impact of latency and jitter on the performance of ... - eso
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Impact of Latency and Jitter on the Performance of Adaptive Optics Systems p p y
for ELTs
L.Pettazzi, E.Fedrigo, R.Clare, g ,ESO
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Motivation (1/2)
Challenging performance requirements for AO systems in new g g p q ygeneration ELTs Higher number of degrees of freedom higher complexity Deliver high Strehl images high-order corrections faster Deliver high Strehl images high-order corrections faster In challenging environmental conditions (e.g. worse maximum seeing,
telescope induced perturbations,…..) I h ll i i l diti In challenging economical conditions
Challenging requirements on the RTC Amount of computations required per cycle Time required to perform the abovementioned computations At lowest possible cost selection of RTC technology needs involved
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
trade-off analysis
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Motivation (2/2)
Impact of RTC latency on the performance of AO loop well studied and p y p punderstood (Fried 1990, Madec 1999, …..)
Classical results apply to a fairly standard AO loop can be used to t id f th i d RTC fget an idea of the required RTC performance
More accurate analysis needed for trade-off analysis
Assumptions matching the ELT’s expected operational conditions
More accurate representation of the control cycle timing sequence
Validation of the analysis tools needed to cross-check the validity of the results
Multi disciplinary approach (e g analysis involving multiple tools: control Multi-disciplinary approach (e.g. analysis involving multiple tools: control model + high fidelity E2E simulators)
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
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Problem set up (1/3)
AO Loop
DMRTC
φtur(t)
D/Aφcorr(t)0
K M
+
-
+
+
p
φres(t)WFS
Meas noiseK4/5 M4/5
+
+
)()()()()()( sDMsHVAsDACsRTCsWFSsL
11
1
)T()sTexp(
)sexp(k)s(RTCsT
)sTexp()s(WFS
)(11)(
sLsS
11
1
mi
ini
sbsa
)s(DM)s(HVA
sT)sTexp()s(DAC
RTC Latency: nominal delay associated to RTC computation (deterministic variable)
RTC Jitter: difference between nominal and actual time delay
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
RTC Jitter: difference between nominal and actual time delay associated to RTC computation (random variable)
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Problem set up (2/4)
Timing definitionsg
1 2 3 4 5D t t
Integration time
e Ts1
Fixed by technology / science requirements
1 2 3 4 5Detector
Read-out 1 2 3 4Tse1
Half frame
Fixed by technology / science requirements
Real Time Computer 1 2 3
1 2 e Ts1
This is what everyone want to squeeze
DAC+HVA 1 2
Mirror 1Tse1
Half frame + rise time
Settling timeFixed by technology
RTC latency
T1T2 T3 T4 T5Sampling time
RTC latency
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
Total latency
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Problem set up (2/4)
Timing definitionsg
1 2 3 4 5D t t
Integration time
e Ts1
Fixed by technology / science requirements
1 1 2 3 4 5Detector
Read-out 1 2 3 4Tse1
Half frame
Fixed by technology / science requirements
0.5
Real Time Computer 1 2 3
1 2 e Ts1
This is what everyone want to squeeze
-0.5
0
DAC+HVA 1 2
Mirror 1Tse1
Half frame + rise time
Settling timeFixed by technology
RTC latency
-1
T1T2 T3 T4 T5Sampling time
RTC latency0 10 20 30 40 50 60 70 80 90 100
-1.5
time
Sample-and-hold followed by Zero-Order Hold
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
Total latency
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Problem set up (3/4)
Timing definitions: Total latency:g y
T/2: statistical delay introduced by the integration of the wavefront sensor T: readout and digitization of the pixels Transmission times between all components Computational time (in every component) T/2: statistical delay introduced by the DAC
τ T/2: statistical delay introduced by the DAC Rise time of the amplifier + settling time of the mirror
Mi i l t I h t l t 1 f d l Minimum latency: Inherent latency: 1 frame delay T/2: statistical delay introduced by the integration of the wavefront sensor Instantaneous readout No communication delay Perfect infinitely powerful real time computer T/2: statistical delay introduced by the DAC
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
Perfect amplifier without rise time and perfect mirror without settling time
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Problem set up (4/4)
Tools
Bench E2E Simulation Control modelMinimum latency 2 frames 1 frame 1 frame
Can simulate • Latency as multiple frames• Jitter• Custom defined exogenous perturbation signalsC li b t
• Latency as multiple frames• Jitter only as frames dropped• Custom defined exogenous perturbation signalsC li b t diff t
• Latency• Jitter with different probability distributions
• Mirror dynamic responseC t d fi d• Cross coupling between
different modes• Mis-registration• Mirror dynamic response
• Cross coupling between different modes
• Mis-registration
• Custom defined exogenous perturbation signals
Cannot simulate • Sub frame latency • Mirror dynamic response • Cross coupling betweenCannot simulate • Sub-frame latency• Sub-frame jitter
(not yet)
• Mirror dynamic response• Sub-frame jitter• Sub-frame latency
• Cross coupling between different modes
• Mis-registration
