OSI-flex: optimization-based shearing interferometry for joint phase and shear estimation using a flexible open-source framework

Abstract Shearing interferometry is a common-path quantitative phase imaging technique in which an object beam interferes with a laterally shifted replica of itself, providing high temporal stability, reduced sensitivity to environmental noise, compact design, and compatibility with partially coherent illumination that suppresses coherence-related artifacts. Its principal limitation, however, is that it yields only sheared phase-difference measurements rather than the absolute phase, thereby requiring an additional reconstruction step. In this work, we introduce OSI-flex, a flexible, open-source computational framework for quantitative phase reconstruction from sheared phase-difference measurements. The method leverages modern machine learning tools, namely automatic differentiation, and the advanced adaptive moment estimation optimizer. The method simultaneously refines the phase distribution and estimates the shear values, enabling adaptation to experimental conditions where the shear cannot be precisely determined. Because defining shear value is inherently difficult in most systems, yet crucial for effective phase reconstruction, this joint optimization leads to robust and reliable phase retrieval. The proposed OSI-flex framework is highly versatile, supporting arbitrary numbers, magnitudes, and orientations of shear vectors. While optimal reconstruction is achieved with two orthogonal shear directions, the inclusion of regularization—specifically total variation minimization and sign constraint—enables OSI-flex to remain effective with nonorthogonal or even single-shear measurements. Moreover, the algorithm accommodates a wide range of shear magnitudes, from subpixel shifts (differential configuration) to several dozen pixels (semi-total shear configuration). Validation with simulations and experimental data confirms quantitative accuracy on calibrated phase objects and demonstrates robustness with 3D-printed cell phantom and follicular thyroid cells.