Wavefront deformation in a rotational shearing interferometer when it no longer finds a derivative

It is a generally accepted belief that a shearing interferometer finds a derivative of the wavefront along the direction of the shear. A shear could be implemented in a form of a linear displacement along an axis, a vector displacement along an arbitrarily chosen direction, a small rotation, and the radial magnification, to list the most popular ones. The shearing function implemented in the interferometer as a device that finds a specific derivative is valid only for a small amount of shear. In fact, in the mathematical definition of a derivative, we arrive at the concept of the derivative of the function, by requiring that that the small change should approach to zero. We examine the range of validity of the shearing-induced change as a derivative of the aberration polynomial in a rotationally sharing interferometer. Furthermore, we propose steps to decrease the errors in the determination of the magnitude of individual aberrations.