臺灣博碩士論文加值系統

粗糙地面對電磁波散射的研究已經有四十年之久了。在理論模式、電腦模擬、以及實驗的量測都曾投入大量的研究心力。以往廣泛使用的散射模式為克希荷夫模式和小擾動模式。然而此兩種模式只能分別使用在地面起伏很大以及很小的情況下。
近年來由所提出的積分方程模式是一個適用範圍更廣的模式，它同時也涵概了兩個以往常用的理論模式。然而若要使得此模式更趨完整精確，有幾個問題尚待修正。其中之一是模式的推導中曾對格林函數的波譜表示式做近似簡化。1997年Dr. Fung所發表的文章中曾探討這個問題並重新修正積分方程模式。然而在其推導過程中，仍然採用舊的近似法來計算模式中的補償場係數。為了得到更加精確的積分方程模式，我們推導出新的補償場係數，且將整個積分方程模式加以整理。將此更精確模式與1997年所發表的模式比較，我們可以發現在地表粗糙起伏偏大時，兩者結果之差距會明顯表現出來。
另一個問題是模式中所需用到的弗芮耳反射係數。傳統上將其近似成入射角或鏡射角之函數。然而這兩種近似的適用範圍有限。本論文提出一個新的反射係數估算模式，在高頻與低頻時此模式相等於以上兩種近似，且很自然地連結前兩種近似。將其應用在積分方程模式上，並與電腦模擬以及實驗量測所得的資料相比對，我們得到了相當好的結果。再者由於自然地表並非單一尺度，某些多重尺度地面的散射機制也將詳細探討。
有了完整的散射理論模式後，我們將它應用於遙測領域中，以實驗室量測資料或衛星影像反衍出地面粗糙度與含水量。我們結合積分方程模式與類神經網路，所得到的參數反衍結果十分良好。

Recently, the Integral Equation Model (IEM) developed for rough surface scattering has been widely used to interpret the measured data from laboratory-controlled experiments and field measurements. Satisfactory results between model and data were reported in the literatures. In this dissertation, two simplifying approximations made in the derivation of IEM are investigated for further improvements of model itself and its applications.
First of all, a more complete expression of the multiple scattering terms in IEM model is developed by removing a simplifying assumption in the spectral representation of the Green''s function used in the scattered field expression of the IEM. The complementary field coefficients in IEM are rederived based on a new surface slope expression. As a result, the effects of multiple scattering can be estimated more accurately. Numerical calculations and comparisons with numerical simulations are provided to demonstrate the results.
Next, instead of the traditional approximations of the Fresnel reflection coefficients used in scattering models, which are only applicable in either a perfectly smooth or a perfectly rough surface, a new reflection coefficient model for an irregular boundary is proposed to account for the roughness dependency. It is demonstrated that the traditional approximations which replace the local incident angle in the Fresnel reflection coefficients, depending on the cases of interest, by either the incident angle or the angle along the specular direction, are special cases of the new model. In our comparisons, when the new reflection coefficient model are incorporated into the IEM, excellent agreements with both simulated data and laboratory measurements are obtained, proving the effectiveness of the new model.
Since the IEM model has been developed to cover a wide range of surface roughness, it thus allows us to study the scattering properties of multiscale rough surfaces in more detail. The insufficiency of using a correlation length to characterize the horizontal scale of the roughness is pointed out and its effect on the backscattering behavior is also discussed. It is concluded that the general description of a multiscale rough surface with a correlation length may not be appropriate to characterize the wave scattering behavior, and, even worse, may lead to misunderstanding of the scattering properties.
Finally, the revised IEM model is applied to the problem of retrieval of parameters from a rough surface. A dynamic learning neural network is used to perform the inversion of surface parameters, where the necessary training data sets are generated using the IEM model. Parameters to be inverted include surface roughness in horizontal and vertical scale and dielectric constant. Applications of the inversion scheme to co-polarized measurements of both laboratory experiment and AIRSAR data result in estimated values of surface parameters for soil surface that compare favorably with the ground truth.

