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 Slide 1 Practical Considerations for Analysis By Synthesis, a Real World Example using DARHT Radiography. By James L. Carroll 2013 LA-UR

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

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 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-upStatic Cylinder shotStatic Cylinder Radiograph

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 Slide 4 DARHT:

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 THE FTO Slide 5

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 Challenges: Dose/Dynamic Range Slide 6

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 Static Test Objects (e.g. FTO) l Allow us to calibrate against objects with known geometry. l Comparison of machines (microtron, PHERMEX, DARHT) l Benchmark radiographic codes (e.g. SYN_IMG, the BIE) l Benchmark scatter codes (MCNP). l Develop understanding and train experimentalists.

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 Collimation l Rough collimation controls angular extent and direction of radiation fan. l Shields from source scatter. l A Graded collimator is an approximate pathlength inverse of object and flattens field for reduced dynamic range and reduced scatter. l An exact graded collimator would produce an image with no features!

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 Challenges Dose/Dynamic Range Slide 9 Graded collimator

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 (FTO+Collimator+Fiducial+plates) Slide 10

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 radiographic physics ? True density (unknown) Inverse approach (approximate physics) 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 radiographic physics ? True density (unknown) Inverse approach (approximate physics) 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 radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) Compare statistically Simulated radiographic physics 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 parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics 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 parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics 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 parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics Transmission (experimental) Transmission (simulated) Model parameters are varied so that the simulated radiograph matches the experiment p(m|r) h(m)

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 Bayesian Analysis Slide 17

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 Assumptions Where n is some independent, additive noise. If n is Gaussian then: Slide 18

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 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 parameterized model of the density (parameters here might be edge locations, density values) True radiographic physics ? True density (unknown) Model density (allowed to vary) Inverse approach (approximate physics) How do we extract density from this transmission? Compare statistically Simulated radiographic physics Transmission (experimental) Transmission (simulated) Model parameters are varied so that the simulated radiograph matches the experiment p(m|r) h(m)

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 The Solution Building h(m) Optimizing parameters m Slide 21

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 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

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 Dealing with Scatter Slide 23

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 Slide 24

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 Example, approximating scatter Slide 25

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 Beautiful, Yes! Slide 26

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 Practical Considerations Slide 27

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 Axis 2, Time 1 Flat Field Slide 28

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 Flatfield Components Slide 29

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 Necessary Assumptions Axis 2 Time 1 FTO Slide 30

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 Necessary Assumptions Slide 31

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 Necessary Assumptions Slide 32

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 Necessary Assumptions Slide 33

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 Necessary Assumptions Slide 34

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 Slide 35

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 Learning Fields Treat entire known chain (FTO+collimator+fiducial plate) as a fiducial Examine fields Produced Slide 36

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 4df s 4df g FTO Residuals 5% residuals Slide 37

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 Nov 2012 FTO Data Scatter and Gain Analysis (5 plates) 4DF S 4DF G 48% 8% Slide 38

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 Axis 2, Time 1 Flat Field Slide 39

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 Center Camera Only FTO Residuals Slide 40

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 Inferred Scatter, FTO Slide 41

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 So What? Simulation is broken, Just learn whatever the field is… Slide 42

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 Width of the Known Ring for FTO Slide 43

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 Additional synthetic fiducials in FTO graded collimator, with FTO Slide 44

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 Width of the Known Ring for FTO Fiducials Slide 45

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 Density in the FTO Ta Slide 46 With Fiducials:Without Fiducials:

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 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

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 Questions Slide 48