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Tomographic imaging reveals internal structures of 3D objects and is crucial for medical diagnoses. Visualizing the morphology and appearance of non-planar sparse anatomical structures that extend over multiple 2D slices in tomographic volumes is inherently difficult but valuable for decision-making and reporting. Hence, various organ-specific unfolding techniques exist to map their densely sampled 3D surfaces to a distortion-minimized 2D representation. However, there is no versatile framework to flatten complex sparse structures including vascular, duct or bone systems. We deploy a neural field to fit the transformation of the anatomy of interest to a 2D overview image. We further propose distortion regularization strategies and combine geometric with intensity-based loss formulations to also display non-annotated and auxiliary targets. In addition to improved versatility, our unfolding technique outperforms mesh-based baselines for sparse structures w.r.t. peak distortion and our regularization scheme yields smoother transformations compared to Jacobian formulations from neural field-based image registration.

Electronically excited atoms or molecules may deexcite by emission of a secondary electron through an Auger-Meitner decay. This deexcitation process is typically considered to be exponential in time. This is strictly speaking, however, only true for the case of an atom. Here, we present a study experimentally demonstrating the non-exponential time dependence of the decay of an inner-shell hole in a diatomic molecule. In addition, we provide an intuitive explanation for the origin of the observed variation of the molecular lifetimes and their dependence on the kinetic energy of the ionic fragments measured in coincidence with the photoelectrons., Comment: 5 pages, 4 figures

The increasing interest in autonomous driving systems has highlighted the need for an in-depth analysis of human driving behavior in diverse scenarios. Analyzing human data is crucial for developing autonomous systems that replicate safe driving practices and ensure seamless integration into human-dominated environments. This paper presents a comparative evaluation of human compliance with traffic and safety rules across multiple trajectory prediction datasets, including Argoverse 2, nuPlan, Lyft, and DeepUrban. By defining and leveraging existing safety and behavior-related metrics, such as time to collision, adherence to speed limits, and interactions with other traffic participants, we aim to provide a comprehensive understanding of each datasets strengths and limitations. Our analysis focuses on the distribution of data samples, identifying noise, outliers, and undesirable behaviors exhibited by human drivers in both the training and validation sets. The results underscore the need for applying robust filtering techniques to certain datasets due to high levels of noise and the presence of such undesirable behaviors., Comment: 8 pages, CoRL 2024 Workshop SAFE-ROL

We derive and study a model of square planar, d8 spin crossover materials that treats elastic, magnetic and spin-orbit interactions on an equal footing. For 1D chains density matrix renormalization group calculations show that the competition between these interactions leads to six different phases. For weak spin-orbit coupling (SOC) and large antiferromagnetic interactions we find a symmetry protected topological (SPT) Haldane phase. This is equivalent to the Haldane-large-D phase transition driven by single ion anisotropy(D) in the spin-one Heisenberg model. For strong SOC the Sz=+-1 HS states are high-energy excitations. Thus, the system can be understood as a transverse field Ising model with the SOC playing the role of the transverse field. Consistent with this, we find a quantum phase transition between the THS phase and a quantum disordered (QD) phase. However, if the magnetic coupling is non-zero or the HS and LS states of a single molecule are non-degenerate the Z2 (Ising) symmetry is broken and the phase transition becomes a crossover. Thus, the QD phase and the THS phases are adiabatically connected, as, equivalently, are the large-D phase of the spin-one Heisenberg model and the quantum disordered phase of the transverse field Ising model. We also find a ferroelastic LS phase, and antierroelastic phase, with alternating HS and LS complexes, and a dimer phase, which results from the competition between antiferromagnetic and antiferroelastic interactions., Comment: 14 pages, 7 figures

We report on strong field ionization of S- and R-propylene oxide in circularly polarized two-color laser fields. We find that the relative helicity of the two single color laser fields affects the photoelectron circular dichroism (PECD). Further, we observe that PECD is modulated as a function of the sub-cycle release time of the electron. Our experimental observations are successfully described by a heuristic model based on electrons in chiral initial states, which are selectively liberated by the laser field and, after tunneling, interact with an achiral Coulomb potential.

