Context and motivation
Near-field measurement systems enable an indirect characterization of the far-field radiation pattern of an antenna under test (AUT) by measuring the electric field that the latter emits within its near-field region (typically in the Fresnel zone).
The near field is often measured over canonical surfaces (planar, spherical and cylindrical) using a simple reference probe. Measurements therefore require a much shorter reading distance than conventional far-field measurements, and make it possible to limit the size of measurement facilities. However, precise and efficient near-field-to-far-field transformations are require to accurately evaluate the radiation pattern of the AUT. Most of these methods are based on a modal expansion of the measured field.

Scientific and technical challenges
Far-field reconstruction from near-field measurements still poses a number of scientific and technical challenges related to practical limitations of the setups and to the accuracy and efficiency of the mathematical transformations used. Standard approaches require the acquisition of a large number of measurement samples on a regular and dense mesh to compute accurately the far-field radiation pattern. This large number of samples results in prohibitively long measurements. Hence, it may be necessary to truncate or under-sample the area where the near field is measured. Furthermore, in a real setup, some samples are not accessible for measurement (e.g. due to the presence of the mount of a robotic arm), which also leads to truncated measurements. The near-field-to-far-field transformation then takes the form of an under-dimensioned system, and constitutes an ill-posed problem. Effective methods to find approximate solutions to them are therefore essential.

Main objectives and description of the work
First, the intern will acquire solid competences on the characteristics of far- and near-fields radiated by an antenna, on the mathematical relations that link both, as well as on conventional systems to measure them. She/he will perform a critical analysis on state-of-the-art near-field-to-far-field transformations. To this end, she/he will use and enhance numerical codes previously developed at CEA-Leti.
The first objective of the internship is to evaluate the impact of a spatial truncation of the acquired near field on the far-field prediction. It will be possible to assess the loss of measurement accuracy for antennas having different values of directivity. This study can be carried out in planar and/or spherical geometry.
The second objective is to develop reconstruction algorithms that will limit this degradation while maintaining reasonable measurement time. These algorithms will leverage either techniques based on Fourier transforms or compressive sensing.The numerical codes will be validated using near and far fields obtained from the full-wave simulations and/or measurements, considering several representative antennas.