Search Results (25)

The Talbot wavemeter has attracted widespread attention from researchers in recent years due to its advantages of miniaturization and low cost. However, the impact of varying incident conditions caused by factors such as alignment has remained a challenge for spectral retrieval. This paper first derives the influence of different incident conditions on the interference pattern based on Fresnel diffraction and verifies the derivation through simulations. We propose a method to address the impact of incident conditions on the interference pattern. By adding a grating with a different periodicity in front of the detector, Moiré fringes are generated in the periodicity dimension, increasing the fringe period and thus enlarging the tolerance for angular misalignment. Finally, we constructed a Talbot wavemeter based on a double-grating structure, achieving a spectral resolution of 9 nm at 360 nm. This method provides a reference for the future development of a high-precision, high-resolution Talbot wavemeter. Full article

X-ray phase-contrast imaging presents a significant advancement in the field of X-ray imaging, surpassing traditional X-ray absorption imaging in detecting hydrogen substances. It effectively addresses the limitations of the latter in providing contrast for imaging weakly absorbing objects, thereby opening up vast potential applications in biomedical research, materials science, and industrial inspection. This article initially explores the fundamental principles of X-ray phase-contrast imaging and several prevalent imaging techniques. Notably, imaging devices such as grating-based Talbot–Lau interferometers emerge as the most promising in phase-contrast imaging due to their exceptional compatibility and imaging quality. Furthermore, this article introduces key parameters for assessing the quality of grating phase-contrast imaging, specifically image noise and sensitivity, along with their calculation methods. These insights are valuable for optimizing grating-based phase-contrast imaging devices. Lastly, this article examines potential applications and advancements in the key components of X-ray phase-contrast imaging while addressing current challenges and future directions in its technological development. This article aims to provide insights and inspiration for scholars interested in this field. Full article

Enrico Van Lint (Pisa, 1808–1884) was a very prolific photographer, active in Pisa in the 19th century where he had a prominent photographic atelier. He was a meticulous experimenter, investigating the evolving photographic activity of his historical period. While his early works included calotypes using Fox Talbot’s methods, he rapidly adopted the collodion processes, becoming one of the most important Italian photographers that used this technique. At the present time, a vast number of examples of the works from Van Lint’s ateliers are preserved and archived in Pisa, under the supervision of the Italian Ministry of Culture in the Photographic Archive of the “Soprintendenza Archeologia, Belle Arti e Paesaggio per le provincie di Pisa e Livorno” (SABAP). This collection is composed of positive prints as well as glass plate negatives, from both Van Lint himself and his colleagues. To this day, Van Lint’s collection has not been studied using analytical techniques, and the identification of the photographic processes involved in the preparation of the positive prints has relied exclusively on thorough observation by historians and conservators. This provides a unique occasion for a first study of Van Lint’s collection, using multiple non-invasive and non-destructive techniques (multispectral imaging, XRF, and FTIR) that can identify the photographic process used to make the positives, as well as highlight significant differences or degradation phenomena. In this preliminary work, we investigated a selection of ten positive prints, attributed to both Van Lint himself and later reproductions from the original glass negatives. The selected samples include prints previously classified as albumen prints and gelatin prints, displaying slight differences in conservation status as well as in print finish. This analytical approach allowed for a proper characterization of these Van Lint’s prints, improving the historical and conservation knowledge to implement the best preventive preservation actions in the near future. Full article

Terahertz radiation patterns can be registered using various detectors; however, in most cases, the scanning resolution is limited. Thus, we propose an alternative method for the detailed scanning of terahertz light field distributions after passing simple and complex structures. Our method relies on using a dielectric waveguide to achieve better sampling resolution. The optical properties of many materials were analyzed using time-domain spectroscopy. A cyclic olefin copolymer (COC) was chosen as one of the most transparent. This study contains a characterization of the losses introduced by the waveguide and a discussion of the setup’s geometry. As a structure introducing the radiation pattern, a 2D quasi-periodic amplitude grating was chosen to observe the Talbot effect (self-imaging). Moreover, some interesting physical phenomena were observed and discussed due to the possibility of detailed scanning, with subwavelength resolution, registering the terahertz wavefront changes behind the structure. Full article

