Beam-Shape Effects and Noise Removal From THz Time-Domain Images in Reflection Geometry in the 0.25–6 THz Range

Abstract

The increasing need of restoring high-resolution hyper-spectral (HS) images is determining a growing reliance on computer vision-based processing to enhance the clarity of the image content. HS images can, in fact, suffer from degradation effects or artefacts caused by instrument limitations. This article focuses on a procedure aimed at reducing the degradation effects, frequency-dependent blur and noise, in Terahertz time-domain spectroscopy (THz-TDS) images in reflection geometry. It describes the application of a joint deblurring and denoising approach that had been previously proved to be effective for the restoration of THz-TDS images in transmission geometry, but that had never been tested in reflection modality. This mode is often the only one that can be effectively used in most cases, for example, when analyzing objects that are either opaque in the THz range, or that cannot be displaced from their location (e.g., museums), such as those of cultural interest. Compared to transmission mode, reflection geometry introduces, however, further distortion to THz data, usually neglected in existing literature. In this work, we successfully implement image deblurring and denoising of both uniform-shape samples (a contemporary 1 Euro cent coin and an inlaid pendant) and samples with the uneven reliefs and corrosion products on the surface, which make the analysis of the object particularly complex (an ancient Roman silver coin). The study demonstrates the ability of image processing to restore data in the 0.25-6 THz range, spanning over more than four octaves, and providing the foundation for future analytical approaches of cultural heritage using the far-infrared spectrum still not sufficiently investigated in the literature.

Integrated Imaging and Spectroscopic Analysis of Painted Fresco Surfaces Using Terahertz Time-Domain Technique

“…Because of the surface curvature, the phase φ(ω) is modified by an additive contribution that linearly increases with axial misalignment and depends on frequency, whereas amplitude variation is much more complex in regard to its non-linear frequency dependence and to intensity beam variation along the axial direction. In the Supplementary Materials (SM) of this work, the experimental evaluation of the consequences of spatial misalignment by measuring the reflected signal from a highly reflective surface, i.e., the metallic mirror, is included to show that such an intensity variation can be neglected if the misalignments are relatively small [4].…”

“…In heritage material studies, this radiation is particularly appreciated for providing a safe and non-invasive method for analyzing objects without posing long-term risks to their chemical stability. In fact, it is non-ionizing and can penetrate many materials that are opaque in the visible and near-infrared frequencies [2][3][4]. When employed with imaging or tomography devices, THz time domain (THz-TD) can enable the investigation of the internal structure of objects and provide information related to their conservation conditions in a completely non-invasive manner [1,5,6].…”

“…Inherently, the presence of tilting or curvature on the sample surface makes it difficult to extract accurate values of the complex refractive index [13]. Finally, various additional secondary effects can complicate the analysis of the THz data, such as Fabry-Perot, multiple-scattering, and water vapor in the atmosphere, which pose significant challenges in data pre-processing, particularly when examining heritage artefacts with multiple material layers and uneven surfaces [4,14].…”

“…The authors proposed an approach specifically tailored for broad-band THz-TDI, starting from image restoration methods commonly applied to remote hyperspectral imaging at visible and near-infrared frequencies. The methodology was extended to the acquisition in reflection geometry for opaque objects and demonstrated to effectively cancel the effects of beam shape and reduce noise between 0.25 and 6 THz [4,12]. The second problematic condition when dealing with heritage object, i.e., studying uneven surfaces, was tackled by A. Artesani and co-authors in 2023 [13].…”

Self-Referenced Method for Geometrical Distortion Removal in THz Time-Domain Reflection Imaging

“…Assuming n 0 equal to the unit and the angle of the impinging beam is θ = 0.14 rad, the axial resolution for the object reliefs can be theoretically evaluated to be around ∆h = 20 µm. The lateral resolution is limited by the point spread function (PSF) of the THz beam [34], the dimension of which changes as a function of the frequency ω, and by the acquisition step size along the x and y axis. Assuming a Gaussian beam approximation [35] [34], the beam waist (2w 0 = 5.094λ) varies between 130 µm and 760 µm, whilst the Rayleigh length (z R = πw 2 0 /λ) varies between 1 mm and 6 mm.…”