My research concerns the theory and numerical solution of the vector radiative transfer equation and its use in retrieving atmospheric and surface properties from spectrally resolved, polarized measurements of scattered light. Applications include retrievals of aerosols, clouds, trace gases and solar-induced fluorescence from Earth-observing satellites, and the interpretation of thermal emission from brown dwarfs and reflected light from directly imaged exoplanets. Polarization and inelastic (Raman) scattering are treated explicitly rather than approximated: both carry information not contained in the scalar intensity, and both bias retrievals when neglected.
1 · Fundamentals of radiative transfer theory
Vector radiative transfer and its derivatives. My PhD work aimed at retrieving aerosol properties from satellite spectra by optimal estimation. This required radiative transfer models that treat aerosol scattering in full detail and provide derivatives with respect to aerosol parameters, which were not readily available at the time. I developed the vector matrix-operator method vSmartMOM, linearized analytically with respect to aerosol and surface properties (Sanghavi, Davis & Eldering 2014; scalar precursor 2013), and extended δ-m and δ-fit truncation to polarized radiative transfer (Sanghavi & Stephens 2015).
Fourier moments of Mie scattering matrices. Radiative transfer codes need the expansion of the aerosol phase matrix in generalized spherical functions. The usual route computes the phase matrix of a size distribution on an angular grid and then integrates it numerically to obtain the expansion coefficients. Domke (1975) proposed going directly from the scattering amplitudes to the coefficients using Wigner 3-j symbols, which skips the intermediate phase matrix. However, the main recurrence relation in his paper was misprinted, and the method was considered impractical for size parameters above about 120. I corrected the recurrence and implemented the method with precomputed 3-j tabulations. Its accuracy is limited only by machine precision; it reproduces the conventional route and is at least 6–8 times faster for polydispersions over size parameters from 0 to beyond 900 (Sanghavi 2014).
Raman scattering from first principles. Rayleigh scattering is not purely elastic: a few percent of molecular scattering is rotational (and vibrational) Raman scattering, which shifts photons in wavelength and fills in solar Fraunhofer and telluric absorption lines. I derived the Cabannes and Raman optical properties of N₂ and O₂ (Part I, 2022), built them into a fully polarized, multiple-scattering framework (Part II, 2023), and quantified the forward-model error of treating Rayleigh scattering as elastic (2026).
Coupled surface–atmosphere radiative transfer. Instead of describing vegetation by a simple BRDF, vSmartMOM now treats the canopy as a scattering medium fully coupled to the atmosphere (including the air within the canopy). The canopy is defined by leaf optical properties and leaf angular distributions, with the soil as the lower boundary condition. This links canopy structure and leaf physiology directly to top-of-atmosphere radiances, polarization and SIF. The coupled model took part in RAMI4ATM, the European Commission Joint Research Centre’s first intercomparison of coupled surface–atmosphere radiative transfer models (paper in preparation). An analogous fully coupled ocean–atmosphere treatment is in development.
3D polarized transfer for oblate, inhomogeneous bodies. A semi-analytic, conics-based scheme computes disk-resolved and disk-integrated Stokes vectors for rapidly rotating, oblate brown dwarfs and giant planets. The body is treated as an ellipsoid, and horizontal structure such as patchy clouds and gravity darkening is included pixel by pixel across the disk (Sanghavi & Shporer 2018), later extended to reflected starlight (2021).
2 · High-performance radiative transfer software
Retrievals from hyperspectral and multi-angle polarimetric instruments require forward models that are both accurate and computationally efficient. I developed vSmartMOM, originally written in Fortran and C++ (Sanghavi, Davis & Eldering 2014). Since 2020 it has been rebuilt as the open-source Julia package vSmartMOM.jl — begun with Christian Frankenberg and Schmidt Software Fellow Rupesh Jeyaram (JOSS 2022). Companion packages provide molecular absorption (HITRAN, ExoMol), canopy, ocean and exoplanet optical properties. I lead its scientific development. The code runs on CPUs and GPUs and is used for Earth-observation studies (SIF and greenhouse-gas retrieval biases, Carbon-I) and for the GPU-accelerated HWO radius–albedo simulations described below. See the software page for milestones.
3 · Planetary atmospheres: Earth
From MAX-DOAS and SCIAMACHY aerosol and cloud retrievals, through MISR multi-angle aerosol inversions, to information-content and error analyses for OCO-2/3 and GOSAT (Sanghavi et al. 2020), my Earth-science work addresses the effect of aerosol and cloud scattering on trace-gas retrievals from space and methods to reduce the resulting errors, e.g. polarimetric O₂ A-band cloud sensing (2015) or N₂O as a light-path proxy (Frankenberg et al. 2025).
