Materials that consist of a random microstructure can affect ultrasonic measurements--reducing signal strength, increasing noise, and reducing measurement accuracy--through scattering and aberration of the acoustic field. To account for these adverse effects a phase screen model, alongside the stochastic wave equation, has been developed. This approach allows the field and study aberrations to be modeled from a statistical point of view. Experimental evidence of aberration and statistical properties of the measured acoustic field are shown. A measured correlation function of the acoustic field is interlinked to mean crystallite size by using a theoretical coherence function that can be mainly described by the correlation length and wave velocity variation of microstructure. The estimation of the mean crystallite size using this technique would provide some insight into material characterization.