合成孔徑雷達（SAR）是一種先進的成像技術，能夠在各種天氣條件和光照情況下獲取地球表面的高解析度圖像。SAR最早於1951年被提出，並在1953年獲得第一幅測量的影像。SAR技術在軍事偵察、地球觀測、環境監測和災害管理等領域得到了廣泛應用。然而，SAR成像技術也面臨諸多挑戰，例如多普勒效應引起的頻率偏移、地面散射體的複雜回波信號處理、成像過程中的噪聲干擾等，這些因素均會影響成像品質。
在本文中，利用有限時域差分法（FDTD）和SAR對不同目標進行掃描。FDTD是一種數值分析技術，用於求解電磁場的時間域麥克斯韋方程組。FDTD方法通過在時間和空間上對電磁場進行離散化處理，逐步模擬電磁波的傳播過程。這種方法具有高度靈活性和準確性，適合處理複雜的邊界條件和異質介質中的波動問題。針對目標的尺寸、形狀和材料做分析，觀察不同情況下，雷達散射截面(RCS)的差異，並成功利用FDTD模擬SAR成像出目標物，在對兩個目標物以上進行掃描時，成像的幾何關係與實際物體位置和距離保持一致，這代表透過模擬結果即可判斷出實際位置為何。
有限時域差分法在計算效率上的優勢，使其在大規模數據處理和實時成像應用中顯示出潛力。未來，隨著研究的深入和技術的進一步成熟，基於FDTD方法的SAR成像技術有望在地球觀測、環境監測、軍事偵察等多個領域取得更加豐碩的成果。

Synthetic Aperture Radar (SAR) is an advanced imaging technology capable of acquiring high-resolution images of the Earth's surface under various weather conditions and lighting situations. SAR was first proposed in 1951 and achieved its first measured image in 1953. SAR technology has been widely used in military reconnaissance, Earth observation, environmental monitoring, and disaster management. However, SAR imaging technology also faces numerous challenges, such as frequency shifts caused by the Doppler effect, complex echo signal processing from ground scatterers, and noise interference during the imaging process, all of which can affect image quality.
In this paper, the Finite-Difference Time-Domain (FDTD) method and SAR are used to scan different targets. FDTD is a numerical analysis technique used to solve Maxwell's equations in the time domain for electromagnetic fields. By discretizing the electromagnetic field in time and space, the FDTD method simulates the propagation of electromagnetic waves step by step. This method is highly flexible and accurate, suitable for addressing wave problems with complex boundary conditions and heterogeneous media.This study analyzes the size, shape, and materials of targets, observing differences in radar cross-section (RCS) under different conditions. The FDTD method successfully simulates SAR imaging of targets, maintaining the geometric relationship of the imaging consistent with the actual positions and distances when scanning more than two targets. This indicates that the actual positions can be determined through simulation results.
The computational efficiency advantages of the Finite-Difference Time-Domain method show its potential in large-scale data processing and real-time imaging applications. In the future, as research deepens and technology matures further, SAR imaging technology based on the FDTD method is expected to achieve even more fruitful results in fields such as Earth observation, environmental monitoring, and military reconnaissance.

[1] C. A. Wiley, “Synthetic aperture radars,” IEEE Trans. Aerosp. Electron. Syst. AES-21 (3), 440–443(1985), doi: 10.1109/TAES.1985.310578.
[2] W. Stecz and K. Gromada, ‘‘UAV mission planning with SAR application,’’ Sensors 20(4), 1080(2020), doi: 10.3390/s20041080.
[3] R. E. Reamer, W. Stockton, and R. D. Stromfors, “New military uses for synthetic aperture radar (SAR),” Proc. SPIE Airborne Reconnaissance XVI 1763, 113–119(1993), doi: 10.1117/12.140829.
[4] S. Huber, F. Q. de Almeida, M. Villano, M. Younis, G. Krieger, and A. Moreira, “Tandem-L: A technical perspective on future spaceborne SAR sensors for earth observation,” IEEE Trans. Geosci. Remote Sens. 56(8), 4792–4807(2018), doi: 10.1109/TGRS.2018.2837673.
[5] L. Jiao, X. Tang, B. Hou, and S. Wang, “SAR images retrieval based on semantic classification and region-based similarity measure for earth observation,” IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens. 8(8), 3876–3891(2015), doi: 10.1109/JSTARS.2015.2429137.
[6] R. K. Sharma, B. S. Kumar, N. M. Desai, and V. R. Gujraty, “SAR for disaster management,” IEEE Aerospace Electron. Syst. Mag. 53(6), 4–9(2008), doi: 10.1109/MAES.2008.4558001.
