Basic radiometry and SNR eq. for CCD, ICCD - UNIS
Basic radiometry and SNR eq. for CCD, ICCD - UNIS
Basic radiometry and SNR eq. for CCD, ICCD - UNIS
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<strong>Basic</strong> <strong>radiometry</strong> <strong>and</strong> <strong>SNR</strong><br />
<strong>eq</strong>uations <strong>for</strong> <strong>CCD</strong>, I<strong>CCD</strong> <strong>and</strong><br />
EM<strong>CCD</strong> imagers<br />
Urban Brändström, 1<br />
1 Swedish Institute of Space Physics, Kiruna, Sweden<br />
Presentation at:<br />
http://alis.irf.se/˜urban/AGF351/Braendstroem-<strong>UNIS</strong>.pdf<br />
<strong>UNIS</strong> 2011-11-15 – p. 1
In memoriam<br />
Professor Ingrid S<strong>and</strong>ahl (1949-2011) <strong>UNIS</strong> 2011-11-15 – p. 2
This is about taking pictures of<br />
darkness, or. . .<br />
<strong>UNIS</strong> 2011-11-15 – p. 3
“Hunting photons with a spoon”<br />
<strong>UNIS</strong> 2011-11-15 – p. 4
Radiometry<br />
<strong>UNIS</strong> 2011-11-15 – p. 5
Radiometry vs. photometry<br />
Holst [1998] defines the term <strong>radiometry</strong>, as the<br />
“energy or power transfer from a source to<br />
a detector”<br />
<strong>UNIS</strong> 2011-11-15 – p. 6
Radiometry vs. photometry<br />
Holst [1998] defines the term <strong>radiometry</strong>, as the<br />
“energy or power transfer from a source to<br />
a detector”<br />
while photometry is defined as<br />
“the transfer from a source to a detector<br />
where the units of radiation have been<br />
normalised to the spectral sensitivity of<br />
the eye.”<br />
<strong>UNIS</strong> 2011-11-15 – p. 6
Radiometry vs. photometry<br />
Holst [1998] defines the term <strong>radiometry</strong>, as the<br />
“energy or power transfer from a source to<br />
a detector”<br />
while photometry is defined as<br />
“the transfer from a source to a detector<br />
where the units of radiation have been<br />
normalised to the spectral sensitivity of<br />
the eye.”<br />
Un<strong>for</strong>tunately the term photometry is often used<br />
instead of <strong>radiometry</strong><br />
<strong>UNIS</strong> 2011-11-15 – p. 6
Radiometry<br />
“Mathematics is often called the queen of the<br />
sciences. Radiometry should then be called the<br />
waiting maid or servant. It is not especially elegant;<br />
it is not very popular, has not been trendy; but it is<br />
essential in almost every part of optical<br />
engineering.” Wolfe [1998]<br />
<strong>UNIS</strong> 2011-11-15 – p. 7
Solid angle<br />
The solid angle Ω sweeps out the area A on the<br />
unit sphere (4π)<br />
Ω = A<br />
[sr]<br />
r2 Think of it as a 3D generalisation of the radian<br />
(arc length on the unit circle)<br />
<strong>UNIS</strong> 2011-11-15 – p. 8
Photon flux:<br />
in energy units:<br />
Flux<br />
Φγ = ∂N<br />
∂t<br />
ΦE = hc<br />
λ<br />
<br />
photons<br />
s<br />
∂N<br />
∂t [W]<br />
<strong>UNIS</strong> 2011-11-15 – p. 9
Radiance<br />
Also known as radiant sterance<br />
In energy units:<br />
LE = ∂2 <br />
Φ(λ) W<br />
∂As∂Ω m2 <br />
sr<br />
In quantum units:<br />
Lγ = λ<br />
hc LE<br />
<br />
photons<br />
s m2 <br />
sr<br />
<strong>UNIS</strong> 2011-11-15 – p. 10
Spectral radiance<br />
Also known as spectral radiant sterance<br />
In energy units:<br />
LλE = ∂L<br />
<br />
W<br />
∂λ m2 <br />
µm sr<br />
In quantum units:<br />
Lλγ = λ<br />
hc LλE<br />
<br />
photons<br />
s m2 <br />
µm sr<br />
<strong>UNIS</strong> 2011-11-15 – p. 11
Spectral radiant emittance<br />
Also known as spectral radiant exitance<br />
Mλγ = ∂Φ<br />
<br />
photons<br />
=<br />
∂As s m2 <br />
Flux per source area.<br />
What you get from a calibration source.<br />
In energy units:<br />
MλE = hc<br />
λ Mλγ<br />
<br />
W<br />
m2 µm sr<br />
<br />
<strong>UNIS</strong> 2011-11-15 – p. 12
Spectral irradiance<br />
Also known as spectral radiant incidance<br />
Eλe = ∂Φ<br />
∂A =<br />
<br />
photons<br />
s m2 <br />
Flux per detector area.<br />
What you get on a detector (or whatever)<br />
In energy units:<br />
EλE = hc<br />
λ Eλγ<br />
<br />
W<br />
m2 µm sr<br />
<br />
<strong>UNIS</strong> 2011-11-15 – p. 13
Transmittance<br />
T = <br />
∀X<br />
TX(λ) = TaToTf . . .<br />
<strong>UNIS</strong> 2011-11-15 – p. 14
At apperture:<br />
Eγapp<br />
= Φγapp<br />
Aapp<br />
Irradiance<br />
= LγAsTaΩds<br />
Aapp<br />
=<br />
<br />
photons<br />
s m 2<br />
At image plane (assuming circular apperture):<br />
Eγi<br />
As<br />
= Lγ<br />
<br />
photons<br />
=<br />
s m2 (1)<br />
<br />
= Φγapp<br />
Ai<br />
Ai<br />
T πd2 app<br />
4r 2 s<br />
<strong>UNIS</strong> 2011-11-15 – p. 15
Photometric units<br />
Φv = KM<br />
750nm<br />
380nm<br />
V (λ)Mp(λ)dλ [lm]<br />
scoptic—rods photoptic—cones After Holst [1998]<br />
<strong>UNIS</strong> 2011-11-15 – p. 16
Photometric units<br />
scoptic—rods (KM = 1746 lm/W) photoptic—cones<br />
