The essence of the paraxial approximation is that we approximate the spherical wavefront (from a point source) as a quadratic surface. Technically, in the paraxial zone, where the observation is near the optical axis, we can approximate r01 by
where we obtain the Fresnel diffraction formula as
More detailed discussion on the accuracy of the Fresnel approximation can be found in chap. 4.2.2 in Goodman.
§ Goodman 2005 - Introduction to Fourier optics.