This is an invited survey article on higher gauge theory for the Encyclopedia of Mathematical Physics, 2nd edition. In particular, we provide a lightning introduction to higher structures and to the construction of the kinematical data of higher gauge theories, i.e. connections on higher principal bundles. We also summarise the most important applications and dynamical principles that have appeared in the literature, and we close with comments on related areas., Comment: 36 pages text, 17 pages references

This study leverages graph neural networks to integrate MELC data with Radiomic-extracted features for melanoma classification, focusing on cell-wise analysis. It assesses the effectiveness of gene expression profiles and Radiomic features, revealing that Radiomic features, particularly when combined with UMAP for dimensionality reduction, significantly enhance classification performance. Notably, using Radiomics contributes to increased diagnostic accuracy and computational efficiency, as it allows for the extraction of critical data from fewer stains, thereby reducing operational costs. This methodology marks an advancement in computational dermatology for melanoma cell classification, setting the stage for future research and potential developments., Comment: Paper accepted at the German Conference on Medical Image Computing 2024

Differentiable rendering methods promise the ability to optimize various parameters of 3d scenes to achieve a desired result. However, lighting design has so far received little attention in this field. In this paper, we introduce a method that enables continuous optimization of the arrangement of luminaires in a 3d scene via differentiable light tracing. Our experiments show two major issues when attempting to apply existing methods from differentiable path tracing to this problem: first, many rendering methods produce images, which restricts the ability of a designer to define lighting objectives to image space. Second, most previous methods are designed for scene geometry or material optimization and have not been extensively tested for the case of optimizing light sources. Currently available differentiable ray-tracing methods do not provide satisfactory performance, even on fairly basic test cases in our experience. In this paper, we propose a novel adjoint light tracing method that overcomes these challenges and enables gradient-based lighting design optimization in a view-independent (camera-free) way. Thus, we allow the user to paint illumination targets directly onto the 3d scene or use existing baked illumination data (e.g., light maps). Using modern ray-tracing hardware, we achieve interactive performance. We find light tracing advantageous over path tracing in this setting, as it naturally handles irregular geometry, resulting in less noise and improved optimization convergence. We compare our adjoint gradients to state-of-the-art image-based differentiable rendering methods. We also demonstrate that our gradient data works with various common optimization algorithms, providing good convergence behaviour. Qualitative comparisons with real-world scenes underline the practical applicability of our method.

In this paper, we introduce and study a remarkable class of mechanisms formed by a $3 \times 3$ arrangement of rigid quadrilateral faces with revolute joints at the common edges. In contrast to the well-studied Kokotsakis meshes with a quadrangular base, we do not assume the planarity of the quadrilateral faces. Our mechanisms are a generalization of Izmestiev's orthodiagonal involutive type of Kokotsakis meshes formed by planar quadrilateral faces. The importance of this Izmestiev class is undisputed as it represents the first known flexible discrete surface -- T-nets -- which has been constructed by Graf and Sauer. Our algebraic approach yields a complete characterization of all flexible $3 \times 3$ quad meshes of the orthodiagonal involutive type up to some degenerated cases. It is shown that one has a maximum of 8 degrees of freedom to construct such mechanisms. This is illustrated by several examples, including cases which could not be realized using planar faces. We demonstrate the practical realization of the proposed mechanisms by building a physical prototype using stainless steel. In contrast to plastic prototype fabrication, we avoid large tolerances and inherent flexibility., Comment: 26 pages, 13 figures. arXiv admin note: text overlap with arXiv:1411.0289 by other authors

Histopathology imaging is crucial for the diagnosis and treatment of skin diseases. For this reason, computer-assisted approaches have gained popularity and shown promising results in tasks such as segmentation and classification of skin disorders. However, collecting essential data and sufficiently high-quality annotations is a challenge. This work describes a pipeline that uses suspected melanoma samples that have been characterized using Multi-Epitope-Ligand Cartography (MELC). This cellular-level tissue characterisation is then represented as a graph and used to train a graph neural network. This imaging technology, combined with the methodology proposed in this work, achieves a classification accuracy of 87%, outperforming existing approaches by 10%., Comment: This work has been submitted to the IEEE for possible publication

