Fig. 1. (a) Problem of reshaping the light of LED is about to map the Vector x of Set S to the Vector y of the Set T; (b) refracting property of ellipsoid. As long as the incident angle is smaller than the critical angle, the light from the focus will be refracted by the upper part of the ellipsoid parallel to its major axis.

Fig. 2. Flowchart of computing the construction ellipsoids of the lens.

Fig. 3. 3D model of the reshaping lens and transmitter.

Fig. 4. Relative LID of the LED and reshaped by the lens.

Fig. 5. Effect of installation error; (a) displacement in xy–plane; (b) displacement in z axis.

Fig. 6. Relative intensity of single optical element and five elements combination.

Fig. 7. Fabricated lens and the optical system installed in an aluminum plate with an LED.

Fig. 8. Relative light intensity of this work (experiment and simulation results).