Mean Opacity Research Articles

ÆSOPUS 2.1: Low-temperature Opacities Extended to High Pressure

We address the critical need for accurate Rosseland mean gas opacities in high-pressure environments, spanning temperatures from 100 K to 32,000 K. Current opacity tables from Wichita State University and ÆSOPUS 2.0 are limited to log(R)≤1 , where R=ρT6−3 in units of gcm−3(106K)−3 . This is insufficient for modeling very low-mass stars, brown dwarfs, and planets with atmospheres exhibiting higher densities and pressures ( log(R)>1 ). Leveraging extensive databases such as ExoMol, ExoMolOP, MoLLIST, and HITEMP, we focus on expanding the ÆSOPUS opacity calculations to cover a broad range of pressure and density conditions ( −8≤log(R)≤+6 ). We incorporate the thermal Doppler mechanism and microturbulence velocity. Pressure-broadening effects on molecular transitions, leading to Lorentzian or Voigt profiles, are explored in the context of atmospheric profiles for exoplanets, brown dwarfs, and low-mass stars. We also delve into the impact of electron degeneracy and nonideal effects, such as ionization potential depression under high-density conditions, emphasizing its notable influence on Rosseland mean opacities at temperatures exceeding 10,000 K. As a result, this study expands the ÆSOPUS public web interface for customized gas chemical mixtures, promoting flexibility in opacity calculations based on specific research needs. Additionally, precomputed opacity tables, inclusive of condensates, are provided. We present a preliminary application to evolutionary models for very low-mass stars.

R-matrix calculations for opacities: I. Methodology and computations

An extended version of the R-matrix methodology is presented for calculation of radiative parameters for improved plasma opacities. Contrast and comparisons with existing methods primarily relying on the distorted wave approximation are discussed to verify accuracy and resolve outstanding issues, particularly with reference to the opacity project (OP). Among the improvements incorporated are: (i) large-scale Breit–Pauli R-matrix calculations for complex atomic systems including fine structure, (ii) convergent close coupling wave function expansions for the (e + ion) system to compute oscillator strengths and photoionization cross sections, (iii) open and closed shell iron ions of interest in astrophysics and experiments, (iv) a treatment for plasma broadening of autoionizing resonances as function of energy-temperature-density dependent cross sections, (v) a ‘top-up’ procedure to compare convergence with R-matrix calculations for highly excited levels, and (vi) spectroscopic identification of resonances and bound (e + ion) levels. The present R-matrix monochromatic opacity spectra are fundamentally different from OP and lead to enhanced Rosseland and Planck mean opacities. An outline of the work reported in other papers in this series and those in progress is presented. Based on the present re-examination of the OP work, opacities of heavy elements might require revisions in high temperature-density plasma sources.

Overview of the contributions from all lanthanide elements to kilonova opacity in the temperature range from 25 000 to 40 000 K

Context. It is now well established that the neutron star (NS) merger is at the origin of the production of trans-iron heavy elements in the universe. These elements are therefore present in large quantities in the ejected matter, whose electromagnetic radiation, called kilonova, is characterized by a significant opacity due to the high density of spectral lines belonging to many heavy ions. Among these, the lanthanide ions play an essential role since, with their open 4f subshell, they have a considerable number of transitions that can absorb emitted light. The knowledge of the atomic structure and the radiative parameters of these ions as well as the determination of the corresponding opacities is therefore of paramount importance for the spectral analysis of kilonovae. Aims. The main goal of the present work is to determine the relative contributions of the different lanthanide elements to the opacity of the emission spectrum of a kilonova in its early phase, that is, a few hours after the NS merger, where the conditions are such that the temperature is between 25 000 and 40 000 K. At these temperatures, the lanthanide ions whose charge states are between V and VII are predominant. Methods. We used the pseudo-relativistic Hartree–Fock (HFR) method extensively to calculate the relevant atomic data (energy levels, wavelengths, and oscillator strengths) in La-Lu V-VII ions. The corresponding monochromatic opacities were estimated from the expansion formalism. Results. We calculated the spectroscopic parameters for a total of more than 800 million radiative transitions in all the ions considered. These data were used to estimate the expansion opacities and Planck mean opacities for all the lanthanide elements at early-phase kilonova conditions between 25 000 and 40 000 K, making it possible to deduce the respective contributions of each element as a function of temperature. Atomic calculations were also carried out with the fully relativistic Multiconfiguration Dirac-Hartree-Fock (MCDHF) method in the specific case of the Yb V ion, as the available experimental data had not yet been compared with the theoretical calculations in our previous studies on lanthanide ions.

