近年來高功率雷射快速的發展，帶動了其雷射頭的開發與設計，在高功率的雷射頭設計中，必須考慮熱透鏡效應造成的焦距位移。熱透鏡效應是當透鏡受到功率雷射照射時，透鏡因為熱膨脹與折射率的改變造成焦距縮短的情形。在設計上消除熱透鏡現象有兩種主要的方法，一是對透鏡進行散熱，讓透鏡維持在可以接受的溫度範圍內，二是以即時補償的方式修正製程參數降低焦距位移的影響。
在焦距變化計算上，為了能預測雷射頭內部在操作時的溫度分布，本文以 Ansys Fluent 建立數值模型，並以熱像儀監控單鏡片升溫的情形取得透鏡材料的吸收係數，並帶入雷射頭模型中的熱源設定，在得到數值模擬的結果後，計算透鏡的曲率半徑變化進而預測其焦距的變化。
本文係以熱膨脹改變的曲率半徑建立與焦距位移之間的關係。利用焦距監測儀以實驗的方式尋找單鏡片在達到熱平衡時的焦距位移。在曲率計算的部分，本文利用簡化的熱膨脹模型描述變形後的透鏡輪廓，再利用其計算曲率的變化。在比較焦距位移與曲率變化時，輔以近軸光線矩陣追蹤法推導得到的解析解而建立兩者的關係。
本文以單鏡片的實驗與模擬建立了焦距位移預測的方法。在預測雷射頭操作時的焦距位移時，先以數值模型計得到雷射頭內透鏡上的溫度分布後，計算透鏡熱變形後相對應的曲率變化，再利用單鏡片實驗建立的預測圖預測其受熱所產生的焦距位移。

When designing a high-power laser head, its proper cooling must be taken into account because of the so-called thermal lensing effect, which in essence is the focus shift of the lenses caused by the energy absorbed from the high-power laser beam. On physical grounds, thermal lensing results from the variation of the refraction index of the lens material with temperature, i.e., a nonzero dn/dT, and thermal expansion. In this study, a series of experiments were carried out using a thermal image camera and the FocusMonitor device to measure the focus movement of lenses. With the help of numerical simulations, a simplified model also is provided for predicting the focus shift by calculating the variation of curvature of the lenses.

[1] E. Kannatey-Asibu Ju., Principles of Laser Materials Processing, 2009.
[2] B. S. Yilbas, "Laser Cutting Quality Assessment and Thermal Efficiency Analysis," Journal of Materials Processing Technology, vol. 155, pp. 2106-2115, Nov 30 2004.
[3] P. Di Pietro and Y. L. Yao, "An Investigation into Characterizing and Optimizing Laser Cutting Quality - a Review," International Journal of Machine Tools & Manufacture, vol. 34, pp. 225-243, Feb 1994.
[4] Y. Arata, "Dynamic Behavior in Laser Gas Cutting of Mild Steel," Transctions of Joining and Welding Research Institute, vol. 8, pp. 175-186, 1979.
[5] M. Radovanovic and P. Dasic, "Research on Surface Roughness by Laser Cut," The Annals of University Dunarea De Jos of Galati Fascicle, vol. 7, pp. 84-88, 2006.
[6] C. Karatas, O. Keles, I. Uslan, and Y. Usta, "Laser Cutting of Steel Sheets: Influence of Workpiece Thickness and Beam Waist Position on Kerf Size and Stria Formation," Journal of Materials Processing Technology, vol. 172, pp. 22-29, Feb 20 2006.
[7] J. P. Gordon, R. C. C. Leite, R. S. Moore, S. P. S. Porto, and J. R. Whinnery, "LongTransient Effects in Lasers with Inserted Liquid Samples," Journal of Applied Physics, vol. 36, 1965.
[8] C. Hu and J. R. Whinnery, "New Thermooptical Measurement Method and a Comparison with Other Methods," Journal of Applied Optics, vol. 12, pp. 72-9, Jan 1 1973.
[9] J. R. Whinnery, "Laser Measurement of Optical Absorption in Liquids," Accounts of Chemical Research, vol. 7, pp. 225-231, 1974.
[10] J. D. Foster and L. M. Osterink, "Thermal Effects in a Nd:YAG Laser," Journal of Applied Physics, vol. 41, pp. 3656-3663, 1970.
[11] W. Koechner, "Thermal Lensing in a Nd:YAG Laser Rod," Journal of Applied Optics, vol. 9, pp. 2548-53, Nov 1 1970.
[12] M. Sparks, "Optical Distortion by Heated Windows in High-Power Laser Systems," Journal of Applied Physics, vol. 42, pp. 5029-&, 1971.
[13] C. A. Klein, "Optical Distortion Coefficients of High-power Laser Windows," Optical Engineering, vol. 29, pp. 343-350, 1990.
[14] C. A. Klein, "High-Power CW Laser Windows: Edge-Cooled or Face-Cooled?," Proceedings of SPIE, vol. 1739, 1992.
[15] E. Beyer, G. Herziger, R. Kramer, and P. Loosen, "A Diagnostic System for Measurement of The Focused Beam Diameter of High Power CO2-Laser," Proceedings of SPIE, vol. 650, 1986.
[16] I. Miyamoto, H. Nanba, and H. Maruo, "Analysis of Thermally Induced Optical Distortion in Lens during Focusing High Power CO2 Laser Beam," Proceedings of SPIE, vol. 1276, 1990.
[17] X. Zhang, W. Chen, J. Ren, G. Huang, and H. Zhang, "Laser Welding Mode Transition and Influence of Thermal Focusing on Mode Transition," Proceedings of SPIE, vol. 2888, 1996.
[18] J. Blecher, T. A. Palmer, S. M. Kelly, and R. P. Martukanitz, "Identifying Performance Differences in Transmissive and Reflective Laser Optics Using Beam Diagnostic Tools," Welding Journal, vol. 91, 2012.
[19] B. McAllister, "Robust Focusing Optics for High-power Laser Welding," Proceedings of SPIE, vol. 8963, 2014.
[20] J. P. Vandoormaal and G. D. Raithby, "Enhancements of the Simple Method for Predicting Incompressible Fluid-Flows," Numerical Heat Transfer, vol. 7, pp. 147-163, 1984.
[21] ANSYS FLUENT Theory Guide: ANSYS, Inc., 2011.
[22] C. J. Kobus and G. L. Wedekind, "An Experimental Investigation into Forced, Natural and Combined Forced and Natural Convective Heat-Transfer from Stationary Isothermal Circular Disks," International Journal of Heat and Mass Transfer, vol. 38, pp. 3329-3339, Dec 1995.
[23] SCHOTT, "N-BK7 data sheet," ed.
[24] I. B. Celik, "Introductory Turbulence Modeling," 1999.
[25] P. Lin, New Computation Methods for Geometrical Optics, 2013.
[26] Newport. The Newport Resource.
[27] Crystran, "N-BK7 data sheet."
[28] E. A. Matzinger, "Finite Element Analysis of The LOLA Receiver Telescope Lens," Proceedings of SPIE, vol. 6675, 2007.