The Z scan theory of thin optically nonlinear medium, by using the fast Hank el transform,is analyzed. The characteristics of Z scan curves under near to p-hat beams are discussed. Meanwhile, the influence of the ratio (diaphragm-gird ling ratio) of the limiting diaphragm radius to the radius of expanded beams on normalized transmittance using near top-hat beams under closed-aperture is analy zed. Through theoretical analysis, the ratio with the best sensitivity is given. Finally, the influence of the size of the far-field diaphragm on normalized tra nsmittance under the experimental configuration with the best sensitivity is ana lyzed.