  The tolerance analysis of freeform surfaces plays a crucial role in the
development of advanced imaging systems. However, the intricate relationship
between surface error and imaging quality poses significant challenges,
necessitating dense sampling of featured rays during the computation process to
ensure an accurate tolerance for different fields of view (FOVs). Here, we
propose an adaptive sampling strategy called "Critical Ray Aiming" for surface
tolerance analysis. By identifying the most sensitive ray to wave aberration at
each surface point, our methodology facilitates flexible sampling of the FOVs
and entrance pupil (EP), achieving computational efficiency without
compromising accuracy in determining tolerable surface error. We demonstrate
the effectiveness of our method through tolerance analysis of two different
freeform imaging systems.