The property of a surface being developable can be expressed in different equivalent ways, by vanishing Gauss curvature, or by the existence of isometric mappings to planar domains. Computational contributions to this topic range from special parametrizations to discrete-isometric mappings. However, so far a local criterion expressing developability of general quad meshes has been lacking. In this paper, we propose a new and efficient discrete developability criterion that is applied to quad meshes equipped with vertex weights, and which is motivated by a well-known characterization in differential geometry, namely a rank-deficient second fundamental form. We assign contact elements to the faces of meshes and ruling vectors to the edges, which in combination yield a developability condition per face. Using standard optimization procedures, we are able to perform interactive design and developable lofting. The meshes we employ are combinatorial regular quad meshes with isolated singularities but are otherwise not required to follow any special curves on a developable surface. They are thus easily embedded into a design workflow involving standard operations like remeshing, trimming, and merging operations. An important feature is that we can directly derive a watertight, rational bi-quadratic spline surface from our meshes. Remarkably, it occurs as the limit of weighted Doo-Sabin subdivision, which acts in an interpolatory manner on contact elements.

A considerable amount of research is concerned with the generation of realistic sensor data. LiDAR point clouds are generated by complex simulations or learned generative models. The generated data is usually exploited to enable or improve downstream perception algorithms. Two major questions arise from these procedures: First, how to evaluate the realism of the generated data? Second, does more realistic data also lead to better perception performance? This paper addresses both questions and presents a novel metric to quantify the realism of LiDAR point clouds. Relevant features are learned from real-world and synthetic point clouds by training on a proxy classification task. In a series of experiments, we demonstrate the application of our metric to determine the realism of generated LiDAR data and compare the realism estimation of our metric to the performance of a segmentation model. We confirm that our metric provides an indication for the downstream segmentation performance., Comment: arXiv admin note: text overlap with arXiv:2109.11775

Ischemic strokes are often caused by large vessel occlusions (LVOs), which can be visualized and diagnosed with Computed Tomography Angiography scans. As time is brain, a fast, accurate and automated diagnosis of these scans is desirable. Human readers compare the left and right hemispheres in their assessment of strokes. A large training data set is required for a standard deep learning-based model to learn this strategy from data. As labeled medical data in this field is rare, other approaches need to be developed. To both include the prior knowledge of side comparison and increase the amount of training data, we propose an augmentation method that generates artificial training samples by recombining vessel tree segmentations of the hemispheres or hemisphere subregions from different patients. The subregions cover vessels commonly affected by LVOs, namely the internal carotid artery (ICA) and middle cerebral artery (MCA). In line with the augmentation scheme, we use a 3D-DenseNet fed with task-specific input, fostering a side-by-side comparison between the hemispheres. Furthermore, we propose an extension of that architecture to process the individual hemisphere subregions. All configurations predict the presence of an LVO, its side, and the affected subregion. We show the effect of recombination as an augmentation strategy in a 5-fold cross validated ablation study. We enhanced the AUC for patient-wise classification regarding the presence of an LVO of all investigated architectures. For one variant, the proposed method improved the AUC from 0.73 without augmentation to 0.89. The best configuration detects LVOs with an AUC of 0.91, LVOs in the ICA with an AUC of 0.96, and in the MCA with 0.91 while accurately predicting the affected side., Comment: PrePrint - Accepted at MICCAI 2022

During the diagnosis of ischemic strokes, the Circle of Willis and its surrounding vessels are the arteries of interest. Their visualization in case of an acute stroke is often enabled by Computed Tomography Angiography (CTA). Still, the identification and analysis of the cerebral arteries remain time consuming in such scans due to a large number of peripheral vessels which may disturb the visual impression. In previous work we proposed VirtualDSA++, an algorithm designed to segment and label the cerebrovascular tree on CTA scans. Especially with stroke patients, labeling is a delicate procedure, as in the worst case whole hemispheres may not be present due to impeded perfusion. Hence, we extended the labeling mechanism for the cerebral arteries to identify occluded vessels. In the work at hand, we place the algorithm in a clinical context by evaluating the labeling and occlusion detection on stroke patients, where we have achieved labeling sensitivities comparable to other works between 92\,\% and 95\,\%. To the best of our knowledge, ours is the first work to address labeling and occlusion detection at once, whereby a sensitivity of 67\,\% and a specificity of 81\,\% were obtained for the latter. VirtualDSA++ also automatically segments and models the intracranial system, which we further used in a deep learning driven follow up work. We present the generic concept of iterative systematic search for pathways on all nodes of said model, which enables new interactive features. Exemplary, we derive in detail, firstly, the interactive planning of vascular interventions like the mechanical thrombectomy and secondly, the interactive suppression of vessel structures that are not of interest in diagnosing strokes (like veins). We discuss both features as well as further possibilities emerging from the proposed concept.

