The technique of VLBI can be described by the fundamental equations of aperture synthesis as given by Clark [1995] and briefly outlined below.
If the electric field produced at a distant (celestial) source of radio emission is 
then the frequency components of the time varying field can be designated 
and are complex quantities. are known as the quasi-monochromatic components of the electric field.
Figure 2.1: Radio source - antenna geometry
The linearity of Maxwell's equations allow each of the quasi-monochromatic components of the field from the source to be superposed at the observer. This superposition can be written as
(refer to Figure 2.1, adopted from Clark 1995). 
is the propagator which describes how the electric field at 
influences the electric field at 
. 
is assumed to be an ordinary scalar function and through empty space takes a simple form, so that
This is the quantity which is observable at a radio telescope. Among the properties of 
is the correlation of the field at two different locations in space,
Upon substitution of the expression for into the above equation and using the simplifying assumptions that the astrophysical radiation is not spatially coherent and that 
, the expression for the correlation of the electric field at two locations is
where s is the vector from the point of observation to a point in the source and 
is the surface brightness distribution of the radio source. 
is known as the spatial coherence function of the field and is the quantity measured by radio interferometers. The above expression can, within well defined limits, be Fourier inverted so that the measurement of 
allows an estimate of 
. This is the fundamental premise of aperture synthesis.
One further simplifying assumption can be made so that the expression for the spatial coherence function can be cast in a more convenient form for Fourier inversion. This assumption is that the radio source is of small angular size and that the vector 
can be expanded as 
,
where 
is a fixed unit vector in the direction of the source, and 
is a perpendicular vector in the plane of sky which describes each point in the radio source.
A suitable coordinate system can be chosen for the interferometer baselines connecting the pairs of locations at which is measured, (u,v), as well as a suitable coordinate system for the plane of the sky, (x,y) [Clark 1995]. The interferometer baselines do not necessarily lie within the u-v plane. It is the projection of the physical baseline into the u-v plane which is important and defines the baseline which measures the spatial coherence function of the electric field. For an array of radio telescopes spanning the Earth, 
can be measured for many points in the u-v plane by observing over a period of time. As the Earth rotates, the baselines of a given array, as projected into the u-v plane, change their orientation and length, sampling different points of the u-v plane. u, v, x, and y are related in the new, simplified expression for ,
When inverted, the above expression for becomes:
However, since an array of radio telescopes forming a set of interferometers does not measure at all points in the u-v plane, but only discretely, a sampling function, S(u,v), must be introduced,
is referred to as the dirty image. It is related to the true brightness distribution of the radio source as follows:
where B is known as the dirty beam, the Fourier transform of the sampling function,
The true brightness distribution, , can then be obtained from and B by deconvolution.