The effects of focused aperture amplitude tapering, both direct and inverse, on axial forelobes and aftlobes are investigated. Taylor tapers give low sidelobes but high forelobes and aftlobes, plus a modest gain degradation. Inverse tapers give low forelobes and aftlobes but high sidelobes and large gain degradation. Uniform excitation gives comparable axial and transverse subsidiary lobes, and is probably the best choice. Focal shift, where the peak axial power density occurs between the aperture and the phase (geometric) focus, due to the 1/R^{2} factor, is accurately calculated for a uniform square aperture. Since peak axial power density available from a focused aperture depends only on aperture size in wavelengths and on distance, these focal shift results allow system trade-offs to be made.

Focal region characteristics of focused array antennas

A formulation is developed for investigating the intensity distribution of Fresnel diffraction by a circular aperture illuminated with partially coherent light. The theory formulated is applied to obtain the intensity distribution along the normal axis to the aperture in the Fresnel diffraction field when the spatially mutual coherence function of the illumination over the aperture takes three different forms. It is shown that the Fresnel diffraction is largely influenced by the coherence condition across the diffracting aperture.

Fresnel Diffraction by a Circular Aperture Illuminated with Partially Coherent Light. I

A method is presented for obtaining the far-field diffraction pattern of a plane aperture when the mutual coherence function of the illumination contains a quadratic phase term. The method is applied to obtain the diffraction pattern of a slit and circular aperture illuminated by an extended quasimonochromatic incoherent slit and circular source, respectively. The phase term has both a quantitative and qualitative effect on the features of the diffraction pattern.

Effect of the Phase Term in the Mutual Coherence Function on Aperture-Diffraction Patterns

The statistical properties of the electromagnetic field diffracted by a plane aperture illuminated by a fluctuating field have been studied in the Fresnel zone on the basis of the theory of partial coherence. The average power distribution and the amplitude and phase of the degree of coherence have been computed for several coherence lengths of the illuminating field ranging from 1/4 to 5 times the dimension of the aperture and for two geometries of the observation points. The obtained results indicate the limits of validity of the often assumed hypothesis of spatial stationarity and of the real Gaussian approximation for the degree of coherence of the diffracted field. It turns out also that the optimum position of a receiving phase-sensitive system placed in the field diffracted by an aperture may not be the focus of the aperture, since there the concentration of average power density is accompanied by a poor coherence of the field.

Statistical properties of the field diffracted by an aperture with partially coherent illumination

Diffraction of partially coherent light by an apodized slit aperture

Fresnel diffraction from an aperture is investigated in order to determine how the focusing property of the aperture depends on the length of coherence of the illuminating field. The computations show how the focusing property becomes poorer as the coherence length decreases and the focus displaces itself toward the aperture.

G. D'Auria

Papers

Fresnel diffraction and focusing properties of apertures under partially coherent illumination