Symmetry Axis Research Articles

Jet rotational metrics

Embedding symmetries in the architectures of deep neural networks can improve classification and network convergence in the context of jet substructure. These results hint at the existence of symmetries in jet energy depositions, such as rotational symmetry, arising from the physical features of the underlying processes. We introduce new jet observables, Jet Rotational Metrics (JRMs), which provide insights into the substructure of jets by comparing them to jets with perfect discrete rotational symmetry. We show that JRMs are formidable jet features, achieving good classification scores when used as inputs to deep neural networks. We also show that when used in combination with other jet observables, like N-subjettiness and EFPs, our features increase classification performance. The results suggest that JRMs may capture information not efficiently captured by the other observables, motivating the design of future jet observables for learning the underlying symmetries in the physical processes.

Sedimentation dynamics of triply twisted Möbius bands: Geometry versus topology

We explore the sedimentation dynamics of triply twisted Möbius bands, each characterized by threefold rotational symmetry but distinguished by its construction and intrinsic geometrical properties. Three types of bands are considered: one with vanishing Gaussian curvature, constructed by isometrically deforming flat rectangular strips through bending without stretching; and two with negative Gaussian curvature, one being constructed by isometrically deforming helicoids. Experiment on these three types of bands, with a focus on varying aspect ratios, reveals a singular phenomenon: while the spin directions of bands not derived from helicoids spin in directions consistent with their inherent chirality, bands derived from helicoids exhibit an aspect-ratio-dependent spin, pointing to the existence of a critical aspect ratio at which geometric factors dominate over chiral influences. Supported by numerical simulations and a detailed analysis of the resistance tensors, we propose the unique response of bands derived from helicoids originates from a complex interaction among geometry, topology, and hydrodynamics. Two explanations are offered for the chiral transition observed in bands derived from helicoid. First, this transition may parallel the dynamics of superhelices, for which competing chiralities influence rotational behavior. Second, the unique geometrical properties of bands derived from helicoids, coupled with deviations between the rotation axis and the local symmetry axis, may underlie the observed aspect-ratio-dependent chiral transition. Our study underscores the significant role of geometrical and topological nuances in determining the behavior of chiral objects suspended in fluids. In addition to offering transformative potential across diverse fields, it promises advancements in mixing, separation processes, and innovative passive swimmers. Published by the American Physical Society 2024

Broadband optically transparent microwave absorber made of interdigital metasurfaces in rotational symmetry with a single air spacer

Broadband optically transparent microwave absorber made of interdigital metasurfaces in rotational symmetry with a single air spacer

Asymmetric dumbbell dimers simultaneously supporting quasi-bound states in continuum and anapole modes for terahertz biosensing

Abstract Multi-resonant metasurfaces are of great significance in the applications of multi-band nanophotonics. Here, we propose a novel metasurface design scheme for simultaneously supporting quasi-bound states in continuum (QBIC) and other resonant modes, in which QBIC resonance is generated by mirror or rotational symmetry breaking in oligomers while other resonant modes can be simultaneously excited by rationally designing the shapes of meta-atoms within oligomers. As an example, the simultaneous excitation of QBIC and anapole modes are demonstrated in a dimer metasurface composed of asymmetric dumbbell-shaped apertures. Based on the far-field multipole decomposition and near-field electromagnetic field distributions, the origin mechanisms of QBIC and anapole mode are elucidated. The symmetry breaking of dumbbell-shaped dimer results in QBIC. Within a certain asymmetric variation range, the contributions of toroidal dipole moment and electric dipole moment with approximately equal magnitudes remain dominant, which allows the anapole mode to always present. The effectiveness of the proposed design scheme is further confirmed by the experimental results identical with the evolutions of numerical simulation. In terahertz biosensing experiments, the anapole mode exhibits a higher sensitivity of 271.3 GHz (nmol/μl)−1, whereas the QBIC can achieve a lower detection limit of 0.015 nmol/μl and expands the detection range by almost an order of magnitude. Our findings are beneficial to designing multi-resonant metasurfaces with different resonance modes and promote the corresponding applications in the fields of biosensing, lasers, filtering, and nonlinearity.

Directed assembly of small binary clusters of magnetizable ellipsoids.

