Ghost Imaging of Space Objects
Dmitry Strekalov, Baris Erkmen, Nan Yu
March 28, 2012 Pasadena, CA
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
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
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
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≈∆
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:
Our model and approach
),(),()(),( 222111212121 xxhxxhxxxdxdxxG ′′′−′Γ′′= ∫∫),()(),(),( 1111111 objbobjobjaobj xxhxTxxhdxxxh ′=′ ∫
),()(),(),( 2222222 objbobjobjaobj xxhxTxxhdxxxh ′=′ ∫
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
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)
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
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
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
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
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
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…