Simulated Fizeau ring fringes in transmission through spherical and plane reflected surfaces

In this paper, we present simulated Fizeau ring fringes. These fringes are constructed due to multiple reflection between
highly reflected partially transmitted spherical and plane surfaces. The real paths of rays and consequently their amplitudes
and phases have been determined when they reached the image plane. This plane is located at a certain distance above the
interferometer. In these calculations, the impact of the image plane position, the radius of the spherical surface and the distance
between the two surfaces on the fringe intensity distribution are investigated. A quite interesting result of our calculation
is that the number of the interfered rays is varied and could be only two, even for a highly reflected surfaces. Three different
estimated visualizations are included to give an overview imagination of the impact of the different parameter variation.
These could be helpful for researchers for testing of spherical surfaces using interference-based methods.