We report the effect of shape anisotropy and material properties on the directed assembly of binary suspensions composed of magnetizable ellipsoids. In a Monte Carlo simulation, we implement the ellipsoid-dipole model to calculate the pairwise dipolar interaction energy as a function of position and orientation. The analysis explores dilute suspensions of paramagnetic and diamagnetic ellipsoids with different aspect ratios in a superparamagnetic medium. We analyze the local order of binary structures as a function of particle aspect ratio, medium permeability, and dipolar interaction strength. Our results show that local order and symmetry are tunable under the influence of a uniform magnetic field when one component of the structure is dilute with respect to the other. The simulation results match previously reported experiments on the directed assembly of binary suspension of spheres. Additionally, we report the conditions on particle aspect ratios and medium properties for various structures with rotational symmetries, as well as open and enclosed structures under the influence of a uniform magnetic field.

Provably Trainable Rotationally Equivariant Quantum Machine Learning

Exploiting the power of quantum computation to realize superior machine learning algorithms has been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes—large regions where cost function gradients vanish exponentially in the number of qubits employed, rendering large models effectively untrainable. A leading strategy for combating this effect is to build problem-specific models that take into account the symmetries of their data in order to focus on a smaller, relevant subset of Hilbert space. In this work, we introduce a family of rotationally equivariant QML models built upon the quantum Fourier transform, and leverage recent insights from the Lie-algebraic study of QML models to prove that (a subset of) our models do not exhibit barren plateaus. In addition to our analytical results we numerically test our rotationally equivariant models on a dataset of simulated scanning tunneling microscope images of phosphorus impurities in silicon, where rotational symmetry naturally arises, and find that they dramatically outperform their generic counterparts in practice. Published by the American Physical Society 2024

Crystal structures of seven gold(III) complexes of the form LAuX 3 (L = substituted pyridine, X = Cl or Br).

The structures of seven gold(III) halide derivatives of general formula LAuX 3 (L = methyl-pyridines or di-methyl-pyridines, X = Cl or Br) are presented: tri-chlorido-(2-methyl-pyridine)-gold(III), [AuCl3(C6H7N)], 1 (as two polymorphs 1a and 1b); tri-bromido-(2-methyl-pyridine)-gold(III), [AuBr3(C6H7N)], 2; tri-bromido-(3-methyl-pyridine)-gold(III), [AuBr3(C6H7N)], 3; tri-bromido-(2,4-di-meth-yl-pyridine)-gold(III), [AuBr3(C7H9N)], 4; tri-chlorido-(3,5-di-methylpyridine)-gold(III), [AuCl3(C7H9N)], 5; tri-bromido-(3,5-di-methyl-pyridine)-gold(III), [AuBr3(C7H9N)], 6, and tri-chlorido-(2,6-di-methyl-pyridine)-gold(III), [AuCl3(C7H9N)], 7. Additionally, the structure of 8, the 1:1 adduct of 2 and 6, [AuBr3(C6H7N)]·[AuBr3(C7H9N)], is included. All the structures crystallize solvent-free, and all have Z' = 1 except for 5 and 7, which display crystallographic twofold rotation symmetry, and 4, which has Z' = 2. 1a and 2 are isotypic. The coordination geometry at the gold(III) atoms is, as expected, square-planar. Four of the crystals (1a, 1b, 2 and 8) were non-merohedral twins, and these structures were refined using the 'HKLF 5' method. The largest inter-planar angles between the pyridine ring and the coordination plane are observed for those structures with a 2-methyl substituent of the pyridine ring. The Au-N bonds are consistently longer trans to Br (average 2.059 Å) than trans to Cl (average 2.036 Å). In the crystal packing, a frequent feature is the offset-stacked and approximately rectangular dimeric moiety (Au-X)2, with anti-parallel Au-X bonds linked by Au⋯X contacts at the vacant positions axial to the coordination plane. The dimers are connected by further secondary inter-actions (Au⋯X or X⋯X contacts, 'weak' C-H⋯X hydrogen bonds) to form chain, double chain ('ladder') or layer structures, and in several cases linked again in the third dimension. Only 1b and 7 contain no offset dimers; these structures instead involve C-H⋯Cl hydrogen bonds combined with Cl⋯Cl contacts (1b) or Cl⋯π contacts (7). The packing patterns of seven further complexes LAuX 3 involving simple pyridines (taken from the Cambridge Structural Database) are compared with those of 1-8.

