Optimization-Based Approach for High- Fidelity Phase Retrieval from Sparse Interferometric Data: Implications for Industry and Biological Research

Optical profilometers provide a non-contact, non-destructive method for swiftly profiling 3D surfaces. White light interferometers, often used for this purpose, employ a 5-phase shifting technique for precise phase maps. However, capturing multiple frames introduces mechanical movement, which impedes imaging of dynamic objects. White light’s low spatial-temporal coherence mitigates speckles and spurious fringes while offering high axial resolution. Creating a high fringe density interferogram with low-coherence light is challenging. Introducing a tilt angle in the interferometer can increase the fringe density, which is still insufficient for phase map retrieval using the single-shot Fourier transform method. We propose an adaptive optimization framework to recover phase maps from single low fringe density interferograms. This method iteratively extracts reference beam information, eliminating mechanical movement and enhancing system stability while reducing costs and system bulkiness. The simulation and experimental results on a step-phase object (etched on silicon) and biological MG63 osteosarcoma cells validate the efficacy of a single-shot optimization scheme. For comparison, the phase maps of the same objects were obtained using the single-shot Fourier transform and multi-shot 5-phase shifted methods. The single-shot optimization technique shows efficient performance, yielding phase maps with reasonable accuracy, potentially replacing the 5-phase shifting technique in industrial and biological diagnostics.