Transcript Lecture 16-Quantum-Limited Detectors

Astronomical Observational Techniques
and Instrumentation
RIT Course Number 1060-771
Professor Don Figer
Quantum-Limited Detectors
1
Aims for this lecture
• Motivate the need for future detectors
• Describe physical principles of future detectors
• Review some promising technologies for future detectors
2
Motivation for Future Detectors
3
Improving Detectors
• Detector properties limit sensitivity in most applications.
• For instance, dark current and read noise are important in low
flux applications.
• Detectivity is a measure of system effectiveness.

F tQE
inst A
S
h
SNR  
N



 

Fback , tQE   idark t  N 2read
F tQE   inst A
inst A
h
h

 

N  tQE
SNR 
N  tQE  N  ,background tQE  n pixidark t  n pix N 2read
Sensit ivity  flux at whichSNR  1
N  , SNR 1tQE
SNR  1 
N  , SNR 1tQE  N  ,background tQE  n pixidark t  n pix N 2read
N  , SNR 1tQE  N  ,background tQE  n pixidark t  n pix N 2read  ( N  , SNR 1tQE) 2
N  , SNR 1 
tQE  (tQE) 2  4(tQE) 2 ( N  ,background tQE  n pixidark t  n pix N 2read )
Detectivity 
Detectivity 
2(tQE) 2
1
1

sensitivity N  , SNR 1
2tQE
1  1  4( N  ,background tQE  n pixidark t  n pix N 2read )
.
4
Detectivity in Broadband Applications
read noise
FOM
0
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Detectivity Metric
Quantum Efficiency
10%
1.5
1.5
1.5
1.4
1.4
1.3
1.3
1.2
1.2
1.1
1.1
1.0
1.0
0.9
0.9
0.9
0.8
0.8
0.8
20%
2.5
2.5
2.4
2.4
2.3
2.3
2.2
2.1
2.1
2.0
1.9
1.9
1.8
1.7
1.7
1.6
1.6
1.5
1.4
30%
3.2
3.2
3.2
3.1
3.1
3.0
3.0
2.9
2.8
2.7
2.7
2.6
2.5
2.4
2.3
2.3
2.2
2.1
2.1
40%
3.9
3.9
3.8
3.8
3.7
3.7
3.6
3.5
3.4
3.4
3.3
3.2
3.1
3.0
2.9
2.9
2.8
2.7
2.6
50%
4.4
4.4
4.4
4.3
4.3
4.2
4.2
4.1
4.0
3.9
3.8
3.7
3.7
3.6
3.5
3.4
3.3
3.2
3.1
60%
4.9
4.9
4.9
4.8
4.8
4.7
4.7
4.6
4.5
4.4
4.3
4.3
4.2
4.1
4.0
3.9
3.8
3.7
3.6
70%
5.4
5.4
5.3
5.3
5.2
5.2
5.1
5.0
5.0
4.9
4.8
4.7
4.6
4.5
4.4
4.3
4.3
4.2
4.1
80%
5.8
5.8
5.7
5.7
5.7
5.6
5.5
5.5
5.4
5.3
5.2
5.1
5.1
5.0
4.9
4.8
4.7
4.6
4.5
90%
6.2
6.2
6.1
6.1
6.1
6.0
5.9
5.9
5.8
5.7
5.6
5.6
5.5
5.4
5.3
5.2
5.1
5.0
4.9
100%
6.6
6.5
6.5
6.5
6.4
6.4
6.3
6.3
6.2
6.1
6.0
5.9
5.8
5.8
5.7
5.6
5.5
5.4
5.3
green=detectivity greater than that for baseline (QE=70%, read noise=5e-)
pink=detectivity less than that for baseline
Figure 3. Detectivity as a function of quantum efficiency and read noise for
broadband astrophysics applications.
5
Detectivity in Low Flux Broadband Applications
read noise
FOM
0
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Detectivity Metric
Quantum Efficiency
10%
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
20%
0.2
0.2
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
30%
0.3
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
40%
0.3
0.3
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
50%
0.4
0.3
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
60%
0.4
0.4
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
70%
0.5
0.4
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
80%
0.5
0.5
0.3
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
90%
0.5
0.5
0.3
0.3
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
100%
0.6
0.5
0.4
0.3
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
green=detectivity greater than that for baseline (QE=70%, read noise=5e-)
pink=detectivity less than that for baseline
Figure 4. Same parameters as used to generate Figure 3, except the exposure
time is only 5 seconds, instead of 10 minutes. It is apparent that read noise
becomes a dominant factor in detectivity for this case.