Analytical Solution to the Steady Navier-Stokes Equation for a Supersonic Cone in the Area of Boundary Layer Behind the Shock Wave by Means Tunnel Mathematics

The means of tunnel mathematics (the theory of functions of a spatial complex variable) allow for an analytical solution to the problem of supersonic flow around a cone in the area of the boundary layer and beyond. The peculiar feature of the Navier-Stokes equations is that they allow for the determination of analytical velocity fields of fluids only for a small number of simple problems. Of course, the problem of the supersonic motion of fluid around a cone is not included in this number. Tunnel mathematics is a method for finding analytical vector velocity fields for steady flows of fluids with axial symmetry. The Navier-Stokes equations are then used to determine pressure and temperature distributions. The main theorem of tunnel mathematics allows for the determination of these distributions for planes z = const (similar to constructing slices of a brain in an MRI procedure). By collecting these “slices,” we can obtain full space distributions of pressure and temperature around a supersonic cone. At this stage of investigation, the conclusions obtained through tunnel mathematics make it possible to qualitatively assess the thickness of the boundary layer on the cone's surface, the shape of the shock wave, and whether the shock wave intersects the boundary layer. First of all, we focused on ensuring that the resulting solutions corresponded to the physical pattern of phenomena. No doubt, solutions obtained through tunnel mathematics must be confirmed experimentally.

Elastic full waveform inversion for tilted transverse isotropic media: A multi‐step strategy accounting for a symmetry axis tilt angle

Elastic full waveform inversion for tilted transverse isotropic media: A multi‐step strategy accounting for a symmetry axis tilt angle

Programmable generation of counterrotating bicircular light pulses in the multi-terahertz frequency range

The manipulation of solid states using intense infrared or terahertz light fields is a pivotal area in contemporary ultrafast photonics research. While conventional circular polarization has been well explored, the potential of counterrotating bicircular light remains widely underexplored, despite growing interest in theory. In the mid-infrared or multi-terahertz region, experimental challenges lie in difficulties in stabilizing the relative phase between two-color lights and the lack of available polarization elements. Here, we successfully generated phase-stable counterrotating bicircular light pulses in the 14–39 THz frequency range circumventing the above problems. Employing spectral broadening, polarization pulse shaping with a spatial light modulator, and intra-pulse difference frequency generation leveraging a distinctive angular-momentum selection rule within the nonlinear crystal, we achieved direct conversion from near-infrared pulses into the designed counterrotating bicircular multi-terahertz pulses. Use of the spatial light modulator enables programmable control over the shape, orientation, rotational symmetry, and helicity of the bicircular light field trajectory. This advancement provides a novel pathway for the programmable manipulation of light fields, and marks a significant step toward understanding and harnessing the impact of tailored light fields on matter, particularly in the context of topological semimetals.

The role of task on the human brain's responses to, and representation of, visual regularity defined by reflection and rotation

Identifying and segmenting objects in an image is generally achieved effortlessly and is facilitated by the presence of symmetry: a principle of perceptual organisation used to interpret sensory inputs from the retina into meaningful representations. However, while imaging studies show evidence of symmetry selective responses across extrastriate visual areas in the human brain, whether symmetry is processed automatically is still under debate. We used functional Magnetic Resonance Imaging (fMRI) to study the response to and representation of two types of symmetry: reflection and rotation. Dot pattern stimuli were presented to 15 human participants (10 female) under stimulus-relevant (symmetry) and stimulus-irrelevant (luminance) task conditions. Our results show that symmetry-selective responses emerge from area V3 and extend throughout extrastriate visual areas. This response is largely maintained when participants engage in the stimulus irrelevant task, suggesting an automaticity to processing visual symmetry. Our multi-voxel pattern analysis (MVPA) results extend these findings by suggesting that not only spatial organisation of responses to symmetrical patterns can be distinguished from that of non-symmetrical (random) patterns, but also that representation of reflection and rotation symmetry can be differentiated in extrastriate and object-selective visual areas. Moreover, task demands did not affect the neural representation of the symmetry information. Intriguingly, our MVPA results show an interesting dissociation: representation of luminance (stimulus irrelevant feature) is maintained in visual cortex only when task relevant, while information of the spatial configuration of the stimuli is available across task conditions. This speaks in favour of the automaticity for processing perceptual organisation: extrastriate visual areas compute and represent global, spatial properties irrespective of the task at hand.

