An approximate algorithm for simulating Fresnel diffraction patterns without Fourier transform

In the study of optical systems, accurately calculating Fresnel diffraction patterns is crucial for understanding and designing various applications, from imaging systems to laser technologies. However, existing commonly used calculation methods each have their limitations. This paper proposes an approximate algorithm for calculating Fresnel diffraction to address these shortcomings. The algorithm is based on the oscillatory characteristics of the quadratic phase exponential function in the Fresnel diffraction integral. By convolving this quadratic phase exponential function with another slowly varying function, it is found that the rapidly oscillating parts cancel each other out, having little impact on the final calculation result. Therefore, only the areas that primarily contribute to the diffraction need to be computed. The study shows that this algorithm significantly reduces the computational load while maintaining a certain level of accuracy. Compared to the direct integration method, it shows a notable improvement in calculation speed. It also maintains high accuracy compared to both the direct integration method and the Fast Fourier Transform (FFT) algorithm. Additionally, since it does not involve the frequency domain transformation used in FFT, it avoids under-sampling issues. This algorithm offers a feasible method for calculating diffraction patterns while ensuring a balance between accuracy and computational efficiency.