The High Mass Accretion in the Innermost Regions of a Viscously Evolved Protoplanetary Disk

In this paper, we investigate the mass accretion properties in the innermost regions of a viscously evolved protoplanetary disk and try to find some clues to the outburst events. In our newly developed one-dimensional time-dependent disk model based on the diffusion equation for surface density, we take into account the following physical effects: the gravitational collapse of the parent molecular cloud core, the irradiation from the central star to the disk, the effect of the photoevaporation mechanism, the viscosity due to the magnetorotational instability (MRI) and the gravitational instability (GI), and the thermal ionization mechanism in the inner regions. We find that the mass accretion rate M·disk in the innermost regions is statistically high enough to generate outbursts, although there are regions where the accretion rate is low. Additionally, we find that there is a weak correlation between the high mass accretion rate M·disk and the molecular cloud core’s properties (angular velocity ω and mass Mcd), as well as a strong correlation with the minimum viscosity parameter αmin. In general, there are two regions of outburst, the inner Region I and outer Region II. The outburst of Region I is caused by the MRI mechanism and thermal instability, while neither the MRI, the GI, nor the thermal instability causes the outburst of Region II. Our analysis suggests that the outer Region II is dominated by, or largely related to, the Rosseland mean opacity κR and the αmin parameter.

ÆSOPUS 2.0: Low-temperature Opacities with Solid Grains

Abstract In this study we compute the equation of state and Rosseland mean opacity from temperatures of T ≃ 30,000 K down to T ≃ 400 K, pushing the capabilities of the ÆSOPUS code into the regime where solid grains can form. The GGchem code is used to solve the chemistry for temperatures less than ≃3000 K. Atoms, molecules, and dust grains in thermodynamic equilibrium are all included in the equation of state. To incorporate monochromatic atomic and molecular cross sections, an optimized opacity sampling technique is used. The Mie theory is employed to calculate the opacity of 43 grain species. Tables of Rosseland mean opacities for scaled-solar compositions are provided. Based on our computing resources, opacities for other chemical patterns, as well as various grain sizes, porosities, and shapes, can be easily computed upon user request to the corresponding author.

Interface of equation of state, atomic data, and opacities in the solar problem

ABSTRACT The dependence of the Rosseland Mean Opacity (RMO) on the equation of state and the number of included atomic levels of iron ions prevalent at the solar radiative/convection boundary is investigated. The ‘chemical picture’ Mihalas–Hummer–Däppen (MHD) equation-of-state (EOS), and its variant QMHD–EOS, are studied at two representative temperature–density sets at the base of the convection zone and the Sandia Z experiment: (2 × 106 K, 1023/cc) and (2.11 × 106 K, 3.16 × 1022/cc), respectively. It is found that whereas the new atomic data sets from accurate R-matrix calculations for opacities (RMOP) are vastly overcomplete, involving hundreds to over a thousand levels of each of the three Fe ions considered – Fe xvii, Fe xviii, Fe xix – the EOS constrains contributions to RMOs by relatively fewer levels. The RMOP iron opacity spectrum is quite different from the Opacity Project distorted wave model and shows considerably more plasma broadening effects. This work points to possible improvements needed in the EOS for opacities in high-energy–density plasma sources.

Feed forward neural network parametrization of the mean radiative properties of the mixture

Fast evaluated and highly accurate parametrization of the radiative properties has important applications where opacity evaluations in situ are frequently needed. Feed forward neural network (FFNN) is successfully developed to fit the average ionization degree, Planck and Rosseland mean opacities of the mixture from the opacity project. Three typical cases are shown: (a) for pure C, FFNNs with different sizes provide low to high representations, and with hundreds of parameters, the root mean square error (RMSE) decreases within 1%. Properties of the complex element such as Fe are also fitted successfully; (b) the mean properties of the CH mixture are fitted with the RMSE less than 2.7% by a 3×30×30×1 FFNN (1081 parameters). Analytical relations between the properties of mixture and each species are discussed; (c) the Rosseland mean opacities of the mixtures from solar model are reconstructed by a 4×20×20×1 FFNN (541 parameters) with the RMSE less than 0.7%, where the mass fractions of H and He are used as the reduced variables to distinguish the compositions at different solar radius. These cases illustrate the key points in the fitting and suggest FFNN as a feasible and powerful tool in the parametrization of mixture properties. This work is essential for practical application and further modelization of the mixture.

