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…