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A double-sided freeform lens is proposed for collimating light emitted from light emitting diodes (LEDs). The surface profiles of the lens are mathematically characterized and precisely determined based on a point-source assumption and differential geometry theory. The proposed lens design method is straightforward, flexible, and effective. Moreover, the optical performance of the lens can be intuitively adjusted by tuning just a small number of design parameters. The simulation results showeddoi:10.3390/app9245452 fatcat:o3vedc4jibhxxbu4yzbxpam4bq