High-resolution 3D phase imaging using a partitioned detection aperture: a wave-optic analysis

Quantitative phase imaging has become a topic of considerable interest in the microscopy community. We have recently described one such technique based on the use of a partitioned detection aperture, which can be operated in a single shot with an extended source [Opt. Lett. 37, 4062 (2012)]. We follow up on this work by providing a rigorous theory of our technique using paraxial wave optics, where we derive fully three-dimensional spread functions for both phase and intensity. Using these functions we discuss methods of phase reconstruction for in- and out-of-focus samples, insensitive to weak attenuations of light. Our approach provides a strategy for detection-limited lateral resolution with an extended depth of field, and is applicable to imaging smooth and rough samples.