CHARACTERISTIC PATHLENGTH FRESNEL NUMBER EQUATIONS AND IDEAL LENS WAVE-FRONT KIRCHHOFF FORMULATION - ANALYSIS OF FOCUSED GAUSSIAN-BEAM DIFFRACTION FIELDS

The characteristic optical pathlength Fresnel number equation for a paraxial lens Gaussian laser beam diffracted and spherically focused by an 'ideal' circular is derived. The maximum inside and outside pathlength Fresnel numbers are quantified. The maximum outside pathlength Fresnel number, simplified via the paraxial approximation, is shown to be equal to the classical focal Fresnel number of the lens-aperture combination. A unique Kirchhoff diffraction integral formulation of this configuration is derived, and calculations show that the diffraction fields for a circular-aperture-truncated focused Gaussian beam are identical in characteristic shape to the same but non-focused diffraction fields, as long as significant focal shift effects are not present. Example applications of the optical pathlength Fresnel number equation are given.