Displacement measurement is a crucial application, with laser-based methods offering high precision and being well established in commercial settings. However, these methods often come with the drawbacks of significant size and exorbitant costs. We introduce a novel displacement measurement method that utilizes the missing-order Talbot effect. This approach circumvents the need to measure contrast in the Talbot diffraction field, opting instead to leverage the displacement within the missing-order Talbot diffraction pattern. Our method only requires parallel light, an amplitude grating, and a detector to achieve displacement measurement. The measurement dynamic range can be adjusted by altering the grating period and the wavelength of the incident light. Through careful simulation and experimental validation, our method exhibits a correlation coefficient R surpassing $0.999$ across a 30 mm dynamic range and achieves a precision superior to 3 $\mathsf{\mu }$m. Full article

The precision of two-dimensional angular sensing is crucial for applications such as navigation, robotics, and optical alignment. Conventional methods often struggle to balance precision, dynamic range, and affordability. We introduce a novel method leveraging the Talbot effect, enhanced by 3D printing technology, to fabricate a grating prototype for high-precision angular measurements. The method detects amplitude grating displacement at the self-imaging position and employs a frequency filtering algorithm for improved accuracy. Rigorous validation through simulations and physical experiments demonstrates that our method achieves a detection resolution of 0.4 arcseconds and a dynamic range exceeding 1400 arcseconds. This research presents a cost-effective, high-precision angular detection solution with potential for broad application in precision mechanical assembly, optical alignment, and other relevant domains. Full article

This article develops a simple hybrid localized mesh-free method (LMM) for the numerical modeling of new mixed subdiffusion and wave-diffusion equation with multi-term time-fractional derivatives. Unlike conventional multi-term fractional wave-diffusion or subdiffusion equations, this equation features a unique time–space coupled derivative while simultaneously incorporating both wave-diffusion and subdiffusion terms. Our proposed method follows three basic steps: (i) The given equation is transformed into a time-independent form using the Laplace transform (LT); (ii) the LMM is then used to solve the transformed equation in the LT domain; (iii) finally, the time domain solution is obtained by inverting the LT. We use the improved Talbot method and the Stehfest method to invert the LT. The LMM is used to circumvent the shape parameter sensitivity and ill-conditioning of interpolation matrices that commonly arise in global mesh-free methods. Traditional time-stepping methods achieve accuracy only with very small time steps, significantly increasing the computational time. To overcome these shortcomings, the LT is used to provide a more powerful alternative by removing the need for fine temporal discretization. Additionally, the Ulam–Hyers stability of the considered model is analyzed. Four numerical examples are presented to illustrate the effectiveness and practical applicability of the method. Full article

To address the increasing demands for cost-effective, large-area, and precisely patterned alignment of liquid crystals, a fractional Talbot lithography alignment technique was proposed. A light intensity distribution with a double spatial frequency of a photomask could be achieved based on the fractional Talbot effect, which not only enhanced the resolution of lithography but also slashed system costs with remarkable efficiency. To verify the feasibility of the alignment method, we prepared a one-dimensional polymer grating as an alignment layer. A uniform alignment over a large area was achieved thanks to the perfect periodicity and groove depth of several hundred nanometers. The anchoring energy of the alignment layer was 1.82 × 10⁻⁴ J/m², measured using the twist balance method, which surpassed that of conventional rubbing alignment. Furthermore, to demonstrate its ability for non-uniform alignment, we prepared polymer concentric rings as an alignment layer, resulting in a liquid-crystal q-plate with q = 1 and ${\alpha }_0$ = π/2. This device, with a wide tuning range (phase retardation of ~6π @ 633 nm for 0 to 5 V), was used to generate special optical fields. The results demonstrate that this approach allows for the uniform large-area orientation of liquid-crystal molecules with superior anchoring energy and customizable patterned alignment, which has extensive application value in liquid-crystal displays, generating special optical fields and intricate liquid-crystal topological defects over a large area. Full article

