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Mathematical Problems in Engineering
Volume 2014, Article ID 535703, 7 pages
Research Article

Design of Elliptic Reflective LED Surgical Shadowless Lamps Using Mathematical Optical Tracing Algorithms

1Department of Mechanical and Electro-Mechanical Engineering, Center for Nanoscience and Nanotechnology, National Sun Yat-Sen University, Kaohsiung 80424, Taiwan
2Department of the Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 811, Taiwan

Received 12 June 2014; Accepted 11 September 2014; Published 29 September 2014

Academic Editor: Teen-Hang Meen

Copyright © 2014 Cheng-Tang Pan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Traditional surgical shadowless halogen lamps are generally designed as projection type with many light bulbs, which can produce not only mercury pollution but also heat radiation that are serious problems to patient. The study utilized Runge-Kutta methods and mathematical algorithms to design and optimize the freeform lens. The LED (light-emitting diode) was adopted to replace the traditional halogen lamp. A uniform lens was designed and fabricated based on the energy conservation. At first, the light field of LED is concentrated through the freeform lens to improve the optical efficiency. Second, the three-shell elliptic curves are applied to the reflective surgical shadowless lamps, where only few LED chips are needed. Light rays emitting from different directions to the target plane can achieve the goal of shadowless. In this study, the LED’s luminance flux is 1,895 lm. The shadow dilution on the target plane is 54%. (central illuminance) is 114,900 lux, and the is 57% which is higher than the regulation by 7%, whereas the power consumption is only 20 W. The energy of reflective surgical shadowless lamps can save more than 50%, compared with the traditional projective one.