6
Detectivity in Narrowband Applications
read noise
FOM
0
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Detectivity Metric
Quantum Efficiency
10%
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
0.0
0.0
20%
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
30%
0.3
0.3
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
40%
0.4
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
50%
0.5
0.5
0.5
0.5
0.5
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
60%
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.2
70%
0.7
0.7
0.7
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
80%
0.8
0.8
0.8
0.8
0.7
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
0.4
0.4
0.3
0.3
90%
1.0
0.9
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
0.4
0.4
100%
1.1
1.1
1.0
0.9
0.9
0.8
0.8
0.7
0.7
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
green=detectivity greater than that for baseline (QE=70%, read noise=5e-)
pink=detectivity less than that for baseline
Figure 5. Detectivity as a function of quantum efficiency and read noise for
narrowband astrophysics applications.
7
Detectivity in Narrowband Applications with Low
Dark Current
read noise
FOM
0
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Detectivity Metric
Quantum Efficiency
10%
1.4
0.7
0.3
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.0
0.0
0.0
20%
2.2
1.3
0.5
0.4
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
30%
2.9
1.8
0.8
0.6
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.1
0.1
0.1
40%
3.5
2.4
1.0
0.8
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.3
0.3
0.2
0.2
0.2
0.2
0.2
0.2
50%
4.0
2.8
1.3
1.0
0.8
0.7
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.2
0.2
0.2
60%
4.5
3.3
1.5
1.2
1.0
0.8
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
70%
4.9
3.7
1.8
1.4
1.1
1.0
0.8
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.4
0.4
0.3
0.3
0.3
80%
5.3
4.1
2.0
1.6
1.3
1.1
0.9
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.4
0.4
0.4
90%
5.7
4.5
2.3
1.8
1.4
1.2
1.1
0.9
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.5
0.4
0.4
0.4
100%
6.1
4.8
2.5
2.0
1.6
1.3
1.2
1.0
0.9
0.8
0.8
0.7
0.6
0.6
0.6
0.5
0.5
0.5
0.4
green=detectivity greater than that for baseline (QE=70%, read noise=5e-)
pink=detectivity less than that for baseline
Figure 6. Same parameters as used to generate Figure 5, except the dark
current is 0.0001 electrons/second/pixel, instead of 0.1 electrons/second/pixel. It
is apparent that read noise becomes a dominant factor in detectivity for this
case. Also, note that the detectivity is comparable to that for the broadband
imaging case modeled in Figure 3.
8
Detectivity in Spectroscopic Applications
read noise
FOM
0
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Detectivity Metric
Quantum Efficiency
10%
0.0004
0.0004
0.0004
0.0004
0.0004
0.0003
0.0003
0.0003
0.0003
0.0003
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
20%
0.0009
0.0009
0.0008
0.0008
0.0007
0.0007
0.0006
0.0006
0.0006
0.0005
0.0005
0.0005
0.0004
0.0004
0.0004
0.0004
0.0004
0.0003
0.0003
30%
0.0013
0.0013
0.0012
0.0011
0.0011
0.0010
0.0010
0.0009
0.0008
0.0008
0.0007
0.0007
0.0007
0.0006
0.0006
0.0006
0.0005
0.0005
0.0005
40%
0.0017
0.0017
0.0016
0.0015
0.0014
0.0014
0.0013
0.0012
0.0011
0.0011
0.0010
0.0009
0.0009
0.0008
0.0008
0.0008
0.0007
0.0007
0.0007
50%
0.0021
0.0021
0.0020
0.0019
0.0018
0.0017
0.0016
0.0015
0.0014
0.0013
0.0012
0.0012
0.0011
0.0010
0.0010
0.0009
0.0009
0.0009
0.0008
60%
0.0026
0.0026
0.0024
0.0023
0.0022
0.0020
0.0019
0.0018
0.0017
0.0016
0.0015
0.0014
0.0013
0.0013
0.0012
0.0011
0.0011
0.0010
0.0010
70%
0.0030
0.0030
0.0028
0.0027
0.0025
0.0024
0.0022
0.0021
0.0020
0.0019
0.0017
0.0016
0.0016
0.0015
0.0014
0.0013
0.0013
0.0012
0.0011
80%
0.0034
0.0034
0.0032
0.0031
0.0029
0.0027
0.0026
0.0024
0.0023
0.0021
0.0020
0.0019
0.0018
0.0017
0.0016
0.0015
0.0014
0.0014
0.0013
90%
0.0039
0.0038
0.0036
0.0034
0.0033
0.0031
0.0029
0.0027
0.0025
0.0024
0.0022
0.0021
0.0020
0.0019
0.0018
0.0017
0.0016
0.0015
0.0015
100%
0.0043
0.0043
0.0040
0.0038
0.0036
0.0034
0.0032
0.0030
0.0028
0.0026
0.0025
0.0023
0.0022
0.0021
0.0020
0.0019
0.0018
0.0017
0.0016
green=detectivity greater than that for baseline (QE=70%, read noise=5e-)
pink=detectivity less than that for baseline
Figure 7. Detectivity as a function of quantum efficiency and read noise for high
resolution spectroscopy astrophysics applications.
