Wrap-type phase unwrapping utilizing arctangent operation as a differential amplifier through shifted phase maps

Area of Science:

• Signal Processing
• Image Analysis
• Computational Mathematics

Background:

• Phase unwrapping is crucial for reconstructing continuous phase from wrapped data.
• The 2π ambiguity problem, or phase wrapping, limits the accuracy of phase measurements.
• Existing methods often struggle with complex surfaces and various wrap types.

Purpose of the Study:

• To introduce a novel phase unwrapping algorithm.
• To leverage the arctangent function for improved wrap-type identification.
• To provide a robust solution for the 2π ambiguity problem.

Main Methods:

• Investigating the properties of the arctangent function as a nonlinear differential amplifier.
• Combining phase jumps from two shifted-wrapped maps as differential mode inputs.
• Developing a mathematical framework to explain shifted wrap effects.

Main Results:

• Successfully distinguished various phase wrap types.
• Differentiated between continuous and discontinuous surfaces using threshold phase values.
• Validated the algorithm's feasibility through simulations and experiments.

Conclusions:

• The proposed arctangent-based algorithm offers a novel approach to phase unwrapping.
• The method effectively addresses the 2π ambiguity by accurately identifying phase wraps.
• This work contributes foundational understanding to phase unwrapping techniques.