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Large Language Models (LLMs) have emerged as powerful tools for addressing modern challenges and enabling practical applications. However, their computational expense remains a significant barrier to widespread adoption. Quantization has emerged as a promising technique to democratize access and enable low resource device deployment. Despite these advancements, the safety and trustworthiness of quantized models remain underexplored, as prior studies often overlook contemporary architectures and rely on overly simplistic benchmarks and evaluations. To address this gap, we introduce OpenSafetyMini, a novel open-ended safety dataset designed to better distinguish between models. We evaluate 4 state-of-the-art quantization techniques across LLaMA and Mistral models using 4 benchmarks, including human evaluations. Our findings reveal that the optimal quantization method varies for 4-bit precision, while vector quantization techniques deliver the best safety and trustworthiness performance at 2-bit precision, providing foundation for future research.

We search for reflection-dominated Compton-thick active galactic nuclei (CT AGN) candidates in the Lockman Hole region using the data of SRG/eROSITA Lockman Hole survey. We selected sources with anomalously hard photon indices in the $0.3 - 8.0$ keV band, untypical for type I AGN. In particular, we required that the upper end of the $90\%$ error interval did not exceed a fiducial boundary of $\Gamma=1.3$. We found 291 sources which constitute a rare subpopulation among extragalactic X-ray sources detected by eROSITA in the Lockman Hole field, $\approx 5\%$. These sources constitute the eROSITA sample of CT AGN candidates in the Lockman Hole field. We further divide the sources into three categories depending on the availability of reliable redshift and statistically significant detection of intrinsic absorption. We present two catalogues: the bright sample (37 sources) and the faint one (254). We estimate the fraction and sky density of reflection-dominated CT AGN candidates. We show examples of individual spectra and use stacking analysis to search for possible redshift evolution of their properties with redshift. We analyse combined eROSITA spectra of bright sources of different categories with a physically motivated spectral model UXCLUMPY and find them fully consistent with the fits to the about $\sim 1$ Msec XMM-Newton data for one of our reflection-dominated CT candidates, Type 2 galaxy $\text{SRGe J105348.6+573032}$. The catalogues of CT AGN candidates could be a good starting point for planning future studies and follow-ups at all wavelengths., Comment: Accepted for publication in MNRAS

Histopathology, the study and diagnosis of disease through analysis of tissue samples, is an indispensable part of modern medicine. However, the practice is time consuming and labor intensive, compelling efforts to improve the process and develop new approaches. One perspective technique involves mapping changes in the polarization state of light scattered by the tissue, but the conventional implementation requires bulky polarization optics and is slow. We report the design, fabrication and characterization of a compact metasurface polarimeter operating at 640 nm enabling simultaneous determination of Stokes parameters and degree of polarization with $\pm$2% accuracy. To validate its use for histopathology we map polarization state changes in a tissue phantom mimicking a biopsy with a cancerous inclusion, comparing it to a commercial polarimeter. The results indicate a great potential and suggest several improvements with which we believe metasurface polarimeter based devices will be ready for practical histopathology application in clinical environment., Comment: Paul Thrane and Chao Meng contributed equally. 23 pages, 10 figures

We consider quantum mechanical systems of spin chain type, with finite-dimensional Hilbert spaces and $\mathcal{N}=2$ or $\mathcal{N}=4$ supersymmetry, described in $\mathcal{N}=2$ superspace in terms of nonlinear chiral multiplets. We prove that they are natural truncations of 1D sigma models, whose target spaces are $\mathsf{SU}(n)$ (co)adjoint orbits. As a first application, we compute the Witten indices of these finite-dimensional models showing that they reproduce the Dolbeault and de Rham indices of the target space. The problem of finding the exact spectra of generalized Laplace operators on such orbits is shown to be equivalent to the diagonalization of spin chain Hamiltonians., Comment: 70 pages, 10 figures

We introduce a notion of Lorentzian metric space which drops the boundedness condition from our previous work and argue that the properties defining our spaces are minimal. In fact, they are defined by three conditions given by (a) the reverse triangle inequality for chronologically related events, (b) Lorentzian distance continuity and relative compactness of chronological diamonds, and (c) a distinguishing condition via the Lorentzian distance function. By adding a countably generating condition we confirm the validity of desirable properties for our spaces including the Polish property. The definition of (pre)length space given in our previous work on the bounded case is generalised to this setting. We also define a notion of Gromov-Hausdorff convergence for Lorentzian metric spaces and prove that (pre)length spaces are GH-stable. It is also shown that our (sequenced) Lorentzian metric space bring a natural quasi-uniformity (resp.\ quasi-metric). Finally, an explicit comparison with other recent constructions based on our previous work on bounded Lorentzian metric spaces is presented., Comment: 68 pages, 1 figure

