[论文解读] Better than a lens - A novel concept to break the SNR-limit, given by Fermat's principle

J. Becker, Ronny Förster+1 more|arXiv (Cornell University)|Nov 20, 2018

Advanced Fluorescence Microscopy Techniques参考文献 14被引用 5

一句话总结

本文提出了一种新颖的单次成像技术，打破了傅里叶空间中由费马原理和光子噪声分布所施加的根本信噪比（SNR）限制。通过将孔径分割为两个子孔径，捕获噪声方差降低的子图像，并在傅里叶空间中通过加权平均重新组合，该方法提升了傅里叶-SNR，并实现了超越传统极限的有效分辨率，实验上已通过使用正交闪耀光栅的纯相位空间光调制器（SLM）验证。

ABSTRACT

The signal in an incoherent imaging system gets transferred worse towards higher spatial frequencies. Since the photon noise is distributed equally in Fourier space, the signal-to-noise ratio (SNR) decreases, and therefore represents a fundamental limit in the field of imaging. Our work aims to go beyond this given SNR-limit, which is directly connected to circumvent Fermats principle (1662). The proposed technique only makes use of a single acquisition process. To our knowledge this hasnt been done before and might have far-reaching impact on a large number of applications ranging from bio-imaging to industrial inspection. Especially in the case of limited photon numbers, e.g. fluorescent emission or a minimum available detector exposure time (temporal resolution), our method represents a new way to improve on SNR, which has been missing so far. We propose a novel and fundamentally new concept, by splitting the pupil of an imaging system into two parts to simultaneously obtain sub-images via each of these sub-pupils. Since the noise variance is proportional to the number of detected photons, it has been reduced in each of the sub-images. Recombining them by weighted averaging in Fourier-space yields an enhancement in (Fourier-) SNR compared to conventional imaging, enabling us to break the aforementioned SNR-limit. This results in an increased effective resolution limit in real space, which is used as an indicator throughout this work. We show a proof-of-concept experiment, in which we split the pupil by displaying orthogonally oriented blazed phase gratings for the different sub-pupils on a phase-only spatial light modulator. Our experiment confirms the improvement in effective resolution and therefore shows that we have overcome the fundamental SNR-limit, by only manipulating the captured light distribution in the pupil plane.

研究动机与目标

• 克服相干成像系统中由傅里叶空间内光子噪声分布均等所导致的根本信噪比限制。
• 解决荧光显微镜和低光照工业检测等应用中光子数有限的挑战。
• 开发一种单次采集方法，在不违反费马原理的前提下提升有效分辨率。
• 展示一种根本上新颖的信噪比提升方法，无需依赖多次曝光或复杂计算重建。

提出的方法

• 利用纯相位空间光调制器（SLM）将成像系统的孔径分割为两个子孔径。
• 在SLM上显示正交闪耀相位光栅，将光束导向两个不同的子孔径区域。
• 同时捕获两幅子图像，每幅图像因子孔径内光子数减少而具有更低的噪声方差。
• 将子图像转换至傅里叶空间，并通过加权平均进行重新组合，以提升傅里叶-SNR。
• 重组合过程利用了独立、低噪声测量组合的统计优势，从而提高整体信号保真度。
• 该方法通过调控孔径平面的能量分布而非改变与射线光学相矛盾的光程长度，避免违反费马原理。

实验结果

研究问题

• RQ1 能否通过单次采集和孔径平面调控克服相干成像中的根本信噪比限制？
• RQ2 将孔径分割为子孔径并在傅里叶空间中重新组合子图像，是否能带来有效分辨率的可测量提升？
• RQ3 与传统成像相比，子图像中噪声方差的降低能在多大程度上提升傅里叶-SNR？
• RQ4 是否可能在不增加光子曝光量或使用多次采集的情况下实现信噪比提升？
• RQ5 能否通过使用正交闪耀光栅的纯相位SLM实现该方法的实验验证？

主要发现

• 实验装置成功通过纯相位SLM调控孔径平面，实现了有效分辨率的提升。
• 采用两个子孔径降低了每幅子图像的噪声方差，使得重新组合后傅里叶-SNR得以提高。
• 在傅里叶空间中对子图像进行加权平均，显著提升了信号保真度，超越了传统成像的极限。
• 该方法在不违反费马原理的前提下实现了信噪比提升，表明其从根本上突破了传统成像的约束。
• 概念验证实验证实，所提出的技术在单次采集中打破了传统信噪比限制，验证了理论框架的有效性。