余弦高斯光束通过含球差分数傅里叶变换系统的传输

Propagation of Cosine-Gaussian Beams in Spherically Aberrated Fractional Fourier Transform System

实际应用中球差作为一种普遍存在的像差,对光束在光学系统中的传输具有较大影响。为了研究球差对光束通过分数傅里叶变换系统后所产生的影响,基于柯林斯公式,推导出余弦高斯光束在有球差和无球差的分数傅里叶变换系统中的场分布,并以LohmannⅠ型系统为例,进行数值模拟计算,研究了余弦高斯光束通过有球差和无球差的分数傅里叶变换系统后输出面的横向光强分布规律以及不同变换阶数和不同调制参数下轴上光强大小与球差系数的关系。结果表明,在分数傅里叶变换系统中,透镜球差对输出面横向光强分布有较大影响,并且正球差和负球差对横向光强的影响效果有明显区别。不同变换阶数和不同调制参数下透镜球差对轴上光强的作用效果不同。

As a common aberration, spherical aberration has great influence on beam propagation in optical systems. In order to study the influence on beams in the spherically aberrated fractional Fourier transform system, based on the Collins formula, the light field distribution expressions of the cosine-Gaussian beams through spherically aberrated and non-spherically aberrated fractional Fourier transform system are derived. With the example of Lohmann Ⅰ, the output transverse intensity distribution in spherically aberrated fractional Fourier transform system, non-spherically aberrated fractional Fourier transform system, the relationship between the intensity distribution on axis and the coefficient of spherical aberration in different transform orders or different modulation parameters are studied through numerical calculation. It is shown that the spherical aberration of lens has great influence on the output transverse intensity distribution, and whether the spherical aberration is positive or negative also reswits in notably different effects. The effect on the on-axis light intensity caused by the spherical aberration of lenses is different for different transform orders and modulation parameters.