Pupil Replication Frank Spaan Alan Greenaway Erwan Prot Vincent Mourai
PREDRIS Pupil Replication for Extreme Dynamic Range Imaging Spectroscopy Start: 1 April 25 Two years, funded by PPARC Publication: Pupil Replication for Exo- Planet Imaging; ApJL, 1 January 25 (referenced in Nature). This presentation: includes new unpublished results. 16 May 25 www.phy.hw.ac.uk/~phyhic 2
Overview Introduction to Pupil Replication Characterization and analysis Error Assessment Experimental proof of principle Simulation of a Coronagraph Comparison with Hyper Telescope principle 16 May 25 www.phy.hw.ac.uk/~phyhic 3
Context Exoplanet indirect detection since 1995 ESA Cosmic Vision 22 (April 25): fundamental physics cosmology solar system planetary formation, life, exoplanets => direct detection of exoplanets => proposals due early 27 16 May 25 www.phy.hw.ac.uk/~phyhic 4
Numbers Dynamic range starflux / planetflux: 1 1 (visual, reflected), 1 6 (infrared, thermal) A planet at 1 AU around a star at 2 pc seen with 3 m telescope at 36 λ/d at 6 nm (stardisk =>.2 λ/d) at 2 λ/d at 1 micron flux: one hour,v-band, efficiency 5% => ~5 photons (planet around magnitude star) ~.5 photons (planet around 1 magnitude star) 16 May 25 www.phy.hw.ac.uk/~phyhic 5
Flux from host star dominates exoplanet: Star flux problem Techniques to suppress scattered host flux: coronography pupil apodisation Log Intensity (normalised) interferometry 5 1 15 2-2 -4-6 -8-1 -12 Off Axis Distance diffraction limited PSF, x-axis in λ/d 16 May 25 www.phy.hw.ac.uk/~phyhic 6
Inner Working Angle Inner working angle (IWA): the minimum angular distance from the star at which a planet can be detected. All techniques need image-plane masks mask size is typically several /D side-lobe suppression often increases star image increasing IWA makes earth-like detection harder => decrease size of star image => pupil replication 5 1 1 5 2 O ff A xis D istan ce 16 May 25 www.phy.hw.ac.uk/~phyhic 7 Log Intensity (normalised) -2-4 -6-8 -1-1 2
Pupil Replication with Apodisation 15 1 energy (normalised) -2-4 15 1 energy (normalised) -2-4 angle (lambda / D) 5-5 -1-15 -15-1 -5 5 1 15 angle (lambda / D) -6 angle (lambda / D) -8-1 -12-14 -16-18 -2 5-5 -1-15 -15-1 -5 5 1 15 angle (lambda / D) -6-8 -1-12 -14-16 -18-2 16 May 25 www.phy.hw.ac.uk/~phyhic 8
Pupil Replication Axial wavefront is continuous (blue), like larger telescope. Non-axial wavefront is discontinuous (red), and appears like a blazed grating Etendue is preserved (pupil area * solid view angle) 16 May 25 www.phy.hw.ac.uk/~phyhic 9
Expected Results Consider 3-fold replication in 1-d Axial pupil wavefront is 3x wider and 3x fainter Image of unresolved axial star is 3x narrower and 3x brighter Sidelobes are 3x fainter Image stop to remove star flux can be smaller Log Intensity (normalised) -2-4 -6-8 -1-12 5 1 15 2 Off Axis Distance 16 May 25 www.phy.hw.ac.uk/~phyhic 1
Expected Limits Violation of homothetic mapping position and orientation of the replicated images is not an exact scaled copy of the unreplicated image => Non-isoplanatic imaging PSF dependent on the viewing direction. => Requirement: Maximum angular diameter of star + telescope pointing error < some limit: θ 16 May 25 www.phy.hw.ac.uk/~phyhic 11
Example General criterion: max wavefront error < λ/4. => For N-fold replication of aperture diameter D and at wavelength λ: Example: 2.5m diameter pupil 8nm wavelength 3-fold pupil replication θ < 5 mas θ < λ 4D( N 1) At angles smaller than θ the image quality should be good (includes pointing error). 16 May 25 www.phy.hw.ac.uk/~phyhic 12
