Interpretation of gravity data warrants uncertainty estimation because of its inherent nonuniqueness. Although the uncertainties in model parameters cannot be completely reduced, they can aid in the meaningful interpretation of results. Here we have employed a simulated annealing (SA)–based technique in the inversion of gravity data to derive multilayered earth models consisting of two and three dimensional bodies. In our approach, we assume that the density contrast is known, and we solve for the coordinates or shapes of the causative bodies, resulting in a nonlinear inverse problem. We attempt to sample the model space extensively so as to estimate several equally likely models. We then use all the models sampled by SA to construct an approximate, marginal posterior probability density function (PPD) in model space and several orders of moments. The correlation matrix clearly shows the interdependence of different model parameters and the corresponding trade-offs. Such correlation plots are used to study the effect of a priori information in reducing the uncertainty in the solutions. We also investigate the use of derivative information to obtain better depth resolution and to reduce underlying uncertainties. We applied the technique on two synthetic data sets and an airborne-gravity data set collected over Lake Vostok, East Antarctica, for which a priori constraints were derived from available seismic and radar profiles. The inversion results produced depths of the lake in the survey area along with the thickness of sediments. The resulting uncertainties are interpreted in terms of the experimental geometry and data error.

Total internal reflection fluorescence (TIRF) microscopy and its variants are key technologies for visualizing the dynamics of single molecules or organelles in live cells. Yet, truely quantitative TIRF remains problematic. One unknown hampering the interpretation of evanescent-wave excited fluorescence intensities is the undetermined cell refractive index (RI). Here, we use a combination of TIRF excitation and supercritical angle fluorescence emission detection to directly measure the average RI in the 'footprint' region of the cell, during imaging. Our RI measurement is based on the determination on a back-focal plane image of the critical angle separating supercritical and undercritial fluorescence emission components. We validate our method by imaging mouse embryonic fibroblasts. By targeting various dyes and fluorescent-protein chimerae to vesicles, the plasma membrane as well as mitochondria and the ER, we demonstrate local RI measurements with subcellular resolution on a standard TIRF microscope with a removable Bertrand lens as the only modification. Our technique has important applications for imaging axial vesicle dynamics, mitochondrial energy state or detecting cancer cells.Total internal fluorescence (TIRF) has evolved from an ex-pert technique to a routine contrast mode used for singlemolecule and single-organelle tracking at or near the basal plasma membrane of cells adherent to a glass substrate [1]. PALM/STORM localization-based super-resolution micro-scopies have further broadened the range of TIRF applica-tions. The emission counterpart of TIRF, supercritical angle fluorescence (SAF) [2] is increasingly being used for sur-face microscopies [3, 4 , 5]. For TIRF, the presence of a re-fractive-index (RI) boundary between the glass substrate (of index n 2 ) and the aqueous sample (n 1 ) results in the emergence of an evanescent wave that provides excitation-light confinement. In SAF microscopies, the otherwise un-detected evanescent emission component of surface-proxi-mal fluorophores couples to the interface where it becomes propagative and detectable in the far field, provided the ob-jective has a sufficiently large numerical aperture (NA= n 2 sin NA , with  NA > c ). The critical angles at the excitation or emission wavelength ,  c =asin[n 2 ()/n 1 ()], the axial decay length =/[4(n 2 2 sin-n 1 2 ) 1/2 ] of the evanescent-wave intensity and the dipole radiation pattern are all modi-fied by the local sample RI n 1 (x,y), which is generally un-determined. Knowledge, even of the average near-mem-brane RI, n 1 , for the very cell under study, would greatly enhance our capacity to chose appropriate incidence and detection angles, to better understand and eliminate image imperfections and to interpret TIRF and SAF in quantita-tive terms, e.g., for axial profilometry, size-or concentra-tion measurements, or for axial single-vesicle tracking. Hilbert-phase microscopy [6], digital confocal microscopy (DCM) [7 , 8] and full-field optical coherence tomography (OCT) [9] all allow RI m...