# Noninvasive cross section reconstruction with transport theory constraints

## Abstract

We consider the inverse problem of identifying the spatially variable absorption and scattering properties of a medium by measuring the exiting radiation when the body is actively interrogated. We formulate this inverse problem as a PDE-constrained optimization problem and solve it iteratively with Newton's method. The constraint is given by the radiative transport equation for neutral particles. Two examples are considered. The first is a dual inclusion domain with no scattering. This problem explores the convergence patterns of the method. The second problem is a central inclusion problem with scattering. This problem explores the optical thickness limit of the method. This optical thickness was determined to be 2-3 mean free paths. (authors)

- Authors:

- Texas A and M Univ., College Station, TX 77843-3133 (United States)

- Publication Date:

- Research Org.:
- American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)

- OSTI Identifier:
- 22105835

- Resource Type:
- Conference

- Resource Relation:
- Conference: PHYSOR 2012: Conference on Advances in Reactor Physics - Linking Research, Industry, and Education, Knoxville, TN (United States), 15-20 Apr 2012; Other Information: Country of input: France; 13 refs.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 22 GENERAL STUDIES OF NUCLEAR REACTORS; CARGO; CROSS SECTIONS; MEAN FREE PATH; NEUTRAL PARTICLES; NEWTON METHOD; OPTIMIZATION; SCATTERING; THICKNESS; TRANSPORT THEORY

### Citation Formats

```
Fredette, N., Ragusa, J., and Bangerth, W..
```*Noninvasive cross section reconstruction with transport theory constraints*. United States: N. p., 2012.
Web.

```
Fredette, N., Ragusa, J., & Bangerth, W..
```*Noninvasive cross section reconstruction with transport theory constraints*. United States.

```
Fredette, N., Ragusa, J., and Bangerth, W.. Sun .
"Noninvasive cross section reconstruction with transport theory constraints". United States.
doi:.
```

```
@article{osti_22105835,
```

title = {Noninvasive cross section reconstruction with transport theory constraints},

author = {Fredette, N. and Ragusa, J. and Bangerth, W.},

abstractNote = {We consider the inverse problem of identifying the spatially variable absorption and scattering properties of a medium by measuring the exiting radiation when the body is actively interrogated. We formulate this inverse problem as a PDE-constrained optimization problem and solve it iteratively with Newton's method. The constraint is given by the radiative transport equation for neutral particles. Two examples are considered. The first is a dual inclusion domain with no scattering. This problem explores the convergence patterns of the method. The second problem is a central inclusion problem with scattering. This problem explores the optical thickness limit of the method. This optical thickness was determined to be 2-3 mean free paths. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Jul 01 00:00:00 EDT 2012},

month = {Sun Jul 01 00:00:00 EDT 2012}

}