Scanning-free digital holography for decoupling the refractive index and thickness via a constrained equation of higher degree

Abstract

Digital holography is one of the most popular quantitative phase imaging techniques, but the refractive index and the thickness are always coupled in the phase. To solve the decoupling problem, multiple scanning methods such as tomography and total reflection are usually used, which is time-consuming. To increase the imaging speed and reduce the system cost, it is urgent to seek the decoupling method of scanning-free digital holography. In this paper, we find that the decoupling method of scanning-free digital holography can be transformed into a problem of solving constrained higher order equations. By introducing the Fresnel reflection formula, a six-degree equation about refractive index is constructed and the corresponding algorithm for solving the equation is given. By using the algorithm, the refractive index and thickness can be decoupled successfully. A series of results show that the proposed method is effective and has high anti-noise performance. This method provides a mathematical possibility for scanning-free digital holography to decouple the refractive index and complex pixel stepped thickness distributions. Therefore, it may provide a theoretical basis for the subsequent development of a real scanning-free digital holography system, which may have potential applications in the measurement of optical devices produced by the modern film deposition process and etching process.