9
Detectivity in Spectroscopic Applications with
Low Dark Current
read noise
FOM
0
1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Detectivity Metric
Quantum Efficiency
10%
0.0036
0.0024
0.0010
0.0008
0.0007
0.0005
0.0005
0.0004
0.0004
0.0003
0.0003
0.0003
0.0003
0.0002
0.0002
0.0002
0.0002
0.0002
0.0002
20%
0.0073
0.0048
0.0021
0.0016
0.0013
0.0011
0.0009
0.0008
0.0007
0.0007
0.0006
0.0006
0.0005
0.0005
0.0004
0.0004
0.0004
0.0004
0.0004
30%
0.0109
0.0072
0.0031
0.0024
0.0020
0.0016
0.0014
0.0012
0.0011
0.0010
0.0009
0.0008
0.0008
0.0007
0.0007
0.0006
0.0006
0.0006
0.0005
40%
0.0146
0.0096
0.0042
0.0032
0.0026
0.0022
0.0019
0.0017
0.0015
0.0013
0.0012
0.0011
0.0010
0.0010
0.0009
0.0008
0.0008
0.0007
0.0007
50%
0.0182
0.0120
0.0052
0.0040
0.0033
0.0027
0.0024
0.0021
0.0018
0.0017
0.0015
0.0014
0.0013
0.0012
0.0011
0.0010
0.0010
0.0009
0.0009
60%
0.0219
0.0144
0.0063
0.0048
0.0039
0.0033
0.0028
0.0025
0.0022
0.0020
0.0018
0.0017
0.0015
0.0014
0.0013
0.0013
0.0012
0.0011
0.0011
70%
0.0255
0.0168
0.0073
0.0056
0.0046
0.0038
0.0033
0.0029
0.0026
0.0023
0.0021
0.0019
0.0018
0.0017
0.0016
0.0015
0.0014
0.0013
0.0012
80%
0.0292
0.0192
0.0084
0.0064
0.0052
0.0044
0.0038
0.0033
0.0030
0.0027
0.0024
0.0022
0.0021
0.0019
0.0018
0.0017
0.0016
0.0015
0.0014
90%
0.0328
0.0215
0.0094
0.0072
0.0059
0.0049
0.0042
0.0037
0.0033
0.0030
0.0027
0.0025
0.0023
0.0022
0.0020
0.0019
0.0018
0.0017
0.0016
100%
0.0365
0.0239
0.0104
0.0080
0.0065
0.0055
0.0047
0.0041
0.0037
0.0033
0.0030
0.0028
0.0026
0.0024
0.0022
0.0021
0.0020
0.0019
0.0018
green=detectivity greater than that for baseline (QE=70%, read noise=5e-)
pink=detectivity less than that for baseline
Figure 8. Same parameters as used to generate Figure 7, except the dark
current is 0.001 electrons/second/pixel, instead of 0.1 electrons/second/pixel. It
is apparent that read noise becomes a dominant factor in detectivity for this
case.
