function, the function is said to be in k-space . Two dimensional k-space has been introduced into MRI as a raw data storage space. The value of each data point in k-space is measured in the unit of 1/meter, i.e. the unit of spatial frequency. It is very common that the raw data in k-space shows features of periodic functions. The periodicity is not spatial frequency, but is temporal frequency. An MRI raw data matrix is composed of a series of phase-variable spin-echo signals. Each of the spin-echo signal is a sinc function of time, which can be described by Spin-Echo = Where Here is the gyromagnetic ratio constant, and is the basic resonance frequency of the spin. Due to the presence of the gradient G, the spatial information r is encoded onto the frequency . The periodicity seen in the MRI raw data is just this frequency , which is basically the temporal frequency in nature. In a rotating frame, , and is simplified to . Just by letting , the spin-echo signal is expressed in an alternative form Spin-Echo = Now, the spin-echo signal is in the k-space. It becomes a periodic function of k with r as the k-space frequency but not as the "spatial frequency", since "spatial frequency" is reserved for the name of the periodicity seen in the real space r. The k-space domain and the space domain form a Fourier pair. Two pieces of information are found in each domain, the spatial information and the spatial frequency information. The spatial information, which is of great interest to all medical doctors, is seen as periodic functions in the k-space domain and is seen as the image in the space domain. The spatial frequency information, which might be of interest to some MRI engineers, is not easily seen in the space domain but is readily seen as the data points in the k-space domain. See also Fourier analysis Superlens Visual perception Fringe visibility k-space References External links Mathematical physics Space