[7] S. Hensley, C. Jones, and Y. Lou, “Prospects for operational use of airborne polarimetric SAR for disaster response and management,” in Proc. Int. Geosci. Remote Sens. Symp., 103–106(2012), doi: 10.1109/IGARSS.2012.6351626.
[8] H. Ling, R.-C. Chou, and S.-W. Lee, “Shooting and bouncing rays: calculating the RCS of an arbitrarily shaped cavity,” IEEE Trans. Antennas Propagat. 37(2), 194–205(1989), doi: 10.1109/8.18706.
[9] C.-L. Dong, L.-X. Guo, X. Meng, and Y. Wang, “An Accelerated SBR for EM Scattering From the Electrically Large Complex Objects,” Antennas Wirel. Propag. Lett. 17(12), 2294–2298(2018), doi: 10.1109/LAWP.2018.2873119.
[10] S. Tebaldini et al., “Sensing the urban environment by automotive SAR imaging: Potentials and challenges,” Remote Sens. 14(14), 3602(2022) , doi: 10.3390/rs14153602.
[11] W.-Q. Wang, “MIMO SAR imaging: Potential and challenges,” IEEE Aerosp. Electron. Syst. Mag. 27(8), 18–23(2013), doi:10.1109/MAES.2013.6575407.
[12] A. R. Brenner and L. Roessing, “Radar imaging of urban areas by means of very high-resolution SAR and interferometric SAR,” IEEE Trans. Geosci. Remote Sens. 46(10), 2971–2982(2008), doi: 10.1109/TGRS.2008.920911
[13] Kane Yee, “Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14(3), 302–307(1966), doi: 10.1109/TAP.1966.1138693.
[14] M. R. Allen and L. E. Hoff, “Wide-angle wideband SAR matched filter image formation for enhanced detection performance,” Proc. SPIE 2093, 381–387(1994), doi: 10.1117/12.177181.
[15] S. Devadithya, A. Pedross-Engel, C. M. Watts, and M. S. Reynolds, “Partitioned inverse image reconstruction for millimeter-wave SAR imaging,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 6060–6064(2017), doi: 10.1109/ICASSP.2017.7953320.
[16] J. Delliere, H. Maître, and A. Maruani, “SAR measurement simulation on urban structures using a FDTD technique,” in Proc. Urban Remote Sens. Joint Event, 1–8(2007), doi: 10.1109/URS.2007.371837.
[17] K. S. Kulpa et al., “An advanced SAR simulator of three-dimensional structures combining geometrical optics and full-wave electromagnetic methods,” IEEE Trans. Geosci. Remote Sens. 52(12), 776– 784(2014), doi: 10.1109/TGRS.2013.2283267.
[18] X. Pan, L. Kang, B. Zou, Y. Zhang, L. Zhang, “ High-resolution SAR signal simulation using parallel FDTD method, ” 2014 IEEE Geoscience and Remote Sensing Symposium (IGARSS), 490 - 493(2014), doi: 10.1109/IGARSS.2014.6946466.
[19] S. Qingwu, Z. Bin, L. Jian, “ High Precision SAR Echo Simulation Based on FDTD Algorithm with Mobile Excitation Source, ”2018 International Conference on Radar (RADAR), doi: 10.1109/RADAR.2018.8557290
[20] S Ray, 14th Annual Review of Progress in APPLIED COMPUTATIONAL ELECTROMAGNETICS, The Applied Computational Electromagnetics Society Naval Postgraduate School, University of Illinois at Urbana-Champaign, Brigham Young University, University of Kentucky, University of Nevada(1998).
[21] W Gronnemose, B Rabus, “ 3-D FDTD Framework for Simulating SAR Imagery of Realistic Near Earth Surface Volumes (Soil, Snow, and Vegetation), ” IEEE Transactions on Geoscience and Remote Sensing 62, doi: 10.1109/TGRS.2024.3391790
[22] 林益謙, “利用有限時域差分法對合成孔徑雷達進行成像, ” 成大光電所碩士論文 (2023)
[23] Uandha Fernandes Barbosa, João Paulo Monteiro Cruvinelda Costa, Raghu Chaitanya Munjulury and Alvaro Martins Abdalla, “ https://www.researchgate.net/publication/312040564,, October (2016)
[24] Armin W. Doerry“Basics of Polar-Format Algorithm for Processing Synthetic Aperture Radar Images, ” SANDIA REPORT(2012)
[25] “Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms, 2nd Edition | Wiley,” Wiley.com.
[26] M. J. Rycroft, “Computational electrodynamics, the finite-difference time-domain method,” Journal of Atmospheric and Terrestrial Physics, vol. 58, no. 15, 1817–1818, Nov.(1996), doi: 10.1016/0021-9169(96)80449-1