Image Formation – Fourier Transform – Gradients

Abstract

The construction of an image entails the assignment of an intensity value (brightness) to each unit of the image (voxel). Our raw data are contained in the FID curve, which comprises overt information about amplitude (intensity) and frequency and covert information about phase (Fig. 31). However, spatial knowledge is “lost” since the signals from the individual voxels have merged into a composite FID wave. Somehow, we need to recover positional information. Now is the time to revisit the Larmor principle: there is a one-to-one correspondence between the proton resonance frequency and the strength of the static field B. So, if we force B to grow in a smooth and continuous manner along a line, then we spread the resonance frequencies, and each voxel along that line is tied to a unique frequency. Thus, the frequency of the received signal betrays the position of the voxel in question.