PSF and Field of View characteristics of imaging and ...francois.henault.free.fr/cv/nullfou_300610.pdf · PSF and FoV characteristics of imaging and nulling ... – Neglecting geometrical

San Diego, June 30th 2010Conference 7734 Optical and Infrared Interferometry II

PSF and FoV characteristics of

imaging and nulling interferometers

1

PSF and Field of View characteristics of


François HénaultUMR CNRS 6525 H. Fizeau – UNS, CNRS, OCA

Avenue Nicolas Copernic06130 Grasse - France




2

- Do nulling maps depend on the type of combining optics(axial vs. multi-axial combination schemes) ?

- Has it some consequence on their “nulling imaging” capacity ?

• “Simple Fourier optics formalism for high angular resolution systems and nulling interferometry,” JOSA A 27, p. 435-449 (2010)

• “Fibered nulling telescope for extra-solar coronagraphy,” Optics Letters 34, n° 7, p. 1096–1098 (2009)

• “Computing extinction maps of star nulling interferometers,” OpticsExpress 16, 4537-4546 (2008)

Previous publications

Opening questions

In the frame of Darwin/TPF-I exoplanet finding space missions…




3

Coordinates systems

X

U

V

D

u

vY

O

Entrance pupil

plane (P)

On-sky angular

coordinates

P1

P2

P3

P4

sO

Sky

object

B

Z

Y’’X’’

O’’

F’

Detection

plane

Exit pupil

plane (P’)

MO’’

X’

D’

Y’

O’P’4

P’1

P’2

P’3

s’B’

M’

s

sO’




4

Image of a sky object O(s) projected back on sky

• PSFT(s) : PSF of one individual collecting telescope, being projected back on-sky

• an : amplitude transmission factor of the nth telescope

• ϕn : phase-shift along the nth interferometer arm for cophasing ornulling purpose

• k = 2π/λ : wavenumber of monochromatic electro-magnetic field

• m : optical compression factor between telescopes and their relay optics

[ ] ( )[ ]∫∫ ∑Ω∈ =

Ω−=

O

O

2N

1n

nnT d/kexpφexpa)-(SFP)O()(I

Os

nnOOO P'O'sOPsssss mii

with




5

General layout of a multi-aperture interferometer

Converging opticsDiverging optics

Fold mirrorBeamsplitter

AcromaticPhase Shifter

Telescope 1

Combining

optics

Z

O

F’

Metrology

beam 1

Metrology

beam 1

Focal plane

Metrology

beam 2

Metrology

beam 2

Telescope 2

P2P1

Relay

optics 1

Relay

optics 2

B

APS 1 APS 2

(P)

(P’)O’

B’

FC

• All telescopes assumed to be identical• All exit pupils optically conjugated with

entrance pupils




6

PSF and Field of View characteristics

• Generalized Point Spread Function (PSF)

– Changing over the whole instrument Field of View

– Object-Image relationship is not a convolution product

• Maximal achievable Field of View (FoV)

– Neglecting any kind of apertures or stops,

– Neglecting geometrical aberrations and diffraction effects

– Suitable for fast polychromatic FoV computations:

[ ] [ ] ( )[ ]2

N

1n

nnTG /kexp/kexpφexpa)(SFP),(PSF ∑=

−−= mimii nnOnO P'O'OPsP'O'ssss

[ ] ( )[ ]2

N

1n

nn /kexpφexpa)(FoV ∑=

−= mii nn P'O'OPss

∫∫=δλ

δλ

δλ

δλλδλ dλ)λ(Bdλ)λ(B)(FoV)(FoV ss




7

• Only occurs when:

• Generalized PSF becomes:

– Constant over the whole FoV

– Classical Object-Image relationship I(s) = O(s) * PSF(s) holds

• Maximal achievable Field of View:– Becomes infinite whatever the wavelength

– Constant transmission equal to:

Golden rule of Fizeau interferometers

[ ] [ ]2

N

1n

nnTG /kexpφexpa)(SFP),(PSF ∑=

−= mii nO P'O'ssss

[ ]2

N

1n

nn φexpa)(FoV ∑=

= is

O’P’n = m OPn

Pupil In Pupil Out

x

x




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• Golden rule extends destructive fringe over the whole FoV, killing thecentral star and all its surrounding planets (this is not what we want )

Numerical simulations: a 8-telescope Fizeau interferometerin imaging and nulling modes

B

X

Y

D

B

X

Y

X

Y

D

Input pupils

00

00

B

X

Y

Dπ

π

π

π

00

00

B

X

Y

Dπ

π

π

π

PSF (FoV center) Maximal

achievable FoV

PSF (half FoV)