Design decisions in urban planning have to be made with particular carefulness as the resulting constraints are binding for the whole architectural design that follows. In this context, investigating and optimizing the airflow in urban environments is critical to design comfortable outdoor areas as unwanted effects such as windy areas and the formation of heat pockets have to be avoided. Our UrbanFlow framework enables interactive architectural design allowing for decision making based on simulating urban flow. Compared to real-time fluid flow simulation, enabling interactive architecture design poses an even higher computational efficiency challenge as evaluating a design by simulation usually requires hundreds of time steps. This is addressed based on a highly efficient Eulerian fluid simulator in which we incorporate a unified porosity model which is devised to encode digital urban models containing objects such as buildings and trees. UrbanFlow is equipped with an optimization routine enabling the direct computation of design adaptations improving livability and comfort for given parameterized architectural designs. To ensure convergence of the optimization process, instead of the classical Navier-Stokes equations, the Reynolds-averaged Navier-Stokes equations are solved as this can be done on a relatively coarse grid and allows for the decoupling of the effects of turbulent eddies which are taken into account using a separate turbulence model. As we demonstrate on a real-world example taken from an ongoing architectural competition, this results in a fast convergence of the optimization process which computes a design adaptation avoiding heat pockets as well as uncomfortable windy areas., Comment: 17 pages, 9 figures

We define the notion of adjustment for strict Lie 2-groups and provide the complete cocycle description for non-Abelian gerbes with connections whose structure 2-group is an adjusted 2-group. Most importantly, we depart from the common fake-flat connections and employ adjusted connections. This is an important generalisation that is needed for physical applications especially in the context of supergravity. We give a number of explicit examples; in particular, we lift the spin structure on $S^4$, corresponding to an instanton-anti-instanton pair, to a string structure, a 2-group bundle with connection. We also outline how categorified forms of Bogomolny monopoles known as self-dual strings can be obtained via a Penrose-Ward transform of string bundles over twistor space., Comment: v3: 77 pages, presentation substantially changed, many results added

In this report we want to present our method and results for the Carotid Artery Vessel Wall Segmentation Challenge. We propose an image-based pipeline utilizing the U-Net architecture and location priors to solve the segmentation problem at hand., Comment: Challenge Report - Preprint

The nuclear-spin chemistry of interstellar water is investigated using the University of Grenoble Alpes Astrochemical Network (UGAN). This network includes reactions involving the different nuclear-spin states of the hydrides of carbon, nitrogen, oxygen and sulphur, as well as their deuterated forms. Nuclear-spin selection rules are implemented within the scrambling hypothesis for reactions involving up to seven protons. The abundances and ortho-to-para ratios (OPRs) of gas-phase water and water ions (H$_2$O$^+$ and H$_3$O$^+$) are computed under the steady-state conditions representative of a dark molecular cloud and during the early phase of gravitational collapse of a prestellar core. The model incorporates the freezing of the molecules on to grains, simple grain surface chemistry and cosmic-ray induced and direct desorption of ices. The predicted OPRs are found to deviate significantly from both thermal and statistical values and to be independent of temperature below $\sim $30~K. The OPR of H$_2$O is shown to lie between 1.5 and 2.6, depending on the spin-state of H$_2$, in good agreement with values derived in translucent clouds with relatively high extinction. In the prestellar core collapse calculations, the OPR of H$_2$O is shown to reach the statistical value of 3 in regions with severe depletion ($n_{\rm H}> 10^7$~cm$^{-3}$). We conclude that a low water OPR ($\lesssim 2.5$) is consistent with gas-phase ion-neutral chemistry and reflects a gas with OPR(H$_2)\lesssim 1$. Available OPR measurements in protoplanetary disks and comets are finally discussed., Comment: 14 pages, 7 figures, accepted for publication in MNRAS on 29 May 2019

The first set of theoretical cross sections for propylene oxide (CH3CHCH2O) colliding with cold He atoms has been obtained at the full quantum level using a high-accuracy potential energy surface. By scaling the collision reduced mass, rotational rate coefficients for collisions with para-H2 are deduced in the temperature range 5-30 K. These collisional coefficients are combined with radiative data in a non-LTE radiative transfer model in order to reproduce observations of propylene oxide made towards the Sagittarius B2(N) molecular cloud with the Green Bank and Parkes radio telescopes. The three detected absorption lines are found to probe the cold (~ 10 K) and translucent (nH ~ 2000 cm-3) gas in the outer edges of the extended Sgr B2(N) envelope. The derived column density for propylene oxide is Ntot ~ 3e12 cm-2, corresponding to a fractional abundance relative to total hydrogen of ~ 2.5e-11. The present results are expected to help our understanding of the chemistry of propylene oxide, including a potential enantiomeric excess, in the cold interstellar medium., Comment: 9 pages, 5 figures, accepted for publication in ApJ (2021/12/14)

The hydronium cation plays a crucial role in interstellar oxygen and water chemistry. While its spectroscopy was extensively investigated earlier, the collisional excitation of H$_3$O$^+$ is not well studied yet. In this work we present state-to-state collisional data for rotational de-excitation of both ortho- and para-H$_3$O$^+$ due to para-H$_2$ impact. The cross sections are calculated within the close-coupling formalism using our recent, highly accurate rigid-rotor potential energy surface for this collision system. The corresponding thermal rate coefficients are calculated up to 100 K. For para-H$_3$O$^+$ the lowest 20 rotation-inversion states were considered in the calculations, while for ortho-H$_3$O$^+$ the lowest 11 states are involved (up to $j\leq5$), so all levels with rotational energy below 420 K (292 cm$^{-1}$) are studied. In order to analyse the impact of the new collisional rates on the excitation of H$_3$O$^+$ in astrophysical environments radiative transfer calculations are also provided. The most relevant emission lines from an astrophysical point of view are studied, taking into account the transitions at 307, 365, 389 and 396 GHz. We show that our new collisional data have a non-negligible impact (from a few percents up to about a factor of 3) on the brightness and excitation temperatures of H$_3$O$^+$, justifying the revision of the physical conditions in the appropriate astrophysical observations. The calculated rate coefficients allow one to recalculate the column density of hydronium in interstellar clouds, which can lead to a better understanding of interstellar water and oxygen chemistry.

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the classical cutoff is found to be vastly different from that below the cutoff. A V-shape structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schr\"odinger equation simulations for different model potentials., Comment: 6 pages, 3 figures

The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules the photoelectron energy does not depend on the electron's emission direction but theoretical studies have questioned this since 1990. Here we provide experimental evidence, that the energies of photoelectrons emitted against the light-propagation direction are shifted towards higher values while those electrons that are emitted along the light-propagation direction are shifted to lower values. We attribute the energy shift to a nondipole contribution from the interaction of the moving electrons with the incident photons., Comment: 6 pages, 4 figures

Molecules are many body systems with a substantial amount of entanglement between their electrons. Is there a way to break the molecular bond of a diatomic molecule and obtain two atoms in their ground state which are still entangled and form a Bell-like state? We present a scheme that allows for the preparation of such entangled atomic states from single oxygen molecules on femtosecond time scales. The two neutral oxygen atoms are entangled in the magnetic quantum number of their valence electrons. In a time-delayed probe step, we employ non-adiabatic tunnel ionization, which is a magnetic quantum number-sensitive mechanism. We then investigate correlations by comparing single and double ionization probabilities of the Bell-like state. The experimental results agree with the predictions for an entangled state., Comment: 20 pages, 7 figures, 1 table

If matter absorbs a photon of sufficient energy it emits an electron. The question of the duration of the emission process has intrigued scientists for decades. With the advent of attosecond metrology, experiments addressing such ultrashort intervals became possible. While these types of studies require attosecond experimental precision, we present here a novel measurement approach that avoids those experimental difficulties. We instead extract the emission delay from the interference pattern generated as the emitted photoelectron is diffracted by the parent ion's potential. Targeting core electrons in CO, we measured a 2d map of photoelectron emission delays in the molecular frame over a wide range of electron energies. The measured emission times depend drastically on the emission direction and exhibit characteristic changes along the shape resonance of the molecule. Our approach can be routinely extended to other electron orbitals and more complex molecules.

