When performing electromagnetic material characterization, an error analysis should be performed to determine the sensitivity of the extracted permittivity and permeability. Traditional error analysis methods such as the error propagation method and Monte Carlo simulations can pose difficulties when analyzing free space material characterization methods. This paper thus shows how interval analysis can be implemented to perform error analysis on free space material characterization methods and provide an alternate means to perform error analysis. Background is presented on interval representations and interval functions, and a procedure for performing error analysis with interval analysis is presented. An error analysis is performed on the free space implementation of the layer-shift method with interval analysis and the subsequent standard deviations computed with interval analysis are compared to standard deviations computed through Monte Carlo simulation.
1. Moore, R. E., Interval Arithmetic and Automatic Error Analysis in Digital Computing, 1962.
2. Snyder, J. M., "Interval analysis for computer graphics," SIGGRAPH Comput. Graph., Vol. 26, No. 2, 121-130, 1992. doi:10.1145/142920.134024
3. Leenaerts, D. M. W., "Application of interval analysis for circuit design," IEEE Journal of Circuits and Systems, Vol. 37, No. 6, 803-807, 1990. doi:10.1109/31.55038
4. Matthews, J., R. Broadwater, and L. Long, "The application of interval mathematics to utility economic analysis," IEEE Transactions on Power Systems, Vol. 5, 177-181, Feb. 1990. doi:10.1109/59.49103
5. Kieffer, M., L. Jaulin, R. Walter, and D. Meizel, "Robust autonomous robot localization using interval analysis," Reliable Computing, Vol. 6, 337-362, 2000, 10.1023/A:1009990700281. doi:10.1023/A:1009990700281
6. Polydorides, N., "Linearization error in electrical impedance tomography," Progress In Electromagnetics Research, Vol. 93, 323-337, 2009. doi:10.2528/PIER09052503
7. Koivisto, P., "Reduction of errors in antenna radiation patterns using optimally truncated spherical wave expansion," Progress In Electromagnetics Research, Vol. 47, 313-333, 2004. doi:10.2528/PIER03120301
8. Ma, L., Z.-F. Li, and G. Liao, "System error analysis and calibration methods for multi-channel SAR," Progress In Electromagnetics Research, Vol. 112, 309-327, 2011.
9. Fenner, R. and E. Rothwell, "Deficiency in the error propagation method for sensitivity analysis of free space material characterization," 2012 15th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM), 1-3, 2012. doi:10.1109/ANTEM.2012.6262408
10. Fenner, R., "Error analysis of reflection-only material characterization," , Ph.D. Thesis, Michigan State University, 2011.
11. Hargreaves, G. I., "Interval analysis in MATLAB," Numerical Analysis Report, Vol. 416, Manchester Center for Computational Mathematics, Manchester, 2002.
12. Moore, R. E., R. B. Kearfott, and M. J. Cloud, "Introduction to interval analysis," SIAM, 2009. doi:10.1007/BF01404681
13. Gargantini, I. and P. Henrici, "Circular arithmetic and the determination of polynomial zeros," Numerische Mathematik, Vol. 18, No. 4, 305-320, 1971. doi:10.1007/BF02281720
14. Klatte, R. and C. Ullrich, "Complex sector arithmetic," Computing, Vol. 24, 139-148, Jun. 1980.
15. Kalachev, A. A., "The methods of investigation of complex dielectric permittivity of layer polymers containing conductive inclusions," Optical and Electrical Properties of Polymers, Materials Reseach Society Symposia Proceedings, Vol. 214, J. A. Emerson and J. M. Torkelson, Eds, 119-124, Pittsburgh, PA, 1991. doi:10.1163/156939306779292264
16. Chen, X., D. Liang, and K. Huang, "Microwave imaging 3-D buried objects using parallel genetic algorithm combined with FDTD technique," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1761-1774, Dec. 2006. doi:10.1029/2011RS004755
17. Fenner, R. A., E. J. Rothwell, and L. L. Frasch, "A comprehensive analysis of free-space and guided-wave techniques for extracting the permeability and permittivity of materials using reflectiononly measurements," Radio Science, Vol. 47, No. 1, n/a-n/a, 2012.