Exploring Canine Picornavirus Diversity in the USA Using Wastewater Surveillance: From High-Throughput Genomic Sequencing to Immuno-Informatics and Capsid Structure Modeling

The SARS-CoV-2 pandemic resulted in a scale-up of viral genomic surveillance globally. However, the wet lab constraints (economic, infrastructural, and personnel) of translating novel virus variant sequence information to meaningful immunological and structural insights that are valuable for the development of broadly acting countermeasures (especially for emerging and re-emerging viruses) remain a challenge in many resource-limited settings. Here, we describe a workflow that couples wastewater surveillance, high-throughput sequencing, phylogenetics, immuno-informatics, and virus capsid structure modeling for the genotype-to-serotype characterization of uncultivated picornavirus sequences identified in wastewater. Specifically, we analyzed canine picornaviruses (CanPVs), which are uncultivated and yet-to-be-assigned members of the family Picornaviridae that cause systemic infections in canines. We analyzed 118 archived (stored at −20 °C) wastewater (WW) samples representing a population of ~700,000 persons in southwest USA between October 2019 to March 2020 and October 2020 to March 2021. Samples were pooled into 12 two-liter volumes by month, partitioned (into filter-trapped solids [FTSs] and filtrates) using 450 nm membrane filters, and subsequently concentrated to 2 mL (1000×) using 10,000 Da MW cutoff centrifugal filters. The 24 concentrates were subjected to RNA extraction, CanPV complete capsid single-contig RT-PCR, Illumina sequencing, phylogenetics, immuno-informatics, and structure prediction. We detected CanPVs in 58.3% (14/24) of the samples generated 13,824,046 trimmed Illumina reads and 27 CanPV contigs. Phylogenetic and pairwise identity analyses showed eight CanPV genotypes (intragenotype divergence <14%) belonging to four clusters, with intracluster divergence of <20%. Similarity analysis, immuno-informatics, and virus protomer and capsid structure prediction suggested that the four clusters were likely distinct serological types, with predicted cluster-distinguishing B-cell epitopes clustered in the northern and southern rims of the canyon surrounding the 5-fold axis of symmetry. Our approach allows forgenotype-to-serotype characterization of uncultivated picornavirus sequences by coupling phylogenetics, immuno-informatics, and virus capsid structure prediction. This consequently bypasses a major wet lab-associated bottleneck, thereby allowing resource-limited settings to leapfrog from wastewater-sourced genomic data to valuable immunological insights necessary for the development of prophylaxis and other mitigation measures.

Searching for a new light gauge boson with axial couplings in muon beam dump experiments

We present a formalism for new U(1) interactions involving weak hypercharge, baryon, and lepton numbers, and a possible axial symmetry generator FA in the presence of a second Brout-Englert-Higgs doublet. The resulting U boson, after mixing with the Z, interpolates between a generalised dark photon, a dark Z, and an axially coupled gauge boson. We especially focus on the axial couplings originating from FA or from mixing with the Z, determined by the scalar sector via parameters like tan β and the v.e.v. of an extra dark singlet.We explore the distinctive features of axially coupled interactions, especially in the ultrarelativistic limit, where the U boson behaves much as an axion-like particle, with enhanced interactions to quarks and leptons. This enhancement is particularly relevant for future muon beam dump experiments, since the muon mass considerably increases the effective coupling, proportional to 2mμ/mU, compared to analogous experiments with electrons.We also analyse the shape of the expected beam dump exclusion or discovery regions, influenced by U boson interactions and the experiment geometry. Different situations are considered, limited in particular by cases for which the U decays before reaching the detector, or has too small couplings to produce detectable events. We also compare to vectorially coupled bosons and axion-like pseudoscalars, highlighting the importance of understanding the parameter space for future experiment design and optimisation.

