During my PhD, I developed a direct approach to calculating thermo-mechanical noise in LIGO interferometers:
Internal thermal noise in the LIGO test masses: A direct approach
The method is computationally cheap, has significant conceptual advantages, and is widely used inside and outside LIGO community. I pointed out that coatings might be the source of noise that people could have missed. This turned out indeed to be the case, and the coating thermal noise is among the dominant sources of noise in many optomechanical experiments. Research on how to reduce it is an active field in precision measurements.
I have also developed a simple method to compute thermo-refractive noise; this is increasingly being used in a number of photonics applications, as devices become increasingly thermal-noise limited:
Fluctuation–dissipation theorem for thermo-refractive noise
One of the first applications of this formalism was to compute thermo-refractive noise in the beamsplitter of GEO600 gravitational-wave interferometer (at the time, there were questions whether the "mystery noise" had thermo-refractive origin). This was the masters thesis project of Bruin Benthem: