Pupil Remapping for high dynamical range imaging Olivier Guyon Subaru Telescope National Astronomical Observatory of Japan Hilo, HI Michelson Summer School, Pasadena, July 2004

What is Pupil Remapping ? PSF is square modulus of Pupil illumination function disk -> Airy pattern (rings are too bright) sparse array -> multiple diffraction peaks (low contrast and not suitable for coronagraphy) Not suitable for high contrast (1e10) imaging !!! A logical solution is to alter the pupil illumination function to make the PSF more “friendly”. Pupil remapping: modify the pupil illumination function using geometrical optics, without removing light.

Pupil Remapping techniques -- Plan Pupil Remapping on sparse pupils : Pupil densification Subpupils magnification Pupil densification with modification of array geometry Pupil densification and redilution 2. Pupil Remapping on single pupils Phase-Induced Amplitude Apodization (PIAA) - Principle and applications - Mirrors shapes PIAA Imager PIAA Coronagraph

Pupil Remapping for interferometers: pupil densification

1. Pupil densification Fizeau image through an interferometer of base B, pupils diameter d. B>>d B ~ d Good angular resolution Many diffraction peaks -> little light per peak -> need big detector -> not compatible with coronagraphs 1 single peak -> contrasted PSF -> small detector OK -> compatible with coronagraphy poor angular resolution

Michelson (1921) B ~ d Motivated by mechanical limitations, but : - lower number of fringes - more light per fringe - wider fringes - SAME FRINGE CONTRAST Possibly easier than if Michelson had been using a ~8m telescope without pupil remapping ? First use of pupil remapping for astronomical imaging.

Pupil Densification (Labeyrie, 1996) Array geometry is preserved PSF is invariant by translation within a small field of view (Zero Order Field, ZOF). -> Hypertelescope

Pupil densification with Array geometry not preserved Tiny field of view PSF is sharp on-axis

Pupil Densification coronagraphy possible “clean” pseudo image in ZOF no coronagraphy possible many diffraction peaks If densification does not preserve the array geometry, the “clean” field of view becomes tiny.

Pupil Densification and redilution For coronagraphy on an interferometer and large field of view: densification -> coronagraphy -> dilution Densification used only to create “intermediate step” suitable for coronagraphy. Why coronagraphy rather than nulling ? (1) produces image (2) photon-efficient (3) simple recombination optics for large N Guyon & Roddier, 2002

Pupil Densification and redilution 10 pc system, 10 micron 60m baseline six 2m telescopes phase mask coronagraph

Pupil remapping on interferometers : summary The pupil of an interferometer is not suitable for either direct imaging or coronagraphy. It is possible to change the pupil geometry (“pupil densification”) to allow efficient imaging in a narrow field or coronagraphy. The more the pupil is modified, the smaller the field of view becomes. If the FOV becomes too small, pupil redilution (inverse pupil remapping) can restore a large FOV. In that case, the pupil densification is only an intermediate step to allow coronagraphy.

Pupil Remapping for single pupil telescopes: Phase-Induced Amplitude Apodization (PIAA)

Pupil apodization techniques The diffraction wings of the PSF can be attenuated by carefully choosing the light distribution in the pupil plane. For example, a pupil with soft edges yields a PSF with lower diffraction wings, and is therefore more suitable for coronagraphic imaging. - The most common technique to obtain the desired light distribution is to put a transmissive mask in the pupil plane. - It is also possible to redistribute the light in the pupil plane without losing flux and without affecting the flatness of the wavefront (PIAA technique, Guyon 2003) - Interfometric apodization (Aime et. al 2001, Pueyo et. al 2004) - Phase-Induced Zonal Zernike Apodization – PIZZA (Martinache 2004)

Apodized Square Aperture Square Aperture Circular Aperture Nisenson & Papaliolios, ApJ, 2001

Classical Pupil Apodization Techniques Only 1 mask required in the pupil plane. Good coronagraphic efficiency at 3 /d and beyond. The PSF is translation-invariant -> insensitive to stellar size/pointing errors achromatic (with binary masks) Large inner working distance (>3  /d) and poor angular resolution because of the apodization of the pupil edges. Low throughput (typically less than 0.3). For some masks, only a fraction of the FOV is usually usable.

C Geometric construction of the optics shapes.

PIAA mirror shapes

PIAA vs Classical apodization 10 flux ratio 0.1 arcsec 0.4  m  m mv=5 star 9

PIAA vs Classical apodization Comparative table Why does it work so well ?