COVER
TABLE OF CONTENTS
ABSTRACT
LIST OF FIGURES
LIST OF TABLES
CHAPTER
1 Introduction
1.1 Background
1.2 Objectives
2 Integral Equation Model
2.1 Estimation of Surface Tangential Fields
2.2 Far-Zone Scattered Field and Scattering Coefficients
2.3 The Simplifying Approximations in the IEM Model
3 A New Expression for the Multiple Scattering in the IEM Model
3.1 Formulation of the Problem
3.2 Numerical Illustrations and Discussion
4 A Reflection Coefficient Model for a Dielectric Irregular Boundary
4.1 The Fresnel Reflection Coefficients
4.2 Model Development
4.3 Validation by Comparisions with the Moment Method
4.3.1 The Effect of Surface Spectrum on the Transition Behaviors
4.3.2 The Effect of Surface Dielectric and RMS Slope on The Transition Behavious
4.4 Validation by Comparisons with Labroatory Measurements
5 The Scattering Properties of Multiscale Rough Surfaces
5.1 Characterization of Two-Scale Rough Surface Scattering
5.2 A Study of Backscattering from Modulated Rough Surface
5.2.1 Analysis of Surface Correlation and Roughness Spectra
5.2.2 Backscsattering Behavior
6 Inversion of Soil Surface Parameters by a Neural Network Trained with the IEM Model
6.1 Earlier Literature Review
6.2 Retrieval Scheme and Sensitivity Analysis
6.3 Numerical Illustrations
6.4 Applications to Labratory Measurement and SAR Data
7 Conclusions
APPENDIX
BIBLIOGRAPHY

1. S. O. Rice, Reflection of Electromagnetic Waves from Slightly Rough Surfaces, Communications in Pure and Applied Mathematics, vol. 4, pp. 361-378, 1951.
2. P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon Press, Oxford, 1963.
3. P. Beckmann, "Scattering by composite rough surfaces," Proc. IEEE, vol. 53, no. 8, pp. 1012-1015, 1965.
4. M. I. Sancer, "An analysis of the vector Kirchhoff equations and the associated boundary-line change," Radio Sci., vol. 3, pp. 141-144, 1968.
5. A. K. Fung and H. J.Eom, "Multiple scattering and depolarization by a randomly rough Kirchhoff surface," IEEE Tran. Ant. and Prop., vol. Ap-29, no. 3, pp. 463-471, 1981.
6. A. K. Fung, and H. J. Eom, "Note on the Kirchhoff rough surface solution in backscattering," Radio Sci., vol. 16, no. 3, pp. 299-302, 1981.
7. F.T. Ulaby, R.K. Moore, and A. K. Fung, Microwave Remote Sensing, Active and Passive, vol.II, chapter 12. Reading, MA: Addison-Wesley, 1982.
8. S. T. Wu and A. K. Fung, "A Noncoherent Model for Microwave Emissions and Backscattering from the Sea Surface," J. Geophys. Res., 77, pp. 5917-5929, 1972.
9. D. E. Barrick and W. H. Peake, "A review of scattering from surfaces with different roughness scales," Radio Sci., vol. 3, no. 8, pp. 865-868, 1968.
10. G. R. Valenzuela, "Scattering of electromagnetic waves from a tilted slightly rough surfaces," Radio Sci., vol. 3, pp.1057-1066, 1968.
11. G. R. Valenzuela, "Depolarization of EM waves by slightly rough surfaces," IEEE Trans. Ant. and Prop, vol. AP-15, no. 4, pp. 552-557, 1967.
12. A. K. Fung, "Theory of cross-polarized power returned from a random surface," Appl. Sci. Res., vol. 18, pp. 50-60, 1967.