The role of outflows in black-hole X-ray binaries

The hot inner flow in black-hole X-ray binaries is not just a static corona rotating around the black hole: it must be partially outflowing. It is therefore a mildly relativistic ``outflowing corona.'' We have developed a model in which Comptonization takes place in this outflowing corona. In all of our previous work, we assumed a rather high outflow speed of $0.8c$. Here, we investigate whether an outflow with a significantly lower speed can also reproduce the observations. Thus, in this work we consider an outflow speed of $0.1c$ or less. As in all of our previous work, we used a Monte Carlo code to compute not only the emergent X-ray spectra, but also the time lags that are introduced to the higher-energy photons with respect to the lower-energy ones via multiple scatterings. We also record the angle (with respect to the symmetry axis of the outflow) and the height at which photons escape. Our results are very similar to those of our previous work, with some small quantitative differences that can be easily explained. We are again able to quantitatively reproduce five observed correlations: (a) the time lag as a function of Fourier frequency, (b) the time lag as a function of photon energy, (c) the time lag as a function of Gamma , (d) the time lag as a function of the cutoff energy in the spectrum, and (e) the long-standing radio--X-ray correlation -- and all of them with only two parameters, which vary in the same ranges for all the correlations. Our model does not require a compact, narrow relativistic jet, although its presence does not affect the results. The essential ingredient of our model is the parabolic shape of the Comptonizing corona. The outflow speed plays a minor role. Furthermore, the bottom of the outflow, in the hard state, looks like a ``slab'' to the incoming soft photons from the disk, and this can explain the observed X-ray polarization, which is along the outflow. In the hard-intermediate state, we predict that the polarization of GX 339-4 will be perpendicular to the outflow.

Observation of In-Gap States in a Two-Dimensional CrI2/NbSe2 Heterostructure.

Low-dimensional magnetic structures coupled with superconductors are promising platforms for realizing Majorana zero modes, which have potential applications in topological quantum computing. Here, we report a two-dimensional (2D) magnetic-superconducting heterostructure consisting of single-layer chromium diiodide (CrI2) on a niobium diselenide (NbSe2) superconductor. Single-layer CrI2 nanosheets, which hold antiferromagnetic (AFM) ground states by our first-principles calculations, were epitaxially grown on the layered NbSe2 substrate. Using scanning tunneling microscopy/spectroscopy, we observed robust in-gap states spatially located at the edge of the nanosheets and defect-induced zero-energy peaks inside the CrI2 nanosheets. Magnetic-flux vortices induced by an external field exhibit broken 3-fold rotational symmetry of the pristine NbSe2 superconductor, implying the efficient modulation of the interfacial superconducting states by the epitaxial CrI2 layer. A phenomenological model suggests the existence of chiral edge states in a 2D AFM-superconducting hybrid system with an even Chern number, providing a qualitatively plausible understanding for our experimental observation.

To the problem of the shielding systems efficiency in constructions of extra-high voltage electrical apparatus

In the article, the authors proposed a method for estimating the electric load parameters to calculate the distribution of the electric field strength of the solid insulating structure of gas-filled high-voltage devices with axial symmetry. This structure consists of a support and insulating busbar filled with SF6 gas as an internal insulating medium. This technique allows to evaluate the parameters of the electrical load (voltage and field strength) depen-ding on the design features of the device and the shielding system used to equalize the electric field. The proposed methodology allows to evaluate the effectiveness of the influence of design parameters of the protection system for gas-filled high-voltage equipment (instrument transformers, arresters, surge arresters, etc.) when designing and improving individual design solutions. The calculation results are in good agreement with the data of experimental studies and statistical information obtained as a result of monitoring the operation of insulating structures, taking into account actual operating conditions and the influence of external factors. The implementation of this technique allows us to take into account the influence of external factors and operational characteristics inherent in instrument transformers and surge suppressors. In the proposed methodology, as an example, we consider a supporting insulating coating that is in operation under the most unfavorable conditions, such as external pollution, moisture and their combination, overvoltage of various origins, etc. The theoretical conclusions are confirmed by the results of calculations using the example of the support-insulating cover of the surge suppressor of the OПН-500 series. A more accurate determination of the effectiveness of the proposed methodology for predicting the field strength distribution parameters under the influence of a shielding system can be achieved by conducting an additional series of calculations and experimental tests of specific insulating structures. Thus, it was concluded that the obtained results can be used to evaluate the external insulation characteristics of both surge suppressors and gas-filled instrument transformers, as well as similar high-voltage equipment of switchgears and transformer substations in conditions of ultra- and transformer substations ultra-high voltages

Combinatorial Optimization Systems Theory Prospected from Rotational Symmetry

Combinatorial optimization systems theory prospected from rotational symmetry involves techniques for improving the quality indices of engineering devices or systems with non-uniform structure (e.g., controllable cyber-physical objects) concerning transformation swiftness, position accuracy, and resolution, using designs based on extraordinary geometric properties and structural excellence of combinatorial conformations, namely the concept of Ideal Ring Bundles. Design techniques based on the underlying combinatorial theory provide configure one- and multidimensional systems with smaller amounts of elements than at present, while maintaining the other substantial operating characteristics of the systems.

