Recursive method for phase retrieval using transport of intensity and its applications

Area of Science:

• Optics and Photonics
• Wave Propagation
• Phase Retrieval

Background:

• Optical field propagation is described by the Helmholtz or paraxial wave equation.
• Transport of Intensity (TIE) is a non-interferometric phase retrieval technique.
• TIE derives from the imaginary part of the paraxial wave equation, relating to energy conservation.

Purpose of the Study:

• To demonstrate a method for retrieving optical field phase by exploiting both real and imaginary parts of the paraxial wave equation.
• To present a recursive approach for simultaneous phase and intensity calculations.
• To showcase applications in imaging phase modulation and surface profiling.

Main Methods:

• Solving the Transport of Intensity Equation (TIE) using standard numerical techniques.
• Solving the real part of the paraxial wave equation (Transport of Phase equation) via a Gauss-Seidel iterative method.
• Recursive calculation of phase and intensity to satisfy both wave equation components.

Main Results:

• Successfully retrieved phase information from optical intensity measurements at different propagation distances.
• Demonstrated phase imaging of self-phase modulation in a liquid medium.
• Obtained 3D surface profiles from phase imaging of reflected light.

Conclusions:

• The combined use of TIE and the transport of phase equation enables accurate optical phase retrieval.
• The recursive method provides a robust framework for phase imaging applications.
• This technique offers a versatile tool for characterizing optical fields and surfaces.