Radiation burnthrough measurements to infer opacity at conditions close to the solar radiative zone–convective zone boundary

Recent measurements at the Sandia National Laboratory of the x-ray transmission of iron plasma have inferred opacities much higher than predicted by theory, which casts doubt on modeling of iron x-ray radiative opacity at conditions close to the solar convective zone-radiative zone boundary. An increased radiative opacity of the solar mixture, in particular iron, is a possible explanation for the disagreement in the position of the solar convection zone-radiative zone boundary as measured by helioseismology and predicted by modeling using the most recent photosphere analysis of the elemental composition. Here, we present data from radiation burnthrough experiments, which do not support a large increase in the opacity of iron at conditions close to the base of the solar convection zone and provide a constraint on the possible values of both the mean opacity and the opacity in the x-ray range of the Sandia experiments. The data agree with opacity values from current state-of-the-art opacity modeling using the CASSANDRA opacity code.

Cross-correlation power spectra and cosmic birefringence of the CMB via photon-neutrino interaction

In the context of the standard model of particles, the weak interaction of cosmic microwave background (CMB) and cosmic neutrino background (CνB), can generate non-vanishing TB and EB power spectra in the order of one loop forward scattering, in the presence of scalar perturbation, which is in contrast with the standard scenario cosmology. Comparing our results with the current experimental data may provide, significant information about the nature of CνB, including CMB-CνB forward scattering for TB, TE, and EB power spectra. To this end, different cases were studied, including Majorana CνB and Dirac CνB. On the other hand, it was shown that the mean opacity due to cosmic neutrino background could behave as an anisotropic birefringent medium and change the linear polarization rotation angle. Considering the contributions from neutrino and anti-neutrino forward scattering with CMB photons (in the case of Dirac neutrino), we introduce relative neutrino and anti-neutrino density asymmetry (δν = Δnν /nν = nν -nν̅ /nν ). Then, using the cosmic birefringence angle reported by the Planck data release β = 0.30° ± 0.11° (68%C.L.), some constraints can be put on δν . Also, the value of cosmic birefringence due to Majorana CνB medium is estimated at about β| ν ≃ 0.2 rad. In this respect, since Majorana neutrino and anti-neutrino are exactly the same, both CB contributions will be added together. However, this value is at least two orders larger than the cosmic birefringence angle reported by the Planck data release, β = 0.30° ± 0.11° (68%C.L.). Finally, we shortly discussed this big inconsistency. It is noteworthy that to calculate the contribution of photon-neutrino forward scattering for cosmic birefringence, we just consider the standard model of particles and the standard scenario of cosmology.

Photoionization and Opacity

Opacity determines radiation transport through material media. In a plasma source, the primary contributors to atomic opacity are bound–bound line transitions and bound-free photoionization into the continuum. We review the theoretical methodology for state-of-the-art photoionization calculations based on the R-matrix method as employed in the Opacity Project, the Iron Project, and solution of the heretofore unsolved problem of plasma broadening of autoionizing resonances due to electron impact, Stark (electric microfields), Doppler (thermal), and core-excitations. R-matrix opacity calculations entail huge amount of atomic data and calculations of unprecedented complexity. It is shown that in high-energy-density (HED) plasmas, photoionization cross sections become 3-D energy–temperature–density-dependent owing to considerable attenuation of autoionizing resonance profiles. Hence, differential oscillator strengths and monochromatic opacities are redistributed in energy. Consequently, Rosseland and Planck mean opacities are affected significantly.

