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U N C L A S S I F I E D Slide 1
Practical Considerations for Analysis By Synthesis, a Real World Example using DARHT
Radiography.
By James L. Carroll2013
LA-UR-13-23130
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA
U N C L A S S I F I E D
Abstract The mathematical theory of inverse problems has been intensely explored for
many years. One common solution to inverse problems involves analysis by synthesis, where a forward model produces a synthetic data set, given model inputs, and optimization is used to find model inputs that minimize the difference between the real data and the synthetic data. Some beautiful mathematical results demonstrate that under ideal situations, this procedure returns the MAP estimate for the parameters of the model. However, many practical considerations exist which makes this procedure much harder to actually use and implement. In this presentation, we will evaluate some of these practical considerations, including: Hypothesis testing over confidence, overfitting systematic errors instead of overfitting noise, optimization uncertainties, and complex measurement system calibration errors. The thrust of this work will be to attempt to qualitatively and quantitatively assess the errors in density reconstructions for the Dual Axis Radiographic Hydrotest Facility (DARHT) and LANL.
Slide 2
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U N C L A S S I F I E D
What is Hydrodynamic Testing? High Explosives (HE) driven experiments to study nuclear weapon
primary implosions.• Radiographs of chosen instants during dynamic conditions.• Metals and other materials flow like liquids under high temperatures and pressures
produced by HE.
Slide 3
Static Cylinder Set-up Static Cylinder shot Static Cylinder Radiograph
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U N C L A S S I F I E D Slide 4
DARHT:
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THE FTO
Slide 5
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Challenges:Dose/Dynamic Range
Slide 6
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U N C L A S S I F I E D
Static Test Objects (e.g. FTO)
Allow us to calibrate against objects with known geometry. Comparison of machines (microtron, PHERMEX, DARHT)Benchmark radiographic codes (e.g. SYN_IMG, the BIE)Benchmark scatter codes (MCNP).Develop understanding and train experimentalists.
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U N C L A S S I F I E D
Collimation
Rough collimation controls angular extent and direction of radiation fan.Shields from source scatter.A Graded collimator is an approximate pathlength inverse of object and flattens field for reduced dynamic range and reduced scatter.An exact graded collimator would produce an image with no features!
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U N C L A S S I F I E D
Challenges
Dose/Dynamic Range
Slide 9
Graded collimator
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(FTO+Collimator+Fiducial+plates)
Slide 10
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U N C L A S S I F I E D
A forward modeling approach is currently used in analysis of (single-time) radiographic data
True radiographicphysics
?
True density(unknown)
Inverse approach(approximatephysics)
Transmission (experimental)
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA
U N C L A S S I F I E D
A forward modeling approach is currently used in analysis of (single-time) radiographic data
True radiographicphysics
?
True density(unknown)
Inverse approach(approximatephysics)
Transmission (experimental)
How do we extract density from this transmission?
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA
U N C L A S S I F I E D
A forward modeling approach is currently used in analysis of (single-time) radiographic data
True radiographicphysics
?
True density(unknown)
Model density(allowed to vary)
Inverse approach(approximatephysics)
Comparestatistically
Simulatedradiographicphysics
Transmission (experimental)
Transmission (simulated)
How do we extract density from this transmission?
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA
U N C L A S S I F I E D
A forward modeling approach is currently used in analysis of (single-time) radiographic data
We develop a parameterizedmodel of the density (parameters here might be edge locations, density values)
True radiographicphysics
?
True density(unknown)
Model density(allowed to vary)
Inverse approach(approximatephysics)
How do we extract density from this transmission?
Comparestatistically
Simulatedradiographicphysics
Transmission (experimental)
Transmission (simulated)
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA
U N C L A S S I F I E D
A forward modeling approach is currently used in analysis of (single-time) radiographic data
We develop a parameterizedmodel of the density (parameters here might be edge locations, density values)
True radiographicphysics
?
True density(unknown)
Model density(allowed to vary)
Inverse approach(approximatephysics)
How do we extract density from this transmission?