13. J. W. Wright, "A new model for sea clutter," IEEE Trans. Ant. and Prop, vol. AP-16, no. 2, pp. 217-223, 1968.
14. M. L. Burrows, "On the composite model for rough-surface scattering," IEEE Trans. Ant. and Prop, vol. AP-21, no. 2, pp. 241-243, March 1973.
15. G. S. Brown, "Backscattering from a Gaussian-distributed perfectly conducting rough surface," IEEE Trans. Ant. and Prop, vol. AP-26, no. 3, pp. 472-482, May 1978.
16. G. S. Brown, "A comparison of approximate theories for scattering from rough surfaces," Wave Motion, vol. 7, pp. 195-205, 1985.
17. A. Guissard, P. Sobieski, "An approximate model for the microwave brightness temperature of the sea," Int. J. Remote Sens., vol. 8, no. 11, pp. 1607-1627, Nov. 1987.
18. P. Sobieski, A. Guissard, C. Baufays, and P. Siraut, "Sea surface scattering calculations in martime satellite communications," IEEE Trans. Comm., vol. 41, no. 10, pp. 1525 - 1533, Oct. 1993.
19. G. S. Brown, "A stochastic Fourier Transform approach to scattering from perfectly conducting randomly rough surfaces," IEEE Trans. Ant. and Prop, vol. AP-30, pp. 1135-1144, May 1982.
20. G. S. Brown, "Simplification in the stochastic Fourier Transform approach to random surface scattering," IEEE Trans. Ant. and Prop, vol. AP-33, pp. 48-55, May 1985.
21. D. P. Winebrenner, and A. Ishimaru, "Application of the phase perturbation technique to randomly rough surfaces," J. Opt. Soc. Am.A, vol. 2, no. 12 pp. 2285-2294, 1985.
22. S. L. Broschat, "The phase perturbation approximation for rough surface scattering from a Pierson-Moskowitz sea surface," IEEE Trans. Geosci. Remote Sensing, vol.31, no. 1, pp. 278-283, 1993.
23. E. Barhar, "Full-wave solutions for the scattered radiation fields from rough surfaces with arbitrary slope and frequency," IEEE Trans. Ant. and Prop, vol. AP-28, pp. 11-21, 1980.
24. E. Barhar, and Y. Zhang, "A new unified full wave approach to evaluate the scatter cross sections of composite random surfaces," IEEE Trans. Geosci. Remote Sensing, vol.34, no. 4, July, pp. 973-980, 1996.
25. A. K. Fung, Z. Li, and K. S. Chen, "Backscattering from a randomly rough dielectric surface," IEEE Trans. Geosci. Remote Sensing, Vol.30, pp. 356-369, 1992.
26. A. K. Fung, Microwave Scattering and Emission Models and Their Applications, Artech House, Norwood, MA, 1994.
27. A. K. Fung, and K. S. Chen, "A validation of the IEM surface scattering model," Proc. IGARSS95, pp.933-935, 1995.
28. G. Nesti, P. Pamploni, P. Coppo, M. Hallikainen, M. Mancini, P. Trouch, and von Shonermark, M., "Experimental reserach at the EMSL on scattering properties of non vegetated terrains," Proc. IGARSS95, pp.2020-2022, 1995.
29. G. Nesti, R. Estevan de Quesada, J.M. Lopez, and A.J. Sieber, "Implementation of the integral equation model for rough surfaces with generic isotropic autocorrelation functions," Proc. IGARSS97, pp. 1361-1364, 1997.
30. P. Coppo, S. Lolli, G. Macelloni, G. Nesti, P. Pampaloni, R. Ruisi, D. Tarchi, "Experimental validation of surface scattering and emission models," Proc. IGARSS97, pp. 904-906, 1997.
31. K. S. Chen, and A. K. Fung, "A comparison of backscattering models for rough surfaces," IEEE Trans. Geosci. Remote Sensing, vol.33, no. 1, Jan, pp. 195-200, 1995.
32. C. Y. Hsieh, A. K. Fung, G. Nesti, A. Sieber and P. Coppo, "A further study of the IEM surface scattering model," IEEE Trans. Geosci. Remote Sensing, Vol. 35, No. 4, pp. 901-909, 1997.