Effect of improved atmospheric opacities in modelling sub-Neptunes

Aims. We investigate the impact of updated atmospheric mean opacity input values on modelled transit radius and the distribution of interior layer mass fractions. Methods. We developed and applied a coupled interior-atmosphere model. Our straightforward semi-grey calculation of atmospheric temperature enables us to perform thousands of model realisations in a Monte Carlo approach to address potential degeneracies in interior and atmospheric mass fraction. Our main constraints are planetary mass and radius from which our model infers distributions of the internal structure of exoplanetary classes ranging from Super-Earth to Mini-Neptune. We varied the relative masses of gas, envelope, mantle, and core layers subject to constraints on the bulk density from observations, and investigated the effect of updating atmospheric mean opacities. Results. First, we validate our model output with observed temperature profiles for modern Neptune. We can reproduce the basic features in the middle atmosphere but not the temperature inversion in the upper layers, which is likely because our model lacks aerosol heating. Calculated interiors are generally consistent with modern Neptune. Second, we compare with the well-studied object GJ 1214 b and obtain results that are broadly consistent with previous findings; they suggest correlations between modelled gas, water, and core mass fractions, although these are generally weak. Updating the opacities leads to a change on the order of a few percent in the modelled transit radius. This is comparable in magnitude to the planned accuracy of the PLATO data for planetary radius, suggesting that the opacity update in the model is important to implement.

Ideas and Tools for Error Detection in Opacity Databases

In this article, we propose several ideas and tools in order to check the reliability of radiative opacity and atomic physics databases. We first emphasize that it can be useful to verify that mathematical inequalities, which impose lower and upper bounds on the Rosseland and/or Planck mean opacities, are satisfied, either for pure elements or mixtures. In the second part, we discuss the intriguing law of anomalous numbers, also named Benford’s law, which enables one to detect errors in line-strength collections, required in order to perform fine-structure calculations. Finally, we point out and illustrate the importance of quantifying the uncertainties due to interpolations in the density-temperature opacity (or more generally atomic-data) tables and performing convergence checks, which are crucial in the accuracy-completeness compromise inherent in opacity computations.

Updated Low-temperature Gas Opacities with ÆSOPUS 2.0

This work introduces new low-temperature gas opacities in the range computed with the ÆSOPUS code under the assumption of thermodynamic equilibrium. In comparison to the previous version, ÆSOPUS 1.0, we updated and expanded molecular absorption to include 80 species, mostly using the recommended line lists currently available from the ExoMol and HITRAN databases. Furthermore, in light of a recent study, we revised the H− photodetachment cross section, added the free–free absorption of other negative ions of atoms and molecules, and updated the collision-induced absorption due to H2/H2, H2/H, H2/He, and H/He pairs. Using the new input physics, we computed tables of Rosseland mean opacities for several scaled-solar chemical compositions, including Magg et al.'s most recent one, as well as α-enhanced mixtures. The differences in opacity between the new ÆSOPUS 2.0 and the original ÆSOPUS 1.0 versions, as well as other sets of calculations, are discussed. The new opacities are released to the community via a dedicated webpage that includes both precomputed tables for widely used chemical compositions and a web interface for calculating opacities on the fly for any abundance distribution.

RAPOC: The Rosseland and Planck opacity converter

RAPOC (Rosseland and Planck Opacity Converter) is a Python 3 code that calculates Rosseland and Planck mean opacities (RPMs) from wavelength-dependent opacities for a given temperature, pressure, and wavelength range. In addition to being user-friendly and rapid, RAPOC can interpolate between discrete data points, making it flexible and widely applicable to the astrophysical and Earth-sciences fields, as well as in engineering. RAPOC uses ExoMol, DACE, or any user defined input data, provided that it is in a readable format. In this paper, we present the RAPOC code and compare its calculated Rosseland and Planck mean opacities with other values in the literature. RAPOC is open-source and available on Pypi and GitHub.

Mean opacities of a strongly magnetized high-temperature plasma

ABSTRACT Geometry and dynamical structure of emission regions in accreting pulsars are shaped by the interplay between gravity, radiation, and strong magnetic field, which significantly affects the opacities of a plasma and radiative pressure under such extreme conditions. Quantitative consideration of magnetic plasma opacities is therefore an essential ingredient of any self-consistent modelling of emission region structure of X-ray pulsars (XRPs). We present results of computations of the Rosseland and Planck mean opacities of a strongly magnetized plasma with a simple chemical composition, namely the solar hydrogen/helium mix. We consider all relevant specific opacities of the magnetized plasma including vacuum polarization effect and contribution of electron–positron pairs where the pair number density is computed in the thermodynamic equilibrium approximation. The magnetic Planck mean opacity determines the radiative cooling of an optically thin strongly magnetized plasma. It is by factor of three smaller than non-magnetic Planck opacity at $k_{\rm B}T \lt 0.1\, E_{\rm cyc}$ and increases by a factor of 102–104 at $k_{\rm B}T \gt 0.3\, E_{\rm cyc}$ due to cyclotron thermal processes. We propose a simple approximate expression which has sufficient accuracy for the magnetic Planck opacity description. We provide the Rosseland opacity in a tabular form computed in the temperature range 1–300 keV, magnetic field range 3 × 1010–1015 G, and a broad range of plasma densities. We demonstrate that the scattering on the electron–positron pairs increases the Rosseland opacity drastically at temperatures > 50 keV in the case of mass densities typical for accretion channel in XRPs.