Manipulating intensity, phase and polarization of the electromagnetic fields on ultrafast timescales is essential for all-optical switching, optical information processing and development of novel time-variant media. Noble metal based plasmonics has provided numerous platforms for optical switching and control, enabled by strong local field enhancement, artificially engineered dispersion and strong Kerr-type free-electron nonlinearities. However, precise control over switching times and spectrum remains challenging, commonly limited by the relaxation of hot-electron gas on picosecond time scales and the band structure of materials. Here we experimentally demonstrate the strong and tuneable nonlinearity in a metamaterial on a mirror geometry, controlled by the wavelength of excitation, which imprints a specific non-uniform hot-electron population distribution and drives targeted electron and lattice dynamics. The interplay of electromagnetic, electronic and mechanical energy exchange allows us to achieve sub-300~fs timescales in the recovery of optical constants in the selected spectral domains, where the modulation surpasses the limitations imposed by the inherent material response of metamaterial components, owing to emergence of a Fano-type destructive interference with acoustic vibrations of the metamaterial, featured in reflection but not in transmission. The observed effects are highly spectrally selective and sensitive to the polarisation properties of light and the Fabry-Perot modes of the metamaterial, opening a pathway for controlling the switching rates by spectral selection and nanostructure design. The capability to manipulate temporal, spectral and mechanical aspects of light-matter interactions underscores new potential nonlinear applications where polarisation diversity, spectral selectivity and fast modulation are important.

We explore quantum-based optical polarimetry as a potential diagnostic tool for biological tissues by developing a theoretical and experimental framework to understand polarization-entangled photon behavior in scattering media. We investigate the mathematical relationship between Wolf's coherency matrix in classical optics and the density matrix formalism of quantum mechanics which allows for the extension of classical Monte Carlo method to quantum states. The developed generalized Monte Carlo approach uniquely integrates the Bethe-Salpeter equation for classical scattering, the Jones vector formalism for polarization, and the density matrix approach for quantum state representation. Therefore, this unified framework can model both classical and quantum polarization states, handle multi-photon states, and account for varying degrees of entanglement. Additionally, it facilitates the prediction of quantum state evolution in scattering media based on classical optical principles. The validity of the computational model is experimentally confirmed through high-fidelity agreement between predicted and measured quantum state evolution in tissue-mimicking phantoms. This work bridges the gap between classical and quantum optical polarimetry by developing and validating a comprehensive theoretical framework that unifies these traditionally distinct domains, paving the way for future quantum-enhanced diagnostics of tissues and other turbid environments., Comment: 21 page, 5 figures + supplementary material 10 pages, 2 figures

The accurate simulation of complex biochemical phenomena has historically been hampered by the computational requirements of high-fidelity molecular-modeling techniques. Quantum mechanical methods, such as ab initio wave-function (WF) theory, deliver the desired accuracy, but have impractical scaling for modelling biosystems with thousands of atoms. Combining molecular fragmentation with MP2 perturbation theory, this study presents an innovative approach that enables biomolecular-scale ab initio molecular dynamics (AIMD) simulations at WF theory level. Leveraging the resolution-of-the-identity approximation for Hartree-Fock and MP2 gradients, our approach eliminates computationally intensive four-center integrals and their gradients, while achieving near-peak performance on modern GPU architectures. The introduction of asynchronous time steps minimizes time step latency, overlapping computational phases and effectively mitigating load imbalances. Utilizing up to 9,400 nodes of Frontier and achieving 59% (1006.7 PFLOP/s) of its double-precision floating-point peak, our method enables us to break the million-electron and 1 EFLOP/s barriers for AIMD simulations with quantum accuracy.

