NMRI Principle Certain nuclei such as 1H nuclei or fermions have spin 1 2 because there are two spin states referred to as up and down states The nuclear magnetic resonance absorption phenomenon occurs when samples containing such nuclear spins are placed in a static magnetic field and a very short radiofrequency pulse is applied with a center or carrier frequency matching that of the transition between the up and down states of the spin 1 2 1H nuclei that were polarized by the static magnetic field Antoine Abragam 1968 Principles of Nuclear Magnetic Resonance 895 pp Cambridge University Press Cambridge UK Very low field schemes have also been recently reported Chemical Shifts NMR is a very useful family of techniques for chemical and biochemical research because of the chemical shift this effect consists in a frequency shift of the nuclear magnetic resonance for specific chemical groups or atoms as a result of the partial shielding of the corresponding nuclei from the applied static external magnetic field by the electron orbitals or molecular orbitals surrounding such nuclei present in the chemical groups Thus the higher the electron density surounding a specific nucleus the larger the chemical shift will be The resulting magnetic field at the nucleus is thus lower than the applied external magnetic field and the resonance frequencies observed as a result of such shielding are lower than the value that would be observed in the absence of any electronic orbital shielding Furthermore in order to obtain a chemical shift value independent of the strength of the applied magnetic field and allow for the direct comparison of spectra obtained at different magnetic field values the chemical shift is defined by the ratio of the strength of the local magnetic field value at the observed electron orbital shielded nucleus by the external magnetic field strength Hloc H0 The first NMR observations of the chemical shift with the correct physical chemistry interpretation were reported for 19F containing compounds in the early 1950 s by Herbert S Gutowsky and Charles P Slichter from the University of Illinois at Urbana USA NMR Imaging Principles A number of methods have been devised for combining magnetic field gradients and radiofrequency pulsed excitation to obtain an image Two major maethods involve either 2D FT or 3D FT reconstruction from projections somewhat similar to Computed Tomography with the exception of the image interpretation that in the former case must include dynamic and relaxation contrast enhancement information as well Other schemes involve building the NMR image either point by point or line by line Some schemes use instead gradients in the rf field rather than in the static magnetic field The majority of NMR images routinely obtained are either by the Two Dimensional Fourier Transform 2D FT technique with slice selection or by the Three Dimensional Fourier Transform 3DFT techniques that are however much more time consuming at present 2D FT NMRI is sometime called in common parlance a spin warp An NMR image corresponds to a spectrum consisting of a number of spatial frequencies at different locations in the sample investigated or in a patient A two dimensional Fourier transformation of such a real image may be considered as a representation of such real waves by a matrix of spatial frequencies known as the k space We shall see next in some mathematical detail how the 2D FT computation works to obtain 2D FT NMR images Two dimensional Fourier transform imaging and spectroscopy A two dimensional Fourier transform 2D FT is computed nume