Simulation Broken line is unreplicated image (diffraction limited) Solid line is replicated image Replicated image is modulated by unreplicated image, as expected mas 5 mas 1 mas y: log(int) x: mas 16 May 25 www.phy.hw.ac.uk/~phyhic 13
Broadband Single pupil, 1 nm (black) 3x Replicated pupil 1 nm (red) 872 nm (green) 76 nm (blue) 1 lo g o f n ormalise d intensit y 2 4 3 3 6 3 3 offaxis anglemaxd 16 May 25 www.phy.hw.ac.uk/~phyhic 14
Analysis (1) in 1 dimension, plane wave on axis, hard edged pupil: wave + pupil: imaged: FT sin(x)/x = sinc(x) = * FT sinc(x) (1+2cos(x)) 16 May 25 www.phy.hw.ac.uk/~phyhic 15
Analysis (2) Input wave at angle α, d = pupil diameter A = amplitude constant 2 x sin wave( x) = Ae π α λ Amplitude of imaged plane wave = T PSF = T 2 T = Asinc 2d x ( ( )) ( ) ( π ( sin α ) λ ) 16 May 25 www.phy.hw.ac.uk/~phyhic 16
Three replications: Analysis (3) single pupil convolved with 3 delta functions Fourier(cosine) = 2 delta functions => sinc multiplied in Fourier domain (image) with 1 + 2cos(x) ( ( ) ) ( 1 2 cos( 2 )) sinc sin ( ) T = A + dπ x λ dπ x α λ Note: Cos( ) is not dependent on angle 16 May 25 www.phy.hw.ac.uk/~phyhic 17
Two dimensions Square pupil (seamless replication) then: 2-D amplitude T T = T T x y T for two replications 1 and 2 1 is on axis, 2 is adjacent T = T T + T T x1 y1 x2 y2 errors imposed on 2 2 1 16 May 25 www.phy.hw.ac.uk/~phyhic 18
Errors Pupil 1: T 1x and T 1y are sinc functions Pupil 2 has errors in x (and y) direction: shift s (and shear h): piston p tilt f (and tip g) T 2x (and similar for T 2y ): ( ( )( )) ( ( )) i2π p x d s x sin Ae + λ + α sinc dπ f λ 16 May 25 www.phy.hw.ac.uk/~phyhic 19
Evaluation 2-D analyses; horizontal crosssection If PSF(no error) - PSF(with error) < 1-1 example: shift = d 1-5 => 1 micron for 1 cm pupil difference image => 1log of normalised intensity 2 4 6 8 1 12 15 1 5 5 1 15 off axis angle Λ d 16 May 25 www.phy.hw.ac.uk/~phyhic 2 15 1 5 5 1 15
Examples Similar results below 1-1 for shear = 1-5 d; piston = 1-6 λ; tip = 1-5 λ/d; tilt = 1-5 λ/d; jitter = 1-6 λ/d No apodisation or star stop applied. Is this peculiar to PR? => Error sensitivity assessed this way is for single pupil of the same order of magnitude. 16 May 25 www.phy.hw.ac.uk/~phyhic 21
Software Simulations 2-D; horizontal crosssections shown Simulations of errors due to shift, shear, piston, tip, tilt, jitter agree with analysis within 1-14 Further simulations: Rotation error, (de-)magnification error, random amplitude errors, random phase errors. Extended sources 16 May 25 www.phy.hw.ac.uk/~phyhic 22
Simulation: Procedure Setup: two square pupils like in analysis wave - pupil - errors - FT - grating - FT -1 - pupil - apodisation - FT - star stop - sampling correction - modulus 2 - store => this for each point source and wavelength and sum the results Adapt for each wavelength: size of pupils, of apodisation, of star stop, of grating. NB: maximum # pixels limited; sampling correction important; accuracy ~1-14 16 May 25 www.phy.hw.ac.uk/~phyhic 23
Rotation error, max = 21 degrees (magenta), and no error (black), diagonal crosssection. 1 Example rotation diagonal crosssection Intensity (normalised) 1 2 1 4 1 6 2 2 4 6 Off Axis Distance (mas) Similar results for (de-)magnification error. Random errors addressed later. 16 May 25 www.phy.hw.ac.uk/~phyhic 24
Extended source Simulation using 5 point sources in broadband (8 wavelengths), source = 5λ/d The cosine term marks the profile (?) black: single pupil red: 3 replications equal normalisation Important when star > λ/2d (sun at 2 pc with 9 m -2-4 telescope at 6 nm) -15-1 -5 5 1 15 16 May 25 www.phy.hw.ac.uk/~phyhic 25
