document: In the Total Focusing Method (TFM) the beam is synthetically focused at every point in the target region [7] as follows. After obtaining the FMC data, the target region, which is in the x–z plane in 2D (Fig. 1), is discretized into a grid. The signals from all elements in the array are then summed to synthesize a focus at every point in this grid. Linear interpolation of the time domain signals is necessary since they are discretely sampled. The intensity of the TFM image ITFM at any point (x,z) is given by:(10)ITFM(x,z)=|∑HTR(1c((xT−x)2+z2+(xR−x)2+z2))|forallT,Rwhere HTR(t) is the Hilbert transform of a signal uTR(t) in the FMC data, xT is the x-position of the transmitting element (T) and xR is the x-position of the receiving element (R). Note that the z-position of all elements is zero (Fig. 3a). The summation is carried out for all possible transmitter–receiver pairs and therefore uses all the information captured with FMC. This algorithm is referred to as ‘conventional TFM’ in this paper.
doc_bio_tags: O O B I I B O O O O O O O O O O O O O O O O O O B O O O O O O O O B I O O O O O B I I I O O O O O O O O O O B O O O O O O O O O B B I O O O O O O O O O O B I O O O O B O O O O O O O O O O O O B I O O O O O O B O O O O O O O B I B O O O O O O O B I B O O O O O O O O O O O O B O O O O O O B I O O O O O O O O B O O O O O O O O O O O
extractive_keyphrases: discretely sampled discretized into a grid fmc grid hilbert transform linear interpolation r receiving element summation summed t tfm total focusing method transmitter–receiver pairs transmitting element x–z plane
abstractive_keyphrases: conventional tfm fmc data synthesize a focus at every point in this grid tfm image tfm image itfm