Fringe pattern distribution in small angle rotationally shearing interferometer

We study the form and shape of the interferometric patterns obtained in a small angle rotationally shearing interferometer (iRSI) and compare them to those obtained in the traditional Mach-Zehnder interferometer (MZI). We concentrate on low order rotationally asymmetric aberrations, tilt, astigmatism, and coma. We find that the iRSI rotates the interferometric pattern by the angle p/(2l), where l is the second summation index of the wavefront polynomial. Thus, the interferometric patterns for the tilt and coma are rotated by 90 degrees, while those for astigmatism by only 45 degrees, relative to those of the MZI. Additionally, when the experimenter wishes to implement a rotation of the interference pattern in the IRSI, he / she needs to incorporate a relative change of the infinitesimal rotation (dj) from some (δφ)min to (δφ)max. However, the true derivative function is accomplished only for an infinitesimal shear angle.