So far: Half-time Pupil Replication as such Analysis, error behaviour To come: Experiment Coronagraph Hyper telescope? 16 May 25 www.phy.hw.ac.uk/~phyhic 26
Experiment A first experiment to verify principle Interferometer beam: 2 coherent beams Monochromatic Circular pupils with Gaussian beams Effect in one dimension only Adjust shear 16 May 25 www.phy.hw.ac.uk/~phyhic 27
PSF, pupils: 5% overlap simulation experiment x 1 4 8 6 energy (J/s) x 1-11 18 16 H:\Work\Education\Erwan\5% OVERLAP PING\P PS F.bmp 1 angle (milli-arcseconds) 4 2-2 -4-6 -8 14 12 1 8 6 4 2 8 6 4 2 x 1 4-5 5 1 angle (milli-arcseconds) x 1 4 energy (J/s) x 1-1 3.5 2 4 6 8 1 H:\Work\Education\Erwan\5% OVERLAP PING\CP SF.bmp 5 3 1 angle (milli-arcseconds) -5 2.5 2 1.5 1 8 6 4-1 -1 -.5.5 1 x 1 5.5 2 4 6 8 1 16 May 25 angle (milli-arcseconds) www.phy.hw.ac.uk/~phyhic 28 2
Cross-sections 1 Blue: simulation, unreplicated Red: simulation, replicated Black: experimental energy (J /s ) 1-1 1-2 1-3 -1 -.8 -.6 -.4 -.2.2.4.6.8 1 angle (milli-arcs econds ) x 1 5 16 May 25 www.phy.hw.ac.uk/~phyhic 29
PSFs, pupils: no overlap angle (milli-arcseconds) simulation experiment x 1 4 energy (J/s) 8 6 4 2-2 -4-6 -8 x 1-11 H:\Work\Education\Erwan\CONTACT\PP S F.bmp 18 11 16 1 9 14 8 12 7 1 6 8 5 4 6 3 4 2 2 1 x 1 4-5 5 angle (milli-arcseconds) energy (J/s) x 1 4 x 1-1 2 4 6 8 1 12 14 H:\Work\Education\Erwan\CONTACT\CP S F.bmp angle (milli-arcseconds) 6 4 2-2 -4-6 3.5 3 2.5 2 1.5 1.5 1 8 6 4 2-8 -5 5 angle (milli-arcseconds) 2 4 6 8 1 12 14 16 May 25 www.phy.hw.ac.uk/~phyhic 3 x 1 4
Cross-sections 1 Blue: simulation, unreplicated Red: simulation, replicated Black: experimental energy (J /s ) 1-1 1-2 1-3 -1 -.8 -.6 -.4 -.2.2.4.6.8 1 angle (milli-arcs econds ) x 1 5 16 May 25 www.phy.hw.ac.uk/~phyhic 31
Replication Use 1 beamsplitter and mirrors Equal: # reflections in each arm polarisation optical path length Adjust last prism to vary replica separation => no shift error Can be cascaded Can be monolithic 16 May 25 www.phy.hw.ac.uk/~phyhic 32
Pupil Apodisation Used simple not optimised function for attenuation B: Super Gaussian x = off-axis angle c is adjusted to attenuate by 1-4 at pupil edge (both un- and replicated) Expect to broaden the image core reduce side-lobes ( ) B x = e ( ) 8 x c 16 May 25 www.phy.hw.ac.uk/~phyhic 33
Simulation Unapodised Black: unreplicated Green: 3-fold replication Apodised Red: unreplicated Blue: 3-fold replication Efficiency: 65% throughput Sidelobes suppressed Units: λ/d 16 May 25 www.phy.hw.ac.uk/~phyhic 34
Off-axis effects 5 mas 1 mas 15 mas Off-axis (planet) images will be distorted: Wavelength dependent => chromatic effects. will these obstruct spectroscopy? what other effects will this have - SNR? y: log(int) x: mas 16 May 25 www.phy.hw.ac.uk/~phyhic 35
Simulation Planets at 7λ/d and 21λ/d, each 1-1 brightness of host star 3 colours shown 76nm (blue), 872nm(green), 1nm (red&black) Log Intensity (normalised) 2 4 6 8 1 12 5 7 1 15 21 Off Axis Distance Units: λ/d (at 1 nm) 21 16 May 25 www.phy.hw.ac.uk/~phyhic 36
Star Stop added 5λ/d half-width solid star stop in image plane second pupil added, no Lyot stop Unreplicated: solid red, replicated: solid blue right: three wavelengths (coloured) -2-2 -4-4 -6-6 -8-8 -1-1 -12-12 5 1 15 2 5 1 15 2 16 May 25 www.phy.hw.ac.uk/~phyhic 37
Coronagraph Broadband (V-band in 8 wavelengths) -2-4 -6-8 -1-12 5 1 15 2 16 May 25 www.phy.hw.ac.uk/~phyhic 38
Sensitivity: amplitude At this accuracy, amplitude errors matter Simulations suggest that better than.1% is required to image exo-earths Simulation: random amplitude error 1-3 max. pixel size ~ 1 cm Log Intensity (normalised) -2-4 -6-8 -1-12 5 1 15 2 Off Axis Distance 16 May 25 www.phy.hw.ac.uk/~phyhic 39
