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

傅里叶成像是一种自由空间的数字成像方式。它基于相干电磁辐射对场景的照明，以及通过光学系统(透镜)在背面焦平面上传输的辐射的记录。其中，场分布表示场景的空间傅里叶频谱，该频谱由传播项修正，传播项包含有关对象距离的信息。傅立叶成像特别适用于太赫兹(THz)频率，在这种情况下，衍射限制迫使人们只能使用有限数量的探测器像素。傅里叶成像覆盖了大视场。再加上焦平面中的场分布紧凑的事实，即使只有很少的像素数可用，这也有利于获得关于整个场景的信息。此外，空间分辨率可以通过测量高傅里叶分量在焦平面上的距离来选择。最重要的是，如果记录了二维焦平面中场分布的幅度和相位，傅里叶成像就可以计算三维图像。我们最近用我们团队开发的、以外差模式工作的基于晶体管的TeraFET探测器展示了这种能力，频率为0.3 THz。为了提高空间分辨率，我们现在将这一研究扩展到0.6 THz，使用亚谐外差检测。将确定可实现的深度分辨率。由于我们之前的工作已经发现了驻波效应造成的相位失真问题，因此将开发抑制它们的装置。其中包括用于缩短辐射相干长度的漫射器，以及基于超材料偏振转换器和偏振滤波的太赫兹光隔离器。直接测量场景的傅里叶频谱的一个有趣的方面是，人们可以利用在图像处理和存储领域所取得的巨大进步，其中傅立叶变换往往是处理概念的核心。傅里叶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，其中只需要有限数量的傅立叶分量来获得良好的图像保真度。我们将探索利用选定的焦平面检测点对简单的三维场景(不同距离的物体)进行压缩传感的潜力。傅里叶成像的另一个优点是它与全息成像技术密切相关。为此，模式识别的深度学习方法在稳健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。这些进展似乎相当直截了当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，我们将探索使这种深度学习方法适用于太赫兹傅立叶成像的方法。

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.