Raman scattering and solar-induced fluorescence. Inelastic scattering produces spurious SIF of up to 0.35 W m⁻² sr⁻¹ µm⁻¹ over vegetation-free regions, and existing zero-level offsets leave residual biases correlated with surface brightness, elevation and geometry. We introduced a lookup-table correction, based on radiative transfer simulations, that estimates and subtracts the inelastic contribution (Sanghavi et al. 2025, GRL).
Mission leadership: Carbon-I. I am the radiative transfer lead of the Carbon-I team, a NASA Earth System Explorer mission concept for imaging the carbon cycle from space, bringing the polarized, inelastic radiative transfer described above into the mission’s forward modeling.
4 · Planets beyond Earth
Breaking the radius–albedo degeneracy for the Habitable Worlds Observatory. Direct imaging measures how bright a planet appears in reflected starlight, but brightness alone cannot tell whether a planet is large and dark or small and bright. For non-transiting planets — including HWO’s prime targets — this degeneracy limits characterization. In Sanghavi, West & Chen (2026) we construct radius-free ultraviolet observables from multi-epoch observations — the normalized 400 nm lightcurve shape, UV intensity and polarization colors, and the degree of linear polarization. Ratios cancel the radius. The approach uses the 360–400 nm window, where Rayleigh scattering is strong, molecular absorption is weak and bright surfaces such as snow or clouds are nearly colorless, so the atmosphere and surface can be described by few parameters. The observables then constrain the atmospheric column, the surface reflectivity and, if unknown, the orbital phases before the radius is inferred.
For a six-phase sequence, spectropolarimetry gives median radius errors of 9.5 %, 3.3 % and 0.45 % at S/N = 5, 20 and 100 with known phases, and 14 %, 3.2 % and 0.47 % with unknown phases. Removing polarimetry degrades these results, especially when the inner working angle restricts phase coverage. For solar-twin systems at 6 and 12 pc, the required six-phase campaigns take a few hundred hours of observing time. The study is a proof of concept; mass constraints from astrometry and radial velocities offer a complementary route to the radius.
In plain terms. Picture the Moon moved so far away that it is a single point of light, smaller than one pixel of a camera. We can watch it brighten and dim as it goes around its star, but brightness alone cannot tell us whether we see a large, dark planet or a small, bright one. What we can measure is how its light changes with color and with polarization at several points along the orbit. In near-ultraviolet light the atmosphere and surface of a rocky planet behave simply, so comparing these measurements tells us how reflective the planet is, independently of its size. Once that is known, the brightness gives the size.
Polarization of brown dwarfs. Brown dwarfs are observed in their own thermal emission, mainly in the near infrared, and polarized emission has been observed from several of them. Thermal emission from a spherically symmetric body has no net polarization, so the signal requires an anisotropy: rotational flattening, patchy clouds, bands or other structure. Modeling these effects together in a single body was the motivation for the oblate 3D framework above. It shows that polarization grows with oblateness and inclination, that gravity darkening can amplify it considerably, and that large cloud grains depolarize (Sanghavi & Shporer 2018). A polarized signal therefore does not by itself indicate clouds. It is more informative about rotational deformation, spin orientation and latitudinal structure.
Spectropolarimetry of brown dwarfs. Coupling the 3D conics framework to molecular opacities gives J, H, K spectropolarimetric simulations as a function of internal energy, surface gravity, grain size and cloud depth. T-dwarf spectra are fit more easily with cloudless atmospheres or high clouds, whereas L-dwarf spectra require deep clouds. Polarimetry provides information complementary to photometry; at current instrument sensitivities it is most informative for high clouds with small grains (Sanghavi & West 2019).
Clouds in reflected light. Widely used approximations — two-term Henyey–Greenstein, or the Henyey–Greenstein–Rayleigh composite — blur the phase-dependent features of exoplanet lightcurves, costing 10–39 % of sensitivity to atmospheric parameters and making clouds appear as polarizing as Rayleigh scatterers regardless of droplet size (Sanghavi, West & Jiang 2021). The Rayleigh-like polarization term gives every cloud scattering event a high polarizability, which, unlike real Rayleigh scattering, does not decrease toward the near infrared. Mie calculations show that cloud particles are depolarizing regardless of chemical species. The expectation that clouds produce strong polarization stems largely from this approximation.