Abstract

The amplitude and phase of the complex optical field in the Helmholtz equation obey a pair of coupled equations, arising from equating the real and imaginary parts. The imaginary part yields the transport of intensity equation (TIE), which can be used to derive the phase distribution at the observation plane. In this paper, we demonstrate the use of TIE to recover the 3D image of an amplitude object embedded in a phase object. The phase object is created by heating a liquid, comprising a solution of red dye in alcohol, using a focused 514 nm laser beam to the point where self-phase modulation of the beam is observed. The induced phase due to the pump beam is also obtained using regular in-line holography and compared with results obtained from TIE. Our work can find applications in, for instance, referenceless 3D imaging of debris in a fireball, and is also well suited for moving objects.

© 2015 Optical Society of America