What is special about the six-port reflectometer is that phase information is obtained by making only amplitude (or power) measurements of four different linear combinations of the two electromagnetic waves. This means that a six-port reflectometer is in principle simply a passive linear circuit with two input ports and four output ports (hence its name), which provides at its outputs four different linear combinations of the waves present at its inputs.
Of course, an indirect measurement technique like this requires both careful calibration of the measurement device (the six-port reflectometer) and a rather sophisticated mathematical procedure to obtain the quantity of interest (the complex reflection coefficient) from the raw measured data (the four amplitudes at the output ports). More details about the operation of the six-port reflectometer can be found in some basic articles on my publications page.
By using two six-port reflectometers in a dual six-port configuration, it is possible to perform the same measurements as with a traditional network analyzer, that is, to measure not only the reflection of waves in order to determine the input impedance, but also the transmission of waves through a two-port DUT in order to determine the gain or attenuation of the DUT.
Around this time, desktop computers became accessible to large laboratories like the NBS. It now made sense to develop measurement devices which no longer directly measured the physical quantities of interest, but where these quantities first had to be calculated from the measured data.
Another advantage is important for metrology laboratories: As the measurement with a six-port reflectoemter contains some redundancy (three of the measured amplitudes determine the fourth up to a choice between two possible values), it is possible to give an estimate of the accuracy of every single measurement.
A six-port reflectometer is also very useful for measuring the behavior of a circuit under high-power signals. This is because in a six-port reflectometer, only the amplitude (or power) of signals needs to be measured. For high-power signals, power measurement devices are much easier to design than the circuits which are used in traditional network analyzers.
There are in my opinion several reasons for this:
For reasons of size, weight, and cost (when produced in large numbers), it is essential for the six-port reflectometer to be integrated in monolithic microwave integrated circuit (MMIC) technology if it is to be used for these applications, which may be part of mobile telephones or other portable devices.
Due to problems in calibrating the device with existing algorithms at some frequencies, I have also developed a new, very robust method for calibration.
Finally, I have participated in the design of a new, very wideband six-port reflectometer covering the frequency range from 2 MHz to 2200 MHz, that is, more than three decades.
A good summary of this work can be found in three articles that have been published in the IEEE Transactions on Instrumentation and Measurement. My complete PhD thesis is also available for download (in French only).