本論文研究新提出的兩種內插演算法: Subsample Waveform Shifting (SWS) 和
Subsample Cross-Correlation (SCC) ，旨在提升混沌光達系統的精準度。混沌光達系統是利用計算混沌調變訊號相關函數之時間延遲獲取目標距離，而渾沌光達的精準度是由類比數位轉換器(ADC)的取樣頻率所影響， SWS 的概念是利用一已知位置的互相關函數作為標準模組，對標準模組的互相關函數進行傅立葉轉換至頻域上，在頻域上可以做連續相位的調整，因此可以得到在時域上不受取樣頻率限制的高解析度移動，並和未知位置的互相關函數進行比對找尋最相似處。 SCC 核心概念和 SWS 相同，不過 SCC 是直接在參考混沌訊號與從目標物反射之混沌訊號間作精細的時間延遲，而得到一高解析度的互相關函數。研究中亦比較了 SWS 、 SCC 和其他內插演算法，並觀察針對在不同操作條件下，如改變光強度、改變同調長度、頻寬及取樣頻率等，各個演算法的表現。研究中成功提升混沌光達的精準度，原始精準度為 3.47 cm ，在適當條件下， SWS 和 SCC 其精準度皆提升近兩個數量級達到 0.05 cm，成功突破了精準度受限取樣頻率的限制。

In this study, we proposed the two new interpolation algoirthms: Subsample Waveform Shifting (SWS) and Subsample Cross-Correlation (SCC) which are designed to enhance the accuracy of chaos lidar system. Chaos lidar system calculated cross-correlation function by the time delay of the chaos signal and reference signal to obtain the target distance. The accuracy of chaos lidar is influenced by the sampling frequency of the analog-to-digital converter (ADC). The concept of SWS use the correlation trace of known location to be the model, and transfer the model into frequency domain by Fourier transform, it can do continuous phase adjustment which is not limited by frequency sampling in frequency domain and find the most similar location with correlation trace of unknown location. The core concept of SCC are the same as SWS, but SCC directly do the fine time delay in the reference chaotic signal and reflected from the target chaos signal, and get a high resolution cross-correlation function. The study also compares SWS , SCC and other interpolation algorithms, discussed the performance of each algorithm under different operating conditions, such as changing optical intensity, correlation length, bandwidth and sampling frequency. In the study, the accuracy of the chaotic lidar was improved. The original accuracy was 3.47 cm . Under the appropriate conditions, the accuracy of SWS and SCC are improved by nearly two orders of magnitude up to 0.05 cm, successfully breakthrough the accuracy limited by sampling frequency.

[1] M. C. Amann, T. Bosch, M. Lescure, R. Myllyla, and M. Rioux, “Laser ranging:
a critical review of usual techniques for distance measurement”, Opt. Eng., 40(1),
pp. 10-19, 2001
[2] G. N. Pearson, P. J. Roberts, J. R. Eacock, and M. Harris, “Analysis of the performance of a coherent pulsed fiber lidar for aerosol backscatter applications,” Appl. Opt., vol. 41, no. 30, pp. 6442–6450, 2002.
[3] A. Rybaltowski and A. Taflove, “Signal-to-noise ratio in direct-detection midinfrared random-modulation continuous-wave lidar in the presence of colored additive noise,” Opt. Express, vol. 9, no. 8, pp. 93–108, Jan. 1992.
[4] T. C. Strand, ”Optical three-dimensional sensing for machine vision,” Opt. Eng., 24(1), pp. 33-40, 1985.
[5] G. C. Luck, “Frequency modulated rader”, New York : McGraw-Hill., pp. 1-466, 1949.
[6] J. Zheng, “Optical frequency-modulated continuous-wave(FMCW) interferometry”, Springer, pp. 1-245, 2005. 30
[7] M. S. Willsey, K. M. Cuomo, and A. V. Oppenheim, “Quasi-orthogonal wideband radar waveforms based on chaotic systems,” IEEE Trans. Aerosp. Electron. Syst., 47(3), pp. 1974–1984, 2011.
[8] F. Y. Lin and J. M. Liu, “Chaotic Radar Using Nonlinear Laser Dynamics”, IEEE J. Quantum Electron., 40(6), pp. 815-820, 2004.
[9] F. Y. Lin and J. M. Liu, “Chaotic Lidar”, IEEE J. Sel. Top. Quantum Electron.,
10(5), pp. 991-997, 2004.
[10] A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. GarciaOjalvo, C. R. Mirasso, L. Pesquera, and K. A. Shore, ”Chaos-based communications at high bit rates using commercial fibre-optic links”, Nature 438, 343–346 (2005).
[11] A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, ”Fast physical
random bit generation with chaotic semiconductor lasers”, Nat. Photonics 2, 728–
732 (2008).
[12] W. T. Wu, Y. H. Liao, and F. Y. Lin “Noise suppressions in synchronized chaos
lidars,” Opt. Express, 18(25), pp. 26155-26162, 2010.
[13] L Schumaker,“ Spline functions: basic theory”,2007
[14] M. Ito ; R. Donaldson,“Zero-crossing measurements for analysis and recognition of speech sounds”,IEEE TRANSACTIONS ON AUDIO AND ELECTROACOUSTICS VOL. AU-19, NO. 3,1971
[15] Quang Minh Tieng ; W.W. Boles,“Recognition of 2D object contours using the
wavelet transform zero-crossing representation”, IEEE Transactions on Pattern Analysis and Machine Intelligence volume: 19,Issue:8,Aug, 1997 31
[16] R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties”, IEEE J. Quantum Electron., 16(3), pp. 347-355, 1980.
[17] T. B. Simpson, J. M. Liu, A. Gavrielides, V. Kovanis, and P. M. Alsing, “Perioddoubling cascades and chaos in a semiconductor laser with optical injection”, Phys. Rev. A: At. Mol. Opt. Phys., 51(5), pp. 4181-4185, 1995.
[18] T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers”, J. Opt. B: Quantum Semiclassical Opt., 9(5), pp. 765-784, 1997.
[19] F.Y.Lin.and J.M.Liu “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback”,Opt. Communications Volume 221, Issues 1–3, 1 June 2003, Pages 173-180