In terahertz (THz) materials science, imaging by scanning prevails when low power THz sources are used. However, the application of array detectors operating with high power THz sources is increasingly reported. We compare the imaging properties of four different array detectors that are able to record THz radiation directly. Two micro-bolometer arrays are designed for infrared imaging in the 8–14 μm wavelength range, but are based on different absorber materials (i) vanadium oxide; (ii) amorphous silicon; (iii) a micro-bolometer array optimized for recording THz radiation based on silicon nitride; and (iv) a pyroelectric array detector for THz beam profile measurements. THz wavelengths of 96.5 μm, 118.8 μm, and 393.6 μm from a powerful far infrared laser were used to assess the technical performance in terms of signal to noise ratio, detector response and detectivity. The usefulness of the detectors for beam profiling and digital holography is assessed. Finally, the potential and limitation for real-time digital holography are discussed.

We realized a phase retrieval technique using terahertz (THz) radiation as an alternative to THz digital holography, named THz ptychography. Ptychography has been used in x-ray imaging as a groundbreaking improvement of conventional coherent diffraction imaging. Here we show that ptychography can be performed at THz frequencies too. We reconstructed an amplitude and a phase object with both simulated and real data. Lateral resolution accounts to <2λ, while depth variations as low as λ/30 can be assessed.

Imaging through scattering materials is of utmost importance, especially for security and biomedical imaging. Unlike the rest of the electromagnetic spectrum, terahertz radiation is a non-ionizing probe and allows imaging deep through non-conducting materials with sub-millimeter resolution. Here, we propose a coherent imaging technique reconstructing two objects, hidden one behind the other, from relative shifts between them. Experimental reconstructions at λ 96.5 μm of amplitude and phase objects hidden behind a glass fabric sample are presented. The hidden objects are retrieved with a lateral resolution of ≈1.5λ and a depth resolution of ≈λ∕10. Besides envisioning its use in noninvasive imaging, we anticipate that, in selected applications, the suggested approach can replace a similar phase retrieval technique, namely ptychography.

We present a method for the separation of the signal scattered from an object hidden behind a THz-transparent sample in the framework of THz digital holography in reflection. It combines three images of different interference patterns to retrieve the amplitude and phase distribution of the object beam. Comparison of simulated with experimental images obtained from a metallic resolution target behind a Teflon plate demonstrates that the interference patterns can be described in the simple form of three-beam interference. Holographic reconstructions after the application of the method show a considerable improvement compared to standard reconstructions exclusively based on Fourier transform phase retrieval.

Three-dimensional X-ray orientation microscopy based on X-ray full-field imaging techniques such as diffraction contrast tomography is a challenging task when it comes to materials displaying non-negligible intragranular orientation spread and/or intricate grain microstructures as a result of plastic deformation and deformation twinning. As shown in this article, the optimization of the experimental conditions and a number of modifications of the data analysis routines enable detection and three-dimensional reconstruction of twin lamellae down to micrometre thickness, as well as more accurate three-dimensional reconstruction of grains displaying intragranular orientation spreads of up to a few degrees. The reconstruction of spatially resolved orientation maps becomes possible through the use of a recently introduced six-dimensional reconstruction framework, which has been further extended in order to enable simultaneous reconstruction of parent and twin orientations and to account for the finite impulse response of the X-ray imaging detector. The simultaneous reconstruction of disjoint orientation domains requires appropriate scaling of the scattering intensities based on structure and Lorentz factors and yields threedimensional reconstructions with comparable density values for all the grains. This in turn enables the use of a global intensity-guided assembly procedure and avoids problems related to the single-grain thresholding procedure used previously. Last but not least, carrying out a systematic search over the list of known twin variants (forward modelling) for each of the indexed parent grains, it is possible to identify additional twins which have been left undetected at the previous stage of grain indexing based on diffraction spot peak positions. The enhanced procedure has been tested on a 1% deformed specimen made from a Ti-4% Al alloy and the result has been cross-validated against a twodimensional electron backscatter diffraction orientation map acquired on one of the lateral sample surfaces.

Imaging with THz radiation has proved an important tool for both fundamental science and industrial use. Here we review a class of THz imaging implementations, named coherent lensless imaging, that reconstruct the coherent response of arbitrary samples with a minimized experimental setup based only on a coherent source and a camera. After discussing the appropriate sources and detectors to perform them, we detail the fundamental principles and implementations of THz digital holography and phase retrieval. These techniques owe a lot to imaging with different wavelengths, yet innovative concepts are also being developed in the THz range and are ready to be applied in other spectral ranges. This makes our review useful for both the THz and imaging communities, and we hope it will foster their interaction.

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hase retrieval consists in the recovery of a complex-valued signal from intensity-only measurements. As it pervades a broad variety of applications, many researchers have striven to develop phase-retrieval algorithms. Classical approaches involve techniques as varied as generic gradient descent routines or specialized spectral methods, to name a few. However, the phase-recovery problem remains a challenge to this day. Recently, however, advances in machine learning have revitalized the study of phase retrieval in two ways: 1) significant theoretical advances have emerged from the analogy between phase retrieval and single-layer neural networks, and 2) practical breakthroughs have been obtained thanks to deep learning regularization. In this tutorial, we review phase retrieval under a unifying framework that encompasses classical and machine learning methods. We focus on three key elements: applications, an overview of recent reconstruction algorithms, and the latest theoretical results.