Spatiotemporally decoupled iterative algorithm using multi-order Taylor expansion for random phase-shifting...

Area of Science:

• Optical metrology
• Interferometry
• Precision measurement

Background:

• Phase-shifting interferometry (PSI) is crucial for measuring ultra-smooth optical components.
• Finite bandwidth light sources introduce random phase-shifting errors and spatiotemporal modulation variations, degrading accuracy.
• Existing algorithms struggle with these complex errors.

Purpose of the Study:

• To develop a novel algorithm for high-precision phase retrieval in PSI under finite bandwidth conditions.
• To overcome limitations of existing algorithms in handling spatiotemporal modulation variations and random phase errors.

Main Methods:

• Proposed a spatiotemporally decoupled iterative algorithm (SDIA).
• Employed multi-order Taylor expansion to decouple spatiotemporally varying modulation amplitude.
• Utilized stepwise separation of time-dependent and space-dependent variables.
• Applied least-squares alternating iteration for linear equation construction.

Main Results:

• Simulations and experiments confirmed the algorithm's feasibility and high accuracy.
• Achieved retrieval residual errors below 1 nm (PV) and 0.1 nm (RMS) for a planar mirror.
• Demonstrated effective handling of random phase-shifting errors and modulation variations.

Conclusions:

• The SDIA effectively addresses random phase-shifting errors and spatiotemporally coupled modulation variations.
• This represents a novel approach to phase retrieval in PSI with finite bandwidth light sources.
• The algorithm offers significant improvements in measurement accuracy for ultra-smooth optical components.