  The efficient design of continuous freeform surfaces, which transform a given
source into an arbitrary target intensity, remains a challenging problem. A
popular approach are ray-mapping methods, where first a ray mapping between the
intensities is calculated and in a subsequent step the surface is constructed.
The challenging part hereby is the to find an integrable mapping ensuring a
continuous surface. Based on the law of reflection/refraction and the
well-known integrability condition, we derive a general condition for the
surface and ray mapping for a collimated input beam. It is shown that in a
small-angle approximation a proper mapping can be calculated via optimal mass
transport. We show that the surface can be constructed by solving a linear
advection equation with appropriate boundary conditions. The results imply that
the optimal mass transport mapping is approximately integrable over a wide
range of distances between the freeform and the target plane and offer an
efficient way to construct the surface by solving standard integrals. The
efficiency is demonstrated by applying it to two challenging design examples.
