Radiation Characteristics of LED with an Elliptic Primary Lens

This paper presents an analytical and numerical study of the radiation characteristics of an LED light source equipped with an elliptic primary lens. The study demonstrates that the elliptical primary lens geometry enables control of the angular intensity distribution through a combination of the lens ellipticity and refractive index. Analytical relations identified the critical eccentricity e min corresponding to the onset of total reflection. For eccentricities below e min , the lens behaves similarly to a spherical one, producing mainly primary refracted rays. For eccentricities above e min , total internal reflection dominates, redistributing a significant portion of the emitted light into secondary rays and enabling efficient side-angle emission. Unlike other studies that rely primarily on numerical optimization or freeform design, this work establishes a closed-form analytical description of light propagation in an elliptic LED primary lens, enabling continuous, physics-based tuning of the LED angular emission. We proposed a simplified 2D model offering a computationally efficient method for predicting lens performance. The analytical model was validated using ray-tracing simulations in Ansys Zemax OpticStudio, showing good agreement between 2D and 3D models for typical LED chip sizes. Comparative analysis with spherical lenses showed that elliptic lenses achieve larger total reflection angles and improved collimation efficiency for identical refractive indices. The elliptic primary lens thus offers a compact and efficient means of controlling the angular light distribution of LEDs, making it suitable for automotive, architectural, and signalling applications.