Quantitative phase retrieval

Imaging the internal structure of quasi-transparent three-dimensional (3D) objects is one of the most challenging tasks for optical systems. If the light propagates coherently through the volumetric object, then collection of phase projections from different angles and tomographic reconstruction are required. However, a single shot from a high space-bandwidth-product camera is often sufficient to yield 3D information if the object is sufficiently sparse. For incoherent 3D sources or scatterers, the mutual intensity of the propagated field has sufficient degrees of freedom to reconstruct the source but it is limited by the sensitivity (contrast) of the interferometric measurement. We describe two complementary methods of phase recovery. (1) For the coherent sparse case, which typically leads to rapid phase oscillations at the exit pupil, we have implemented several generations of digital holographic imaging systems which can be deployed underwater to image, e.g. aquatic organisms, seed particles, or bubbles in a flow. (2) For slowly varying optical density profiles, we have been investigating phase recovery via the Transport of Intensity Equation (TIE) and we have developed methods to improve contrast and eliminate the inherent scanning requirement by exploiting the (known) object dispersion. We will present experimental results and discuss these methods comparatively.