Cosmic Reionization on Computers: Physical Origin of Long Dark Gaps in Quasar Absorption Spectra

I explore the properties of “dark gaps”—regions in quasar absorption spectra without significant transmission—with several simulations from the Cosmic Reionization On Computers (CROC) project. The CROC simulations in the largest available boxes (120 cMpc) come close to matching both the distribution of mean opacities and the frequency of dark gaps, but alas not in the same model: the run that matches the mean opacities fails to contain enough dark gaps and vice versa. Nevertheless, the run that matches the dark gap distributions serves as a counterexample to claims in the literature that the dark gap statistics requires a late end to reionization—in that run reionization ends at z = 6.7 (likely too early). While multiple factors contribute to the frequency of large dark gaps in the simulations, the primary factor that controls the overall shape of the dark gap distribution is the ionization level in voids—the lowest-density regions produce the highest transmission spikes that terminate long gaps. As the result, the dark gap distribution correlates strongly with the fraction of the spectrum above the gap detection threshold and the observed distribution is matched by the simulation in which this fraction is 2%. Hence, the gap distribution by itself does not constrain the timing of reionization, although it may do so in combination with the distribution of mean opacities.

Theoretical investigation of energy levels and transitions for Pr iv

ABSTRACT We present extensive energy levels (1110 levels) and transition data for the Pr iv. We also show the effect of such atomic data on opacity for neutron star (NS) merger. We performed energy spectra and transition data calculations using the GRASP2018 package, which is based on the multiconfiguration Dirac–Hartree–Fock and relativistic configuration interaction methods. Using the GRASP2018 data, the opacities in the NS merger ejecta containing pure Pr are calculated. Energy levels are compared with recommended values from the NIST Atomic Spectra Database and other available works. Furthermore, electric dipole (E1) transition data, line strengths, weighted oscillator strengths, and transition rates are computed between the above levels. We estimate the uncertainties of the computed line strengths giving the accuracy class. The computed line strengths are also compared with other theoretical computations. We proposed few ways to estimate the uncertainties of the line strengths of the E1 transitions. Our calculation for opacity for a typical condition of NS merger ejecta at t ∼ 1 d shows that the Planck mean opacity of Pr3 + reaches $\sim 1\, \rm cm^{2}\, g^{-1}$ at $T\, \sim \, 15000$ K. The opacity is higher than that by the previous studies, thanks to the higher completeness of the atomic data. We also highlight the importance of accurate atomic data for the opacity by comparing it with the opacity using the atomic calculation from HULLAC. Moreover, we identify the important configurations, especially for the transitions between the high-lying levels for the opacity of 3+ ionized lanthanides.

