The general theory of phase shifting algorithms.

Area of Science:

• Optical Metrology
• Interferometry
• Signal Processing

Background:

• Phase Shifting Interferometry (PSI) is a key technique in optical metrology.
• Existing PSI methods have limitations in analysis and synthesis.
• The Frequency Transfer Function (FTF) offers a novel approach for PSI.

Purpose of the Study:

• To present a general, holistic theory of PSI algorithms.
• To expand upon previous work using the Frequency Transfer Function (FTF).
• To introduce new methods for PSI analysis and synthesis.

Main Methods:

• Application of the Frequency Transfer Function (FTF) for PSI analysis and synthesis.
• Development of complex PSI algorithms using quadrature filters.
• Formulation of new methods for detuning error estimation and phase noise analysis.

Main Results:

• Achieved rotational invariant spectrum in PSI.
• Synthesized complex PSI algorithms from simpler filters.
• Developed more accurate formulae for detuning error estimation.
• Introduced methods for output-power phase noise estimation.
• Presented a novel way to combine PSI algorithms with recursive linear PSI algorithms for resonant quadrature filters.

Conclusions:

• The FTF provides a powerful, general framework for PSI.
• The presented holistic theory unifies and expands PSI algorithm development.
• New methods offer enhanced accuracy and capabilities in optical metrology applications.