Abstract
Accurate and reproducible measurement of optical parameters such as refractive index (RI) and thickness is central to quantitative phase imaging (QPI) and its applications in biology and material science. A long-standing challenge in QPI systems is the intrinsic coupling between RI and thickness in the reconstructed phase distribution, which limits the metrological value of QPI for uniquely and robustly separating the sample’s RI and physical thickness. Unlike previous decoupling strategies that rely on multi-wavelength or tomographic recording, this work presents a measurement-oriented computational framework, the Cauchy-based Inverse Phase Hybrid Error Reduction (CIPHER) algorithm, designed to decouple RI and thickness from a single reconstructed phase map. By incorporating Cauchy’s dispersion model into the inverse problem, i.e., n(λ) = n1 + n2/λ2, CIPHER provides a physically constrained measurement model that reduces solution ambiguity and improves estimation stability. The algorithm incorporates GPU acceleration and an optimized CIPHER implementation based on a coarse-to-fine full-grid search with fast thickness selection and deterministic tie-breaking, preserving the full-grid solution while reducing computation time by nearly an order of magnitude for high-resolution phase imaging applications. The performance of CIPHER is validated using both simulated and experimental datasets, including a calibrated phase target with traceable thickness standards and an array of microlenses with unknown parameters. Experimental results demonstrate that CIPHER accurately estimates thickness and RI maps, achieving accuracy above 95% for both calibrated and non-calibrated targets. By enabling accurate RI and thickness measurements without assumptions about sample geometry or the surrounding medium, CIPHER advances the state of the art in optical metrology. CIPHER represents a generalizable measurement model for phase-based systems, with potential applications spanning biomedical diagnostics, materials inspection, and optical manufacturing where traceable, uncertainty-aware quantification of optical parameters is required.