Sphere-to-sphere diffraction propagation method for a phase-retrieval algorithm in the measurement of optical...

Area of Science:

• Optics
• Metrology
• Computational Physics

Background:

• Optical surface testing requires precise phase retrieval.
• Conventional methods can be computationally intensive.
• The Sziklas and Siegman coordinate transformation (SSCT) offers a potential simplification.

Purpose of the Study:

• To present an improved phase-retrieval algorithm for optical surface testing.
• To leverage the SSCT for enhanced computational efficiency.
• To validate the algorithm's accuracy and feasibility.

Main Methods:

• Utilized the Sziklas and Siegman coordinate transformation (SSCT) to convert spherical-wave diffraction to plane-wave diffraction.
• Applied the fast Fourier transform directly in propagation computations.
• Performed analysis and simulations to verify diffraction computation and phase-retrieval capability.

Main Results:

• The SSCT-based algorithm demonstrated simplicity and improved speed compared to conventional methods.
• Simulation results confirmed accurate diffraction computation and effective phase retrieval.
• Experimental testing of a 200 mm diameter, f/5 spherical surface showed excellent agreement with a ZYGO interferometer.

Conclusions:

• The improved phase-retrieval algorithm based on SSCT is feasible and accurate for optical surface testing.
• The method offers a practical and efficient alternative to existing techniques.
• This approach enhances computational efficiency in phase-retrieval applications.