Resolution and quality enhancement in terahertz in-line holography by sub-pixel sampling with double-distance reconstruction

Flyscan terahertz multi-plane lensless imaging with suppressed coherent noise

Coherent lensless imaging usually suffers from coherent noise and twin-image artifacts. In the terahertz (THz) range, where wavelengths are 2 to 4 orders of magnitude longer than those in the visible spectrum, the coherent noise manifests primarily as parasitic interference fringes and edge diffraction, rather than speckle noise. In this work, to suppress the Fabry-Pérot (F-P) interference fringes, we propose a novel method, which involves the averaging over multiple diffraction patterns that are acquired at equal intervals within a sample's half-wavelength axial shift. To address edge diffraction, as well as non-uniform illumination, a normalization operation is applied. As the twin-image disturbances when dealing with a single diffraction pattern, multi-plane configuration is employed. With all these strategies combined, we propose a flyscan THz multi-plane lensless imaging technique that enables subwavelength resolution, and high-quality, full-field, and rapid complex-valued THz imaging. Furthermore, we refine two algorithms for image reconstruction: one based on the regular multi-plane alternating projection and the other based on an optimization model with total variation regularization. We experimentally verify the proposed methods, achieving a lateral resolution of 88 µm (0.74λ) at 2.52 THz, and showcase its potential for biomedical applications by imaging a section of mouse brain tissue.

High-throughput terahertz imaging: progress and challenges

Many exciting terahertz imaging applications, such as non-destructive evaluation, biomedical diagnosis, and security screening, have been historically limited in practical usage due to the raster-scanning requirement of imaging systems, which impose very low imaging speeds. However, recent advancements in terahertz imaging systems have greatly increased the imaging throughput and brought the promising potential of terahertz radiation from research laboratories closer to real-world applications. Here, we review the development of terahertz imaging technologies from both hardware and computational imaging perspectives. We introduce and compare different types of hardware enabling frequency-domain and time-domain imaging using various thermal, photon, and field image sensor arrays. We discuss how different imaging hardware and computational imaging algorithms provide opportunities for capturing time-of-flight, spectroscopic, phase, and intensity image data at high throughputs. Furthermore, the new prospects and challenges for the development of future high-throughput terahertz imaging systems are briefly introduced.

Single-pixel three-dimensional imaging of the terahertz-wave by complex-field synthesis

We propose a novel three-dimensional (3D) imaging technique by terahertz (THz) waves. Specifically, we modulate the THz wave using diffusers to produce three different speckle-like illumination patterns. The object is raster scanned by the three illumination patterns to generate three raw images via the single-pixel detection method. Subsequently, we synthesize a complex field using the three raw images. Finally, the retrieved image is calculated using the phase correlation of the complex point spread function. The proposed imaging system is simple and highly cost-effective. Therefore, it is a promising technique that can be adopted for industrial inspection and security screening.

Terahertz referenceless wavefront sensing by means of computational shear-interferometry

In this contribution, we demonstrate the first referenceless measurement of a THz wavefront by means of shear-interferometry. The technique makes use of a transmissive Ronchi phase grating to generate the shear. We fabricated the grating by mechanical machining of high-density polyethylene. At the camera plane, the +1 and -1 diffraction orders are coherently superimposed, generating an interferogram. We can adjust the shear by selecting the period of the grating and the focal length of the imaging system. We can also alter the direction of the shear by rotating the grating. A gradient-based iterative algorithm is used to reconstruct the wavefront from a set of shear interferograms. The results presented in this study demonstrate the first step towards wavefield sensing in the terahertz band without using a reference wave.

Terahertz phase retrieval imaging in reflection

Terahertz phase retrieval is a promising technique able to assess the complex diffracted wave properties through an iterative processing algorithm. In this Letter, we demonstrate the implementation of this technique in reflection geometry with a continuous wave acquisition system working at 0.287 THz. To ensure a high signal-to-noise ratio in the measured dataset, we proposed a double parallel recording scheme with one detector and two lock-in amplifiers operating with the complimentary sensitivity setting. This provided a higher numerical aperture than conventional raster-scanning focal plane imaging. A specialized digital interferometric postprocessing procedure was applied to obtain a surface height map from the reconstructed phase distribution in the object's irradiated area.

Holography and Coherent Diffraction Imaging with Low-(30-250 eV) and High-(80-300 keV) Energy Electrons: History, Principles, and Recent Trends

In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

THz coherent lensless imaging

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.

