Zhao Lujia, Liu Yu-Ang, Ji Huiru, Wang Haibo, Tan Hao, Mo Yan, Ma Donglin
National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China.
Institute of Optics, University of Rochester, 480 Intercampus Dr., Rochester, NY 14627, USA.
Sensors (Basel). 2025 Feb 27;25(5):1454. doi: 10.3390/s25051454.
In the simulation of partially coherent light propagation within optical systems utilizing the Wigner function, the constraints imposed by the Fourier transform necessitate that the dimensions of the input and output matrices remain congruent. Consequently, the extent of the image plane is dictated by the dimensions of the light source matrix and the propagation distance. For optical systems of greater complexity, such simulations are highly memory-intensive. This paper innovatively incorporates the displacement theorem of the chirp z-transform and integrates it with the Wigner function. This approach affords enhanced flexibility in the simulation of partially coherent light transmission, enabling the targeted simulation of regions of interest within the frequency domain of the optical system, thereby significantly improving simulation efficiency. The efficacy of this novel method is demonstrated through the simulation of a Wigner transmission algorithm based on the chirp z-transform, applied to an RC (Ritchey-Chrétien) telescope system. The RC telescope, known for its optical design that minimizes aberrations and provides high-quality imaging, serves as a critical foundation for the simulation. The resultant simulations exhibit a high degree of consistency with traditional methods while offering increased flexibility, thus corroborating the validity and effectiveness of the proposed approach.
在利用维格纳函数对光学系统内部分相干光传播进行模拟时，傅里叶变换所施加的约束要求输入矩阵和输出矩阵的维度保持一致。因此，像平面的范围由光源矩阵的维度和传播距离决定。对于更复杂的光学系统，此类模拟对内存要求极高。本文创新性地引入了线性调频z变换的位移定理，并将其与维格纳函数相结合。这种方法在部分相干光传输模拟中提供了更高的灵活性，能够在光学系统的频域内对感兴趣的区域进行有针对性的模拟，从而显著提高模拟效率。通过基于线性调频z变换的维格纳传输算法对RC（里奇 - 克莱琴）望远镜系统进行模拟，验证了这种新方法的有效性。RC望远镜以其能将像差降至最低并提供高质量成像的光学设计而闻名，是该模拟的关键基础。所得模拟结果与传统方法高度一致，同时具有更高的灵活性，从而证实了所提方法的有效性。
