text: An acoustic slowness surface can be determined for each pixel by propagating the acoustic wave in several directions. Having measured the SAW velocity in multiple directions the challenge is then to convert this information into the measurement of crystallographic orientation. The direct calculation of the orientation from velocity is a difficult problem. However, the numerical calculation of the SAW velocity as a function of SAW velocity is relatively simple, as first outlined by Farnell. Therefore, a database of possible slowness surfaces can be pre-calculated and compared to the measurement values. For each measurement pixel the orientation is given by the orientation of the pre-calculated velocity surface which best matches the measured data. These maps can spatially describe the crystal orientation of the material being interrogated and can be used to examine microtexture and sample morphology. The technique is applicable to any crystal structure, however transverse isotropy means the full orientation cannot be determined in hexagonal materials, such as titanium.
  In order to calculate the predicted SAW velocity of the sample, the materials density and elastic constants must be known. Elastic constants are typically measured by ultrasonic techniques such as resonant ultrasound spectroscopy, with well-established values for most common engineering materials. However, it is possible to attempt the full inverse problem to determine both the elastic constants and crystallographic orientation from only the measured SAW velocity.
  From orientation data, a wealth of information can be devised that aids in the understanding of the sample's microstructure and processing history. Recent developments include understanding: the prior texture of parent phases at elevated temperature; the storage and residual deformation after mechanical testing; the population of various microstructural features, including precipitates and grain boundary character.