<strong>UNIS</strong> 2011-11-15 – p. 17
Photometric units<br />
Φv lm luminous flux<br />
Lv cd/m 2 or nits luminance<br />
Mv lux or lm/m 2 luminous emmitance<br />
Ev lux or lm/m 2 illumniance<br />
<strong>UNIS</strong> 2011-11-15 – p. 18
The foot-lambert<br />
A foot-lambert or footlambert (fL, sometimes fl or<br />
ft-L) is a unit of luminance in U.S. customary<br />
units <strong>and</strong> some other unit systems. A<br />
foot-lambert <strong>eq</strong>uals 1/π c<strong>and</strong>ela per square foot,<br />
or 3.426 c<strong>and</strong>ela per square meter (the<br />
corresponding SI unit).<br />
1 [ftL] = 1<br />
π<br />
cd<br />
ft 2<br />
<br />
≈ 3.426<br />
cd<br />
m 2<br />
<br />
<strong>UNIS</strong> 2011-11-15 – p. 19
The Rayleigh<br />
<strong>UNIS</strong> 2011-11-15 – p. 20
The Rayleigh (1)<br />
Consider a cylindrical column of cross-sectional<br />
area 1 m 2 extending away from the detector into<br />
the source.<br />
The volume emission rate from a volume<br />
element of length dl at distance l is<br />
ǫ(l, t, λ) photons m −3 s −1 . The contribution to Lγ is<br />
given by:<br />
(2)<br />
dLγ =<br />
ǫ(l, t, λ)<br />
4π<br />
dl<br />
<br />
photons<br />
s m2 <br />
sr<br />
<strong>UNIS</strong> 2011-11-15 – p. 21
The Rayleigh (2)<br />
Integrating along the line of sight l [m]:<br />
∞<br />
(3) 4πLγ = ǫ(l, t, λ)dl<br />
0<br />
This quantity is the column emission rate, which<br />
Hunten et al. [1956] proposed as a radiometric unit<br />
<strong>for</strong> the aurora <strong>and</strong> airglow.<br />
<strong>UNIS</strong> 2011-11-15 – p. 22
The Rayleigh (3)<br />
In SI-units the Rayleigh becomes<br />
[Baker <strong>and</strong> Romick, 1976]:<br />
(4)<br />
1 [Rayleigh] ≡ 1 [R] 10 10<br />
<br />
photons<br />
s m 2 (column)<br />
The word column denotes the concept of an<br />
emission-rate from a column of unspecified<br />
length, as discussed above. It should be noted<br />
that the Rayleigh is an apparent emission rate,<br />
not taking absorption or scattering into account.<br />
<br />
<strong>UNIS</strong> 2011-11-15 – p. 23
The Rayleigh (4)<br />
However (un<strong>for</strong>tunately. . . )<br />
“the Rayleigh can be used as defined without any<br />
commitment as to its physical interpretation, even<br />
though it has been chosen to make interpretation<br />
convenient.” Hunten et al. [1956]<br />
And then there is the clarifications by: Baker<br />
[1974]; Baker <strong>and</strong> Romick [1976]; Chamberlain [1995]<br />
<strong>UNIS</strong> 2011-11-15 – p. 24
By now you should realized<br />
that. . .<br />
<strong>UNIS</strong> 2011-11-15 – p. 25
. . . God said:<br />
Go to, let us go down, <strong>and</strong> there confound their<br />
language, that they may not underst<strong>and</strong> one<br />
another’s speech. [Bible Gen11:7]<br />
<strong>UNIS</strong> 2011-11-15 – p. 26
. . . God said:<br />
Go to, let us go down, <strong>and</strong> there confound their<br />
language, that they may not underst<strong>and</strong> one<br />
another’s speech. [Bible Gen11:7]<br />
And there was: stilb, Rayleighs, footlamberts, Irradiance,<br />
spectral-radiant sterance, lumens, lux, c<strong>and</strong>ela, <strong>radiometry</strong>,<br />
nit, luminance, illuminance, emittance, apostilb, phot, skot,<br />
lambert, foot-c<strong>and</strong>le, photometry, DIN, ASA, ISO. . .<br />
<strong>UNIS</strong> 2011-11-15 – p. 26
. . . God said:<br />
Go to, let us go down, <strong>and</strong> there confound their<br />
language, that they may not underst<strong>and</strong> one<br />
another’s speech. [Bible Gen11:7]<br />
And there was: stilb, Rayleighs, footlamberts, Irradiance,<br />
spectral-radiant sterance, lumens, lux, c<strong>and</strong>ela, <strong>radiometry</strong>,<br />
nit, luminance, illuminance, emittance, apostilb, phot, skot,<br />
lambert, foot-c<strong>and</strong>le, photometry, DIN, ASA, ISO. . .<br />
—Help! We are sinking!<br />
<strong>UNIS</strong> 2011-11-15 – p. 26
<strong>and</strong> now. . .<br />
<strong>UNIS</strong> 2011-11-15 – p. 27
The 4π confusion<br />
<strong>UNIS</strong> 2011-11-15 – p. 28
The 4π confusion<br />
There<strong>for</strong>e, we propose that photometric<br />
measurements of the airglow <strong>and</strong> aurora be<br />
reported in terms of 4πB rather than the surface<br />
brightness B itself. Further, we suggest that 4πB<br />
be given the unit “rayleigh” (symbol R), where B is<br />
in units of 10 6 quanta cm −2 s −1 sr −1 . Hence<br />
1 R = 10 6 quanta cm −2 (column) −1 s −1 .<br />
Hunten et al. [1956]<br />
<strong>UNIS</strong> 2011-11-15 – p. 29
The 4π confusion<br />
There<strong>for</strong>e, we propose that photometric<br />
measurements of the airglow <strong>and</strong> aurora be<br />
reported in terms of 4πB rather than the surface<br />
brightness B itself. Further, we suggest that 4πB<br />