PIAA: The Field of view issue

Pupil remapping and phase

optical axis Remapped pupil phase map for off-axis source PSF of off-axis source separation = 10 lambda/d linear brightness scale

PIAAI and PIAAC : extending the field of view 2 more optical elements can be used to restore the original pupil. The optical quality of these 2 elements does not have to be nearly as good as the first PIAA optics (before the occulting mask).

PIAAI and PIAAC Benefits of the PIAAC : - large field of view - removes light from central star -> easier on the detector - easy to work at small separations: no need for the detector to separate the 2 PSFs - builds lambda/d PSF through diffraction, not deconvolution: - not very sensitive to zodi and exo-zodi - behaves well in multiple planets systems

PIAA: The FOV issue is stellar size a problem ? on-axis source off-axis source PIAA acts like an imaging system and is not sensitive to small pointing errors and stellar size. In the PIAAC, focal mask should be sized to accommodate pointing errors

(Nearly) optimal solution for PIAA Guyon et. al 2004, in preparation

Corresponding PSF

Phase slope amplification factor Slope after remapping: Incoming wavefront of slope Sl1 along x axis. r2 = f(r1) Distance to optical axis :

Phase slope amplification factor

Off-axis throughput Very good agreement between simple geometric model and diffractive simulation results. inner working angle of the (classical) apodization profile peak intensity in the apodization profile

Classical Apodization 4m 0.5 micron solar system at 10pc same apodization profile for all images 1 mas diameter star Earth contrast = Separation = 3.45 lambda/d Mars contrast =

PIAA Imager (with focal plane mask) 4m 0.5 micron solar system at 10pc same apodization profile for all images 1 mas diameter star

PIAA Coronagraph 4m 0.5 micron solar system at 10pc same apodization profile for all images 1 mas diameter star

The PIAA Coronagraph Good coronagraphic efficiency at 1.2 /d and beyond. Achromatic technique Not sensitive to stellar diameter Imaging technique The PSF is translation-invariant No loss of flux : optimal throughput. No loss of angular resolution. The full FOV is usable. No amplitude mask required: fully reflective optics. The PIAA optics can be physically small and can be quickly inserted in the telescope beam. Not compatible with central obstruction (stellar size problem + optics difficult to polish)

PIAAC : summary High performance : -small IWD, good contrast, high throughput : TPF with a 2m telescope -simple design (2 mirrors + 2 low quality mirrors), achromatic Flexible: - Can be combined with classical apodization. - Can be combined with other coronagraph designs to get smaller than 1 lambda/d IWD (and make the optics easier to polish) : - Apodized pupil Lyot coronagraph - Phase mask coronagraph -> loss of achromaticity Same technique can be used to improve beam transport and fiber coupling for TPF interferometer. Attractive coronagraph for ground-based telescopes with AO.

PIAAC : summary

PSF imaging -> <- pupil imaging The lab experiment with lenses Galicher et. al, 2004 in preparation

Lab experiment with lenses 2 lenses have been polished for a preliminary demonstration of the PIAA concept. Plastic lenses diamond turned by Masashi Otsubo (NAOJ)

Without PIAA With PIAA Demonstration of lossless apodization with PIAA bright rings are due to surface errors on the lenses (diamond turning)

Geometric transformation of the beam Without PIAA With PIAA

Pupil radial profiles Bright rings due to polishing errors (diamond turning) Total flux preserved !

Wavefront quality Shearing interferometer fringes. Without (left) and with (right) PIAA. The results obtained have been limited by the optical quality of the lenses.

Off-axis PSFs with PIAA imager PSFs agree with simulations left : experiment right : simulation scales are different between simulation and experiment

Lab experiment We have demonstrated : -lossless apodization of a beam -the algorithm used to compute lenses/mirrors shapes is correct -no phase aberrations introduced other than the optics aberrations for on-axis -the algorithm used to compute off-axis PSFs is “qualitatively” correct We have not yet demonstrated high dynamical range imaging because of insufficient wavefront quality. We have gained experience on how to align the optics, using visual inspection of the PSF as a diagnostic. Next step: high quality mirrors to demonstrate high contrast. Funding provided by JPL and NAOJ.

Summary If you don't like your pupil, remap it !!! The more you remap your pupil, the more you will lose Field of View. -> once the stellar flux has been removed, the pupil can remapped again in its original configuration to restore Field of View. The above statements apply to interferometers and single pupil telescopes.