The operation of a small-size Cherenkov gamma-ray telescope TAIGA-IACT with camera on SiPMs OnSemi MicroFJ-60035 has been modelled by multiparticle Monte Carlo (MC) methods. The model implies that telescope camera is equipped with two specific types of filters of 290-590 nm (visible+NUV) and 220-320 nm (MUV+UVB)-bands, each covering half of the camera pixels in some uniform order. This allows one to measure the fraction of UV-radiation in total amount of Cherenkov radiation of an extensive air shower (EAS), that can be used for efficient gamma-hadron separation. The corresponding quality factor takes values up to 5.07 in the 10-100 TeV range depending on the distance to EAS axis and camera orientation., Comment: 22 pages, 5 figures, 10 tables, accepted to Research in Astronomy and Astrophysics

We applied synchrotron single-crystal X-ray diffraction in a diamond anvil cell at 48-51 GPa and first-principles theoretical calculations to study the crystal structure of solid atomic iodine at high pressure. We report the synthesis of two phases of atomic iodine at 48-51 GPa via laser heating of I-N2 mixtures. Unlike the familiar monatomic I4/mmm structure, which consists of crystallographically equivalent atoms, a new Pm-3n structure is of inclusion type, featuring two distinct kinds of atoms: a central detached one and peripheral ones forming the linear chains. Moreover, we observe crystallization of the familiar high-pressure face centered cubic (fcc) structure, albeit at much lower pressures compared to cold compressed iodine. The discovery of Pm-3n structure in iodine marks an important step in understanding of the pressure induced phase transition sequence in halogens., Comment: 9 pages, 6 figures in the main text. 5 supplementary figures and 1 supplementary table

We report the discovery of a short, large amplitude X-ray flare from AT2019vcb (aka Tormund), a tidal disruption event at $z=0.088$. The discovery is based on the data from the SRG/eROSITA X-ray telescope which happened to observe the source seven months after the onset of the optical TDE. eROSITA observation occurred 13 days after a soft flare was detected in the XMM-Newton data by Quintin et al. 2023. Both events bear similar characteristics in terms of timing and spectral properties. eROSITA spectrum is described as an accretion disk with a characteristic temperature of $\sim180$ eV and luminosity $\sim8\times10^{43}$ erg/s. The eROSITA flare lasted less than 12 hours and had an amplitude $\ge70$ with respect to the quiescent level, no flares were detected in later eROSITA observations (6-18 months later). The XMM-Newton and eROSITA flares provide strong evidence that the TDE AT2019vcb is a bona fide QPE source. Our work further strengthens the direct connection between TDEs and QPE following similar recent results in a TDE AT2019qiz by Nicholl et al. 2024., Comment: submitted to MNRAS, comments welcome

Photonic skyrmion and meron lattices are structured light fields with topologically protected textures, analogous to magnetic skyrmions and merons. Here, we report the theoretical existence of mixed skyrmion and meron quasicrystals in an evanescent optical field. Topological quasiperiodic tilings of even and odd point group symmetries are demonstrated in both the electric field and spin angular momentum. These quasicrystals contain both skyrmions and merons of N\'eel-type topology. Interestingly, the quasiperiodic tilings are in agreement with the observations of quasiperiodic arrangements of carbon nanoparticles in water driven by ultrasound, and pave the way towards engineering hybrid topological states of light which may have potential applications in optical manipulation, metrology and information processing., Comment: 6 pages, 4 figures, Letter, to be submitted for publication

We argue that the North Polar Spur (NPS) and many less prominent structures are formed by gaseous metal-rich plumes associated with star-forming regions (SFRs). The SFRs located at the tangent to the 3-5~kpc rings might be particularly relevant to NPS. A multi-temperature mixture of gaseous components and cosmic rays rises above the Galactic disk under the action of their initial momentum and buoyancy. Eventually, the plume velocity becomes equal to that of the ambient gas, which rotates with different angular speed than the stars in the disk. As a result, the plumes acquire characteristic bent shapes. An ad hoc model of plumes' trajectories shows an interesting resemblance to the morphology of structures seen in the radio continuum and X-rays., Comment: A&A (accepted, unformatted version)

We revisit the classical aspects of $\mathcal{N}=(2,2)$ supersymmetric sigma models with Hermitian symmetric target spaces, using the so-called Gross-Neveu (first-order GLSM) formalism. We reformulate these models for complex Grassmannians in terms of simple supersymmetric Lagrangians with polynomial interactions. For maximal isotropic Grassmannians we propose two types of equivalent Lagrangians, which make either supersymmetry or the geometry of target space manifest. These reformulations can be seen as current-current deformations of curved $\beta \gamma$ systems. The $\mathsf{CP}^{1}$ supersymmetric sigma model is our prototypical example., Comment: 37 pages

