Pupil Remapping for high dynamical range imaging

Olivier Guyon Subaru TelescopeNational Astronomical Observatory of JapanHilo, HIguyon@naoj.org

Michelson Summer School, Pasadena, July 2004

What is Pupil Remapping ?

PSF is square modulus of Pupil illumination functiondisk -> Airy pattern (rings are too bright)sparse array -> multiple diffraction peaks (low contrast and not

suitablefor coronagraphy)

Not suitable for high contrast (1e10) imaging !!!

A logical solution is to alter the pupil illumination function to make the PSFmore “friendly”.

Pupil remapping: modify the pupil illumination function using geometrical optics, without removing light.

Pupil Remapping techniques-- Plan --

1. Pupil Remapping on sparse pupils : Pupil densificationSubpupils magnificationPupil densification with modification of array geometryPupil densification and redilution

2. Pupil Remapping on single pupils Phase-Induced Amplitude Apodization (PIAA)

- Principle and applications- Mirrors shapes

PIAA ImagerPIAA Coronagraph

Pupil Remapping for interferometers: pupil densification

1. Pupil densification

Fizeau image through an interferometer of base B, pupils diameter d.

B>>dB ~ d

Good angular resolutionMany diffraction peaks -> little light per peak -> need big detector -> not compatible with coronagraphs

1 single peak -> contrasted PSF -> small detector OK -> compatible with coronagraphypoor angular resolution

Michelson (1921)

B ~ dMotivated by mechanical limitations, but : - lower number of fringes - more light per fringe - wider fringes - SAME FRINGE CONTRAST

Possibly easier than if Michelson had been usinga ~8m telescope withoutpupil remapping ?

First use of pupil remapping forastronomical 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 possiblemany diffraction peaks

If densification does not preservethe array geometry, the “clean”field of view becomes tiny.

Pupil Densification and redilution

For coronagraphy on an interferometerand large field of view:densification -> coronagraphy -> dilution

Densification used only tocreate “intermediate step”suitable for coronagraphy.

Why coronagraphy rather thannulling ?

(1) produces image(2) photon-efficient(3) simple recombination

optics for large N

Guyon & Roddier, 2002

Pupil Densification and redilution

10 pc system, 10 micron60m baselinesix 2m telescopesphase 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 AmplitudeApodization (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)

ApodizedSquareAperture

SquareAperture

CircularAperture

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 ratio0.1 arcsec 0.4 m - 0.6 mmv=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

Pupil remapping and phase

opticalaxis

Remapped pupil phase mapfor off-axis source

PSF of off-axis sourceseparation = 10 lambda/dlinear 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 toseparate 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 issueis stellar size a problem ?

on-axis source

off-axis source

off-axis source

PIAA acts like an imaging system and is not sensitiveto 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 amplificationfactor

Slope after remapping:

Incoming wavefront of slope Sl1 along x axis.

r2 = f(r1)

Distance to optical axis :

Phase slope amplificationfactor

Off-axis throughput

Very good agreement between simple geometric model and diffractivesimulation results.

inner working angleof the (classical) apodization profile

peak intensity in theapodization profile

Classical Apodization4m telescope @ 0.5 micronsolar system at 10pcsame apodization profile for all images1 mas diameter star

Earth contrast = 3 10

-11Separation = 3.45 lambda/d

Mars contrast = 1.5 10

-10

PIAA Imager(with focal plane mask)4m telescope @ 0.5 micron

solar system at 10pcsame apodization profile for all images1 mas diameter star

PIAA Coronagraph4m telescope @ 0.5 micronsolar system at 10pcsame apodization profile for all images1 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 couplingfor TPF interferometer.

Attractive coronagraph for ground-based telescopes with AO.

PIAAC : summary

PSF imaging ->

<- pupil imaging

The lab experimentwith lenses

Galicher et. al, 2004in 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 polishingerrors (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 PSFswith PIAAimager

PSFs agree withsimulations

left : experimentright : simulationscales are different betweensimulation 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 ofinsufficient wavefront quality.We have gained experience on how to align the optics, using visual inspectionof 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 againin its original configuration to restore Field of View.

The above statements apply to interferometers and single pupil telescopes.