A statistical examination of the Fry method of strain analysis

The statistics of the Fry method of strain analysis are examined in this paper. Point objects in the pre-deformed state are assumed in the Poisson distribution that is truncated at the maximum probability density function (PDF) of a certain point object. The mean log likelihood function (MLLF) is defined as the average sum of the log PDF of each individual point in the deformed state, and is maximized by use of a grid search to solve for unknown parameters, strain and cutoff radius. In order to demonstrate the feasibility of the new strain method, it is applied to artificial sets of point objects generated at the prescribed parameters. Results deliver a very high accuracy of the strain estimate even for artificial sets with many less packed point objects. Increasing the number of point objects in the MLLF tends to give a higher accuracy of strain estimate, particularly for a smaller point number, less than 60 in this case. A deformed conglomerate is analyzed to illustrate the new approach. A probable spurious point in these data is identified using the detection method proposed in this paper. Its removal leads to a more robust estimate of the strain.