TFM calculates the time taken for a wave to travel from each generating array element to each possible scattered in the imaging region (the area the operator wishes to inspect), and then back to each detecting element. For this work, the total path must include the wedge attached to the phased array probe, including the refraction at the wedge/steel boundary. The speed in each region must be known for the times of flight to be calculated accurately. Each possible scatterer is then a focusing point, forming a rectangular array (dimensions of X-position and Y-position), with each element of the array representing the combined magnitude of the waves scattered from that point; this can be referred to as the image array. For each generation–detection pair, and each point in the image array, the analytic signal component (where the analytic signal is the real original signal combined with the Hilbert transform of the original signal [37]) at the time point representing the generation–scatterer–detection flight time is added to the image array. Using the analytic signal allows the TFM process to take advantage of the phase and magnitude of any received signals. All of these contributions are summed, and the magnitude taken of the result (simply the absolute value of each image element), to produce the final TFM image