3D imaging at THz frequencies based on 2D fundamental and sub-harmonic heterodyne detection of the spatial Fourier spectrum

傅立叶成像是一种自由空间的数字成像方式。它基于通过相干电磁辐射照射场景并记录通过背面焦平面中的光学系统（"透镜"）传输的辐射。在那里，场分布表示由传播项修改的场景的空间傅立叶频谱，该传播项包含关于物体距离的信息。傅立叶成像本身特别适合太赫兹（THz）频率制度，其中衍射限制迫使人们使用有限数量的检测器像素。傅立叶成像覆盖大的视场。与焦平面中的场分布紧凑的事实一起，这有益于获得关于整个场景的信息，即使只有少量像素可用。此外，可以通过在焦平面中测量高傅立叶分量的距离来选择空间分辨率。最重要的是，傅立叶成像使得能够计算三维图像，如果记录二维焦平面中的场分布的振幅和相位。我们已经证明了这种能力，最近在0.3太赫兹与基于晶体管的TeraFET探测器，在我们的小组开发和外差模式下运行。为了提高空间分辨率，我们现在将这项研究扩展到0.6太赫兹，使用次谐波外差检测。将确定可实现的深度分辨率。由于我们先前的工作已经确定了驻波效应的相位失真问题，将开发抑制它们的设备。这些包括用于减少辐射的相干长度的漫射器，以及基于超材料偏振转换器和偏振滤波的THz光学隔离器。 直接测量场景的傅立叶光谱的一个有趣的方面是，人们可以利用在成像处理和存储领域中取得的巨大进步，其中傅立叶变换通常位于处理概念的核心。傅立叶频谱的一个特性是它们通常是稀疏的。这导致了压缩检测方案，其中对于良好的图像保真度仅需要有限数量的傅立叶分量。我们将探索压缩感知的潜力与选定的焦平面检测点的简单三维场景（物体在不同的距离）。傅立叶成像的另一个优点是它与全息成像技术的密切关系。对于这些，模式识别的深度学习方法在鲁棒的相位恢复方面取得了令人印象深刻的进展，这使得景深和超分辨率得以增强。这些进展似乎可以相当简单地扩展到相干太赫兹傅里叶成像。在与深度学习专家团队的合作中，我们将探索如何使这种深度学习方法适用于太赫兹傅立叶成像。

Fourier imaging is a free-space, digital imaging modality. It is based on the illumination of a scene by coherent electromagnetic radiation and the recording of the radiation transmitted through an optical system (“lens”) in the backside focal plane. There, the field distribution represents the scene’s spatial Fourier spectrum modified by a propagation term, which contains the information about the object distances. Fourier imaging lends itself especially well for the terahertz (THz) frequency regime where the diffraction limitation forces one to work with a limited number of detector pixels. Fourier imaging covers a large field-of-view. Together with the fact that the field distribution in the focal plane is compact, this is beneficial to obtain information about a whole scene even if only a low number of pixels is available. Furthermore, the spatial resolution can be selected by how far out in the focal plane the high Fourier components are measured. Most importantly, Fourier imaging enables the computation of three-dimensional images, if amplitude and phase of the field distribution in the two-dimensional focal plane are recorded. We have demonstrated this capability recently at 0.3 THz with a transistor-based TeraFET detector, developed in our group and operated in heterodyne mode. In order to improve the spatial resolution, we now extend this research to 0.6 THz, using sub-harmonic heterodyne detection. The achievable depth resolution will be determined. As our prior work has identified phase distortion problems by standing-wave effects, devices for their suppression will be developed. These include both a diffuser for a reduction of the radiation's coherence length, and a THz optical isolator based on a metamaterial polarization converter and polarization filtering. An intriguing aspect of directly measuring the Fourier spectra of scenes, is, that one can take advantage of the vast progress achieved in the field of imaging processing and storage, where Fourier transformation often lies at the core of the processing concepts. A property of Fourier spectra is that they are often sparse. This has led to compressed detection schemes, where only a limited number of Fourier components is needed for a good image fidelity. We will explore the potential of compressed sensing with selected focal-plane detection points for simple three-dimensional scenes (objects at different distances). Another advantage of Fourier imaging is its close relationship with holographic imaging techniques. For these, deep learning approaches of pattern recognition have brought impressive progress with regard to a robust phase recovery, which has enabled an enhancement of the depth-of-field as well as super-resolution. These advances appear rather straightforward to extend to coherent THz Fourier imaging. In a collaboration with a team of experts on deep learning, we will explore ways to make such deep-learning approaches applicable to THz Fourier imaging.