Numerical calculation of the Fresnel transform

Area of Science:

• Optics and Photonics
• Computational Physics

Background:

• Accurate calculation of Fresnel diffraction integrals is crucial in optics.
• Existing methods may lack efficiency or general applicability for varying propagation distances.

Purpose of the Study:

• To develop general and simple sampling rules for Fresnel diffraction integrals.
• To enhance the efficiency of these calculations, particularly for arbitrary propagation distances.
• To integrate these rules with fast Fourier transform (FFT) algorithms.

Main Methods:

• Derivation of general sampling rules for Fresnel diffraction.
• Extension of sampling rules for FFT-based computation.
• Comparative analysis with existing theoretical diffraction calculation methods.

Main Results:

• Established practical sampling rules for Fresnel diffraction calculations.
• Demonstrated increased computational efficiency using FFT-based algorithms.
• Validated the accuracy and applicability across different propagation distances.

Conclusions:

• The derived sampling rules provide an efficient and accurate method for Fresnel diffraction.
• FFT-based extensions offer significant computational advantages.
• This approach is broadly applicable for various optical propagation scenarios.