This paper presents a design for a high-efficiency, low-beam headlamp with Oliker's ellipses technology [Computing Lett. 2, 29 (2006)]. In addition to the one-time intrinsic light absorption of reflection, the designed low-beam lampshade can reflect all the light from the LED in the on-demand illumination range. This study proposes and adopts a matrix calculation method to accelerate the calculation speed of constructing an Oliker's composite ellipsoidal reflector, which in turn increases the ellipsoidal facet number of the compound ellipsoidal reflector. In the design of the low-beam headlamp, the illumination weight on the target plane is defined by the method of curve fitting, which ensures that the light-field pattern of the low-beam headlamp changes smoothly rather than in a patchy distribution. The content of this study itself also provides a design method and example for applying Oliker's ellipses technology to on-demand spatial lighting.
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