Chaotic Imaging

PhD Student: Emiliano PudduTutor: Prof. A. Andreoni

XX Ciclo di DottoratoA.A. 2004/05

Email: Emiliano.Puddu@uninsubria.it

Index

Three wave interaction

Chaotic imaging

Image enhancement & recovery

Imaging Configurations

Maxwell’s equations for the three wave interaction

kzjajga=dzda exp*

231

2 3 2 1 2 32 g = ω ω ω η d

123 kkk=Δk

213 ω+ω=ω

...3)3(4220 EdEEP

2 *3 1

expda = jga a j kzdz

kzjajga=dzda exp21

3

k 3

k 2

k 1

z

E2

E1

E3

42 I Type OBaBβ

3k

k 2

k 1

k 3

k 2

k 1

Sum and Difference frequency

Lower frequency fields are injected: Sum frequency interaction

Higher frequency field is injected: Difference frequency interaction

Phases of the involved fields

a)

b)

c)

Virtual image

Virtual image

Real image

a) b) c)

O' O

L

BBO

telescope dO

CCD355 nm

1064 nm

O''

k3

k2

k1

Sum Frequency

532 nm

case a)

dO'

IMAGING CONFIGURATION: I

Real Object O, Virtual Image, O’, transformed into real O’’

O'O

LBBO

telescopedO

x

ldO'

CCD

355 nm

1064 nmO''

k3

k2

k1

Difference Frequency

532 nm

case b)

IMAGING CONFIGURATION : II

Real Object O, Virtual Image, O’, transformed into Real O’’

O BBO

dO'

CCD

355 nm

1064 nmO'

k3

k2

k1

532 nm

dO

case c)

Difference Frequency - Real Object

IMAGING CONFIGURATION : III

Real Object O, Real Image O’

O'O

L BBOdO

CCD

355 nm

1064 nmO''

k3

k2

k1

Difference Frequency

532 nmcase b)

2f 2f

IMAGING CONFIGURATION : IV

Real Object O, transformed into Virtual O’, Real Image O’’

dO’

What if….

…one of the injected beam has thermal statistic?

We realise the situation of…

Puddu et al., O. L. 30, 1294-1296, 2005

…chaotic imaging!

case b) at degeneracy

L1

L2

...

NLC

E1(ω)

E3(2ω)

E2(ω)

U0(x,y)

2f1

2f1 d

d/ 2f2

D

Case b) at degeneracy

Experimental result

The three holes are not recognizable!

L1

L2

...

NLC

E1(ω)

E3(2ω)

E2(ω)

U0(x,y)

2f1

2f1 d

d/ 2f2

D

Fourier optic: interpretation

Correlation protocol

Bondani, Puddu, Andreoni, J.M.O., in press

Geometria d’interazione

2 Ground Glass Plates

Correlation protocol II

6000 samples 250 samples

2

'

f d

ˆ ˆx y x y

Andreoni, Puddu, Bondani, Manuscript in preparation

2 2

, 3 3', ' , ', ' ', ' 'i jG i j a i j i j a i i j j

Phase – Matching conditions in the chaotic imaging

i

j

Image Enhancement

Shift and Average:add only the maps that respect the condition

2

'

f d

Averages over a sample of 7 correlations

Image Recovery

The same procedure is applied to an insufficient sample of images!

Results

Reduction of the noise:

Reduction of the number of the samples: 250 Vs 6000

02.0 Vs 01.0 0.06 Vs 0.10

6000 samples250 samples{

Perspectives:

Can chaotic imaging generate ghost imaging?

Can chaotic imaging be applied to cryptography?

I.E.N. ISTITUTO ELETTRONICO NAZIONALE

GALILEO FERRARIS

Dott. S. Castelletto Dott. I. Degiovanni