Towards optical intensity interferometry for high angular ...pnunez/defense.pdf · Introduction...

Introduction ACTs and γ-ray astronomy SII with IACTS The imaging problem Experimental efforts Closing

Towards optical intensity interferometry for highangular resolution stellar astrophysics

Paul D. NunezDept. of Physics & Astronomy

University of Utah

June 4 2012


Talk outline

Motivations.

Background.

Cherenkov telescope arrays.

The imaging problem: Phase recovery.

Simulations of future intensity interferometers.

Experimental efforts.

Conclusions.


Motivations for stellar intensity interferometry

0.1mas resolution

λ = 400nm

(Simulation by B.Freitag)

∼ 1km baseline

Disk-like stars: Diameters atdifferent wavelengths.

Rotating stars: Oblatenessand pole brightening.

Interacting binaries.

Mass loss and mass transfer.

Altair (CHARA)

α − Arae (VLTI)


Complex Degree of Coherence γ

γ(ri , ti ; rj , tj) ≡〈E ∗(ri , ti ) · E (rj , tj)〉√〈|E ∗(ri , ti )|2〉〈|E ∗(rj , tj)|2〉

Amplitude Interferometry Intensity Interferometry (I.I.)γ(x) = F [O(θ)] |γ(x)|2 = |F [O(θ)]|2

Star

E i

E j

.





Star

Inte

nsity

Phase

E i

E j

.





Star

Correlator

Analysis

Cij =<∆Ii ∆Ij><Ii><Ij>

|Fourier Trans|2

I iI j

.


Intensity Interferometry

Cij =< ∆Ii ∆Ij >

< Ii >< Ij >

Hanbury Brown & Twiss.1950’s

Correlation of Intensities.

No need for sub-wavelengthprecision.

Insensitive to turbulence.

Narrabri 1963


Gamma-ray astronomy

Primary γ ray initiates electromagneticcascade, which in turn emitsCherenkov radiation.

γ

e +

e −

VERITAS array in southern arizona


X-ray binary LSI+ 61◦303

Be star and compactcompanion.

TeV emission is maximum atapastron.

TeV attenuation due tointeractions with stellarphotons and circumstellarhydrogen.

Compact object is ablack hole.Nunez, P.D., LeBohec, S., &

Vincent, S. 2011, ApJ, 731,

105-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Rat

e (1

/min

)

Phase

2006-2007 Veritas


X-ray binary LSI+ 61◦303

Be star and compactcompanion.

TeV emission is maximum atapastron.

TeV attenuation due tointeractions with stellarphotons and circumstellarhydrogen.

Compact object is ablack hole.Nunez, P.D., LeBohec, S., &

Vincent, S. 2011, ApJ, 731,

105-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.2 0.4 0.6 0.8 1 1.2 1.4

Rat

e (1

/min

)

Phase

i=64°, nH=5x1019m-3

i=22°, nH=1x1020m-3

i=22°, nH=2x1020m-3

2006-2007 Veritas


Air Cherenkov telescope arrays

The Cherenkov Telescope Array (CTA)

ACTs are ideal SII receivers.

Easily adapted for optical SII (λ ∼ 400 nm)

Future arrays will provide thousands of simultanous baselines.

SII working group in CTA.


Array design and (u, v) coverage

λ = 400nm∆θmin ∼ λ

∆xmax∼ 0.01mas

∆θmax ∼ λ∆xmin

∼ 1mas



1.4

km


∆xmax∼ 0.01mas


∼ 1mas



35m


∆xmax∼ 0.01mas


∼ 1mas


Data simulation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Magnitude

-1200-1000-800 -600 -400 -200 0 200 400 600 800 1000

x [m]

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

1000

y [m

]

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200 1400 1600

|γ|

R [m]

0.9

0.95

1

1.05

0 20 40 60 80 100

|γ|

R [m]

0.1mas, mv = 3, 10 hrs (Nunez et al. 2012)


The imaging problem

γ ∼ Fourier transform of the radiance distribution of the star.

γ(x) ∼∫O(θ)e ikxθdθ

In SII we have access to the squared modulus of the complexdegree of coherence |γ|2

When |γ|2 is measured, the phase of the Fourier transform islost.

How can we recover images?


Some alternatives?

Model fitting.Maximum likelihood approach. (Thiebaut 2006).

Phase recovery

Three point correlations. 〈Ii Ij Ik〉 (Ribak 2006)

Analytic approach. (Holmes 2004).

The Fourier transform of an object of finite size (e.g. a star)is an analytic function.Relate magnitude to phase through Cauchy-Riemannequations.