Iterative phase retrieval for digital holography: tutorial

This paper provides a tutorial of iterative phase retrieval algorithms based on the Gerchberg-Saxton (GS) algorithm applied in digital holography. In addition, a novel GS-based algorithm that allows reconstruction of 3D samples is demonstrated. The GS-based algorithms recover a complex-valued wavefront using wavefront back-and-forth propagation between two planes with constraints superimposed in these two planes. Iterative phase retrieval allows quantitatively correct and twin-image-free reconstructions of object amplitude and phase distributions from its in-line hologram. The present work derives the quantitative criteria on how many holograms are required to reconstruct a complex-valued object distribution, be it a 2D or 3D sample. It is shown that for a sample that can be approximated as a 2D sample, a single-shot in-line hologram is sufficient to reconstruct the absorption and phase distributions of the sample. Previously, the GS-based algorithms have been successfully employed to reconstruct samples that are limited to a 2D plane. However, realistic physical objects always have some finite thickness and therefore are 3D rather than 2D objects. This study demonstrates that 3D samples, including 3D phase objects, can be reconstructed from two or more holograms. It is shown that in principle, two holograms are sufficient to recover the entire wavefront diffracted by a 3D sample distribution. In this method, the reconstruction is performed by applying iterative phase retrieval between the planes where intensity was measured. The recovered complex-valued wavefront is then propagated back to the sample planes, thus reconstructing the 3D distribution of the sample. This method can be applied for 3D samples such as 3D distribution of particles, thick biological samples, and other 3D phase objects. Examples of reconstructions of 3D objects, including phase objects, are provided. Resolution enhancement obtained by iterative extrapolation of holograms is also discussed.

Lensfree on-chip microscopy based on dual-plane phase retrieval

In lensfree on-chip microscopy, the iterative phase retrieval with defocused images easily enables a high-resolution and whole field reconstruction. However, on the reconstruction of the dense sample, conventional methods suffer from the stagnation problem and noise affection under two intensity measurements, which gives rise to a remarkable loss of the image contrast and resolution. Here we propose a novel dual-plane phase retrieval algorithm to perform a stable and versatile lensless reconstruction. A weighted feedback constraint was utilized to speed up the convergence. Then, a gradient descent minimization based on total variation metric was proposed to suppress the noise affection. With these two object constraints, a smoothed but resolution-preserving result can be achieved. Numerical simulations of Gaussian and Poisson noise were given to prove the noise-robustness of our method. The experiments of USAF resolution target, H&E stained pathological slide, and label-free microglia cell demonstrated the superior performance of our approach compared to other state-of-the-art methods.

Iterative phase-retrieval-assisted off-axis terahertz digital holography

In terahertz digital holography, the off-axis configuration is the appropriate choice when the investigated object is non-sparse and complex. The limitation of recording distance in the off-axis configuration restricts the imaging quality. Either low-resolution or spectra overlap can potentially occur. We propose an iterative phase-retrieval approach to improve the quality of reconstruction results obtained from an off-axis hologram. One additional capture of object wave intensity is recorded to perform iterative phase retrieval with off-axis reconstruction as the initial guess. Apodization operation can be applied to the object wave intensity capture to suppress undesired border diffraction effects. The image quality using the proposed method has been improved both from simulation and experimental verification.

Broadband terahertz antireflective microstructures on quartz crystal surface by CO2 laser micro-processing

Anti-reflection (AR) coating is a critical technology and an ongoing challenge for terahertz systems. The subwavelength structure (SWS) is an effective AR method, whereas the current manufacturing techniques, such as chemical etching and ultrafast laser processing, are low-efficient and low-quality for processing structures at the hundred-micron scale on hard brittle materials. We present a study of broadband SWSs directly ablated on the surface of quartz crystal by precisely controlled CO₂ laser pulses, instead of commonly used ultra-fast lasers. The processing time of SWS can be shortened by two orders of magnitude compared with that by ultra-fast laser pulses. The SWS samples exhibit excellent AR properties with maximum transmittance of 97% at 0.71 THz, peak transmittance improvement of 13.5%, and optimal efficiency spectrum of 0.28-1.21 THz with transmittance >90%. The AR properties of SWS samples are in agreement with the simulated expectation and exist over a wide range of incidence angles up to ∼40°. The imaging of an object using SWS as the substrate shows an obvious improvement in imaging quality. We present an efficient and practical way to improve the transmission of optical components of materials, such as quartz crystal, alumina, and sapphire, in the terahertz band.

Sparsity-based continuous wave terahertz lens-free on-chip holography with sub-wavelength resolution

We demonstrate terahertz (THz) lens-free in-line holography on a chip in order to achieve 40 μm spatial resolution corresponding to ~0.7λ with a numerical aperture of ~0.87. We believe that this is the first time that sub-wavelength resolution in THz holography and the 40 μm resolution were both far better than what was already reported. The setup is based on a self-developed high-power continuous wave THz laser at 5.24 THz (λ = 57.25 μm) and a high-resolution microbolometer detector array (640 × 512 pixels) with a pitch of 17 μm. This on-chip in-line holography, however, suffers from the twin-image artifacts which obfuscate the reconstruction. To address this problem, we propose an iterative optimization framework, where the conventional object constraint and the L₁ sparsity constraint can be combined to efficiently reconstruct the complex amplitude distribution of the sample. Note that the proposed framework and the sparsity-based algorithm can be applied to holography in other wavebands without limitation of wavelength. We demonstrate the success of this sparsity-based on-chip holography by imaging biological samples (i.e., a dragonfly wing and a bauhinia leaf).