10
Read Noise
The Importance of Read Noise in Imaging
Images of the Arches cluster near the Galactic center, based on real data obtained with
Keck/LGSAO. Each image has synthetic shot noise and increasing read noise (left to right and
top to bottom: 0, 5, 10, 100 electrons).
11
Aperture vs. Read Noise
Effective Telescope Size vs. Read Noise
Telescope Diameter (m)
80
70
60
50
40
30
20
0
1
2
3
4
5
6
Read Noise (electrons)
This plot shows a curve of constant sensitivity for a range
of telescope diameters and detector read noise values in
low-light applications. A 30 meter telescope and zero read
noise detector would deliver the same signal-to-noise ratio
as a 60 meter telescope with current detectors.
12
Very Low Light Level - ExoPlanet Imaging
• The exposure time required to achieve SNR=1 is dramatically
reduced for a zero read noise detector, as compared to
detectors with state of the art read noise.
read noise
FOM
0
1
2
3
4
5
6
7
Exposure Time (seconds) for SNR = 1
Quantum Efficiency
10%
6,600
7,159
8,486
10,148
11,954
13,830
15,745
17,684
20%
2,300
2,674
3,457
4,363
5,312
6,281
7,259
8,244
30%
1,311
1,591
2,141
2,760
3,402
4,053
4,709
5,368
40%
900
1,123
1,547
2,016
2,500
2,990
3,484
3,979
50%
680
865
1,209
1,587
1,976
2,369
2,764
3,161
60%
544
703
992
1,309
1,633
1,961
2,291
2,621
70%
453
591
841
1,113
1,392
1,673
1,956
2,239
80%
388
510
730
968
1,212
1,459
1,706
1,954
90%
338
448
645
857
1,074
1,293
1,513
1,734
100%
300
400
577
768
964
1,161
1,359
1,558
mag_star=5, mag_planet=30, R=100, i_dark=0.0010
13
Principles of Quantum Limited Detectors
14
Key Capabilities for Future Improvement
•
•
•
•
•
•
•
•
•
photon-counting (zero read noise)
wavelength-resolving
polarization-measuring
low power
large area
in-pixel processing
high dynamic range
high speed
time resolution
15
QLID Technology Contenders
Table 1. Quantum-limited Detector Technologies.
Superconductors
Semiconductors
Transition Edge Sensor (TES)
energy resolution
operating temperature of tens of mK
Electron Multiplying CCD (EMCCD)
commercially available
excess noise factor
Superconducting Tunnel Junction (STJ)
energy resolution
operating temperature of mK, leakage
current
Linear Mode Avalance Photodiode
(LM-APD)
ns time constant
excess noise factor (although MCT
has ~no excess noise)
Kinetic Inductance Detector (KID)
energy resolution
ms time constant
Geiger Mode Avalance Photodiode
(GM-APD)
large pulse per photon
afterpulsing
Superconducting Single Photon Detectors
(SSPD)
ns time constant
low fill-factor, polarized, few K
16
Key to Single-Photon Counting
• A photon-counting system requires that the ratio of signal
from a single photon to the noise of the system be big enough
to detect.
photo- generatedsignal
 big enough
noise of system
• This can be achieved by:
–
–
–
–
increasing numerator (e.g., charge gain)
decreasing denominator (e.g., cooling, better circuits)
decreasing what is “big enough” (e.g., better processing)
combination of all
17
Superconductors
• Most metals have descreased resistance with lower
temperature, but they still have finite resistance at T=0 K.
• Superconductors lose all resistance to electrical current at
some temperature, Tc. Examples include: Pb, Al, Sn, and Nb.
• Electrons in superconductors bond as “Cooper pairs” that do
not interact with the ion lattice below Tc because the required
interaction energy exceeds the thermal energy in the crystal.
• In general, Tc<4.2 K.
• Recent developments have produced “high” temperature
superconductors, for which Tc>77 K (temperature of liquid
nitrogen).
