Three-dimensional phase imaging with the intensity transport equation

Phase can be retrieved from intensity measurements with the intensity transport equation. Three-dimensional image formation of weak phase objects based on this method is investigated. It is shown that, although the refractive index of a thin object can be measured, the three-dimensional variation of refractive index of an arbitrary object cannot, in general, be reconstructed, as spatial frequencies with a zero-axial component are not detected. However, this may not be a problem if regions with known refractive index are present in the sample.