We report on a joint experimental and theoretical study of photoelectron circular dichroism (PECD) in methyloxirane. By detecting O 1s-photoelectrons in coincidence with fragment ions, we deduce the molecule's orientation and photoelectron emission direction in the laboratory frame. Thereby, we retrieve a fourfold differential PECD clearly beyond 50%. This strong chiral asymmetry is reproduced by ab initio electronic structure calculations. Providing such a pronounced contrast makes PECD of fixed-in-space chiral molecules an even more sensitive tool for chiral recognition in the gas phase., Comment: 5 figures

Elastic geodesic grids (EGG) are lightweight structures that can be deployed to approximate designer-provided free-form surfaces. Initially, the grids are perfectly flat, during deployment, a curved shape emerges, as grid elements bend and twist. Their layout is based on networks of geodesic curves and is found geometrically. Encoded in the planar grids is the intrinsic shape of the design surface. Such structures may serve purposes like free-form sub-structures, panels, sun and rain protectors, pavilions, etc. However, so far the EGG have only been investigated using a generic set of design surfaces and small-scale desktop models. Some limitations become apparent when considering more sophisticated design surfaces, like from free-form architecture. Due to characteristics like high local curvature or non-geodesic boundaries, they may be captured only poorly by a single EGG. We show how decomposing such surfaces into smaller patches serves as an effective strategy to tackle these problems. We furthermore show that elastic geodesic grids are in fact well suited for this approach. Finally, we present a showcase model of some meters in size and discuss practical aspects concerning fabrication, size, and easy deployment., Comment: 15 pagers, 20 figures. arXiv admin note: substantial text overlap with arXiv:2010.08062

Scalable systems for automated driving have to reliably cope with an open-world setting. This means, the perception systems are exposed to drastic domain shifts, like changes in weather conditions, time-dependent aspects, or geographic regions. Covering all domains with annotated data is impossible because of the endless variations of domains and the time-consuming and expensive annotation process. Furthermore, fast development cycles of the system additionally introduce hardware changes, such as sensor types and vehicle setups, and the required knowledge transfer from simulation. To enable scalable automated driving, it is therefore crucial to address these domain shifts in a robust and efficient manner. Over the last years, a vast amount of different domain adaptation techniques evolved. There already exists a number of survey papers for domain adaptation on camera images, however, a survey for LiDAR perception is absent. Nevertheless, LiDAR is a vital sensor for automated driving that provides detailed 3D scans of the vehicle's surroundings. To stimulate future research, this paper presents a comprehensive review of recent progress in domain adaptation methods and formulates interesting research questions specifically targeted towards LiDAR perception., Comment: Accepted at IEEE Intelligent Vehicles Symposium (IV) 2021 Workshop on Autonomy at Scale. 8 pages, 5 figures

We present an experimental and theoretical study of core-level ionization of small hetero- and homo-nuclear molecules employing circularly polarized light and address molecular-frame photoelectron angular distributions in the light's polarization plane (CP-MFPADs). We find that the main forward-scattering peaks of CP-MFPADs are slightly tilted with respect to the molecular axis. We show that this tilt angle can be directly connected to the molecular bond length by a simple, universal formula. The extraction of the bond length becomes more accurate as the photoelectron energy is increased. We apply the derived formula to several examples of CP-MFPADs of C 1s and O 1s photoelectrons of CO, which have been measured experimentally or obtained by means of ab initio modeling. The photoelectron kinetic energies range from 70 to 1000~eV and the extracted bond lengths agree well with the known bond length of the CO molecule in its ground state. In addition, we discuss the influence of the back-scattering contribution that is superimposed over the analyzed forward-scattering peak in case of homo-nuclear diatomic molecules as N$_2$.