18
Slide Title
19
Avalanche Photodiodes (APDs)
20
Geiger-Mode Imager:
Photon-to-Digital Conversion
Pixel circuit
Digital
timing
circuit
photon
APD
Quantum-limited sensitivity
Noiseless readout
Photon counting or timing
Digitally
encoded
photon
flight time
APD/CMOS array
Lenslet
array
Focal-plane
concept
21
Geiger-Mode Operation
22
Gain of an APD
M
Ordinary
photodiode
Linear-mode
APD
Geiger-mode
APD
100
10
1
0
Response
to a photon
Breakdown
I(t)
1
M
∞
23
Operation of Avalanche Diode
Linear
on
Geiger
mode
mode
on
Linear
Geiger
quench
mode
mode
avalanche
Current
off
off
arm
Vdc + V
Vbr
Voltage
24
Avalanche Diode Architecture
-V
hν
Quartz substrate
p+ implant (collects holes)
low E-field
10 µm
p+ implant
high E-field
n+ implant (collects electrons)
metal
metal
metal
0.5 µm
bump bond
ROIC
+V
25
Performance Parameters
 Photon detection efficiency
(PDE)
 The probability that a single
incident photon initiates a
current pulse that registers in a
digital counter
 Dark count Rate
(DCR)/Probability (DCP)
Single photon input
APD output
 The probability that a count is
triggered by dark current
instead of incident photons
time
Discriminator
level
Digital comparator output
time
time
Successful
single photon
detection
Photon absorbed
but insufficient
gain – missed
count
Dark count –
from dark
current
26
APD Charge Gain
• Show animation with thumping euro-techno disco music
http://techresearch.intel.com/spaw2/uploads/files/SiliconPhotonics.html
27
32x32 Timing Circuit Array
Pixels
0.35-mm CMOS process
fabricated through MOSIS
1.2 GHz on-chip clock
Two vernier bits
0.2-ns timing quantization
100-mm spacing to match the
32x32 APD array
Time bin
Vernier bits
Counter
Timing image/histogram measuring propagation of
electronic trigger signal
28
32x32 APD/CMOS Array with
Integrated GaP Microlenses
29
Shortcomings of Conventional Imaging
• When the 3D world is projected
into a flat intensity image, there is
a huge information loss.
• Image processing algorithms
attempt to use intensity edges to
infer properties of 3D objects.
• Consequences of lost information
for automated image segmentation
and target detection/recognition:
– Depth ambiguity
– Sensitivity to lighting, reflectivity
patterns, and point of observation
– Obscuration and camouflage
30
Ladar Imaging System
Microchip laser
Geiger-mode
APD array
• Imaging system photon starved
– Each detector must precisely time a weak
optical pulse
– Sub-ns timing, single photons
Color-coded
range image
31
Laser Radar Brassboard System (Gen I)
Taken at noontime on a sunny day
• 4  4 APD array
• External rack-mounted timing circuits
• Doubled Nd:YAG passively Q-switched microchip laser
(produces 30 µJ, 250 ps pulses at  = 532 nm)
• Transmit/receive field of view scanned to generate 128  128 images
32
Conventional vs Ladar Image
Conventional image
3D image
33
Foliage Penetration Experiment
View from
100 m tower
Laser radar
on tower
elevator
Objects
under trees
34
Foliage Penetration Imagery
35
Transition Edge Sensors (TESs)
36
Transition Edge Sensors (TES)
• A TES is similar to a bolometer, in that photon energy is
detected when it is absorbed in a material that changes
resistance with temperature.
• The difference is that a TES is held at a temperature just below
the transition temperature at which the material becomes
supconducting.
• The effective change in resistance when photons are absorbed
is very large (and easy to detect).
• One of the disadvantages of using TES’s is that the transition
temperature is usually very low, requiring exotic cooling
techniques.
37
TES Schematic
38
Slide Title
• xxxxxx
39
TES Wavelength Resolution
40
Slide Title
41
Prototype TES Device
42
Superconducting Tunneling Junctions
(STJs)
43
Superconducting Tunneling Junctions (STJs)
• An STJ uses the current response of a Josephson junction (aka
STJ) when struck by a photon to detect light.
• The junction is similar to semiconducting junction and is
composed of superconductor-insulator-superconductor.
• The gap energy is generally much less than for silicon, so
optical photons induce charge gain that depends on photon
energy.
44
TES vs. STJ
45
Superconducting Single Photon Detectors
(SSPDs)
46
Slide Title
47
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48
Slide Title
49
Slide Title
50
Slide Title
51
Slide Title
• xxxxxx
52
Slide Title
53