33. L. Tsang, J.A. Kong, and R.T. Shin, Theory of Microwave Remote Sensing, New York: Wiley, 1985.
34. M. F. Chen, and A. K. Fung, "A numerical study of the regions of validity of the Kirchhoff and small perturbation rough surface scattering models," Radio Science, vol. 23, no. 2, pp.163-170, 1988.
35. R. M. Axline and A. K. Fung, "Numerical computation of scattering from a perfectly conducting random surface," IEEE Trans. Antennas. Propagat., vol. AP-26, no. 3, pp.482-488, May, 1978.
36. M.F.Chen, K. S. Chen and A. K. Fung, "A study of the validity of the Integral Equation Model by moment method simulation: cylindrical case," Remote Sensing of Environment, Vol. 29, pp. 217-228, 1989.
37. M. F.Chen and S. Y. Bai, "Computer simulation of wave scattering from a dielectric random surface in two dimensions: cylindrical case," J. Electromagnetic Waves and Applications, Vol. 4, no. 10, pp.963-982, 1990.
38. L. Tsang, C.H. Chan, K. Park, H. Sangani, A. Ishimaru, and P. Phu, "Monte Carlo simulations of large scale composite random rough surface scattering based on the banded matrix iterative approach," J. Opt. Soc. Amer., vol. 11, pp.691-696, 1994.
39. A. Beaudoin, T. L. Toan, and Q. H. J. Gwyn, "SAR observations and modeling of the C-band backscatter variability due to multiscale geometry and soil moisture" IEEE Trans. Geosci. Remote Sensing, vol.28, no. 5, pp. 886-895, Sep. 1990.
40. A. T. Manninen, "Multiscale surface roughness and backscattering - Summary," Journal of Electromagnetic Waves and Applications, vol. 11, pp.471-475, 1997.
41. Y. C. Tzeng, K. S. Chen, W. L. Kao, and A. K. Fung, "A dynamic learning neural network for remote sensing applications," IEEE Trans. Geosci. Remote Sensing, vol.32, pp. 1096-1102, Sept. 1994.
42. A. J. Poggio and E. K. Miller, "Integral equation solution of three dimensional scattering problems," Computer Techniques for Electromagnetics, Pergamon, New York, 1973, Ch. 4.
43. A. K. Fung, M. R. Shah, and S. Tjuatja, "Numerical simulation of scattering from three-dimensional randomly rough surfaces, " IEEE Trans. Geosci. Remote Sensing, vol.32, no. 5, pp. 986-994, 1994.
44. L. Tsang, C. H. Chan, K. Park, and H. Sangani, "Monte Carlo simulations of large scale problems of random rough surface scattering and applications to grazing incidence with the BMIA/canonical grid method," IEEE Trans. Antennas Propagat., vol. 43, pp.851-859, 1995.
45. L. Tsang, C. H. Chan, and K. Park, "Backscattering enhancement of a two-dimensional rough surface (three-dimensional scattering) based on Monte Carlo simulations," J. Opt. Soc. Amer. A, vol. 11, pp.711-715, 1994.
46. J. T. Johnson, R. T. Shin, J. A. Kong, L. Tsang, and K. Park, "A numerical study of the composite surface model for ocean backscattering, " IEEE Trans. Geosci. Remote Sensing, vol. 36, pp. 72-83, 1998.
47. K. Pak, L. Tsang and J. Johnson, "Numerical simulations and backscattering enhancement of electromagnetic waves from two-dimensional dielectric random rough surfaces with the sparse-matrix canonical grid method," J. Opt. Soc. Am. A. vol. 14, pp. 1515-1529, 1997.
48. F. Mattia, J. C. Souyris, T. L. Toan, D. Casarano, F. Posa, and M. Borgeaud, "On the surface roughness characterization for SAR data analysis," Proc. IGARSS97, pp. 898 - 900, Singapore, 1997.
