RESUMEN
We present an erratum to J. Opt. Soc. Am. A, 39, 2376 (2022)JOAOD60740-323210.1364/JOSAA.476200. This erratum adds the mathematical proof of the unique solution of Eq. (3) in Appendix A. At the same time, we correct an unintended error in which the phase step in Fig. 3(a2) and Fig. 4(a2) did not exceed 2π. The signal-to-noise ratio (SNR) required in the proposed method is related to the step size. We analyze the required SNR under different step sizes and find that the smaller the step size, the higher the SNR that is required.
RESUMEN
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.
RESUMEN
It is known that phase ambiguity is always an inherent problem in digital holography. In this paper, a 2π ambiguity-free digital holography method is proposed. The method naturally avoids phase ambiguity by a quasianalytic method. This quasianalytic method accurately calculates the true phase by constructing an equation and solving the solution of the equation. Thus, the inherent wrapping problem in digital holography is eliminated. For example, our experimental result shows that the true phase of the stepped specimen with the phase distributed in [0, 16π] can be obtained unambiguously. Since the proposed method naturally avoids the phase ambiguity problem, it may be beneficial to enlarge the application potential of the digital holography. The effectiveness and accuracy of the proposed method are verified by both numerical simulations and experimental results.