Within the last several years, the field of terahertz science and technology has changed dramatically. Many new advances in the technology for generation, manipulation, and detection of terahertz radiation have revolutionized the field. Much of this interest has been inspired by the promise of valuable new applications for terahertz imaging and sensing. Among a long list of proposed uses, one finds compelling needs such as security screening and quality control, as well as whimsical notions such as counting the almonds in a bar of chocolate. This list has grown in parallel with the development of new technologies and new paradigms for imaging and sensing. Many of these proposed applications exploit the unique capabilities of terahertz radiation to penetrate common packaging materials and provide spectroscopic information about the materials within. Several of the techniques used for terahertz imaging have been borrowed from other, more well established fields such as x-ray computed tomography and synthetic aperture radar. Others have been developed exclusively for the terahertz field, and have no analogies in other portions of the spectrum. This review provides a comprehensive description of the various techniques which have been employed for terahertz image formation, as well as discussing numerous examples which illustrate the many exciting potential uses for these emerging technologies.

We describe a terahertz imaging system that uses a single pixel detector in combination with a series of random masks to enable high-speed image acquisition. The image formation is based on the theory of compressed sensing, which permits the reconstruction of a N-by-N pixel image using much fewer than N 2 measurements. This approach eliminates the need for raster scanning of the object or the terahertz beam, while maintaining the high sensitivity of a single-element detector. We demonstrate the concept using a pulsed terahertz time-domain system and show the reconstruction of both amplitude and phase-contrast images. The idea of compressed sensing is quite general and could also be implemented with a continuous-wave terahertz source.

We design and implement a multipixel spatial modulator for terahertz beams using active terahertz metamaterials. Our first-generation device consists of a 4×4 pixel array, where each pixel is an array of subwavelength-sized split-ring resonator elements fabricated on a semiconductor substrate, and is independently controlled by applying an external voltage. Through terahertz transmission experiments, we show that the spatial modulator has a uniform modulation depth of around 40% across all pixels, and negligible crosstalk, at the resonant frequency. This device can operate under small voltage levels, at room temperature, with low power consumption and reasonably high switching speed.

We describe a novel, high-speed pulsed terahertz (THz) Fourier imaging system based on compressed sensing (CS), a new signal processing theory, which allows image reconstruction with fewer samples than traditionally required. Using CS, we successfully reconstruct a 64 x 64 image of an object with pixel size 1.4 mm using a randomly chosen subset of the 4096 pixels, which defines the image in the Fourier plane, and observe improved reconstruction quality when we apply phase correction. For our chosen image, only about 12% of the pixels are required for reassembling the image. In combination with phase retrieval, our system has the capability to reconstruct images with only a small subset of Fourier amplitude measurements and thus has potential application in THz imaging with cw sources.

We describe a new terahertz imaging method for high-speed image acquisition using a compressed sensing phase retrieval algorithm. This technique permits image reconstruction using a limited and randomly chosen subset of a Fourier image.With applications to homeland security, medical imaging, and quality control of packaged goods, commercial time-domain THz imaging systems can achieve a spatial resolution of less than 1 mm. However, these systems are generally limited by slow image acquisition rate [1,2]. Meanwhile, developments of THz imaging techniques using more sophisticated image processing approaches, such as the Radon transform [3,4] and interferometric imaging [5], have shown preliminary successes but face similar limitations in speed, resolution and/or hardware requirements. Here we describe a new approach which addresses these problems by partial sampling of the amplitude image in the Fourier plane and reconstruction of the target based on its spatial structure. This work is motivated by the possibility of reconstructing an image using many fewer measurements than are traditionally required.Integral to our approach is a new signal processing scheme that combines the recent theory of compressed sensing (CS) [6-8] with traditional phase retrieval (PR) algorithms [9]. Traditional PR algorithms recover the Fourier phase from modulus-only measurements of an image's entire Fourier transform. CS theory enables image recovery from a small, random subset of Fourier measurements (magnitude and phase). In general, an infinite number of signals can be found that match these few measurements; CS uses an optimization procedure to find the "best" solution. This notion of "best" is based on assumptions of the objects' spatial structure, e.g., the sparsest solution in terms of some basis. We combine CS and PR to reconstruct the object with a small subset of the Fourier transform modulus. Our Compressed Sensing Phase Retrieval algorithm (CSPR) iterates in a way similar to the classic Hybrid Input-Output (HIO) algorithm [6] in order to find the phase of the limited measurements, but in each step also performs a CS optimization. The CS-scheme we use is orthogonal matching pursuit (OMP) [10].Our imaging system consists of a THz transmitter, a receiver, and two lenses, one of which collimates the THz beam while the other focuses the beam (Fig.