We investigate the topological properties of reflection zeros of three-layer structures consisting of a dielectric layer sandwiched between two metal layers, which can be used as optical differentiators. We show that the reflection zeros possess non-zero topological charges, which makes them topologically protected. With a small perturbation of the parameters of the structure (e.g., a change in one of the layer thicknesses), the reflection zero does not disappear, but shifts in the parameter space, i.e., appears at different wavelength and angle of incidence. We demonstrate that with a further parameter change, two zeros with opposite topological charges (+1 and -1) approach each other, merge, and then disappear. We believe that the obtained results give useful insight regarding the operation of layered metal-dielectric-metal structures possessing reflection zeros., Comment: 8 pages, 2 figures

We consider the design of cascaded diffractive optical elements (DOEs) for generating specified intensity distributions for several incident beams with different wavelengths. For each incident beam with a given wavelength, the cascaded DOE forms a different specified intensity distribution. The problem of DOE design is formulated as the problem of minimizing a functional that depends on the functions of diffractive microrelief height of the cascaded DOE and represents the deviations of the intensity distributions generated at the operating wavelengths from the specified ones. Explicit expressions are obtained for the derivatives of the functional, and on this basis, a gradient method for calculating a cascaded DOE is formulated. The proposed gradient method is used for the calculation of cascaded DOEs focusing radiation of three different wavelengths into different areas. In particular, the calculation of a cascaded DOE generating a complex color image of parrots is considered. The presented numerical simulation results demonstrate high performance of the proposed method., Comment: 11 pages, 7 figures

We consider the problem of designing a diffractive neural network (DNN) consisting of a set of sequentially placed phase diffractive optical elements (DOEs) and intended for the optical solution of several given classification problems at different operating wavelengths, so that each classification problem is solved at the corresponding wavelength. The problem of calculating the DNN is formulated as the problem of minimizing a functional that depends on the functions of the diffractive microrelief height of the DOEs constituting the DNN and represents the error in solving the given classification problems at the operating wavelengths. We obtain explicit and compact expressions for the derivatives of this functional and, using them, formulate a gradient method for the DNN calculation. Using this method, we design DNNs for solving the following three classification problems at three different wavelengths: the problem of classifying handwritten digits from the MNIST database, the problem of classifying fashion products from the Fashion MNIST database, and the problem of classifying ten handwritten letters from the EMNIST database. The presented simulation results of the designed DNNs demonstrate high performance of the proposed method., Comment: 19 pages, 11 figures

A wide range of practically important problems is nowadays efficiently solved using artificial neural networks. This gave momentum to intensive development of their optical implementations, among which, the so-called diffractive neural networks (DNNs) constituted by a set of phase diffractive optical elements (DOEs) attract considerable research interest. In the practical implementation of DNNs, one of the standing problems is the requirement for high positioning accuracy of the DOEs. In this work, we address this problem and propose a method for the design of DNNs for image classification, which takes into account the positioning errors (transverse shifts) of the DNN elements. In the method, the error of solving the classification problem is represented by a functional depending on the phase functions of the DOEs and on random vectors describing their transverse shifts. The mathematical expectation of this functional is used as an error functional in the gradient method for calculating the DNN taking into account the transverse shifts of the DOEs. It is shown that the calculation of the derivatives of this functional corresponds to the DNN training method, in which the DOEs have random transverse shifts. Using the proposed gradient method, DNNs are designed that are robust to transverse shifts of the DOEs and enable solving the problem of classifying handwritten digits at a visible wavelength. Numerical simulations demonstrate good performance of the designed DNNs at transverse shifts of up to 17 wavelengths., Comment: 16 pages, 7 figures, 2 tables

We theoretically describe and numerically investigate the operation of "vectorial" optical differentiation of a three-dimensional light beam, which consists in simultaneous computation of two partial derivatives of the incident beam profile with respect to two spatial coordinates in different transverse electric field components. It is implemented upon reflection of the beam from a layered structure by simultaneously utilizing the effect of optical resonance and the spin Hall effect of light. As an example of a layered structure performing this operation, we propose a three-layer metal-dielectric-metal (MDM) structure. We show that by choosing the parameters of the MDM structure, it is possible to achieve the so-called isotropic vectorial differentiation, for which the intensity of the reflected optical beam (squared electric field magnitude) is proportional to the squared absolute value of the gradient of the incident linearly polarized beam. The presented numerical simulation results demonstrate high-quality vectorial differentiation and confirm the developed theoretical description., Comment: 12 pages, 4 figures

