Original sentence: For Fresnel diffraction the electric field at point (x,y,z) is given by:.Moreover, if we are interested in the behaviour of the field only in a small area close to the origin, i.This equation, then, is the Fresnel approximation, and the inequality stated above is a condition for the  approximation's validity.Unlike Fraunhofer diffraction, Fresnel diffraction has to account for the curvature of the wavefront, in order to correctly calculate the relative phase of interfering waves.for values of x and y much smaller than z, then we can assume , that means  and the r in the denominator of the Fresnel integral can be approximated by.is the cosine of the angle between z and r.is the imaginary unit,
Edited sentence: For Fresnel diffraction the electric field at point (x,y,z) is then given by:.For the r in the denominator we go one step further, and approximate it with only the first term,.In addition, it is always valid if in addition to the Fresnel condition, we have.This equation, then, is the Fresnel approximation, and the inequality stated above is a condition for the approximation's validity.This is valid in particular if we are interested in the behaviour of the field only in a small area close to the origin, where the values of x and y are much smaller than z.Unlike Fraunhofer diffraction, Fresnel diffraction accounts for the curvature of the wavefront, in order to correctly calculate the relative phase of interfering waves.is the imaginary unit