Cauchy-Riemann phase recovery in 1-D (Holmes 2004)

γ(z) =∑j

I (j∆θ)z j ; z ≡ exp(i mk∆x∆θ) ≡ e iφ

z ≡ ξ + iψ ; γ ≡ Re iΦ

∂Φ

∂ψ=

∂ lnR

∂ξ≡ ∂s

∂ξ

∂Φ

∂ξ= −∂ lnR

∂ψ≡ − ∂s

∂ψ

∆s|| =∂s

∂ξ∆ξ +

∂s

∂ψ∆ψ =

∂Φ

∂ψ∆ξ − ∂Φ

∂ξ∆ψ ≡ ∆Φ⊥

Log-Magnitude differences ⇔ Phase differences.


1D example

0

1

2

3

4

5

6

7

8

9

10

0 100 200 300 400 500 600 700 800 900 1000

Mag

nitu

de

m

Magnitude 1D

Magnitude

-3

-2

-1

0

1

2

3

0 100 200 300 400 500 600 700 800 900 1000

Φ

m

Reconstructed ΦReal Φ

Phase

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7

∝ In

tens

ity

θ(k ∆x)-1

Reconstructed ImageReal Image

Image


1D examples

-3

-2

-1

0

1

2

3

0 100 200 300 400 500 600 700 800 900 1000

Φ

m


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7

∝ In

tens

ity

θ(k ∆x)-1


-3

-2

-1

0

1

2

3

0 100 200 300 400 500 600 700 800 900 1000

Φ

m


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.5 1.52 1.54 1.56 1.58 1.6 1.62 1.64 1.66 1.68 1.7

∝ In

tens

ity

θ(k ∆x)-1



Simulation/Analysis overview

Pristine

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200 1400 1600

|γ|

R [m]

0.9

0.95

1

1.05

0 20 40 60 80 100

|γ|

R [m]

Data Hermite fit

Cauchy-RiemannGerchberg-SaxtonMiRA

∂Φ∂ψ = ∂ lnR

∂ξ∂Φ∂ξ = −∂ lnR

∂ψ

arg min{χ2}

Thiebaut 2006


0

0.2

0.4

0.6

0.8

1

Reconstructed Image

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

θx [mas]

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

θ y [m

as]

0

0.5

1 0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.1 0.2 0.3 0.4 0.5 0.6

Rec

rad

ius

(mas

)

Real vs. Reconstructed radii

ErrorReal=Rec

Rec radius

-0.03-0.02-0.01

0 0.01 0.02 0.03

0 0.1 0.2 0.3 0.4 0.5 0.6Res

idua

l (m

as)

Real radius (mas)

PSF

0.185

0.19

0.195

0.2

0.205

0.19 0.195 0.2 0.205 0.21

Error close-up

0

0.2

0.4

0.6

0.8

1

Reconstructed Image

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1θx [mas]

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

θ y [m

as]

PSF

Pristine

1

1.2

1.4

1.6

1.8

2

1 1.2 1.4 1.6 1.8 2R

ec a

/bReal a/b

Real vs. Reconstructed a/b

Nunez, et. al. 2012,

MNRAS, 419, 172

0

0.2

0.4

0.6

0.8

1

Reconstructed Image

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1θx [mas]

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

θ y [m

as]

PSF

Pristine

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Re

c s

ep

ara

tio

n (

ma

s)

Real separation (mas)


Post-processing example: Star spots

mv = 3, 10 hrs of observation

∆T = 500◦K

Nunez et al. 2012, MNRAS


Post-processing example: Star spots

Effect of finite telescope size?

electronic noise, stray light?

Rou et al. in prep.


Attempts to measure |γ|2 in the lab

Light source .

Pinhole

.

BS PMT1

PMT2

..

Correlator.



Light source .

Pinhole

.

BS PMT1

PMT2

..

Correlator

Artificial star

.



Light source .

Pinhole

.

BS PMT1

PMT2

..

Correlator

Artificial star

Miniature telescopes

.



Light source .

Pinhole

.

BS PMT1

PMT2

..

Correlator

Artificial star

Miniature telescopes

Analog or digital

David Kieda



Light source .

Pinhole

.

BS PMT1

PMT2

..

Correlator

Artificial star



Light source .

Pinhole

.

BS PMT1

PMT2

..

Correlator

Artificial star

θ ≈ 1×10−4 m3m = 10−4rad

θ = 1.22λ/d

⇒ d = 6.5mm


Results with the pseudo-thermal light source

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-15 -10 -5 0 5 10 15

|γ|2

Baseline (mm)

0.2 mm0.3 mm0.5 mm


Results with the pseudo-thermal light source

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-15 -10 -5 0 5 10 15

|γ|2

Baseline (mm)

0.2 mm0.3 mm0.5 mm

.

d = 1.22λ/θ


Imaging from autocorrelation data

Laser Beam expander .

Mask

.

.

Rough surface

.

CCD

.

.

.

CPU

In collaboration with Ryan Price and Erik Johnson. .




Mask

.

.

Rough surface

.

CCD

.

.

.