be given the unit “rayleigh” (symbol R), where B is<br />
in units of 10 6 quanta cm −2 s −1 sr −1 . Hence<br />
1 R = 10 6 quanta cm −2 (column) −1 s −1 .<br />
Hunten et al. [1956]<br />
So does both Hunten et al. [1956] <strong>and</strong> Chamberlain<br />
[1995] claim that 4π × 10 6 = 10 6 ???<br />
<strong>UNIS</strong> 2011-11-15 – p. 29
Can we agree on this?<br />
The apparent radiance (Lγ) can be obtained from<br />
the column emission rate I (in Rayleighs)<br />
according to Baker <strong>and</strong> Romick [1976]:<br />
(5)<br />
Lγ = 1010 I<br />
4π<br />
photons<br />
s m 2 sr<br />
<br />
<strong>UNIS</strong> 2011-11-15 – p. 30
Can we agree on this?<br />
The apparent radiance (Lγ) can be obtained from<br />
the column emission rate I (in Rayleighs)<br />
according to Baker <strong>and</strong> Romick [1976]:<br />
(7)<br />
Or is it:<br />
(8)<br />
Lγ = 1010 I<br />
4π<br />
Lγ = 10 10 I<br />
photons<br />
s m 2 sr<br />
<br />
<br />
photons<br />
s m2 <br />
sr<br />
<strong>UNIS</strong> 2011-11-15 – p. 30
Still confused. . .<br />
. . . but at a different level.<br />
<strong>UNIS</strong> 2011-11-15 – p. 31
Signal<br />
<strong>UNIS</strong> 2011-11-15 – p. 32
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
<strong>UNIS</strong> 2011-11-15 – p. 33
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
• Apperture of the optics<br />
<strong>UNIS</strong> 2011-11-15 – p. 33
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
• Apperture of the optics<br />
• Area of detector (pixel-area <strong>for</strong> imagers)<br />
<strong>UNIS</strong> 2011-11-15 – p. 33
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
• Apperture of the optics<br />
• Area of detector (pixel-area <strong>for</strong> imagers)<br />
• Number of photoelectrons collected in a pixel<br />
n −<br />
e = QE(λ)Eγi γ tintApix<br />
−<br />
e <br />
(15)<br />
<strong>UNIS</strong> 2011-11-15 – p. 33
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
• Apperture of the optics<br />
• Area of detector (pixel-area <strong>for</strong> imagers)<br />
• Number of photoelectrons collected in a pixel<br />
n −<br />
e = QE(λ)Eγi γ tintApix<br />
−<br />
e <br />
(17)<br />
(18)<br />
n e − γ ≈ QE(λ)TtintApix<br />
10 10 I<br />
16f 2 #<br />
e − <br />
<strong>UNIS</strong> 2011-11-15 – p. 33
Noise<br />
<strong>UNIS</strong> 2011-11-15 – p. 34
What is noise?<br />
<strong>UNIS</strong> 2011-11-15 – p. 35
Some peoples noise are other<br />
peoples signal<br />
<strong>UNIS</strong> 2011-11-15 – p. 36
Notation<br />
〈X〉 2 variance of X<br />
〈X〉 st<strong>and</strong>ard deviation of X<br />
X mean value of X<br />
Photon arrival is Poisson distributed<br />
It can be shown that <strong>for</strong> a Poisson distributed<br />
signal variance is <strong>eq</strong>ual to the mean<br />
<strong>UNIS</strong> 2011-11-15 – p. 37
<strong>CCD</strong> principle of operation<br />
After Janesick et al. [1987]<br />
<strong>UNIS</strong> 2011-11-15 – p. 38
E2V TECH <strong>CCD</strong>201<br />
<strong>UNIS</strong> 2011-11-15 – p. 39
What is the <strong>SNR</strong> of an ideal<br />
photon detector?<br />
<strong>UNIS</strong> 2011-11-15 – p. 40
<strong>CCD</strong>-noise sources<br />
<strong>UNIS</strong> 2011-11-15 – p. 41
(19)<br />
〈n e −<br />
<strong>CCD</strong><br />
〉 =<br />
<strong>CCD</strong> noise<br />
<br />
〈n −<br />
e 〉 s 2 + 〈n −<br />
e 〉 r 2 + 〈n −<br />
e 〉 p 2 e − <br />
RMS<br />
<strong>UNIS</strong> 2011-11-15 – p. 42
(20)<br />
(21)<br />
(22)<br />
〈n e − s 〉 =<br />
=<br />
Shot Noise<br />
<br />
<br />
CTE N<br />
CTE N<br />
≈<br />
<br />
〈n −<br />
e 〉 γ 2 + 〈n −<br />
ed 〉2<br />
<br />
<br />
n e − γ + n e −<br />
d<br />
<br />
n e − γ + n e −<br />
d<br />
<br />
≈<br />
=<br />
<strong>UNIS</strong> 2011-11-15 – p. 43
<strong>CCD</strong> Noise sources<br />
After Holst [1998] <strong>UNIS</strong> 2011-11-15 – p. 44
(23)<br />
(24)<br />
〈n e − p 〉 =<br />
Pattern Noise<br />
<br />
〈n −<br />
eFPN 〉2 + 〈n −<br />
ePRNU 〉2 ≈ 〈n −<br />
e 〉 ≈<br />
PRNU<br />
≈ Un e − γ ≈ n e − γ<br />
√ ne − max<br />
e − RMS<br />
<br />
<strong>UNIS</strong> 2011-11-15 – p. 45
(25)<br />
〈n −<br />
e 〉 ≈<br />
<strong>CCD</strong><br />
<strong>CCD</strong> Noise<br />
<br />
n −<br />
e + n −<br />
γ ed + 〈ne − r 〉2 e − <br />
RMS<br />
<strong>UNIS</strong> 2011-11-15 – p. 46
Signal-to-noise ratio <strong>for</strong> a <strong>CCD</strong><br />
• Measured signal-to-noise ratio:<br />
(26)<br />
<strong>SNR</strong><strong>CCD</strong> = DN signal<br />
DN noise<br />
≈ n e − γ<br />
〈n e −<br />
<strong>CCD</strong> 〉<br />
<strong>UNIS</strong> 2011-11-15 – p. 47
Signal-to-noise ratio <strong>for</strong> a <strong>CCD</strong><br />
• Measured signal-to-noise ratio:<br />
(29)<br />
• thus <strong>for</strong> a <strong>CCD</strong>:<br />
(30)<br />
