Christiansen filters realized with cylindrical lenses of even symmetry

Authors：Xie, Kang^*; Ma, Dianguo; Ma, Ji; Liang, Lanju; Wei, Dequan; Wang, Xueqin; Wang, Meng; Hu, Zhijia; Zhang, Junxi; Mao, Qiuping

Source：Journal of the Optical Society of America A: Optics and Image Science, and Vision , 2022, 39(3): 431-439.

DOI：10.1364/JOSAA.446633

A type of Christiansen filter that takes the form of a smooth cylindrical lens of even symmetry is proposed. By varying the shape of the lens, the filter can be made to realize many common filtering responses, including the polynomial function response, the Gaussian function response, and the sinc function response. A systematic design technique based on inverse scattering is established, and a desired, prescribed response can be tailored by properly shaping the lens of the filter. Three prototypical Christiansen filters, namely, a second-order all-real-roots filter, a second-order sinc filter, and a Gaussian filter, are synthesized using the proposed method. A prescribed response at 545 nm with a FWHM of 2 nm is achieved systematically by all of the three Christiansen filters.