Fast and accurate phase-unwrapping algorithm based on the transport of intensity equation: reply

Area of Science:

• Optics
• Image Processing
• Computational Physics

Background:

• A previous study introduced a phase-unwrapping algorithm utilizing the transport of intensity (TIE) equation.
• A specific derivation of the axial intensity derivative using the paraxial angular spectrum (AS) method was presented in that work.

Purpose of the Study:

• To address a recent comment that misinterpreted the utility of the angular spectrum method.
• To resolve ambiguity in the derivation of the axial intensity derivative.
• To correct a typographical error in the original manuscript.

Main Methods:

• Revisiting the derivation of the axial intensity derivative.
• Applying the paraxial angular spectrum (AS) method.
• Correcting a specific typo in the calculation.

Main Results:

• The angular spectrum (AS) method's utility in deriving the axial intensity derivative is confirmed.
• A corrected analytical expression for the axial intensity derivative is provided.
• The ambiguity raised by Yoneda et al. is resolved.

Conclusions:

• The transport of intensity (TIE) equation based phase-unwrapping algorithm is robust.
• The paraxial angular spectrum (AS) method is a valid approach for this derivation.
• Clear communication and precise derivations are crucial in scientific publications.