In the framework of the theory of linear viscoelasticity, we derive an analytical expression of the relaxation modulus in the Andrade model $G_{\alpha }\left(t\right)$ for the case of rational parameter $\alpha =m/n\in (0,1)$ in terms of Mittag–Leffler functions from its Laplace transform ${\tilde{G}}_{\alpha }\left(s\right)$. It turns out that the expression obtained can be rewritten in terms of Rabotnov functions. Moreover, for the original parameter $\alpha =1/3$ in the Andrade model, we obtain an expression in terms of Miller-Ross functions. The asymptotic behaviours of $G_{\alpha }\left(t\right)$ for $t\to 0^{+}$ and $t\to +\infty$ are also derived applying the Tauberian theorem. The analytical results obtained have been numerically checked by solving the Volterra integral equation satisfied by $G_{\alpha }\left(t\right)$ by using a successive approximation approach, as well as computing the inverse Laplace transform of ${\tilde{G}}_{\alpha }\left(s\right)$ by using Talbot’s method. Full article

Surface runoff flows must be drained safely through culverts in ephemeral flow streams and bridges in perennial streams without any damage to the road or highway infrastructure stability. In practice, bridges cross drainage basin channels reliably, and they are more carefully planned, designed, constructed, and maintained against extreme water passages, but culverts are subject to even less frequent and intensive rainfall consequent surface runoff occurrences with higher risk potential. It is, therefore, necessary to design culverts more carefully in such a way that they drain down the upstream surface water without any critical problem to the road downstream of the road stream channels. Most of the hydrological, hydraulic, and sedimentological formulations are empirical expressions that are widely valid for locations where culverts are suitably developed based on simple bivalent logical rules between factors involved in upstream inlet locations of culverts. One of the first logic rule-based methods in the literature is Talbot’s procedural approach to culvert design. This approach is based not only on an explicit equation, but also on a set of linguistically proposed design rules that are expressed deterministically to effectively eliminate most of the ambiguities. This paper proposes a modified approach with additional logistic structural features based on a bivalent logic inference system, which is an improved version of the Talbot procedure and leads to better culvert transition surface flow prediction. The proposed method is applied to a local area in Tekirdağ City, Türkiye, where a serious train accident occurred due to a poorly maintained culvert. Full article

The selection of an affordable method to fabricate plasmonic metasurfaces needs to guarantee complex control over both tunability and reproducibility of their spectral and morphological properties, making plasmonic metasurfaces suitable for integration into different sensing devices. Displacement Talbot lithography could be a valid solution thanks to the limited fabrication steps required, also providing the highly desired industrial scalability. Fabricated plasmonic metasurfaces are represented by a gold nanohole array on a glass substrate based on a triangular pattern. Scanning electron microscopy measurements have been recorded, showing the consistency of the surface features with the optimized design parameters. Reflectance and transmittance measurements have also been carried out to test the reliability and standardization of the metasurface’s optical response. Furthermore, these plasmonic metasurfaces have also been successfully tested for probing refractive index variations in a microfluidic system, paving the way for their use in sensitive, real-time, label-free, and multiplexing detection of bio-molecular events. Full article

