The process of nulling in ellipsometry is studied by a graphical presentation using the trajectories of two significant polarization states in the complex plane, XPC and XSA. These states are determined by (1) the polarizer and compensator (XPC) and (2) the specimen and the analyzer (XSA) in the polarizer-compensator-specimen-analyzer ellipsometer arrangement. As the azimuth angles of the ellipsometer elements are varied, XPC and XSA move closer to one another in a stepwise fashion until they coincide when a null is reached. Thus, at null, the polarization states are matched, and XPC = XSA. For an isotropic reflector, the trajectory of XSA is a straight line, which simplifies the development of a criterion for achieving the most rapid nulling for two nulling procedures.
D. L. Confer, R. M. A. Azzam, and N. M. Bashara, "Ellipsometer nulling: convergence and speed," Appl. Opt. 15, 2568-2575 (1976) http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-15-10-2568.