volume | PIER Journals

Abstract

Spectral decomposition in 2-D k_z-m space is used to develop transfer functions that relate modal electromagnetic fields on concentric cylindrical surfaces. It is shown that all time-average radiated power is generated by superluminal modes (phase velocity v_z > c) which are confined to the baseband |k_z| > k₀. Subluminal modes, with k_z outside of the radiated band, are radially evanescent but permit recovery of imaging resolution that exceeds the usual diffraction limit provided by the radiated fields. Outward translation between cylinder surfaces is found to have a stable low-pass 2-D transfer characteristic in k_z-m space, where spatial resolution decreases with increased radius. The inverse transfer functions for inward translation of field components (termed backpropagation) employ a high-pass process that amplifies subluminal evanescent modes, thus potentially enhancing resolution while also amplifying measurement noise. A 2-D filter with flat elliptical passband and Gaussian roll-off is used to mitigate noise amplification with backpropagation. Outward translation and backpropagation are tested using sampled data on finite-length cylinders for various noise levels.

1. Ransom, P. L. and R. Mittra, "A method of locating defective elements in large phased arrays," Proc. IEEE, Vol. 59, 1029-1030, 1971.

2. Harms, P. H., J. G. Maloney, M. P. Kesler, E. J. Kunster, and G. S. Smith, "A system for unobtrusive measurement of surface currents," IEEE Trans. Antennas Propagat., Vol. 49, 174-185, 2001.
doi:10.1109/8.914266 Google Scholar

3. Guler, M. G. and E. B. Joy, "High resolution spherical microwave holography," IEEE Trans. Antennas Propagat., Vol. 43, 464-472, 1995.
doi:10.1109/8.384190 Google Scholar

4. Joy, E. B.M. G. Guler, C. H. Barrett, A. R. Dominy, and R. E. Wilson, "Near-field measurement of radome anomalies," Proc. 9th Antenna Measurement Tech. Assoc. Symposium, No. 10, 235-240, 1987.

5. Guler, M. G., "Spherical microwave holography," Ph.D. dissertation, No. 12, 1993. Google Scholar

6. Medgyesi-Mitchang, L. N., P. G. Moore, D. L. Smith, and S. G. Lambrakos, "Ultra-near fields of bodies of translation with discontinuities: Ï‰-k representations," J. Electromagn. Waves Appl., Vol. 15, 1701-1723, 2001. Google Scholar

7. Medgyesi-Mitchang, L. N., P. G. Moore, D. L. Smith, and S. G. Lambrakos, "Ultra-near fields of penetrable bodies of translation: Ï‰-k representations," J. Electromagn. Waves Appl., Vol. 16, 1467-1483, 2002. Google Scholar

8. Wawrzyniak, D. J., "Electromagnetic imaging of electromagnetic scatterers," M.S. thesis, No. 6, 1997. Google Scholar

9. Williams, E. G., Fourier Acoustics: SoundR adiation and NearfieldA coustical Holography, Academic Press, 1999.

10. Williams, E. G., "Supersonic acoustic intensity," J. Acoust. Soc. Am., Vol. 97, 121-127, 1995.
doi:10.1121/1.412991 Google Scholar

11. Williams, E. G., B. Houston, and J. A. Bucaro, "Experimental investigation of the wave propagation on a point-driven, submerged capped cylinder using k-space analysis," J. Acoust. Soc. Am., Vol. 87, 513-522, 1990.
doi:10.1121/1.398922 Google Scholar

12. Williams, E. G., H. D. Dardy, and K. B. Washburn, "Generalized nearfield acoustical holography for cylindrical geometry: Theory and experiment," J. Acoust. Soc. Am., Vol. 81, 389-407, 1987.
doi:10.1121/1.394904 Google Scholar

13. Morgan, M. A., "Electromagnetic source imaging using superluminal cylindrical modes," Abstracts for USNC/URSI Radio Science Meeting, No. 7, 1999. Google Scholar

14. Morgan, M. A., "Near-field imaging using cylindrical harmonic backpropagation," Abstracts for Progress in Electromagnetics Research Symposium, No. 7, 2000.

15. Stutzman, W. L. and G. A. Thiele, Antenna Theory andDesign, 2nd Ed., 1998.

16. Silver, S., Microwave Antenna Theory andDesign, Chapter 7, 1949.

17. Ramo, S., J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communications Electronics, 3rd Ed., 1994.

18. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Chapter 9, 1970.

19. Papoulis, A., Signal Analysis, Chapter 3, 1977.