49. J. A. Ogilvy, Theory of wave scattering from random rough surfaces, Philadelphia : Institute of Physics Publishing, 1992.
50. K. S. Chen, T. D. Wu, and A. K. Fung, "Modulation effects on surface scattering," PIERS 1997, Cambridge, 1997.
51. K. S. Chen, T. D. Wu and A. K. Fung, "A study of backscattering from multiscale rough surfaces," J. Electromagnetic Waves and Appl., vol. 12, pp. 961-978, 1998.
52. Y. Oh, K. Sarabandi, and F. T. Ulaby, "An empirical model and inversion technique for radar scattering from bare soil surface," IEEE Trans. Geosci. Remote Sensing, vol.30, pp. 370-381, Mar. 1992.
53. P. C. Dubois, J. J. Van Zyl, and E. T. Engman, "Measuring soil moisture with imaging radar," IEEE Trans. Geosci. Remote Sensing, vol.33, pp. 195-926, July 1992.
54. J. Shi et al., "Estimation of bare surface soil moisture and surface roughness parameter using L-band SAR image data," IEEE Trans. Geosci. Remote Sensing, vol.35, pp. 1254-1265, Sep. 1997.
55. L. Tsang, Z. Chen, S. Oh, R. J. Mark II, and A. T. C. Chang, "Inversion of snow parameters from passive microwave remote sensing measurements by a neural network trained with a multiple scattering model," IEEE Trans. Geosci. Remote Sensing, vol.30, pp. 1015-1024, Sep. 1992.
56. D. T. Davis, Z. Chen, L. Tsang, J. N. Hwang, and A. T. C. Chang, "Retrieval of snow parameters by interactive inversion of a neural network," IEEE Trans. Geosci. Remote Sensing, vol.31, pp. 842-851, July 1993.
57. L. Li, J. Vivekanandan, C. H. Chan, and L. Tsang, "Microwave radiometric technique to retrieve vapor, liquid and ice, part I - development of a neural network-based inversion method," IEEE Trans. Geosci. Remote Sensing, vol.35, pp. 224-236, Mar. 1997.
58. J. Vivekanandan, L. Li, L. Tsang, and C. H. Chan, "Microwave radiometric technique to retrieve vapor, liquid and ice, part II - joint studies of radiometer and radar in winter clouds," IEEE Trans. Geosci. Remote Sensing, vol.35, pp. 224-236, Mar. 1997.
59. M. S. Dawson, A. K. Fung, and M. T. Manry, "Surface parameter retrieval using fast learning neural networks," Remote Sensing Reviews, vol.7, pp. 1-18, 1993.
60. M. S. Dawson, A. K. Fung, and M. T. Manry, "A robust statistical-based estimator for soil moisture retrieval from radar measurements," IEEE Trans. Geosci. Remote Sensing, vol.35, pp. 57-67, 1997.
61. K. S. Chen, W. L. Kao, and Y. C. Tzeng, "Retrieval of surface parameters using dynamic learning neural network," Int. J. Remote Sensing, vol. 16, pp. 801-809, 1995.
62. K. S. Chen, Y. C. Tzeng, and P. T. Chen, "Retrieval of ocean winds from satellite scatterometer by a neural network," IEEE Trans. Geosci. Remote Sensing, in press 1999.
63. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, in Numerical Recipes in Fortran. NY: Cambridge University Press, 1992
64. M. C. Dobson, F. T. Ulaby, and M. T. Hallikainen, and M. A. El-Rayes, "Microwave dielectric behavior of wet soil, Part II: Dielectric mixing model," IEEE Trans. Geosci. Remote Sensing, vol.23, pp. 35-46, Jan. 1985.
65. N. P. Peplinski, F. T. Ulaby, and M. C. Dobson, "Dielectric properties of soil in the 0.3-1.3 GHz range," IEEE Trans. Geosci. Remote Sensing, vol.33, pp. 803-807, May. 1995.