We show here that highly polarized X-ray synchrotron radiation from young supernova remnants (SNRs) can be modeled within the framework of diffusive shock acceleration (DSA) and nonlinear magnetic turbulence generation.Cosmic ray acceleration by SNR shocks to very high energies requires efficient magnetic turbulence amplification in the shock precursor.As the strong turbulence generated by Bell's instability far upstream from the viscous subshock convects through the subshock, nonlinear dynamical effects on the compressible fluctuations produce a downstream layer filled with strong anisotropic turbulence with predominantly radial magnetic fields.The synchrotron radiation from shock accelerated electrons in the turbulent downstream layer has a high degree of polarization shown to be consistent with recent observations of young SNRs by IXPE.In the case of Tycho's SNR, the measured X-ray radiation constrains the thickness of the energy containing interval and the amplitude of cosmic ray driven magnetic turbulence, as well as the maximal energy of accelerated protons.The preferential direction of the X-ray polarization depends sensitively on the SNR shock velocity and the ambient density.A unique feature of our model is the sensitive dependence of the degree and direction of X-ray polarization on the spatial overlap between regions of amplified magnetic turbulence and TeV electron populations.While this overlap occurs on scales orders of magnitude below the resolution of IXPE,its polarization measurement allows testing of turbulent plasma processes on unprecedented scales.The mechanism of formation of highly polarized X-ray synchrotron radiation in fast shocks with high level of anisotropic turbulent magnetic field preferentially directed along the shock normal may be applied to other systems like shocks produced by black hole jets., Comment: Physical Review in print, 14 pages, 6 figures

The Laser Interferometer Space Antenna (LISA) is a gravitational wave detector in space. It relies on a post-processing technique named time-delay interferometry (TDI) to suppress the overwhelming laser frequency noise by several orders of magnitude. This algorithm requires intersatellite-ranging monitors to provide information on spacecraft separations. To fulfill this requirement, we will use on-ground observatories, optical sideband-sideband beatnotes, pseudo-random noise ranging (PRNR), and time-delay interferometric ranging (TDIR). This article reports on the experimental end-to-end demonstration of a hexagonal optical testbed used to extract absolute ranges via the optical sidebands, PRNR, and TDIR. These were applied for clock synchronization of optical beatnote signals sampled at independent phasemeters. We set up two possible PRNR processing schemes: Scheme 1 extracts pseudoranges from PRNR via a calibration relying on TDIR; Scheme 2 synchronizes all beatnote signals without TDIR calibration. The schemes rely on newly implemented monitors of local PRNR biases. After the necessary PRNR treatments (unwrapping, ambiguity resolution, bias correction, in-band jitter reduction, and/or calibration), Scheme 1 and 2 achieved ranging accuracies of 2.0 cm to 8.1 cm and 5.8 cm to 41.1 cm, respectively, below the classical 1 m mark with margins., Comment: 17 pages, 13 figures

A crucial aspect of understanding the complex nature of Deep Neural Networks (DNNs) is the ability to explain learned concepts within their latent representations. While methods exist to connect neurons to human-understandable textual descriptions, evaluating the quality of these explanations is challenging due to the lack of a unified quantitative approach. We introduce CoSy (Concept Synthesis), a novel, architecture-agnostic framework for evaluating textual explanations of latent neurons. Given textual explanations, our proposed framework uses a generative model conditioned on textual input to create data points representing the explanations. By comparing the neuron's response to these generated data points and control data points, we can estimate the quality of the explanation. We validate our framework through sanity checks and benchmark various neuron description methods for Computer Vision tasks, revealing significant differences in quality., Comment: 10 pages, 5 figures

The low efficiency of conventional liquefaction technologies based on the Joule-Thomson expansion makes liquid hydrogen currently not attractive enough for large-scale energy-related technologies that are important for the transition to a carbon-neutral society. Magnetocaloric hydrogen liquefaction has great potential to achieve higher efficiency and is therefore a crucial enabler for affordable liquid hydrogen. Cost-effective magnetocaloric materials with large magnetic entropy and adiabatic temperature changes in the temperature range of 77 $\sim$ 20 K under commercially practicable magnetic fields are the foundation for the success of magnetocaloric hydrogen liquefaction. Heavy rare-earth-based magnetocaloric intermetallic compounds generally show excellent magnetocaloric performances, but the heavy rare-earth elements (Gd, Tb, Dy, Ho, Er, and Tm) are highly critical in resources. Yttrium and light rare-earth elements (La, Ce, Pr, and Nd) are relatively abundant, but their alloys generally show less excellent magnetocaloric properties. A dilemma appears: higher performance or lower criticality? In this review, we study how cryogenic temperature influences magnetocaloric performance by first reviewing heavy rare-earth-based intermetallic compounds. Next, we look at light rare-earth-based, "mixed" rare-earth-based, and Gd-based intermetallic compounds with the nature of the phase transition order taken into consideration, and summarize ways to resolve the dilemma.