CPU

Artificial star





Mask

.

.

Rough surface

.

CCD

.

.

.

CPU

Speckle image





Mask

.

.

Rough surface

.

CCD

.

.

.

CPU

Speckle image AutocorrelationAutocorrelation





Mask

.

.

Rough surface

.

CCD

.

.

.

CPU

Speckle image AutocorrelationAutocorrelation Reconstruction

Analysis





Mask

.

.

Rough surface

.

CCD

.

.

.

CPU



StarBase


StarBase camera


Starting observations of Spica


Starting observations of Spica

-100

-80

-60

-40

-20

0

20

40

0 500 1000 1500 2000

Dig

ital c

ount

s

Time (ns)

Channel 1Channel 2

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0 50 100 150 200 250 300 350 400

Cor

rela

tion

Time lag (ns)

Analyzed 1 s of data.

Need several hours of data to detect a correlation.

Expect to see modulation of correlation as a function of time.


Conclusions

Fast electronics and IACT arrays will allow to measure |γ|2

SII will provide high angular resolution images of stars.

Advantages when compared to amplitude interferometry.

Phase can be recovered via several techniques.

Images can be used for stellar astrophysics.

Experimental efforts allow to understand the advantages anddifficulties of modern SII.


Thanks to:

Stephan LeBohec, Dave Kieda and Janvida Rou.

Lina Peralta.

Physics dept: Jackie Hadley, Heidi Frank.

Michelle Hui, Gary Finnegan, Nick Borys ...

...

THE END


JUST IN CASE


Two component Fourier model (Hanbury Brown 1974)Detected currents at A and B

iA = KA(E1 sin(ω1t + φ1) + E2 sin(ω2t + φ2))2

iB = KB(E1 sin(ω1(t + d1/c) + φ1) + E2 sin(ω2(t + d2/c) + φ2))2

Band pass of electronics ∆f ≈ 100MHz

iA = KAE1E2 cos((ω1 − ω2)t + (φ1 − φ2))

iB = KBE1E2 cos((ω1 − ω2)t + (φ1 − φ2) + ω1d1/c − ω2d2/c)

iA and iB are correlated.


Intensity fluctuations and correlations⟨∆n2

⟩=〈n〉 + 〈n〉2 τc

T

Shot noise Wave noise

0

0.02

0.04

0.06

0.08

0.1

0.12

0 5 10 15 20 25 30 35 40

P(N

)

(N) Counts per electronic time resolution

PoissonSuper Poisson

Fit

Wave noise is small but correlatedbetween neighboring detectors.


Cauchy-Riemann phase recovery (1D)

γ(m∆x) =∑j

I (j∆θ)exp(i mk∆x j∆θ)

γ [z(m∆x)] =∑j

I (j∆θ)z j ; z ≡ exp(i mk∆x∆θ) ≡ e iφ

z ≡ ξ + iψ ; γ ≡ Re iΦ (1)

∂Φ

∂ψ=

∂ lnR

∂ξ≡ ∂s

∂ξ

∂Φ

∂ξ= −∂ lnR

∂ψ≡ − ∂s

∂ψ


Cauchy-Riemann phase recovery

γ(m∆x) =∑j

I (j∆θ)exp(i mk∆x j∆θ) (2)

γ [z(m∆x)] =∑j

I (j∆θ)z j ; z ≡ exp(i mk∆x∆θ) ≡ e iφ (3)

z ≡ ξ + iψ ; γ ≡ Re iΦ (4)

∂Φ

∂ψ=

∂ lnR

∂ξ≡ ∂s

∂ξ(5)

∂Φ

∂ξ= −∂ lnR

∂ψ≡ − ∂s

∂ψ(6)


∆sξ =∂s

∂ξ∆ξ =

∂Φ

∂ψ∆ξ (7)

∆sψ =∂s

∂ψ∆ψ = −∂Φ

∂ξ∆ψ (8)

(9)

Since |z | = 1 ⇒ we can only access to the log-magnitude s alongthe unit circle in the ξ − ψ plane.

∆s|| =∂s

∂ξ∆ξ +

∂s

∂ψ∆ψ =

∂Φ

∂ξ(−∆ψ) +

∂Φ

∂ψ∆ξ ≡ ∆Φ⊥


Φ is in general a solution to the Laplace equation in the ξ − ψplane.

Φ(φ) =∑j

ajcos(jφ) + bjsin(jφ) (10)

∆Φ⊥(φ) =∑j

{(1− 2sin(∆φ/2))j − 1

}(ajcos(jφ) + bjsin(jφ))

(11)

There is a relation between the log-magnitude differences andthe phase.

There will be ambiguities in the phase were the magnitude iszero.

Reconstructed phase will have an unknown gross piston andtilt.

Towards optical intensity interferometry for high angular ...pnunez/defense.pdf · Introduction...

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