Controlling the aliasing by zero-padding in the digital calculation of the scalar diffraction

Area of Science:

• Optics and Photonics
• Computational Physics
• Digital Signal Processing

Background:

• Digital simulations of scalar diffraction are crucial in optics and photonics.
• Common methods include the Huygens convolution method (HCM), angular spectrum method (ASM), and Fresnel diffraction integral (FDI).
• Well-sampling conditions and potential artifacts like aliasing require careful consideration.

Purpose of the Study:

• To analyze the well-sampling conditions for digital diffraction calculation methods.
• To identify the optimal method and parameters for accurate diffraction field simulation.
• To provide guidelines for avoiding aliasing in numerical diffraction.

Main Methods:

• Discussion of digital calculation methods: Huygens convolution method (HCM), angular spectrum method (ASM), and Fresnel diffraction integral (FDI).
• Analysis of aliasing occurrence and the role of zero-padding.
• Evaluation of method applicability based on propagation distance and interest in intensity vs. phase.

Main Results:

• Aliasing is an unavoidable artifact in digital diffraction unless zero-padding is applied.
• The ASM is suitable for short distances, while HCM is better for long distances, but HCM's point spread function degrades with distance.
• FDI can be used for long distances if only intensity is needed; phase calculations require zero-padding and restrict distance.

Conclusions:

• Sufficient zero-padding is critical for accurate digital diffraction simulations, particularly for the ASM.
• The ASM with adequate zero-padding is recommended for calculating the diffraction field when phase information is important.
• The FDI offers a simpler alternative for intensity-only calculations over long distances without zero-padding.