The supporting quadric method (SQM) is a versatile method for the design of a wide class of freeform optical elements. In the present work, a novel SQM-based approach for the computation of total internal reflection (TIR) optical elements generating arbitrary narrow-angle light distributions is proposed. High performance of the presented method is confirmed by two designed optical elements: the first one forms an illuminance distribution in a square region with angular size of 17°, and the second one generates a bat-shaped uniformly illuminated area with an angular size of 43.6° x 22.6°. The lighting efficiencies in both cases exceed 90%, and the relative root-mean-square deviations of the generated light distributions from the required ones are less than 6%.
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