A recursive phase retrieval technique using transport of intensity : reconstruction of imaged phase and 3D surfaces

Date of Award


Degree Name

Ph.D. in Electrical and Computer Engineering


Department of Electrical and Computer Engineering


Advisor: Partha P. Banerjee


Transport of intensity is a noninterferometric method to find the phase of an object by recording optical intensities at different distances of propagation. The transport of intensity equation results from the imaginary part of the complex paraxial wave equation and is equivalent to the principle of conservation of energy. The real part of the paraxial wave equation gives the eikonal equation in the presence of diffraction, which can be also termed the transport of phase equation. The amplitude and phase of the optical field must simultaneously satisfy both the real and imaginary parts of the paraxial wave equation during propagation. In this dissertation, it is demonstrated, using illustrative examples, how to exploit this to retrieve the phase through recursive calculations of the phase and intensity. This is achieved using the transport of intensity equation which is solved using standard Fourier transform techniques and the transport of phase equation, which is solved using a Gauss-Seidel iterative method. Examples include calculation of the imaged phase induced through self-phase modulation of a focused laser beam in a liquid, and the imaged phase of light reflected from a surface which yields its 3d surface profile.


Optics Mathematical models, Optical measurements, Electrical Engineering, Optics, TPE, TIE, Transport of Intensity, Transport of Phase, Recursive

Rights Statement

Copyright 2016, author