<strong>SNR</strong><strong>CCD</strong> = DN signal<br />
DN noise<br />
<strong>SNR</strong><strong>CCD</strong> ≈<br />
≈ n e − γ<br />
〈n e −<br />
<strong>CCD</strong> 〉<br />
n −<br />
eγ <br />
n −<br />
e + n −<br />
γ ed + 〈ne − r 〉2<br />
<strong>UNIS</strong> 2011-11-15 – p. 47
Signal-to-noise ratio <strong>for</strong> a <strong>CCD</strong><br />
• Measured signal-to-noise ratio:<br />
(32)<br />
• thus <strong>for</strong> a <strong>CCD</strong>:<br />
(33)<br />
<strong>SNR</strong><strong>CCD</strong> = DN signal<br />
DN noise<br />
<strong>SNR</strong><strong>CCD</strong> ≈<br />
≈ n e − γ<br />
〈n e −<br />
<strong>CCD</strong> 〉<br />
n −<br />
eγ <br />
n −<br />
e + n −<br />
γ ed + 〈ne − r 〉2<br />
• <strong>and</strong> <strong>for</strong> an ideal photon detector:<br />
<strong>SNR</strong>γideal =<br />
<br />
n e − γ<br />
(34) <strong>UNIS</strong> 2011-11-15 – p. 47
Threshold of detection<br />
The threshold of detection is usually defined as<br />
<strong>SNR</strong> = 2 while the Noise Equivalent Exposure<br />
NEE, is obtained when <strong>SNR</strong> = 1. For a <strong>CCD</strong> the<br />
maximum signal, or Saturation Equivalent<br />
Exposure, SEE is obtained when the charge well<br />
capacity n e − max [e − ], is reached. This occurs when:<br />
(35)<br />
n e − γ ≥ n e − max − n e −<br />
d<br />
In most cases the maximum charge-well capacity<br />
DN SEE [counts], is matched to the maximum<br />
ADC output DN max.<br />
<strong>UNIS</strong> 2011-11-15 – p. 48
Dynamic range (1)<br />
The Dynamic Range is defined as the peak<br />
signal divided by the RMS noise <strong>and</strong> the<br />
DC-bias-level, (if any). The minimum ADC<br />
output, is subtracted in the case of a signed<br />
integer output. DR is usually expressed in<br />
decibels.<br />
<br />
<br />
DN SEE − DN min<br />
DR = 20 log10 DN DC + DN NEE − DN min<br />
(36)<br />
[dB]<br />
<strong>UNIS</strong> 2011-11-15 – p. 49
Dynamic range (2)<br />
An approximate theoretical value <strong>for</strong> DR is<br />
obtained by dividing the maximum signal by the<br />
total noise<br />
(37)<br />
DR ≈ 20 log 10<br />
n e − max − n e −<br />
d<br />
〈n e − tot 〉<br />
[dB]<br />
<strong>UNIS</strong> 2011-11-15 – p. 50
I<strong>CCD</strong><br />
<strong>UNIS</strong> 2011-11-15 – p. 51
I<strong>CCD</strong><br />
After Holst [1998] <strong>UNIS</strong> 2011-11-15 – p. 52
<strong>SNR</strong> <strong>for</strong> a <strong>CCD</strong><br />
• Measured signal-to-noise ratio:<br />
<strong>SNR</strong><strong>CCD</strong> = DN signal<br />
DN noise<br />
≈ n e − γ<br />
〈n e −<br />
<strong>CCD</strong> 〉<br />
<strong>UNIS</strong> 2011-11-15 – p. 53
<strong>SNR</strong> <strong>for</strong> a <strong>CCD</strong><br />
• Measured signal-to-noise ratio:<br />
<strong>SNR</strong><strong>CCD</strong> = DN signal<br />
DN noise<br />
• For an ideal photon detector:<br />
<strong>SNR</strong>γideal =<br />
≈ n e − γ<br />
〈n e −<br />
<strong>CCD</strong> 〉<br />
<br />
n e − γ<br />
<strong>UNIS</strong> 2011-11-15 – p. 53
<strong>SNR</strong> <strong>for</strong> a <strong>CCD</strong><br />
• Measured signal-to-noise ratio:<br />
<strong>SNR</strong><strong>CCD</strong> = DN signal<br />
DN noise<br />
• For an ideal photon detector:<br />
• <strong>and</strong> <strong>for</strong> a <strong>CCD</strong>:<br />
<strong>SNR</strong><strong>CCD</strong> ≈<br />
<strong>SNR</strong>γideal =<br />
≈ n e − γ<br />
〈n e −<br />
<strong>CCD</strong> 〉<br />
<br />
n e − γ<br />
n e − γ<br />
<br />
n e − + n e − + 〈n e −〉 2 <strong>UNIS</strong> 2011-11-15 – p. 53
<strong>SNR</strong> <strong>for</strong> an I<strong>CCD</strong><br />
Noting that <strong>for</strong> an I<strong>CCD</strong>:<br />
n e − γ,pc ≈ QEpc (λ)TtintM 2 FOApix<br />
10 10 I<br />
16f 2 #<br />
−<br />
eRMS <strong>UNIS</strong> 2011-11-15 – p. 54
<strong>SNR</strong> <strong>for</strong> an I<strong>CCD</strong><br />
• The signal-to-noise ratio <strong>for</strong> an I<strong>CCD</strong> can be<br />
estimated as:<br />
<strong>SNR</strong>I<strong>CCD</strong> ≈<br />
<br />
n e − γ,pc<br />
k2 MCP (ne − γ,pc + ne −<br />
d,pc ) + n e −<br />
d<br />
+〈n e − r 〉 2<br />
g 2<br />
<strong>UNIS</strong> 2011-11-15 – p. 55
<strong>SNR</strong> <strong>for</strong> an I<strong>CCD</strong><br />
• The signal-to-noise ratio <strong>for</strong> an I<strong>CCD</strong> can be<br />
estimated as:<br />
<strong>SNR</strong>I<strong>CCD</strong> ≈<br />
<br />
n e − γ,pc<br />
k2 MCP (ne − γ,pc + ne −<br />
d,pc ) + n e −<br />
d<br />
+〈n e − r 〉 2<br />
• As seen, increasing the gain of the image<br />
intensifier makes the <strong>CCD</strong> noise-sources<br />
negligible, but does not increase the <strong>SNR</strong><br />
beyond that. For very high gain, we see that:<br />
<strong>SNR</strong>I<strong>CCD</strong> ≈<br />
g 2<br />
<br />
n −<br />
eγ,pc 2(n −<br />
