Metrology and the linear canonical transform

It is shown experimentally that both surface tilt and in-plane translation motion can be independently estimated using the speckle photographic correlation technique by capturing consecutive images in two linear canonical transform domains (using two different quadratic phase systems). A geometric interpretation, based on use of the Wigner distribution function is presented to describe the method and a simple matrix approach, based on the ABCD matrix, is used to quantify it. It is shown that the sensitivity and dynamic range of measurement of both tilt and translation are both variable and depend on the parameters of the ABCD matrix.