Stepwise Fourier correction algorithm for enhancing the robustness of dispersion fringe sensing to tip/tilt errors

Area of Science:

• Optical Metrology
• Interferometry
• Wavefront Sensing

Background:

• Dispersion Fringe Sensing (DFS) is a technique for optical measurements.
• Tip/tilt errors are common in optical systems and can degrade measurement quality.
• Accurate co-phase sensing is crucial for applications like adaptive optics and interferometry.

Purpose of the Study:

• To investigate the impact of tip/tilt errors on Dispersion Fringe Sensing (DFS) performance.
• To develop and validate a novel algorithm for correcting DFS results affected by tip/tilt errors.
• To demonstrate the feasibility of high-precision co-phase sensing using DFS in the presence of tip/tilt errors.

Main Methods:

• Development of a dispersion fringe model that incorporates tip/tilt error effects.
• Theoretical analysis of how tip/tilt errors influence fringe quality and optical path difference.
• Implementation of a two-step correction algorithm based on Fourier transform analysis.
• Numerical simulations to evaluate the algorithm's precision in piston sensing.

Main Results:

• Tip/tilt errors were found to blur dispersion fringes and introduce optical path differences.
• The proposed two-step algorithm effectively corrects for tip/tilt induced errors.
• Numerical simulations achieved high-precision piston sensing with an RMS error of approximately 0.005 µm.
• The developed method demonstrates robustness against tip/tilt disturbances.

Conclusions:

• Dispersion Fringe Sensing (DFS) can maintain high precision for co-phase sensing despite tip/tilt errors.
• The novel Fourier transform-based algorithm offers a viable solution for error correction in DFS.
• This research supports the use of DFS in demanding optical metrology applications requiring precise wavefront control.