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
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Impact of the latency
More delay smaller gain with same margin smaller bandwidthy g g
Delay 0 1 2 3 4 5Gain 1.4 0.38 0.22 0.16 0.12 0.10
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
The performance variation (residuals) depends on the input PSD
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Validation of analysis method
Comparison with E2E casep
OCTOPUS Simulation Transfer Function Anasysis
0.7
0.75
0.8
0.7
0.75
0.8Delay= 1Delay= 2Delay= 3D l 4
0 55
0.6
0.65
Stre
hl R
atio
0 55
0.6
0.65
Stre
hl R
atio Delay= 4
Delay= 5
0.45
0.5
0.55
0.45
0.5
0.55
Analysis confirms that the control model captures the most important
0.1 0.2 0.3 0.40.4
I-Controller Gain0.1 0.2 0.3 0.4
0.4
I-Controller Gain
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
Analysis confirms that the control model captures the most important contributors to system performance
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E-ELT AO Loop
100
rad2 /H
z
eq mode # 2 100
rad2 /H
z
eq mode # 3
AO loop target: reject atmospheric + telescope
100
Hz100
Hz
100
Hz
eq mode # 4
100
Hz
eq mode # 7
atmospheric + telescope-induced perturbations
M5 removes low
100
Hz
rad2 /H
100
Hz
rad2 /H
mode # 8 mode # 11
frequency large stroke perturbations
AO loop (driving M4
100
100
rad2 /H
z
eq mode # 8
100
100
rad2 /H
z
eq mode # 11 AO loop (driving M4 mirror) to cope with remaining perturbations
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
10Hz
10Hz
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Latency Analysis Results
T/2 WFS: included in model T readout: assumed 2ms Transmission times between all components
To be considered in given delayg yComputational time (in every component)
150us in Mirror Controller includedRequirement: 1ms for the RTCIdeal case q
WPU included in RTC T/2 DAC: included in modelRise time of the amplifier + settling time of the
Median ELT seeing conditions High flux
Rise time of the amplifier settling time of the mirror Ideal amplifier, settling time included in model
High flux Specification: 70% Strehl Achieved
■ M4 expected response fitted from VLT/DSM measurements
■ Gain achieving maximum specified robustness
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
72% (1ms Latency) 74% (0.5ms Latency)
■ Gain achieving maximum specified robustness margin (6dB Modulus margin)
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Jitter Simulations (1/2)
Residuals
In1 Out1
WFS
SimIn
Turbulence
O t1Out1
Scheduler
NoOp
In1Out1 -6Z
num(z)
den(z)In1Out1
Controller output update executed at randomly variable time
RODMdelayDMController
Controller output update executed at randomly variable time instants
Can simulate violation of Hard-RT constraints producing dropped measurements
Can use different jitter probability distributions Low impact on simulation time (10 sec ELT simulation performed
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
Low impact on simulation time (10 sec ELT simulation performed on a laptop within 15mins)
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Jitter Simulations (2/2)
Example: jitter llnormally
distributed around mean latency
Tail probability < mean cut to keep causalitycausality
Other distributions can be easily i l t d (simulated (e.g.
uniform) Jitter+Latency can y
be > than integration time
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
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Jitter Simulations (2/2)
Ideal (no jitter) vs. l lif t llreal-life controller
Time line:1 received1. received
measurement event (green)
2 t ll t t2. controller output update (blue w/o jitter, red w/ jitter)
Missed frames are also simulated
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
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Results of Jitter Simulations
Latency requirement for t t ELT WFRTCprototype ELT WFRTC
20μs (1% sampling time) Assumed optimal gain p g
configurations computed for latency study
Jitter up to 1% fully negligible
@10% Jitter some (small) @10% Jitter some (small) performance degradation observable
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
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More insight into Jitter Results
Control Jitter:
Multiplicative perturbation in output to the controller
Weighted by derivative-like actiong y
Modulated by jitter noise
Jitter induced perturbation expected to increase if:
Exogenous signals with higher power @ high freqs interaction with Exogenous signals with higher power @ high freqs interaction with measurement noise/ higher order systems
High controller gain @ high freqs more sophisticated control
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012
algorithms are considered.
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Conclusions
Set up of methodologies to analyze impact of latency and jitter on AO p g y p y jsystem performance focusing on realistic operational scenarios
Analysis proposed includes the major contributors to AO system performance in ELTsperformance in ELTs
Results of the analysis to be used to identify best cost effective technology for WFRTC
Future work
Evaluate realistic models of computer jitter Extend the analysis beyond SCAO systemsy y y Evaluate Jitter trade off considering more involved control strategies Validate analysis using laboratory facilities
Impact of Latency and Jitter in AOS performance for ELTs | Dec. 2012