Pixel size 1-3 random amplitude errors, with 25, 251, 251 pupil pixels (1, 1, 1 mm/pixel) Log Intensity (normalised) -2-4 -6-8 -1-12 Log Intensity (normalised) -2-4 -6-8 -1-12 Log Intensity (normalised) -2-4 -6-8 -1-12 5 1 Off Axis Distance 5 1 Off Axis Distance 5 1 Off Axis Distance 16 May 25 www.phy.hw.ac.uk/~phyhic 4
Sensitivity: phase Log Intensity (normalised) -2-4 -6-8 -1-12 Higher sensitivity to phase errors Simulation suggests that better than /1 is needed to image exo-earths Pixel size 1 cm Random phase error max. 5 1 15 2 Off Axis Distance 1 3 λ 1-4 λ 1-5 λ Log Intensity (normalised) -2-4 -6-8 -1-12 5 1 15 2 Off Axis Distance 5 1 15 2 Off Axis Distance 16 May 25 www.phy.hw.ac.uk/~phyhic 41 Log Intensity (normalised) -2-4 -6-8 -1-12
Hyper Telescope? Pupil Replication =/ / Hyper Telescope? Assessment of the hyper telescope principle using analysis like before simplified situation characterisation only adding to discussion... 16 May 25 www.phy.hw.ac.uk/~phyhic 42
Overview On axis: Pupil Replication = Hyper Telescope pupil replication Off axis: hyper telescope 16 May 25 www.phy.hw.ac.uk/~phyhic 43
Hyper Telescope 1-D, 3 pupils with equal spacing h between the telescopes and joined: ( ( ( ) ( )) ) ( 1 2cos 2 ( ) 1 sin ) sinc sin ( ) => similar to pupil replication but: => cos( ) now dependent on angle on axis (star light suppression) equal to PR ( ( ) ) T = A + dπ x + h d α λ dπ x α λ 16 May 25 www.phy.hw.ac.uk/~phyhic 44
HT Analysis PSF: α =.3 λ/d of single pupil, h = 2d (3d centre to centre) Pupil Replication (PR) Hyper Telescope (HT) 3 3 3 3 1 lo g o f n ormalise d intensit y 2 4 6 1 lo g o f n ormalise d intensit y 2 4 6 3 3 offaxis angle maxd 3 3 offaxis angle maxd 16 May 25 www.phy.hw.ac.uk/~phyhic 45
HT Analysis Same as last slide but: PSF: α = 1.6 λ/d of single pupil, Pupil Replication (PR) Hyper Telescope (HT) 3 3 3 3 1 lo g o f n ormalise d intensit y 2 4 6 1 lo g o f n ormalise d intensit y 2 4 6 3 3 offaxis angle maxd 3 3 offaxis angle maxd 16 May 25 www.phy.hw.ac.uk/~phyhic 46
Combine? HT-PR PR-HT 16 May 25 www.phy.hw.ac.uk/~phyhic 47
Analysis HT-PR: the hyper telescope is replicated 3 times: T HT THT PR = + 3 ( ( )) ( 1 2cos( 6π d x sin α λ )) PR-HT: the 3 replications are made in each of the hyper telescopes: THT TPR HT = + d x + h d 3 ( 1 2cos ( 6 π ( (( ) 1 ) sin ( α )) λ )) 16 May 25 www.phy.hw.ac.uk/~phyhic 48
HT-PR or PR-HT 3 3 3x3 pupils α =.3 λ/d 1 lo g o f n ormalise d intensit y 2 4 6 3 3 offaxis anglemaxd 3 3 3 3 1 lo g o f n ormalise d intensit y 2 4 6 1 lo g o f n ormalise d intensit y 2 4 6 3 3 offaxis angle maxd 3 3 offaxis angle maxd 16 May 25 www.phy.hw.ac.uk/~phyhic 49
H = 3 d, α =.1 λ/d 3 3 3 3 2 4 6 2 4 6 3 3 offaxis angle maxd 3 3 offaxis angle maxd 16 May 25 www.phy.hw.ac.uk/~phyhic 5 1l og of normalise dintensit y 1l og of normalise dintensit y 3 3 3 3 2 4 6 2 4 6 3 3 offaxis angle maxd 3 3 offaxis angle maxd 1l og of normalise dintensit y 1l og of normalise dintensit y
Evaluation? Based on this analysis only: Options: pupil replication hypertelescope combined other... Criteria: on-axis behaviour: star suppression off-axis behaviour: planet detection 16 May 25 www.phy.hw.ac.uk/~phyhic 51
Information Pupil Replication for Exo-Planet Imaging; A. H. Greenaway, F. H. P. Spaan and V. Mourai, The Astrophysical Journal Letters, Vol. 618-2, pp L165-L168, 1 January 25. Analysis of Pupil Replication (to be published). www.phy.hw.ac.uk/~phyhic energy (normalised) 1-2 -4 angle (lambda / D) 5-6 -8-1 -12-14 -5-16 -18-5 5 1 angle (lambda / D) 16 May 25 www.phy.hw.ac.uk/~phyhic 52-2