  Several precise and computationally efficient results for pointing errors
models in two asymptotic cases are derived in this paper. The normalized
mean-squared error (NMSE) performance metric is employed to quantify the
accuracy of different models. For the case that the beam width is relatively
larger than the detection aperture, we propose the three kinds of models that
have the form of $c_1\exp(-c_2r^2) $.It is shown that the modified intensity
uniform model not only achieves a comparable accuracy with the best linearized
model, but also is expressed in an elegant mathematical way when compared to
the traditional Farid model. This indicates that the modified intensity uniform
model is preferable in the performance analysis of free space optical (FSO)
systems considering the effects of the pointing errors. By analogizing the beam
spot with a point in the case that beam width is smaller than the detection
aperture, the solution of the pointing errors model is transformed to a smooth
function approximation problem, and we find that a more accurate approximation
can be achieved by the proposed point approximation model when compared to the
model that is induced from the Vasylyev model in some scenarios.
