A piecewise thickness-function to the interferometric measurement of the optically transparent thin films

A new piecewise function to determine the thickness profile of transparent thin films, is built from a piecewise scaled function of the 1D gray value plot obtained through monochromatic-light-interferometry. In the gray value piecewise function each subfunction contains the information of the physical phenomena related to fringe pattern formation and corresponds to an interferometric branch. The interference phenomenon is studied by assuming that the scaled function is the normalized intensity that comes from light interference in an infinite thin-layer material inserted between two half-spaces of other two different materials. The scaled function is introduced to the model through the relative reflectivity and from this the piecewise thickness function. The scaled gray-values piecewise function is in the interval [0,1], which avoids divergences in the reflectivity function and reproduce adequately the phase difference in the extrema values, then the thickness profile is obtained. The thickness function approach was tested by obtaining the meniscus thickness of a water droplet. We got an adsorbed layer thickness of 21 ± 2.2 nm. In addition, we demonstrated numerically that our proposal includes or improves other methods previously reported. The process was validated by simulation and compared with previous works. Finally, the application of our data analysis procedure to obtain dynamic meniscus thickness in real time is discussed.