First 3D radiation-hydrodynamic simulations of Wolf-Rayet winds

Context. Classical Wolf-Rayet (WR) stars are direct supernova progenitors undergoing vigorous mass loss. Understanding the dense and fast outflows of such WR stars is thus crucial for understanding advanced stages of stellar evolution and the dynamical feedback of massive stars on their environments, and for characterizing the distribution of black hole masses. Aims. In this paper, we develop the first time-dependent, multidimensional, radiation-hydrodynamical models of the extended optically thick atmospheres and wind outflows of hydrogen-free classical WR stars. Methods. A flux-limiting radiation hydrodynamics approach is used on a finite volume mesh to model WR outflows. The opacities are described using a combination of tabulated Rosseland mean opacities and the enhanced line opacities expected within a supersonic flow. Results. For high-luminosity models, a radiation-driven, dense, supersonic wind is launched from deep subsurface regions associated with peaks in the Rosseland mean opacity. For a model with lower luminosity, on the other hand, the Rosseland mean opacity is not sufficient to sustain a net-radial outflow in the subsurface regions. Instead, what develops in this case, is a "standard" line-driven wind launched from the optically thin regions above an extended, moderately inflated, and highly turbulent atmosphere. We thus find here a natural transition from optically thick outflows of classical WR stars to optically thin winds of hot, compact subdwarfs; in our simulations, this transition occurs approximately at a luminosity that is ~40% of the Eddington luminosity. Because of the changing character of the wind-launching mechanism, this transition is also accompanied by a large drop (on the low-luminosity end) in the average mass-loss rate. Since the subsurface opacity peaks are further associated with convective instabilities, the flows are highly structured and turbulent, consisting of coexisting regions of outflowing, stagnated, and even pockets of infalling gas. Typical velocity dispersions in our 3D models are high, 100–300 km s−1, but the clumping factors are rather modest, fc1 ≡ 〈ρ2〉/〈ρ〉2 ~ 2. We further find that, while the low-density gas in our simulations is strongly radiation-driven, the overdense structures are, after their initial launch, primarily advected outward by ram-pressure gradients. This inefficient radiative acceleration of dense "clumps" reflects the inverse dependence of line driving on mass density and leads to a general picture wherein high-density gas parcels move significantly slower than the mean and low-density wind material.

A comprehensive study of the radiative properties of NO—a first step toward a complete air opacity

In this paper we propose a methodology to calculate the radiative properties of the diatomic molecular constituents of air, and utilize the present approach to model the radiative properties of nitrogen monoxide, NO. We also investigate the important physics involved in calculating accurate radiative quantities for air, such as the Planck and Rosseland mean opacities, and emission and absorption coefficients, as well as the couplings accounted for in rovibrational calculations. Complete active space self-consistent field multi-reference configuration interaction (CAS-MRCI) calculations were performed in order to model the NO X 2Π, a 4Π, b 4Σ−, 12Σ+, 22Σ+, 32Σ+, G 2Σ−, B′2Δ, (C, B) 22Π, (H′, L) 32Π, and 12Φ adiabatic states, and calculate the respective molecular data. The γ X 2Π − A 2Σ+, ɛ X 2Π − D 2Σ+, β′ X 2Π − B′2Δ, ‘11 000 Å’ A 2Σ+ − D 2Σ+, ‘infrared’ X 2Π − X 2Π and X 2Π − (C, B) 22Π (δ and β) band systems are investigated in monochromatic spectra calculations, as well as the Ogawa a 4Π − b 4Σ− band and several other band systems. Several conclusions are drawn, such as the importance of including the Ogawa band, which has not been included in previous air radiative models or comprehensive line-list calculations, as well as the importance of performing coupled rovibrational line-list calculations in order to accurately calculate the Rosseland means. We also found that the additional band systems modeled here contribute significantly to the total Planck and Rosseland means.

Characterization of Dysfunctional Lens Index and Opacity Grade in a Healthy Population.

This study enrolled 61 volunteers (102 eyes) classified into subjects < 50 years (group 1) and subjects ≥ 50 years (group 2). Dysfunctional Lens Index (DLI); opacity grade; pupil diameter; and corneal, internal, and ocular higher order aberrations (HOAs) were measured with the i-Trace system (Tracey Technologies). Mean DLI was 8.89 ± 2.00 and 6.71 ± 2.97 in groups 1 and 2, respectively, being significantly higher in group 1 in all and right eyes (both p < 0.001). DLI correlated significantly with age (Rho = −0.41, p < 0.001) and pupil diameter (Rho = 0.20, p = 0.043) for all eyes, and numerous internal and ocular root-mean square HOAs for right, left, and all eyes (Rho ≤ −0.25, p ≤ 0.001). Mean opacity grade was 1.21 ± 0.63 and 1.48 ± 1.15 in groups 1 and 2, respectively, with no significant differences between groups (p ≥ 0.29). Opacity grade significantly correlated with pupil diameter for right and all eyes (Rho ≤ 0.33, p ≤ 0.013), and with some ocular root-mean square HOAs for right and all eyes (Rho ≥ 0.23, p ≤ 0.020). DLI correlates with age and might be used complementary to other diagnostic measurements for assessing the dysfunctional lens syndrome. Both DLI and opacity grade maintain a relationship with pupil diameter and internal and ocular HOAs, supporting that the algorithms used by the device may be based, in part, on these parameters.