5 arcsec

5 arcsec




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Monolithic

telescope

Beam combiner(exit pupil plane)

Z

O’

F’

Beam

densifier

Primary Mirror

SecondaryMirror

Metrologybeam 2

Metrologybeam 2

Metrologybeam 1

Metrologybeam 1

B’

P’2

Focal plane

Relay

optics

P’1

(P)

(P’)

Sheared-Pupil Telescopes (SPT)

Z

F’

Focal plane

(P’)

APS 1

Metrology

beams

Metrology

beams

O’

APS 2

and OPDcompensation

May be replacedwith a modifiedMach-Zehndercombiner

[or Michelsonequipped withcube-corners]




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Two different types of Sheared-Pupil Telescope

Masked output

sub-pupils

B’

D’X’

Y

’

O’

Input pupil plane Output pupil plane

B’

D’

D

X

Y

X’

Y

’

O’OUnmasked output

sub-pupils

B

DX

Y

O

Monolithic

pupil

telescopeLyot stop on

Exit pupil




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• Usable for exploratory science missions: exo-zodi

characterization, Jupiter-like planets…

• If rotating, allow to validate most of the Darwin/TPF-I

algorithms envisaged for planets finding and characterization

• When unmasked, they concentrate energy in very small core, overcoming Rayleigh’s diffraction limit

• But no real super-resolving power , since PSF are sharpened after sub-aperture filtering:

Interest and limitations of nulling SPTs

Specific Object-Image relationship:

[ ] [ ] [ ])O(*)(PSF/kexpφexpa)( T

2N

1n

nn ssP'O'ss n ×−=Ι ∑=

mii




12

• Unmasked SPT: high throughput, residual star leakage

• Masked SPT: no leakage, enlarged nulled area of low throughput

PSF and Field of View simulations of SPTs

Sh

eare

d-P

up

il

Te

lesc

op

eD

= 5

m

Ma

ske

d S

PT

B =

0.5

mD

= 4

m

Ma

ske

d S

PT

B =

1 m

D =

3 m

5 a

rcs

ec




13

Telescope 1

Axial beam

combiner

Z

O

F’

Fringe

tracker

Fringe

tracker

Metrology

beam 1

Metrology

beam 1

Focal plane

Metrologybeam 2

Metrologybeam 2

Telescope 2

P2P1

Relay

optics 1

Relay

optics 2

B

APS 1 APS 2

(P)

(P’)

O’

Axially Combined Interferometer (ACI)

• Co-axial recombination by means of a balanced set

of beamsplitters

• Equivalent to the previous

monolithic, masked SPT

• Nulls all diffracted light

originating from central

star

• Specific Object-Image

relationship:

[ ] [ ]

=Ι ∑=

)O(kexpφexpa*)(PSF)(

2N

1n

nnT sOPsss nii




14

• No gain in angular resolution, but diffracted starlight cleaned before final image blurring

• Progressive leakage from central objects (to be traded against throughput)

Nulling imaging capacities of SPT

Ma

ske

d S

PT

B =

0.5

mD

= 4

m

Ma

ske

d S

PT

B =

1 m

D =

3 m

2 a

rcs

ec

Fic

titi

ou

s

sk

y o

bje

ct




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AC

IB

= 2

0 m

D =

5 m

AC

IB

= 1

0 m

D =

5 m

• For longer baselines, nulling ACI behaves as a single-dish telescope Nulling capacity seems to be lost

Nulling imaging capacities of ACI

2 a

rcs

ec

Fic

titi

ou

s

sk

y o

bje

ct




16

Conclusions

• Nulling maps and nulled images produced by different types

of multi-aperture optical systems can be rapidly evaluated by

means of a simple Fourier optics formalism

• From the results of theory and first numerical computations:

– “Golden rule for interferometric imaging” extends the destructive fringe pattern of nulling interferometers over their whole Field of View

– A nulling monolithic, sheared-pupil telescope is an attractive solution Requires further tradeoff on throughput/leakage

– Theoretical Object-Image relationship of the Bracewell interferometer allows full extinction of diffracted starlight, but no super-resolution is possible

– In the case of fibered nulling interferometers, best throughput are achieved using axial recombination schemes (nulling ACIs)[ ]Please retain: this is all very preliminary, eventually anecdotal

and somewhat heuristic. Further work is required and

cooperations are welcome

Documents

PSF and Field of View characteristics of imaging and ...francois.henault.free.fr/cv/nullfou_300610.pdf · PSF and FoV characteristics of imaging and nulling ... – Neglecting geometrical