Detailed historical account of LAOS rheometry can be found else where. I add here only my own interest in obsolete instrument designs.
The history of LAOS as a test condition is as old as that of oscillatory shearing rheometry. The use of Lissajous figure was first proposed as early as 1944. K. Weissenberg first proposed a harmonic analysis of LAOS data in 1964. In fact it was not easy for early experimentalists to maintain or measure small deformation esp. for complex fluids before necessary technology break through in actuators and transducers (e.g. linear voltage differential transformer, LVDT). LAOS was therefore more frequently reached in the past than in today whenever an oscillatory shearing was performed.
Harmonic decomposition of the LAOS data was done in various way before the age of computer. One way was fitting the data with a Volterra intergral equation of a limited number of orders to find the corresponding high order kernels (which was not a real decomposition).
The commercial success of Weissenberg rheogoniometer series evoke the desire to extract higher harmonics from the electric signals. One noticeable idea by Harris and Bogie was using the once-called ‘dynamic analysis’ system, product of Solartron Electronic Groups Ltd. It was in essence a cross-correlation method to obtain higher harmonic information on an analog circuit design. The system consisted of a resolved component indicator (or transfer function analyser, as it was more frequently called) excited by a pair of in-phase / quadratic signals from a mechanical reference generator†.
The transfer function analyser technique lasted for as long as one decade on Weissenberg rheogoniometer as its model upgraded from R16 to R18, but bolder try on a computer using FFT was performed in as early as 1971. The analog signal was sampled and input in a signal averager to raise the S/N ratio. From then on, the later development was not hard to imagine: smaller and faster computers coupled with more sensitive and accurate measurement systems.
A major transition occurred, though, from Weissenberg rheogoniometer to the Rheometrics mechanic spectrometer (RMS) series during the 1970s, which also shift the LAOS and harmonic analysis to the new device. The device had a few of new feature compared to the Weissenberg counterpart. First, it directly gave the result of G’ and G”, otherwise the earlier rheologists had to manually calculated from the Lissajous curves. Second, it provided an oven chamber to perform high temperature experiment, a feature not easily achievable with old rheogoniometers. And third, it upgrade the driving system from gears-based to electronic motor††. These features gained a wide acceptance very fast, and ARES soon became a standard of rheometer as well as the platform for LAOS, as the Weissenberg rheogoniometer once had been.
† Interested readers may refer to a technical report of the former Royal Aircraft Establishment in 1964 about a measurement system for amplitude and phase available here, which may give a brief description of the technical status at that time.
†† Interested readers are referred to Rev. Sci. Instrum. 1984, 55, 1675.