Ge-Se-Te based penrose photonic quasi-crystal fiber for SCG covering 2–21 μm MIR regime

This work proposes a Penrose-based photonic quasi-crystal fiber (PQF) composed of Arsenic-free, non-toxic chalcogenide glass for Supercontinuum (SC) generation consisting of quasi-crystal lattice of air holes having eight-fold rotational symmetry. Following optimizing the structural parameters, the proposed PQF offers zero dispersion wavelength (ZDW) at around 3.8 μm, an effective mode area of 30 μm2, and a respective high nonlinearity of 824 W−1Km−1 at 2 μm wavelength. By injecting a secant hyperbolic optical pulse having a central wavelength of 4 μm with 20 kW peak power and pulse width of 50 fs, a broadband SC of 2–21 μm is generated, which mostly covers the transparency range of the proposed material as well as Mid-IR regime. To the best of our understanding, this particular type of PQF for broadband SC generation has been proposed for the first time, serving as the novelty factor. Apart from novelty, the wide-band SC assists the proposed PQF in becoming a better counterpart for applications like optical coherence tomography (OCT), frequency metrology, and other Mid-IR applications.

Evaluation of Point Group Symmetry in Lanthanide(III) Complexes: A New Implementation of a Continuous Symmetry Operation Measure with Autonomous Assignment of the Principal Axis.

The structure of molecular systems dictates the physical properties, and symmetry is the determining factor for all electronic properties. This makes group theory a powerful tool in quantum mechanics to compute molecular properties. For inorganic compounds, the coordination geometry has been estimated as idealized polyhedra with high symmetry, which, through ligand field theory, provides predictive capabilities. However, real samples rarely have ideal symmetry, and although continuous shape measures (CShM) can be used to evaluate deviation from an ideal reference structure σideal, this often fails for lanthanide(III) complexes with high coordination numbers, no obvious choice of principal axes, and no obvious reference structure. In lanthanide complexes, the unique electronic structures and associated properties are intricately tied to the symmetry around the lanthanide center. Therefore, robust methodologies to evaluate and estimate point group symmetry are instrumental for building structure-property relationships. Here, we have demonstrated an algorithmic approach that orients a molecular structure Q in the best possible way to the symmetry axis of any given point group G and computes a deviation from the ideal symmetry σsym(G,Q). This approach does not compute the deviation from an ideal reference system, but the intrinsic deviation in the structure induced by symmetry operations. If the structure contains the symmetry operation, there is no deviation and σsym(G,Q) = 0. The σsym deviation is generated from all of the symmetry operation ÔS in a point group G using the most correct orientation of the sample structure in each group G. The best orientation is found by an algorithm that minimizes the orientation of the structure with respect to G. To demonstrate the methodology, we have investigated the structure and symmetry of 8- and 9-coordinated lanthanide(III) aqua complexes and correlated the luminescence from 3 europium(III) crystals to their actual symmetry. To document the methodology, the approach has been tested on 26 molecules with different symmetries. It was concluded that the method is robust and fully autonomous.

Electronic analogue of Fourier optics with massless Dirac fermions scattered by quantum dot lattice

Abstract The field of electron optics exploits the analogy between the movement of electrons or charged quasiparticles, primarily in two-dimensional materials subjected to electric and magnetic (EM) fields and the propagation of electromagnetic waves in a dielectric medium with varied refractive index. We significantly extend this analogy by introducing an electronic analogue of Fourier optics dubbed as Fourier electron optics (FEO) with massless Dirac fermions (MDF), namely the charge carriers of single-layer graphene under ambient conditions, by considering their scattering from a two-dimensional quantum dot lattice (TDQDL) treated within Lippmann-Schwinger formalism. By considering the scattering of MDF from TDQDL with a defect region, as well as the moir'{e} pattern of twisted TDQDLs, we establish an electronic analogue of Babinet's principle in optics. Exploiting the similarity of the resulting differential scattering cross-section with the Fraunhofer diffraction pattern, we construct a dictionary for such FEO. Subsequently, we evaluate the resistivity of such scattered MDF using the Boltzmann approach as a function of the angle made between the direction of propagation of these charge-carriers and the symmetry axis of the dot-lattice, and Fourier analyze them to show that the spatial frequency associated with the angle-resolved resistivity gets filtered according to the structural changes in the dot lattice, indicating wider applicability of FEO of MDF.