A new piecewise thickness-function to determine the thickness of extremely transparent thin films, through the monochromatic-light-interferometric data, is proposed. The piecewise thickness-function is based on the gray values interference patterns, studied as a piecewise function as well. In the gray value piecewise function each subfunction corresponds to an interferometric branch, which is related to reflectivity from where a new rescaled gray value piecewise function is proposed to obtain the piecewise thickness function. The rescaled gray-values piecewise function is in the interval [0,1], which avoids divergences on the reflectivity function. The thickness function approach was tested by obtaining the meniscus thickness of a water droplet. We got an adsorbed layer thickness of \(21\pm 2.2 \text{n}\text{m}\). In addition, we demonstrated numerically that our proposal includes or improves other methods previously reported. The process was validated in two ways, i) numerical simulation and ii) comparison with previous works. Finally, the application of our data analysis procedure to obtain dynamic meniscus thickness in real-time is discussed.