In an optical time domain reflectometer type strain measurement system, we theoretically derive the shape of the Brillouin gain spectrum produced in an optical fiber under a parabolic strain distribution which is formed in a uniformly loaded beam. Based on the derived result, we investigate the effects of the parabolic strain distribution parameters and the measurement conditions such as the launched pulse width and the measurement position on the beam on the deformation of the Brillouin backscattered-light power spectrum shape. In addition, we investigate the strain measurement error resulting from the deformation of the power spectrum shape by analyzing the peak-power frequency at which the power spectrum is maximized.

In order to estimate elasticity distribution of living soft tissue by ultrasonic pulse-echo method, we developed an algorithm by which we estimate 2-D displacement vector field from two successive rf echo data frames. The algorithm estimates a displacement vector iteratively by matching the phase characteristics of the local regions of two data frames. The estimation process is composed of coarse one and the fine one. In the coarse estimation process, the displacement is estimated by detecting the peak of the 2-D cross-correlation function. In the fine process, the displacement is estimated iteratively by shifting the 2nd frame data so that the phase characteristics matches with that of the 1st frame data. In each iterative step of both processes, the estimated displacement vector field is spatially smoothed. This proposed algorithm exhibits excellent performance in obtaining accurate and smooth distribution of displacement vector which is required to obtain strain distribution and finally shear modulus distribution. We conducted an experiment on an agar phantom which has inhomogeneous shear modulus distribution. Using the proposed method, we obtained 2-D displacement field with reasonable accuracy. We reconstructed a relative shear modulus map using axial strain assuming 1-D stress condition. The reconstructed map using the calculated axial strain through 2-D displacement estimation algorithm was satisfactory, and was clearly superior to the one through 1-D displacement estimation algorithm. The proposed 2-D displacement field estimation algorithm seems to be a versatile and powerful tool to measure strain distribution for the purpose of tissue elasticity estimation under various deformation conditions.