ghost imaging of space objects - nasa
TRANSCRIPT
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Ghost Imaging of Space Objects
Dmitry Strekalov, Baris Erkmen, Nan Yu
March 28, 2012 Pasadena, CA
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Challenges of Astronomy and Astrophysics
Time (hrs)
Francois et al., Nature 482, 195-198 (2012)
Earth-like planets finding
290 pc away
Gravitational lens detections
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The UMBC Ghost Imaging experiment
(x,y)
f
a1
a2
b
Photon pairs source
• Background suppression • Imaging of difficult to access objects • Dual-band imaging • Relaxed requirements on imaging optics
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Spontaneous Parametric Down Conversion
JPL 2001
Pump
Signal
Idler
Phase matching conditions:
321 ωωω =+
321
→→→
=+ kkk
(photon energy conservation)
(photon momentum conservation)
Wavelength
Ang
le
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Using thermal light Theory: Experiment:
x'
Object 50/50 beam splitter
Image
x2
x1
),(),()(),( 222111212121 xxhxxhxxxdxdxxG ′′′−′Γ′′= ∫∫
).,()(),(),( 1111111 objbobjobjaobj xxhxTxxhdxxxh ′=′ ∫
Transverse mode (speckle) size:
Mathematics of Ghost Imaging:
a
zx
πλ
2≈∆
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Can an object replace the beam splitter?
x
Object Image
x2
x1
),(),()(),( 222111212121 xxhxxhxxxdxdxxG ′′′−′Γ′′= ∫∫),()(),(),( 1111111 objbobjobjaobj xxhxRxxhdxxxh ′=′ ∫
),()(),(),( 2222222 objbobjobjaobj xxhxTxxhdxxxh ′=′ ∫
Object
k2
k1
Source
Shadow size:
star
star
d
L
πλ
2
obj
obj
d
L
πλ
2
Speckle size:
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Our model and approach
),(),()(),( 222111212121 xxhxxhxxxdxdxxG ′′′−′Γ′′= ∫∫),()(),(),( 1111111 objbobjobjaobj xxhxTxxhdxxxh ′=′ ∫
),()(),(),( 2222222 objbobjobjaobj xxhxTxxhdxxxh ′=′ ∫
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Gaussian absorber:
−
−=2
2
2exp1)(
obj
objobj R
xxT
50 cm 50 cm ρ ρ
Rs = 1 cm
Ro = 1, 2, 3 mm
3 mm
1 mm
3 mm 1 mm
No object
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Gaussian absorber
50 cm 50 cm
Rs = 1 cm Ro = 3 mm
∆R = 0, 3, 5, 10, 30 mm
10 30
0
(going off axis)
∆R (cm)
Spec
kle
wid
th (µ
m)
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Kepler 20e example
Time (hrs)
Francois et al., Nature 482, 195-198 (2012)
Planet displacement (star radia)
Flux
0.9998
1
2.55169 km Speckle size when occluded
Speckle size when not occluded 2.55198 km 0.999885
Dips to
0.9999
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In different regimes, the correlation measurement SNR can be below or above the direct intensity measurement SNR
Intensity measurement
0.1 photons/coincidence window
0.5 photons/coincidence window
1 photon/coincidence window
observation time = 100*coherence time
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Thin lens 50 cm 50 cm ρ ρ
Rs = 1 cm f, Ro
R0 = 20 cm
R0 = 5 mm
R0 = 2 mm
f = 1 m
f = -1 m
R0 = 20 cm
R0 = 5 mm
R0 = 2 mm
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50 cm 50 cm
Rs = 1 cm Ro = 3 mm f = 1 m
∆R
Thin lens (going off axis)
∆R (cm) Sp
eckl
e w
idth
(µm
) ∆R (cm)
Inte
nsity
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Application to gravity lenses and gas clouds
Gravity lenses are not thin lenses!
Lens Axicon Scwarzchild’s lens
= + +
R
Rs2≈α
2
4
12 sR
kRf ≈
Speckle size variation:
+
−≈∆
s
s
LL
LL
fd
d 11
α
R
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Summary and conclusions
Ghost Imaging - a “spooky” relative of the intensity interferometry – is a technique that works
Steps towards astronomy applications: • from quantum to natural light sources • from bucket to remote “fair sampling” detection • now, from beam splitter to sub-mode detection
What could be the objects? • Exoplanets • Gas or dust clouds • Gravitational lenses due to black holes Wavelength-specific, suitable for spectrally resolved imaging A possibility of distributing the “instrumental burden” between the space- and ground-based detectors. More resources to explore: higher-order correlations, information compression, computational imaging…