基于傅里叶对映射的光整形的可积解

IF 1.9 4区 物理与天体物理 Q3 OPTICS Journal of the European Optical Society-Rapid Publications Pub Date : 2021-07-26 DOI:10.1186/s41476-021-00161-y
Liangxin Yang, Irfan Badar, Christian Hellmann, Frank Wyrowski
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引用次数: 0

摘要

在远场光整形中,其中一种设计方法是基于源和目标辐照度之间的一对一映射。然而,在这种算法中可能会出现可积性问题,无论是在设计自由曲面的光线映射方法中,还是在实现所需输出相位的基于几何光学的方法中。我们引入另一种映射型算法来解决可积性问题,该算法不是在空间域中建立源和目标辐照度之间的映射,而是在空间域和空间频域之间的傅里叶对电场上假设映射。通过求解傅里叶对的映射,得到了输出相位的梯度,该梯度等价于得到的映射函数。此外,映射的存在性和刻划性保证了梯度的可积性,从而可以直接积分光滑的输出相位。基于获得的光滑输出相位,可以设计用于光整形任务的自由曲面。通过数值算例对不同映射假设下的方法进行了比较。
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Integrable solution for light shaping based on a Fourier-pair mapping

In far-field light shaping, one of the design methods is based on a one-to-one map between the irradiance of the source and target. However, an integrability issue may occur in this kind of algorithms, either in the ray mapping method for designing a freeform surface or in those geometric-optics-based methods for achieving a required output phase. We introduce another mapping-type algorithm to tackle the integrability problem, which instead of establishing a mapping between both the source and target irradiance in the space domain, the mapping is assumed on electric fields of a Fourier pair between the space domain and the spatial-frequency domain. By solving the mapping from the Fourier pair, the gradient of the output phase is achieved, that the gradient is equivalent to the obtained mapping function. Moreover, the existence and the characterization of the mapping guarantees the integrability of the gradient so that a smooth output phase can be directly integrated. Based on the obtained smooth output phase, a freeform surface can then be designed for the light-shaping task. Numerical examples are demonstrated for the comparison of the approaches with different mapping assumptions.

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来源期刊
CiteScore
2.40
自引率
0.00%
发文量
12
审稿时长
5 weeks
期刊介绍: Rapid progress in optics and photonics has broadened its application enormously into many branches, including information and communication technology, security, sensing, bio- and medical sciences, healthcare and chemistry. Recent achievements in other sciences have allowed continual discovery of new natural mysteries and formulation of challenging goals for optics that require further development of modern concepts and running fundamental research. The Journal of the European Optical Society – Rapid Publications (JEOS:RP) aims to tackle all of the aforementioned points in the form of prompt, scientific, high-quality communications that report on the latest findings. It presents emerging technologies and outlining strategic goals in optics and photonics. The journal covers both fundamental and applied topics, including but not limited to: Classical and quantum optics Light/matter interaction Optical communication Micro- and nanooptics Nonlinear optical phenomena Optical materials Optical metrology Optical spectroscopy Colour research Nano and metamaterials Modern photonics technology Optical engineering, design and instrumentation Optical applications in bio-physics and medicine Interdisciplinary fields using photonics, such as in energy, climate change and cultural heritage The journal aims to provide readers with recent and important achievements in optics/photonics and, as its name suggests, it strives for the shortest possible publication time.
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