Numerical solution of nonparaxial scalar diffraction integrals for focused fields.

Area of Science:

• Computational physics
• Wave propagation modeling
• Numerical methods

Background:

• Accurate field propagation is crucial for optical system design and analysis.
• Existing methods often require high sampling rates, increasing computational cost.
• Optimizing sampling for fast Fourier transform (FFT)-based methods is an ongoing challenge.

Purpose of the Study:

• To derive novel sampling criteria for FFT-based field propagation.
• To ensure accurate calculation results in the output plane.
• To balance computational load and accuracy, particularly for focal field calculations.

Main Methods:

• Combined analysis of input field and propagation kernel to derive sampling criteria.
• Application of geometrical optics for a priori knowledge in focal field calculations.
• Investigation of chirp z-transform-based zoom algorithms using similar techniques.

Main Results:

• Developed sampling criteria applicable to general field propagation.
• Demonstrated accurate results with sub-Nyquist sampling rates in numerical examples.
• Showcased optimization of computational load versus accuracy using a priori knowledge.

Conclusions:

• The derived sampling criteria enhance the efficiency and accuracy of FFT-based field propagation.
• The methodology provides a framework for analyzing sampling in related algorithms like chirp z-transform.
• This work offers practical guidelines for computational optics and wave propagation simulations.