e + n −<br />
e<br />
<strong>UNIS</strong> 2011-11-15 – p. 55<br />
)
<strong>SNR</strong> <strong>for</strong> an em<strong>CCD</strong><br />
The signal-to-noise ratio <strong>for</strong> an<br />
electron-multiplication <strong>CCD</strong> can be estimated as:<br />
<strong>SNR</strong>em<strong>CCD</strong> ≈<br />
<br />
n e − γ<br />
k2 em (n −<br />
e + n −<br />
γ ed + 〈ne −<br />
cic 〉2 ) + 〈n e − r 〉2<br />
g2 Please note:<br />
For an EM<strong>CCD</strong> kem ≈ √ 2 while kMCP (I<strong>CCD</strong>) is<br />
taken as √ 2 here, which is somewhat too good to<br />
be true. In real cases kMCP ≥ 1.6<br />
<strong>UNIS</strong> 2011-11-15 – p. 56
<strong>SNR</strong> example: <strong>CCD</strong> vs. I<strong>CCD</strong><br />
<strong>SNR</strong><br />
1000<br />
100<br />
10<br />
1<br />
Ideal <strong>CCD</strong> (a)<br />
ALIS <strong>CCD</strong> (b)<br />
PAI ideal <strong>CCD</strong> (c)<br />
PAI I<strong>CCD</strong> (d)<br />
PAI <strong>CCD</strong> (e)<br />
t=16.7 ms, T=0.5, f/3.9, ALIS <strong>CCD</strong>CAM5, PAI I<strong>CCD</strong><br />
0.1<br />
10000 100000 1e+06 1e+07 1e+08 1e+09 1e+10<br />
Column emission rate Rayleighs 557.7 nm<br />
<strong>UNIS</strong> 2011-11-15 – p. 57
<strong>SNR</strong> vs. of integration time<br />
<strong>SNR</strong><br />
10000<br />
1000<br />
100<br />
10<br />
1<br />
1 MR (a)<br />
100 kR (b)<br />
10 kR (c)<br />
1 kR (d)<br />
100 R (e)<br />
T=0.5, f/3.5, ALIS <strong>CCD</strong>CAM5 557.7 nm<br />
0.1<br />
0.001 0.01 0.1 1 10 100 1000 10000<br />
Integration time [s]<br />
<strong>UNIS</strong> 2011-11-15 – p. 58
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
<strong>UNIS</strong> 2011-11-15 – p. 59
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
• Apperture of the optics<br />
<strong>UNIS</strong> 2011-11-15 – p. 59
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
• Apperture of the optics<br />
• Area of detector (pixel-area <strong>for</strong> imagers)<br />
<strong>UNIS</strong> 2011-11-15 – p. 59
Where are my photons?<br />
• Transmittance (atmosphere, optics, filters. . . )<br />
• Apperture of the optics<br />
• Area of detector (pixel-area <strong>for</strong> imagers)<br />
• Number of photoelectrons collected in a pixel<br />
n −<br />
e = QE(λ)Eγi γ tintApix<br />
−<br />
e <br />
(44)<br />
(45)<br />
n e − γ ≈ QE(λ)TtintApix<br />
10 10 I<br />
16f 2 #<br />
e − <br />
<strong>UNIS</strong> 2011-11-15 – p. 59
<strong>SNR</strong><br />
<strong>SNR</strong> <strong>and</strong> on-chip binning<br />
1000<br />
100<br />
10<br />
1<br />
0.1<br />
bin 1,1 (a)<br />
bin 2,2 (b)<br />
bin 4,4 (c)<br />
bin 8,8 (d)<br />
bin 16,16 (e)<br />
t=1 s, T=0.5, f/3.5, ALIS <strong>CCD</strong>CAM5, PAI I<strong>CCD</strong><br />
1 100 10000 1e+06 1e+08 1e+10<br />
Column emission rate Rayleighs 557.7 nm<br />
<strong>UNIS</strong> 2011-11-15 – p. 60
<strong>SNR</strong>: <strong>CCD</strong>, I<strong>CCD</strong> <strong>and</strong> em<strong>CCD</strong><br />
<strong>SNR</strong><br />
1000<br />
100<br />
10<br />
1<br />
Ideal SI003AB (a)<br />
SI003AB (b)<br />
Ideal PAI <strong>CCD</strong> (c)<br />
PAI I<strong>CCD</strong> (d)<br />
Ideal <strong>CCD</strong>201-20 (g)<br />
<strong>CCD</strong>201-20 (h)<br />
bin 2,2 <strong>CCD</strong>201-20 (h)<br />
t=1/25 s, T=0.5, f/1.6, bin=1x1<br />
0.1<br />
1000 10000 100000 1e+06 1e+07 1e+08 1e+09 1e+10<br />
Column emission rate Rayleighs 557.7 nm<br />
<strong>UNIS</strong> 2011-11-15 – p. 61
When do we need EM-gain?<br />
<strong>UNIS</strong> 2011-11-15 – p. 62
<strong>SNR</strong><br />
Fast: ≈ 2900 photons/pixel<br />
100<br />
10<br />
1<br />
0.1<br />
0.01<br />
Ideal <strong>CCD</strong>201-20<br />
EM OFF 10 MHz <strong>CCD</strong>201-20<br />
EM ON 10 MHz <strong>CCD</strong>201-20<br />
EM ON vs. EM OFF at 10 MHz<br />
1 10 100 1000 10000<br />
photons/pixel (assuming 90% QE)<br />
<strong>UNIS</strong> 2011-11-15 – p. 63
Always <strong>for</strong> high temporal<br />
resolution<br />
<strong>UNIS</strong> 2011-11-15 – p. 64
<strong>SNR</strong><br />
Slow: ≈ 42 photons/pixel<br />
100<br />
10<br />
1<br />
0.1<br />
Ideal <strong>CCD</strong>201-20<br />
1 MHz Con. <strong>CCD</strong>201-20<br />
EM ON 1 MHz <strong>CCD</strong>201-20<br />
Slow readout EM ON vs. Conventional Ampl.<br />
1 10 100 1000<br />
photons/pixel (assuming 90% QE)<br />
<strong>UNIS</strong> 2011-11-15 – p. 65
Not always <strong>for</strong> low temporal<br />
resolution<br />
<strong>UNIS</strong> 2011-11-15 – p. 66
Intercalibration<br />
<strong>UNIS</strong> 2011-11-15 – p. 67
Intercalibration<br />
This is the process of intercalibrating calibration<br />
sources <strong>and</strong> to transfer absolute calibration<br />
in<strong>for</strong>mation between different instruments <strong>and</strong><br />
research groups.<br />
Hans Lauches intercalibration photometer (responsible<br />
