The exact calculation of the field at a point due to a single Fresnel zone is carried out by using the Maggi—Rubinowicz contour integral. The result agrees with the Fresnel theorem in the limit for k very large, k being the propagation constant of the incident wave. The results obtained suggest a new interpretation of the physical meaning of the Maggi—Rubinowicz contour integral in diffraction theory as representing a contribution of elementary or Fresnel zones, in exactly the same manner that the Kirchhoff integral does when considered as an expression of Huygens’ principle.
© 1969 Optical Society of America
RASHAD MOUNIR SHOUCRI, "Exact Calculation of the Field Due to a Single Fresnel Zone by the Use of the Maggi-Rubinowicz Contour Integral," J. Opt. Soc. Am. 59, 1158-1161 (1969)