Amplitude and Phase Detection

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THALES RESEARCH & TECHNOLOGY FRANCE

This document and any data included are the property of THALES. They cannot be reproduced, disclosed or used without THALES'
pri
or written approval. ©THALES 2002. Modèle trtco V 5.1.0

Amplitude and Phase Detection

J
-
C Lehureau

Thales Research and Technology

THALES RESEARCH & TECHNOLOGY FRANCE

This document and any data included are the property of THALES. They cannot be reproduced, disclosed or used without THALES'
pri
or written approval. ©THALES 2002. Modèle trtco V 5.1.0

Frequency of electronic components

0.0001
0.001
0.01
0.1
1
10
100
1000
10000
100000
1950
1960
1970
1980
1990
2000
2010
2020
2030
Optics
Frequency (GHz)
Ge Si GaAs WDM

THALES RESEARCH & TECHNOLOGY FRANCE

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pri
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Heterodyne Detection

X

DS





|s+p|²
-
|s
-
p|²

Radio signal







Optical interference

THALES RESEARCH & TECHNOLOGY FRANCE

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pri
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Coherent
-
incoherent interference

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Power detection

s
int

=


N


p

s
shot
=

N

s
tot

=


s
int
2
+
s
shot
2
=

N *(1+ p)

N photons

p photon

s

THALES RESEARCH & TECHNOLOGY FRANCE

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pri
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Power detection

s
tot

=

N *(1+ p) is a quantum limited detector

if:


shot noise
>>
additive noise


Example of microbolometer:


NETD=50 mK on 2500µm²


NEP =.75 nW


NEW =30 pJ = 10
10
photons


The pump must be nearly 1 Joule per pixel!!


Example of CMOS addressed photodiode:


reading noise = 1000 electrons


N >> 1 million photons = 0.01 pJ

THALES RESEARCH & TECHNOLOGY FRANCE

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Amplitude and phase detection

signal


XOR

THALES RESEARCH & TECHNOLOGY FRANCE

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t

Physical measurement

Signal processing

+

wavefront
sensor

Image

Field

measurements

Synthesis

Propagation

model

Phase

calibration

Laser source

speckle

field

Phase detection & image reconstruction

THALES RESEARCH & TECHNOLOGY FRANCE

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pri
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Short range experimentation


Digital holography enables wavefront estimation on a great number of
pixels


12 bits 512x512 CCD frames


Synthesis by means of object rotation


overlapping holograms increases resolution


aberration correction by calculus

Pz
BS1
BS2
CCD
L1
O1
Scattering
Object
HeNe
laser
Z=1.5 m
D
Reference
wavefront
Object
wavefront
Z=50m

THALES RESEARCH & TECHNOLOGY FRANCE

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pri
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Black body radiation
0
2E-16
4E-16
6E-16
8E-16
1E-15
1.2E-15
1.4E-15
1.6E-15
1.8E-15
2E-15
0
9E+13
2E+14
3E+14
4E+14
4E+14
5E+14
6E+14
7E+14
8E+14
9E+14
1E+15
1E+15
1E+15
1E+15
1E+15
intensity
Thermal source

A mode is defined by geometrical extent and time
-
bandwidth:


the population of a mode is p= 1/(exp(h
n
/kT
-

1)

p=1% at peak

THALES RESEARCH & TECHNOLOGY FRANCE

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An example of phase detection

incoherent holography

FFT

CCD

Color filter

Quadrator

Integrator

At T=3300K,
l
=900nm, P
photon
=1%

For each shot:


S/N=
-
20dB

After 10000 shots

S/N= +20dB

THALES RESEARCH & TECHNOLOGY FRANCE

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signal

Faint correlation

Let us normalize the pump to unity:

each output gives a signal:


s1=s2=

p cos
f

where

p is the population of a mode


f

is a random phase

The correlation of the two outputs:


S= s1*s2 = p

is to be compared to the unity noise


One needs N>>1/p² samples to overcome

the noise

THALES RESEARCH & TECHNOLOGY FRANCE

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An astronomic example

2 telescopes make an observation at 100 light
-
years

The resolution of each is 1µRd i.e. 10 a.u./pixel

l

is chosen such that p~
1

(
l
=5
l
peak
)

Cross section of the star is 1/1 000 000 of a pixel

Light from a planet is 1/1 000 000 000 of the star


At 1000 billion samples/second:


the star generates correlation within 1s


the planet can be seen within 10000 days

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Image formation by a rotating linear antenna

The
N>>1/p² rules generates

a dramatic loss in information

capacity; this can be compensated

by generating more correlation

function than the number of
detectors

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%decoded %erreur capacity

Maximum entropy of low S/N

The capacity of a channel is

increased by erasing samples

below a threshold

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Conclusions


Modern infrared detectors (InP, QWIP) have a bandwidth which

allows the analysis of a significant part of optical spectrum.


Optical heterodyne power detection has the same theoretical

limit as quantum limited detector but will find application only

where detailed analysis of optical spectrum is needed.


Heterodyne detector is cheap: multichannel structure is possible


Phase and amplitude detection generates a non material link

between remote telescopes. The number of correlation function

varies as the square of detecting sites.


Computer correlation allow image formation with “a posteriori”

phase correction.


There is a need for information link/storage in the peta/exa byte

range