person: 1981–1999 Lauche, 1999-2011 Widell, SSC,<br />
2011– Brändström, IRF)<br />
<strong>UNIS</strong> 2011-11-15 – p. 68
The European Rayleigh<br />
<strong>UNIS</strong> 2011-11-15 – p. 69
Intercal. procedure<br />
• Calibrators are compared at calibration<br />
workshops using a calibration-photometer<br />
with 7 filters <strong>and</strong> a reference source.<br />
<strong>UNIS</strong> 2011-11-15 – p. 70
Intercal. procedure<br />
• Calibrators are compared at calibration<br />
workshops using a calibration-photometer<br />
with 7 filters <strong>and</strong> a reference source.<br />
• Last known absolute callibration of the<br />
calibration <strong>eq</strong>uipment against a national<br />
st<strong>and</strong>ard (NBS) was done by [Torr <strong>and</strong> Espy,<br />
1981].<br />
<strong>UNIS</strong> 2011-11-15 – p. 70
Intercal. procedure<br />
• Calibrators are compared at calibration<br />
workshops using a calibration-photometer<br />
with 7 filters <strong>and</strong> a reference source.<br />
• Last known absolute callibration of the<br />
calibration <strong>eq</strong>uipment against a national<br />
st<strong>and</strong>ard (NBS) was done by [Torr <strong>and</strong> Espy,<br />
1981].<br />
• Known calibration workshops at the optical<br />
meetings were: Aberdeen 1981, Lindau 1983,<br />
Lysebu 1985, Saskatoon 1987, Lindau 1989,<br />
Wien 1991, Lindau 1999, Stockholm 2000,<br />
Oulu 2001, Kiruna 2006, Andøya 2007 <strong>and</strong><br />
Sodankylä 2011.<br />
<strong>UNIS</strong> 2011-11-15 – p. 70
25<br />
20<br />
15<br />
10<br />
5<br />
Intercal. workshops<br />
Number of participating calibrationsources in intercalibration workshops 1981-2011<br />
0<br />
1980 1985 1990 1995 2000 2005 2010<br />
<strong>UNIS</strong> 2011-11-15 – p. 71
Sodankylä 2011<br />
<strong>UNIS</strong> 2011-11-15 – p. 72
<strong>and</strong> the FMI-sphere<br />
<strong>UNIS</strong> 2011-11-15 – p. 73
To be done here<br />
After Sigernes et al. [2008]<br />
<strong>UNIS</strong> 2011-11-15 – p. 74
[Rayleighs/Angstrom]<br />
1000<br />
100<br />
10<br />
1<br />
0.1<br />
0.01<br />
Y275<br />
L1614<br />
920B<br />
Intercal. results<br />
0.001<br />
3500 4000 4500 5000 5500 6000 6500 7000 7500<br />
Wavelength [Angstrom]<br />
<strong>UNIS</strong> 2011-11-15 – p. 75
atio [%]<br />
30<br />
20<br />
10<br />
0<br />
-10<br />
-20<br />
-30<br />
Intercal. errors<br />
Confusogram of calibration ratios [1985,1999,2000,2001 to 2006]<br />
4000 4500 5000 5500 6000 6500 7000<br />
Wavelength [Angstrom]<br />
y275 1985<br />
y275 1999<br />
y275 2000<br />
y275 2001<br />
l1614 1985<br />
l1614 1999<br />
l1614 2000<br />
l1614 2001<br />
920b 1985<br />
920b 1999<br />
920b 2000<br />
920b 2001<br />
<strong>UNIS</strong> 2011-11-15 – p. 76
Calibration issues<br />
<strong>UNIS</strong> 2011-11-15 – p. 77
Calibration<br />
Calibration is the process of answering the<br />
following two basic questions:<br />
1. What physical value does the pixel represent?<br />
(absolute calibration)<br />
2. How is each pixel mapped to the observed<br />
object? (geometrical calibration)<br />
<strong>UNIS</strong> 2011-11-15 – p. 78
Abs. calibration (ALIS)<br />
<strong>UNIS</strong> 2011-11-15 – p. 79
Challenge<br />
Read the “28. Appendix” <strong>and</strong> compare to<br />
Sigernes et al. [2008]. You might also want to<br />
compare to Torr <strong>and</strong> Espy [1981]<br />
Calculate R/Å <strong>for</strong> the IRF-UJO-Y275 radioactive<br />
source around 5577 Å using the result in “28.<br />
Appendix” <strong>and</strong> compare to latest intercalibration<br />
result from Sodankylä. (That source is marked<br />
15 µlm<br />
<strong>UNIS</strong> 2011-11-15 – p. 80
ALIS<br />
<strong>UNIS</strong> 2011-11-15 – p. 81
ALIS 2009–2012<br />
A<br />
N<br />
F<br />
K<br />
O<br />
B<br />
T<br />
Norway<br />
D<br />
I<br />
E<br />
R<br />
Sweden<br />
S<br />
M<br />
Y<br />
Finl<strong>and</strong><br />
<strong>UNIS</strong> 2011-11-15 – p. 82
Spectroscopic imaging<br />
4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000<br />
Wavelength [Å]<br />
<strong>UNIS</strong> 2011-11-15 – p. 83
Selectable common volumes<br />
100<br />
50<br />
0<br />
−50<br />
−100<br />
Abisko<br />
Silkimuotka<br />
Nikaluokta Kiruna<br />
Merasjaervi<br />
Tjautjas<br />
−150<br />
−200 −100 0 100 200<br />
surveilance<br />
50<br />
0<br />
−50<br />
−100<br />
−150<br />
−200<br />
400<br />
300<br />
200<br />
100<br />
0<br />
Abisko<br />
Silkimuotka<br />
Nikaluokta Kiruna<br />
Merasjaervi<br />
Tjautjas<br />
−200 −100 0<br />
south<br />
100 200<br />
Abisko<br />
Nikaluokta Kiruna<br />
Silkimuotka<br />
Tjautjas<br />
Merasjaervi<br />
−400 −200 0<br />
east−west<br />
200 400<br />
400<br />
300<br />
200<br />
100<br />
0<br />
−200 0<br />
eiscat<br />
200<br />
Approximate field of view at 110 km<br />
