Surface Shape Detection with a Single Far-Field Intensity by Combined Amplitude and Phase Retrieval

Table 1

List of symbols.

Symbol	Unit	Meaning
a		Far field of the tested antenna, complex-valued
A		Aperture field of the tested antenna, complex-valued
b		Far-field amplitude of an ideal antenna, real and even
B		Aperture amplitude of an ideal antenna, real and even
C		Relative aperture amplitude increase caused by δ
E	rad	Aperture phase aberration caused by δ
f	GHz	Frequency of the source in the measurement
F, F^−1		FFT, inverse FFT
FL	m	Focal length of tested antenna
G		A matrix determined by antenna geometry [12]
k		Wavenumber
LN		Laplacian matrix extended to size N × N [12]
N		Data size N × N
δ	mm	Surface shape error of the tested antenna
η		Oversampling factor in the far-field scanning