Tailored optics for extended sources

In this contribution we present a rigorous tailoring method of designing a free-form surface for a given extended source. In contrast to point sources, an extended source cannot realize every desired distribution. Our approach, however, unequivocally indicates whether a given desired distribution can be realized with a given extended source or not. In case it cannot, a realizable distribution close to the originally desired is suggested. First we compute the transformation function which converts the light pattern on the target for a point source into the light pattern the same optics produces when the extended source is used in lieu of the point source. We call this the blurring transformation. This linear function is computed with detail and accuracy avoiding shot noise using differential ray tracing. Then we compute the inverse of this transformation, which we call the de-blurring function. Applying the de-blurring function to the distribution desired with an extended source allows to compute the distribution created in the hypothetical case of using a point source in lieu of the extended source. Finally we compute the shape of the free-form optics in the conventional tailoring process based on a point source and the computed de-blurred distribution. We will show examples and discuss the conditions for a solution to exist.