Abisko<br />
Nikaluokta Kiruna<br />
Silkimuotka<br />
Tjautjas<br />
Merasjaervi<br />
50<br />
0<br />
−50<br />
−100<br />
−150<br />
100<br />
50<br />
0<br />
−50<br />
−100<br />
300<br />
200<br />
100<br />
0<br />
Abisko<br />
Silkimuotka<br />
Nikaluokta Kiruna<br />
Merasjaervi<br />
Tjautjas<br />
−100 0<br />
mag_zen<br />
100 200<br />
Abisko<br />
Silkimuotka<br />
Nikaluokta Kiruna<br />
Merasjaervi<br />
Tjautjas<br />
−200 −100 0 100<br />
core<br />
400<br />
300<br />
200<br />
100<br />
Abisko<br />
Silkimuotka<br />
Nikaluokta Kiruna<br />
Merasjaervi<br />
Tjautjas<br />
−300 −200 −100<br />
north<br />
0 100 200<br />
0<br />
Abisko<br />
Nikaluokta Kiruna<br />
Silkimuotka<br />
Tjautjas<br />
Merasjaervi<br />
−200 0<br />
heating<br />
200<br />
[km]<br />
250<br />
200<br />
150<br />
100<br />
50<br />
0<br />
W<br />
o<br />
50 90 o<br />
−150 −100 −50 0 100 200<br />
β<br />
S<br />
00 11<br />
00 11<br />
00 11<br />
α<br />
z<br />
N y<br />
β<br />
a φ<br />
[km]<br />
E<br />
x<br />
Azimuth<br />
<strong>UNIS</strong> 2011-11-15 – p. 84
Scientific results <strong>and</strong> capabilities<br />
<strong>UNIS</strong> 2011-11-15 – p. 85
Altitude (km)<br />
Altitude (km)<br />
Altitude (km)<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
20:09:00<br />
−50 0 50<br />
20:10:00<br />
−50 0 50<br />
20:11:00<br />
−50 0 50<br />
North (km)<br />
Auroral tomography<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
40 km west of Kiruna<br />
90<br />
20:09:30<br />
−50 0 50<br />
20:10:30<br />
−50 0 50<br />
20:11:30<br />
−50 0 50<br />
North (km)<br />
Altitude (km)<br />
Altitude (km)<br />
Altitude (km)<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
20:09:00<br />
−50 0 50<br />
20:10:00<br />
−50 0 50<br />
20:11:00<br />
−50 0 50<br />
North (km)<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
90<br />
160<br />
150<br />
140<br />
130<br />
120<br />
110<br />
100<br />
70 km west of Kiruna<br />
1997-02-16 ALIS/FAST/EISCAT<br />
90<br />
20:09:30<br />
−50 0 50<br />
20:10:30<br />
−50 0 50<br />
20:11:30<br />
−50 0 50<br />
North (km)<br />
<strong>UNIS</strong> 2011-11-15 – p. 86
<strong>UNIS</strong> 2011-11-15 – p. 87
<strong>UNIS</strong> 2011-11-15 – p. 88
electron energy<br />
10 2<br />
10 1<br />
10 0<br />
Auroral electron spectras,<br />
from tomography,<br />
log 10 electron energy flux<br />
200 400 600 800 1000 1200<br />
time after 23:20:00 UT (s)<br />
9<br />
8.5<br />
8<br />
7.5<br />
7<br />
6.5<br />
6<br />
5.5<br />
5<br />
4.5<br />
<strong>UNIS</strong> 2011-11-15 – p. 89
electron energy<br />
10 2<br />
10 1<br />
10 0<br />
Auroral electron spectras,<br />
from tomography,<br />
log 10 electron energy flux<br />
200 400 600 800 1000 1200<br />
time after 23:20:00 UT (s)<br />
<strong>and</strong> from spectroscopic<br />
ratios (right panel).<br />
After Gustavsson et al. [2001b], Phys. Chem. Earth 26.<br />
9<br />
8.5<br />
8<br />
7.5<br />
7<br />
6.5<br />
6<br />
5.5<br />
5<br />
4.5<br />
N−S distance<br />
N−S distance<br />
80<br />
60<br />
40<br />
20<br />
0<br />
−20<br />
−40<br />
−60<br />
0 500 1000<br />
time after 23:20:00 UT (s)<br />
80<br />
60<br />
40<br />
20<br />
0<br />
−20<br />
−40<br />
−60<br />
Characteristic energy (keV)<br />
Oxygen scaling factor<br />
0 500 1000<br />
time after 23:20:00 UT (s)<br />
0.9<br />
0.8<br />
0.7<br />
0.6<br />
0.5<br />
0.4<br />
0.3<br />
0.2<br />
0.35<br />
0.3<br />
0.25<br />
0.2<br />
0.15<br />
N−S distance<br />
N−S distance<br />
N−S distance<br />
50<br />
0<br />
−50<br />
0 500 1000<br />
time after 23:20:00 UT (s)<br />
8446 A<br />
50<br />
0<br />
−50<br />
4278 A<br />
0 500 1000<br />
time after 23:20:00 UT (s)<br />
6300 A<br />
50<br />
0<br />
−50<br />
0 500 1000<br />
time after 23:20:00 UT (s)<br />
160<br />
140<br />
120<br />
100<br />
80<br />
60<br />
40<br />
110<br />
100<br />
90<br />
80<br />
70<br />
60<br />
50<br />
40<br />
30<br />
250<br />
200<br />
150<br />
100<br />
50<br />
<strong>UNIS</strong> 2011-11-15 – p. 89
<strong>UNIS</strong> 2011-11-15 – p. 90
Bus<br />
Kiruna<br />
Optlab<br />
Abisko<br />
filter/expose s<strong>eq</strong>uence<br />
Filter/exposure s<strong>eq</strong>uence: sync−rapid−aeronomi<br />
0 2 4 6 8 10 12 14 16 18 20<br />
time (s)<br />
<strong>UNIS</strong> 2011-11-15 – p. 91
<strong>UNIS</strong> 2011-11-15 – p. 92
<strong>UNIS</strong> 2011-11-15 – p. 93
<strong>UNIS</strong> 2011-11-15 – p. 94
Daylight aurora<br />
After Rees et al. [2000], GRL, 27.<br />
<strong>UNIS</strong> 2011-11-15 – p. 95
Radio-induced optical emissions<br />
<strong>UNIS</strong> 2011-11-15 – p. 96
RIOE<br />
ALIS made the first unambigous observation of<br />
high-latitude RIOE 1999-02-16<br />
17:40:15 17:40:35 17:40:55 17:41:15 17:41:35 17:41:55<br />
17:43:55 17:44:05 17:44:15 17:44:25 17:44:35 17:44:45<br />
