot coronagraphs (Kern) 5 Implementation SpeckleCam design No polarizing beamsplitter 7 reflections before occulter –Includes 3 rd DM (sequential) for redundancy Relatively simple design (Krist, Trauger & Moody 2006) 3 rd DM

6. Band-limited Lyot coronagraphs (Kern) 6 Throughput and IWA Throughput vs angle is determined by width of occulter –Throughput linearly related to occulter transmission and Lyot area –Linear 4 th -order max throughput 0.45 @ 4 /D, 0.16 @ 2 /D –Linear 8 th -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 zodi Linear sinc 2 (4 th order) adjustable width

7. Band-limited Lyot coronagraphs (Kern) 7 IWA considerations Stellar size limits contrast for 4 th -order mask –4 th -order mask loses 34 of top 100 stars 8 th -order mask can observe all top 100 stars (Crepp 2006)

8. Band-limited Lyot coronagraphs (Kern) 8 Optical bandwidth – DM correction Optical surface requirements depend on bandwidth –For sequential DMs, amplitude-induced phase errors and 2 nd - order propagation of phase and reflectivity variations set bandpass –Requirements are linear in R =  / (Shaklan & Green 2006) R=6.3

9. Band-limited Lyot coronagraphs (Kern) 9 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

10. Band-limited Lyot coronagraphs (Kern) 10 Aberration sensitivity: I 8 th -order masks have greatly reduced sensitivities compared to 4 th -order masks (Shaklan & Green 2005)

11. Band-limited Lyot coronagraphs (Kern) 11 Aberration sensitivity: II Polarization of FB1 is a non-issue with 8 th -order mask –Allows design with no beamsplitter With standard coatings, 4 th -order FB1 with no polarization control limits contrast to ~ 10 -9 –Polarization-induced aberrations are predominately low-order (Balasubramanian et al. 2005)

12. Band-limited Lyot coronagraphs (Kern) 12 Aberration sensitivity: III DM cannot correct random occulter transmission errors over wide bandpass because errors are in focal plane Requirements are consistent with superpolished surfaces Linear occulter can be translated to avoid “bad spots” (Duparre & Jakobs 1996) (Lay et al. 2005)

13. Band-limited Lyot coronagraphs (Kern) 13 Requirements (STDT 2006) (Shaklan STDT 2005) Dynamic error budget dominated by pointing error Reminder of relaxation allowed by 8 th -order mask 8 th order

14. Band-limited Lyot coronagraphs (Kern) 14 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 2 nd -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. Band-limited Lyot coronagraphs (Kern) 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. Band-limited Lyot coronagraphs (Kern) 16 Model validation testbed High Contrast Imaging Testbed (HCIT) provides experimental validation and guidance to models occulter Lyot DM

17. Band-limited Lyot coronagraphs (Kern) 17 Testbed layout Testbed is classical Lyot arrangement –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. Band-limited Lyot coronagraphs (Kern) 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

19. Band-limited Lyot coronagraphs (Kern) 19 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. Band-limited Lyot coronagraphs (Kern) 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 (10 8 ), good spatial resolution –Different exposure levels show different absorptive spectra, exposure changes index of refraction (dispersion also changes)

21. Band-limited Lyot coronagraphs (Kern) 21 Occulting mask experiments - I Binary mask polarization models validated on HCIT –Prediction was that orthogonal linear polarizations see different occulting mask phase –Resulting contrast should be different in two polarizations Data Models Nulled polarization Orthogonal polarization > 10 -7 < 10 -8 (Hoppe 2006)

22. Band-limited Lyot coronagraphs (Kern) 22 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. Band-limited Lyot coronagraphs (Kern) 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. Band-limited Lyot coronagraphs (Kern) 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

25. Band-limited Lyot coronagraphs (Kern) 25 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 Lyot occulter FT

26. Band-limited Lyot coronagraphs (Kern) 26 Sensing for null - II Bordé-Traub algorithm senses entire correction at pupil using complicated “test pattern” –Uses linear-phase approximation (e i  = 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

27. Band-limited Lyot coronagraphs (Kern) 27 Model of nulling algorithm Monochromatic Bordé-Traub nulling algorithm Start from “blank” DM setting 20 iterations to 10 -9, 30 to 6x10 -10 Includes optical effects not present in linear-phase analysis (Krist & Bordé / PROPER)

28. Band-limited Lyot coronagraphs (Kern) 28 Summary Con: Band-limited masks have lower throughput, larger PSF than some coronagraph designs Pro: 8 th -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)