Abstract
Quantitative Phase Imaging (QPI) provides valuable insights into the morphological and chemical properties of biological systems. Among the different QPI methods, Digital Holographic Microscopy (DHM) is one of the most promising because of its high spatial resolution and sensitivity, allowing for the reconstruction of two-dimensional (2D) phase distributions in a single shot (i.e., a single recorded image is required). These 2D phase distributions encode critical information about a sample’s refractive index (RI) and thickness, which are vital parameters for studying cellular structures and dynamics. However, interpreting QPI-DHM phase measurements poses a significant challenge due to the intrinsic coupling between the sample’s refractive index (RI) and thickness (t). This coupling complicates the accurate retrieval of both parameters, limiting the potential of QPI-DHM in advancing biological research and enhancing the precision of cellular diagnostics. This Master’s Thesis is focused on the investigation of a mathematical framework designed to accurately estimate both the refractive index and thickness of a sample using 2D phase data by leveraging the wavelength dependence of the sample’s refractive index using Cauchy’s equation. The proposed computational framework decouples the RI and thickness distributions from reconstructed phase measurements by minimizing the error between the theoretical and measured phase data. The performance of the proposed method, referred to as Cauchy-Based Inverse Phase Hybrid Error Reduction or CIPHER in this Master’s research thesis, has been demonstrated using both simulated and experimental datasets. Both the simulated and experimental results show that the proposed CIPHER approach estimates both the RI and thickness with a low error, even with the presence of noise. In addition, the performance of the CIPHER method has also been compared using simulated data with the Spherical Phase-based Holistic INdex-thickness eXtraction(SPHINX) approach, which assumes that the sample is spherical and estimates its thickness from a fitting of the 2D sample’s morphology. This comparison shows that the CIPHER method outperforms the SPHINX approach, decoupling both parameters with a lower percentage error. The main advantages of the proposed approach are: (1) it does not include any change of the experimental QPI systems, (2) it requires fewer input images or data, reducing the acquisition time required for measurements, and (3) it eliminates the need for prior assumptions regarding the sample’s morphology or the surrounding medium, making it a versatile tool for a wide range of applications. We believe that this framework can be transformative in biomedical research, improving our understanding of biological systems.