Is the Rayleigh-Sommerfeld diffraction always an exact reference for high speed diffraction algorithms?

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Wave Propagation

Background:

• Scalar diffraction theory is crucial for calculating electromagnetic wave behavior in optics and photonics.
• Fast Fourier Transform (FFT)-based algorithms approximate the Rayleigh-Sommerfeld-diffraction (RSD) theory for high-speed computations.
• Existing methods face limitations in accurately sampling the RSD integral.

Purpose of the Study:

• To demonstrate a novel sampling condition for well-sampling the Riemann integral of the RSD.
• To discuss the fundamental restrictions imposed by this sampling condition.
• To present a unified approach for applying RSD outside its conventional sampling domain.

Main Methods:

• Development of a new sampling condition for the RSD Riemann integral.
• Analysis of sampling restrictions and their implications.
• Implementation of a unified approach for extended RSD application.

Main Results:

• A novel sampling condition for accurate RSD integral evaluation is demonstrated.
• Fundamental restrictions associated with the sampling condition are identified and discussed.
• Sampling below the Abbe resolution limit completely removes these restrictions.
• A general unified approach for applying RSD beyond its sampling domain is provided.

Conclusions:

• The novel sampling condition enhances the accuracy of computational diffraction methods.
• The proposed approach broadens the applicability of the Rayleigh-Sommerfeld-diffraction theory.
• This work offers a more versatile tool for wave propagation simulations in optics and photonics.