This thesis describes a method developed to quickly measure the Rayleigh wave Q for a test material using a minimally invasive laser probe. The probe was donated to our lab by Dr. Alex Maznev at Phillips AMS in Natick, Ma. The machine was originally used to measure ultra thin film metal thicknesses; however we have utilized it to suit our needs. The optics head relies on a technique known as the transient grating method to generate a dispersion curve. This dispersion curve is then operated on by a local approximation for the Kramers-Kronig relations. The Kramers-Kronig relations for acoustic waves relate the real and imaginary parts of the dynamic compressibility to one another. The real part of the compressibility relates to the phase velocity of the wave and the imaginary part relates to the attenuation. Once the attenuation for the corresponding range of frequencies is determined the last step is to apply both the dispersion data and the attenuation data to the material Q equation to find Q over a range of frequencies. This thesis discusses the design of the machine, the theory behind the Kramers-Kronig relations and surface acoustic waves, the experimental procedure, and lastly results generated by the technique.