A brief review of the main effects associated with low Fresnel number N in optical system with circular and elliptical pupil shape under uniform and Gaussian illumination is given. The attention is drawn more specifically on the focal shift and its impact on static resolution and depth-of-focus. This is illustrated by several examples of imaging systems in the terahertz spectral region, where diffraction effect tends to dominate. Recently developed in the mm-wave range, compact passive THz imagers often require large depth-of-field at a nominal distance of several meters leading to a value of the Fresnel number N<1. Typically far-infrared and submm space-based astronomical instrumentation with or without direct spatial sampling (i.e. Nyquist or better) requires compactness inducing small internal pupil size leading to N<5 across a larger spectral bandwidth, putting restrictive constraints on the design and/or the operation of the imaging system. Some application-specific design guidelines are also derived from the good agreement found between optical modeling and experimental measurements on prototypes. Finally mention is made of shorter wavelength optical instruments or devices in which similar effect can occur showing the general nature of the phenomenon.