Comparestatistically
Simulatedradiographicphysics
Transmission (experimental)
Transmission (simulated)
Model parameters are varied so that the simulated radiograph matches the experiment
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA
U N C L A S S I F I E D
A forward modeling approach is currently used in analysis of (single-time) radiographic data
We develop a parameterizedmodel of the density (parameters here might be edge locations, density values)
True radiographicphysics
?
True density(unknown)
Model density(allowed to vary)
Inverse approach(approximatephysics)
How do we extract density from this transmission?
Comparestatistically
Simulatedradiographicphysics
Transmission (experimental)
Transmission (simulated)
Model parameters are varied so that the simulated radiograph matches the experiment
p(m|r)
h(m)
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U N C L A S S I F I E D
Bayesian Analysis
Slide 17
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Assumptions
Where n is some independent , additive noise. If n is Gaussian then:
Slide 18
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U N C L A S S I F I E D
Plug that in:
If I assume a uniform prior then:
Slide 19
Operated by Los Alamos National Security, LLC for the U.S. Department of Energy’s NNSA
U N C L A S S I F I E D
A forward modeling approach is currently used in analysis of (single-time) radiographic data
We develop a parameterizedmodel of the density (parameters here might be edge locations, density values)
True radiographicphysics
?
True density(unknown)
Model density(allowed to vary)
Inverse approach(approximatephysics)
How do we extract density from this transmission?
Comparestatistically
Simulatedradiographicphysics
Transmission (experimental)
Transmission (simulated)
Model parameters are varied so that the simulated radiograph matches the experiment
p(m|r)
h(m)
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U N C L A S S I F I E D
The Solution Building h(m) Optimizing parameters m
Slide 21
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U N C L A S S I F I E D
Using the Prior Computer vision is notoriously under constrained. Penalty terms on the function to be optimized can often overcome this
problem. These terms can be seen as ill-posed priors
• GGMRF
Slide 22
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Dealing with Scatter
Slide 23
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U N C L A S S I F I E D Slide 24
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U N C L A S S I F I E D
Example, approximating scatter
Slide 25
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Beautiful, Yes!
Slide 26
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Practical Considerations
Slide 27
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Axis 2, Time 1 Flat Field
Slide 28
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Flatfield Components
𝑭=𝑩𝒑𝑫𝒓+𝑺 𝒇Slide 29
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U N C L A S S I F I E D
Necessary Assumptions Axis 2 Time 1 FTO
Slide 30
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U N C L A S S I F I E D
Necessary Assumptions Axis 2 Time 1 FTO
Slide 31
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U N C L A S S I F I E D
Necessary Assumptions Axis 2 Time 1 FTO
Slide 32
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U N C L A S S I F I E D
Necessary Assumptions Axis 2 Time 1 FTO
Slide 33
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Necessary Assumptions Axis 2 Time 1 FTO
Slide 34
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Produce Low Frequency Fit to Flat Field
Slide 35
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Learning Fields Treat entire known chain
(FTO+collimator+fiducial plate) as a fiducial
Examine fields Produced
Slide 36
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4df s 4df g FTO Residuals
5% residuals
Slide 37
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Nov 2012 FTO Data Scatter and Gain Analysis (5 plates) 4DF S 4DF G
48% 8%
Slide 38
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Axis 2, Time 1 Flat Field
Slide 39
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Center Camera Only FTO Residuals
Slide 40
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Inferred Scatter,FTO
Slide 41
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So What? Simulation is broken, Just learn whatever the field is…
Slide 42
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Width of the Known Ring for FTO
5.4-4.5 5.4-4.25 5.4-3.5 5.4-0
Slide 43
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Additional synthetic fiducials in FTO graded collimator, with FTO
Slide 44
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Width of the Known Ring for FTO
5.4-4.5 5.4-4.25 5.4-3.5 5.4-0 Fiducials
Slide 45
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Density in the FTO Ta
Slide 46
With Fiducials: Without Fiducials:
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U N C L A S S I F I E D
Conclusion Scatter is more curved than previously thought Curved fields can’t be learned accurately in existing thin fiducial ring Fiducials inside unknown objects don’t perfectly solve the problem But they can help
Slide 47
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Questions
Slide 48