ECEG398 Quantum Optics Course Notes Part 2: Thermal Imagers Prof. Charles A. DiMarzio and Prof.

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Transcript ECEG398 Quantum Optics Course Notes Part 2: Thermal Imagers Prof. Charles A. DiMarzio and Prof. 

ECEG398 Quantum Optics
Course Notes
Part 2: Thermal Imagers
Prof. Charles A. DiMarzio
and Prof. Anthony J. Devaney
Northeastern University
Spring 2006
February 2006
Chuck DiMarzio, Northeastern University
10842-2-1
Thermal Fields
• Mean Number (Text Eq.2.141): n 
1
e
h / k B T
1
• Std. Deviation (Text Eq. 2.149):   n  n
• Energy Density (Text Eq. 2.151):
4h 3
1
U    hn     3 h / kBT
c e
1
February 2006
Chuck DiMarzio, Northeastern University
10842-2-2
2
Single-Mode Mean
February 2006
Chuck DiMarzio, Northeastern University
10842-2-3
Single Mode SNR
SNR :
Red Solid : T 300 K,
Grn Dash : 5000 K
Upper Trace is Poisson
0.1
0.001
0.00001
0.1mm
lambda , Wavelength
100
February 2006
500
1000
5000 10000
50000100000.
Chuck DiMarzio, Northeastern University
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, nm
Spectral Radiant Exitance
U
M   hn c
Watch the Units:
dM
dM
M 
 2
 2M 
d
d
M 
February 2006
dM d dM
c dM
c

 2
 2 M
d
d d
 d 
Chuck DiMarzio, Northeastern University
10842-2-5
Signal & Noise Radiant Exitance
M   hn c
Spect . Rad . Ex ., W m^3:
Red Solid : T 300 K,
Grn Dash : 5000 K
1.
10
1.
10
1.
M  ( noise)  h n  n c
2
13
10
10
7
10000
10
0.01
100
February 2006
200
500
1000
2000
5000 10000
Chuck DiMarzio, Northeastern University
lambda , Wavelength
, nm
10842-2-6
Lambert’s Law
A’
A
February 2006
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Spectral Radiance
z
dq
q
y
df
f
x
February 2006
Chuck DiMarzio, Northeastern University
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M , Spectral Radiant Exitance, W/m /  m
Black-Body Equation (1)
10
10
5
10
0
10
-5
10
-1 0
2
10
February 2006
10
Chuck DiMarzio, Northeastern University
-1
0
1
10
10
 , Wavelength,  m
10
2
10842-2-9
2
/ m
M, Spectral Radiant Exitance, W/m
Black Body Equations (2)
February 2006
10
10
10
5
10
0
10
-5
10
-10
10000
5000
2000
10
500
1000
-1
T=300k
0
1
10
10
 , Wavelength,  m
Chuck DiMarzio, Northeastern University
10
2
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Solar Irradiance on Earth
Data from The Science of Color, Crowell, 1953
3000
Exoatmospheric
Sea Level
filename=m1695.m
5000 K Black Body Normalized to 1000 W/m 2
2500
E , Spectral Irradiance, W/m 2/ m
6000 K Black Body Normalized to 1560 W/m 2
2000
1500
1000
500
0
0
February 2006
200
400
600
800 1000 1200
, Wavelength, nm
1400
Chuck DiMarzio, Northeastern University
1600
1800
2000
10842-2-11
Typical Outdoor Radiance Levels
Ultraviolet
Visible
Near IR
6000K Sun
6.9 G Lux
Sunlit
Cloud
6.9 k Lux
Blue
Sky
Mid IR
Far IR
300K
night sky
Atmospheric Passbands
February 2006
Chuck DiMarzio, Northeastern University
10842-2-12
.5
0 -1
10
6
0
1
0
1
2
10 T = 500 K 10
10
4
2
0 -1
10
February 2006
T = 300 K
1
D M/Delta T
D M/Delta T
Thermal Imaging
Chuck DiMarzio, Northeastern University
10
10
, Wavelength,  m
10842-2-13
10
2
Etendue
P    L dW dA
AW is
Constant
AW
Viewed
W  2 1  1  NA  by Pixel


2
NA of
Area of PRC Detector Lens
W   NA
2
Single Mode
NA   / d
WA  
2
February 2006
NA of
Objective
NA of
PRC
Chuck DiMarzio, Northeastern University
Pixel
Area
10842-2-14
Spectral Flux (Power) Per Mode
Pl , W m mode :
Red Solid : T 300 K,
Grn Dash : 5000 K
1
0.001
1.
10 6
1.
10
9
1.
10 12
1.
10 15
lambda , Wavelength
100
February 2006
200
500
1000
2000
5000
Chuck DiMarzio, Northeastern University
, nm
10000
10842-2-15
Probability Distributions
(Delta)
Laser
Mode
Re(E)
Thermal
Mode
Many
Thermal
Modes
February 2006
Im(E)
(Delta)
|E|
(Gaussian)
(Rayleigh)
Summed
on
Detector
Chuck DiMarzio, Northeastern University
(Poisson)
|E|2
n
(BoseEinstein)
(Exponential)
(Poisson)
10842-2-16
Detected Photons (Signal & Bkg)
nDet
Ps
PBKG
AW 1
 q   D n c
 B
Filter
Amp
Preamp
q
BPF
PNoise
February 2006
Chuck DiMarzio, Northeastern University
10842-2-17
Detector Examples: Spectral
Photon Radiance
10464-3-32
February 2006
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Detector Examples: Total
Background Power
10464-3-31
February 2006
Chuck DiMarzio, Northeastern University
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Noise Photons (Bkg. Limited)
nDet
AW 1
 q   D n c
 B
AW 1
  q  D n c
 B
February 2006
Chuck DiMarzio, Northeastern University
10842-2-20
Noise-Equivalent Power
nDet
P
LAW
 q
 q
hB
hB

NEP
  q
hB
LAW
  q
hB
LAW 1
hB LAW
NEP  hB q

hB q
q
February 2006
Chuck DiMarzio, Northeastern University
10842-2-21
Detector Examples: NEP
10464-3-3
February 2006
Chuck DiMarzio, Northeastern University
10842-2-22
D-Star
NEP 
NEP 
February 2006
hB LAW
q
ABD 
*
D

h L D W AB
q
*
max
D
Chuck DiMarzio, Northeastern University
q

h LW
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Detector Examples:
Detectivity, D*
10464-3-34
February 2006
Chuck DiMarzio, Northeastern University
10842-2-24
Estimating the Temperature
nDet
n
AW 1
 q   D n c
 B
e
1
e
h / k B T
1
h / k BT
h
2
k BT
dn
 h / k T
C
2
dT e B  1
AW 1
DnDet   q  D Cc
DT 
 B
February 2006
Chuck DiMarzio, Northeastern University
10842-2-25
Noise-Equivalent Delta T
AW 1
DnDet   q  D Cc
DT 
 B
AW 1
  q  D n c
 B
AW 1
NEDT 
  q   D Cc
 B
February 2006
Chuck DiMarzio, Northeastern University
10842-2-26
Calculating NEDT
AW 1
AW 1
NEDT 
q  D n c
 q  D Cc
 B
 B
B
n
NEDT  
q  D cAW C
T=300Kelvin, q=0.8, B=30 Hz, D=1m, A=(10mm)2, W=0.1 sr
7 X 106 Photons/Kelvin
February 2006
NEDT=5 mKelvin
Chuck DiMarzio, Northeastern University
10842-2-27