Reconstruction of the Under-sampled High-frequency Data in a Broadband Planar Near-field Test Based on the Asymptotic Field Similarity

This work introduces an effective planar far-field reconstruction method. The proposed method uses spatial convolution to derive the complex electric fields on the far-field planes for different frequency points. If the frequencies and observation distances of the two convoluted far fields satisfy f
2
/f
1
= d
2
/d
1
= N, then the two far fields have high asymptotic similarity. Notably, the sampling interval of the multi-frequency near-field test may cause the under-sampling issue, and the array elements might not work properly at some higher frequency range causing some data loss for the measured samples. For this regard, the electric field asymptotic similarity can be used to reconstruct the faulty under-sampled high-frequency far field by providing highly similar data from the over-sampled low-frequency far field, where the condition of f
2
/f
1
= d
2
/d
1
= N is satisfied. From the comparisons of the complex far fields between the reconstructed one and the directly sampled one, it is clear that the reconstructed result is highly consistent with the theoretically over-sampled far field, and accordingly the effectiveness and accuracy of the proposed reconstruction method based on the high asymptotic similarity can be well proved.