We can determine the beam profile at the aperture plane Ea by propagating the field by applying the Hygen-Fresnel principle through a Hankel transformation of to yield
Where d is the distance between the beamwaist and the aperture plane and is the Bessel function of the zeroth order.
The normalized transmittance of the aperture can be calculated as
(26.20)
Numerator gives the nonlinear aperture transmission and the denominator is the aperture transmission in the linear regime i.e. corresponding to large Z and will reduce to
(26.21)
Where is the input power and S is the aperture transmittance in linear regime.
(26.22)
is the aperture linear transmittance, with denoting the beam radius at the aperture in the linear regime.
Hence, by measuring the transmission T as afunction of sample position Z, one can deduce and thus n2 which is related to .
by applying the Hygen-Fresnel principle through a Hankel transformation of 
to yield
is the Bessel function of the zeroth order.
of the aperture can be calculated as
is the input power and S is the aperture transmittance in linear regime.
denoting the beam radius at the aperture in the linear regime.
and thus n2 which is related to 
.