Quantitative phase imaging with optical differentiation by spatially variable amplitude filters

We present a non-interferometric technique for quantitative phase imaging (QPI) that is cost-effective, easily integrated into standard microscopes, and capable of wide-field imaging with noncoherent light. Our method measures the phase gradient through optical differentiation using spatially variable amplitude filters, accommodating a range of transmission functions, including commercially available variable neutral-density filters. This flexibility is made possible by a general relationship we derive. The approach is demonstrated by recovering phase information from a microsphere with a phase shift exceeding 2π, without the need for phase unwrapping. Additionally, we image multiple HeLa cells across a large field of view.