Comparison of Fresnel Diffraction Beams and Fraunhofer Diffraction Beams: Analysis and Simulation Approaches

Fresnel diffraction beams and Fraunhofer diffraction beams represent two fundamental diffraction phenomena in optics, widely applied in optical field analysis and imaging technologies. Their core distinctions lie in observation distance and approximation conditions, which directly influence beam propagation characteristics and computational methods. Fresnel diffraction occurs in the near-field region, relatively close to the diffracting object. At this range, the spherical wave nature of light remains significant, requiring consideration of quadratic phase factors in calculations, thus resulting in more complex mathematical expressions. Simulations of Fresnel diffraction typically employ Fresnel integrals or angular spectrum propagation theory, providing accurate descriptions of amplitude and phase evolution during beam propagation. In code implementation, this often involves discretizing the diffraction integral using Fast Fourier Transform (FFT) algorithms with appropriate sampling intervals to maintain numerical accuracy. Fraunhofer diffraction constitutes a far-field approximation, applicable when the observation plane is sufficiently distant from the diffracting object. Here, light waves can be approximated as plane waves, with diffraction patterns directly related to the object's Fourier transform, leading to computationally efficient solutions. Fraunhofer diffraction simulations commonly utilize a single FFT operation, where the computed field represents the Fourier transform of the input aperture function. This approach is particularly useful for analyzing optical system spectral characteristics, such as focal spot distributions in lens systems. When simulating these diffraction phenomena, Fresnel diffraction demands higher computational precision as it preserves propagation distance effects, while Fraunhofer diffraction simplifies calculations at the cost of near-field detail resolution. Practical applications determine model selection based on specific experimental conditions and accuracy requirements. For instance, laser beam shaping or holographic imaging may require Fresnel diffraction models, whereas far-field spot analysis typically employs Fraunhofer approximations. By comparing simulation results of both diffraction types, one can visually observe beam evolution from near-field to far-field regions, elucidating core physical mechanisms of diffraction phenomena. Such comparisons not only facilitate optical system design but also provide theoretical foundations for optimizing related algorithms, including improvements in numerical propagation methods and computational efficiency enhancements.