6.1 Processing in frequency and space domains

Section 2.4.2 discussed the tomographic approach to target imaging in two-dimensional (2D) viewing geometry. We suggested an algorithm for processing in the frequency domain, which finds the reflectivity function ?( x, y) from Eq. (2.48).

The first procedure to be performed is to reconstruct an image in the frequency domain by calculating the N number of discrete Fourier transform (DFT) records of the echo complex envelope

for each of the M number of the target angular positions m ? ?, m = 0, , M ? 1. The pixels found in this way are located at the polar grid nodes formed by the interceptions of concentric circumferences separated by the frequency step 1/ N ? t and rotated by the radial beam angle ? ? from one another.

Since an inverse DFT can be made only on a rectangular grid, the second procedure should include the finding of pixels at the equidistant nodes of a rectangular grid, using the P _? ( l, m) values obtained by the first procedure. This is followed by a 2D inverse DFT computation of the target reflectivity ?( x _i, y _j) at the rectangular grid nodes.

This algorithm has two important features that deserve attention. First, since the complex envelope of an echo signal is finite, there are distortions near the I/2 ? t boundaries of the major period of...