  In computational optics, numerical modeling of diffraction between arbitrary
planes offers unparalleled flexibility. However, existing methods suffer from
the trade-off between computational accuracy and efficiency. To resolve this
dilemma, we present a novel approach that rigorously and efficiently models
wave propagation between two arbitrary planes. This is achieved by rearranging
the angular spectrum of the source field, coupled with linear algebraic
computations. Notably, our method achieves comparable computational efficiency
to the control method for both scalar and vectorial diffraction modeling, while
eliminating nearly all numerical errors. Furthermore, we selectively merge the
angular spectrum to further enhance the efficiency at the expense of precision
in a controlled manner. Thereafter, the time consumption is reduced to at most
3% of that before merging.