After [Brändström et al., 1999], GRL, 26.<br />
4000<br />
3000<br />
2000<br />
1000<br />
0<br />
4000<br />
3000<br />
2000<br />
1000<br />
0<br />
<strong>UNIS</strong> 2011-11-15 – p. 97
Tomography of RIOE<br />
After Gustavsson et al. [2001a], JGR<br />
106, 29<br />
ALIS made the first tomographic<br />
estimate of volume<br />
distribution of RIOE.<br />
<strong>UNIS</strong> 2011-11-15 – p. 98
<strong>UNIS</strong> 2011-11-15 – p. 99
<strong>UNIS</strong> 2011-11-15 – p. 100
Meteor research<br />
<strong>UNIS</strong> 2011-11-15 – p. 101
A strange meteor trail<br />
130<br />
120<br />
110<br />
100<br />
95<br />
x 10 4<br />
10<br />
9<br />
8<br />
7<br />
6<br />
5<br />
4<br />
3<br />
2<br />
1<br />
110<br />
100<br />
4227 Å (left) 5893 Å (right)<br />
After Pellinen-Wannberg et al. [2004, GRL 31], GRL 31.<br />
95<br />
5000<br />
4500<br />
4000<br />
3500<br />
3000<br />
2500<br />
2000<br />
<strong>UNIS</strong> 2011-11-15 – p. 102
Polar-Stratospheric clouds<br />
70<br />
60<br />
50<br />
40<br />
26<br />
Triangulation<br />
24<br />
23<br />
25<br />
21 22<br />
−20 −10 0<br />
After Enell [2002], IRF Sci. Rep. 278<br />
<strong>UNIS</strong> 2011-11-15 – p. 103
Future plans <strong>and</strong> challenges<br />
<strong>UNIS</strong> 2011-11-15 – p. 104
Small structure<br />
The aurora is extremly rich in small structure<br />
“With respect to underst<strong>and</strong>ing the<br />
dynamic coupling between the<br />
magnetosphere <strong>and</strong> the auroral<br />
ionosphere the observational bias toward<br />
bright aurora is physically unjustified”<br />
[Semeter 2001]<br />
<strong>UNIS</strong> 2011-11-15 – p. 105
We do not underst<strong>and</strong>:<br />
• Creation of narrow arcs<br />
<strong>UNIS</strong> 2011-11-15 – p. 106
We do not underst<strong>and</strong>:<br />
• Creation of narrow arcs<br />
• Diffuse aurora<br />
<strong>UNIS</strong> 2011-11-15 – p. 106
We do not underst<strong>and</strong>:<br />
• Creation of narrow arcs<br />
• Diffuse aurora<br />
• Pulsating aurora<br />
<strong>UNIS</strong> 2011-11-15 – p. 106
We do not underst<strong>and</strong>:<br />
• Creation of narrow arcs<br />
• Diffuse aurora<br />
• Pulsating aurora<br />
• The role of the ionosphere in the<br />
magnetosphere-ionosphere coupling<br />
<strong>UNIS</strong> 2011-11-15 – p. 106
We do not underst<strong>and</strong>:<br />
• Creation of narrow arcs<br />
• Diffuse aurora<br />
• Pulsating aurora<br />
• The role of the ionosphere in the<br />
magnetosphere-ionosphere coupling<br />
• How are different scales related to each<br />
other?<br />
<strong>UNIS</strong> 2011-11-15 – p. 106
We do not underst<strong>and</strong>:<br />
• Creation of narrow arcs<br />
• Diffuse aurora<br />
• Pulsating aurora<br />
• The role of the ionosphere in the<br />
magnetosphere-ionosphere coupling<br />
• How are different scales related to each<br />
other?<br />
Thus we need instruments measuring different<br />
scales with high temporal <strong>and</strong> spatial resolution,<br />
e.g. Polar/VIS, ASC, ALIS, ASK<br />
<strong>UNIS</strong> 2011-11-15 – p. 106
ALIS 2010–2014<br />
• Electrodynamics of auroral structures: get<br />
most out of EISCAT-UHF<br />
• ALIS/EISCAT/REIMEI<br />
• Improve temporal resolution: EM<strong>CCD</strong><br />
• Review which sites to use<br />
• Ionospheric sounding rockets?<br />
• Collaboration <strong>for</strong> development of methods<br />
<strong>and</strong> models<br />
• Calibration!!!<br />
• Improve access to data<br />
<strong>UNIS</strong> 2011-11-15 – p. 107
In particular<br />
we will work to answer the following specific<br />
questions:<br />
1. What is the temporal <strong>and</strong> spatial scale<br />
distribution of small (less than a few km)<br />
auroral structures?.<br />
2. What are the temporal <strong>and</strong> spatial variations<br />
of the primary particle distributions causing<br />
small auroral structures?<br />
3. What is the detailed 3D electrodynamics of<br />
small auroral structures?<br />
4. How does ionospheric feedback influence<br />
auroral structure?<br />
<strong>UNIS</strong> 2011-11-15 – p. 108
<strong>and</strong> now. . .<br />
<strong>UNIS</strong> 2011-11-15 – p. 109
My brain hurts!<br />
Mr. T. F. Gumby:—Doctor! Doctor! DOCTOR! DOCTOR! Doctor!<br />
— Are you the brain specialist? — My brain hurts!<br />
http://www.mwscomp.com/mpfc/gumbrain.ht<br />
<strong>UNIS</strong> 2011-11-15 – p. 110
It’s<br />
The end!<br />
<strong>UNIS</strong> 2011-11-15 – p. 111
THE END!<br />
<strong>UNIS</strong> 2011-11-15 – p. 112
The end?<br />
Kiruna ASC 2007-02-05 17.39.00 UTC 10s exp.<br />
<strong>UNIS</strong> 2011-11-15 – p. 113
References<br />
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Torr, M. R., <strong>and</strong> P. Espy, Intercalibration of instrumentation<br />
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