In the present paper we consider two related problems, i.e. the description of geodesics and the calculation of the spectrum of the Laplace-Beltrami operator on a flag manifold. We show that there exists a family of invariant metrics such that both problems can be solved simply and explicitly. In order to determine the spectrum of the Laplace-Beltrami operator, we construct natural, finite-dimensional approximations (of spin chain type) to the Hilbert space of functions on a flag manifold., Comment: 40 pages, 11 figures

Radiofrequency traps are used to confine charged particles but are only stable for a narrow range of charge-to-mass ratios. Here, we confine two particles -- a nanoparticle and an atomic ion -- in the same radiofrequency trap although their charge-to-mass ratios differ by six orders of magnitude. The confinement is enabled by a dual-frequency voltage applied to the trap electrodes. We introduce a robust loading procedure under ultra-high vacuum and characterize the stability of both particles. It is observed that slow-field micromotion, an effect specific to the dual-field setting, plays a crucial role for ion localization and will be important to account for when engineering controlled interactions between the particles., Comment: 4 figures

Fast blue optical transients (FBOTs) represent a new class of highly energetic sources observed from radio to X-rays. High luminosity, light curves and spectra of the sources can be understood if they are associated with supernova-like or tidal disruption events. Radio observations of the transient sources revealed a mildly relativistic expansion of some of the remnants. The high power and mildly relativistic shock velocities are providing favorable conditions for very high energy particle acceleration. In this paper we present a model of particle acceleration in mildly relativistic magnetohydrodynamic (MHD) outflow of the transient source. To construct the non-thermal radiation and cosmic ray spectra in a broad range of energies we combined the microscopic particle-in-cell (PIC) simulations of electron and proton injection at mildly relativistic shock with Monte Carlo technique for high energy particle transport and acceleration. The kinetic PIC simulations provided the energy partition parameter $\epsilon_{e}$ used to fit the observed non-thermal radio emission using the magnetic field amplification mechanisms modelled with Monte Carlo simulations. The model allowed to describe the radio-spectrum of CSS161010 and it's X-ray luminosity. The high X-ray luminosity of AT2018 and AT2020mrf detected during the first weeks can be connected to the jet interaction with the stellar companion in a binary system. The model predicts that FBOTs can accelerate cosmic rays to energies above 10 PeV with a possible upper limit of maximum energy of 100 PeV. With the expected event rate of FBOTs they can contribute to the very high energy cosmic rays population in galaxies., Comment: 11 pages, 8 figures

We report on the optical realization of the magneto-intersubband oscillations that have been measured in the sub-terahertz transmittance of a GaAs quantum well with two subbands occupied. Following their dc analogue, the oscillations are periodic in the inverse magnetic field with the period governed by the subband gap. Their magnitude and polarization dependence accurately follow the presented simplified version of the dynamic magneto-intersubband oscillations equation that naturally combines dc magneto-intersabband oscillations with microwave-induced resistance oscillations (MIRO). Simultaneously measured photoresistance also reveals its strong sensitivity to the sign of the circular polarization, proving the used theoretical modeling., Comment: 5 pages, 2 figures

Levitated dipolar scatterers exhibit exceptional performance as optomechanical systems for observing quantum mechanics at the mesoscopic scale. However, their tendency to scatter light in almost any direction poses experimental challenges, in particular limiting light collection efficiencies and, consequently, the information extractable from the system. In this article, we present a setup designed to enhance the information gleaned from optomechanical measurements by constraining the back action to a specific spatial direction. This approach facilitates achieving Heisenberg-limited detection at any given numerical aperture. The setup consists of a hollow hemispherical mirror that controls the light scattered by the dipolar emitter, particularly at high scattering angles, thereby focusing the obtained information. This mirror is compatible with existing setups commonly employed in levitated optomechanics, including confocal lenses and optical resonators.