Alignment precision is a crucial factor that directly impacts overlay accuracy, which is one of three fundamental indicators of lithography. The alignment method based on the Moiré fringe has the advantages of a simple measurement optical path and high measurement accuracy. However, it requires strict control of the distance between the mask and wafer to ensure imaging quality. This limitation restricts its application scenarios. A depth–DOF (depth of focus) Moiré fringe alignment by broad–spectrum modulation is presented to enhance the range of the alignment signals. This method establishes a broad–spectrum Moiré fringe model based on the Talbot effect principle, and it effectively covers the width of dark field (WDF) between different wavelength imaging ranges, thereby extending the DOF range of the alignment process, and employs a hybrid of genetic algorithms and the particle-swarm optimization (GA–PSO) algorithm to combine various spectral components in a white spectrum. By calculating the optimal ratio of each wavelength and using white light incoherent illumination in combination with this ratio, it achieves the optimal DOF range of a broad–spectrum Moiré fringe imaging model. The simulation results demonstrate that the available DOF range of the alignment system has been expanded from 400 μm to 800 μm. Additionally, the alignment precision of the system was analyzed, under the same conditions, and the accuracy analysis of the noise resistance, translation amount, and tilt amount was conducted for the Moiré fringe and broad–spectrum Moiré fringe. Compared to a single wavelength, the alignment precision of the broad–spectrum Moiré fringe decreased by an average of 0.0495 nm, equivalent to a 1.5% reduction in the original alignment precision, when using a 4 μm mask and a 4.4 μm wafer. However, the alignment precision can still reach 3.795 nm, effectively enhancing the available depth of focus range and reducing the loss of alignment precision. Full article

We provide a simple analysis based on ray optics and Dirac notation for 1D (one-dimensional) and 2D (two-dimensional) non-diffracting modes in the cosine profile, which are often called Cosine beams. We explore various kinds of structured modes formed by the superposition of two 1D Cosine beams. We then went on to understand the properties of the Bessel beams in terms of Cosine beams. For the first time, we report on the generation of three-dimensional tunable needle structures based on the interference of 1D Cosine beams. These size-tunable optical needles can have multiple advantages in material processing. Also, we report, for the first time, on the Talbot effect in Cosine beams. Straightforward mathematical calculations are used to derive analytical expressions for Cosine beams. The present method of demonstrating Cosine beams may be utilized to understand other structured modes. The Dirac notation-based interference explanation used here can provide new researchers with an easy way to understand the wave nature of light in a fundamental aspect of interferometric experiments as well as in advanced-level experiments such as beam engineering technology, imaging, particle manipulation, light sheet microscopy, and light–matter interaction. We also provide an in-depth analysis of similarities among Cosine, Bessel, and Hermite–Gaussian beams. Full article

This work presents a highly accurate method for the numerical solution of the advection–diffusion equation of fractional order. In our proposed method, we apply the Laplace transform to handle the time-fractional derivative and utilize the Chebyshev spectral collocation method for spatial discretization. The primary motivation for using the Laplace transform is its ability to avoid the classical time-stepping scheme and overcome the adverse effects of time steps on numerical accuracy and stability. Our method comprises three primary steps: (i) reducing the time-dependent equation to a time-independent equation via the Laplace transform, (ii) employing the Chebyshev spectral collocation method to approximate the solution of the transformed equation, and (iii) numerically inverting the Laplace transform. We discuss the convergence and stability of the method and assess its accuracy and efficiency by solving various problems in two dimensions. Full article

Siliceous diatom frustules present a huge variety of shapes and nanometric pore patterns. A better understanding of the light modulation by these frustules is required to determine whether or not they might have photobiological roles besides their possible utilization as building blocks in photonic applications. In this study, we propose a novel approach for analyzing the near-field light modulation by small pennate diatom frustules, utilizing the frustule of Gomphonema parvulum as a model. Numerical analysis was carried out for the wave propagation across selected 2D cross-sections in a statistically representative 3D model for the valve based on the finite element frequency domain method. The influences of light wavelength (vacuum wavelengths from 300 to 800 nm) and refractive index changes, as well as structural parameters, on the light modulation were investigated and compared to theoretical predictions when possible. The results showed complex interference patterns resulting from the overlay of different optical phenomena, which can be explained by the presence of a few integrated optical components in the valve. Moreover, studies on the complete frustule in an aqueous medium allow the discussion of its possible photobiological relevance. Furthermore, our results may enable the simple screening of unstudied pennate frustules for photonic applications. Full article