Abstract In multispectral digital in-line holographic microscopy (DIHM), aberrations of the optical system affect the repeatability of the reconstruction of transmittance, phase and morphology of the objects of interest. Here we address this issue first by model fitting calibration using transparent beads inserted in the sample. This step estimates the aberrations of the optical system as a function of the lateral position in the field of view and at each wavelength. Second, we use a regularized inverse problem approach (IPA) to reconstruct the transmittance and phase of objects of interest. Our method accounts for shift-variant chromatic and geometrical aberrations in the forward model. The multi-wavelength holograms are jointly reconstructed by favouring the colocalization of the object edges. The method is applied to the case of bacteria imaging in Gram-stained blood smears. It shows our methodology evaluates aberrations with good repeatability. This improves the repeatability of the reconstructions and delivers more contrasted spectral signatures in transmittance and phase, which could benefit applications of microscopy, such as the analysis and classification of stained bacteria.
In this paper we present a general method for multichannel image restoration based on regularized χ2. We introduce separable regularizations that account for the dynamics of the model and take advantage of the continuities present in the data, leaving only two hyper-parameters to tune. We illustrate a practical implementation of this method in the context of host galaxy subtraction for the Nearby SuperNova Factory (SNfactory). We show that the image restoration obtained fulfils the stringent requirements on bias and photometricity needed by this programme. The reconstruction yields sub-per cent integrated residuals in all the synthetic filters considered both on real and simulated data. Even though our implementation is tied to the SNfactory data, the method translates to any hyper-spectral data. As such, it is of direct relevance to several new generation instruments like MUSE. Also, this technique could be applied to multiband astronomical imaging for which image reconstruction is important, for example, to increase image resolution for weak-lensing surveys.
SUMMARY Inverse problems occur in many fields of geophysics, wherein surface observations are used to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness inherent in these problems, a standard strategy is to incorporate a priori information regarding the unknown model. Sometimes a solution is obtained by imposing that the inverted model remains close to a reference model and with smooth lateral variations (e.g. a correlation length or a minimal wavelength are imposed). This approach forbids the presence of strong gradients or discontinuities in the recovered model. Admittedly, discontinuities, such as interfaces between layers, or shapes of geological provinces or of geological objects such as slabs can be a priori imposed or even suggested by the data themselves. This is however limited to a small set of possible constraints. For example, it would be very challenging and computationally expensive to perform a tomographic inversion where the subducting slabs would have possible top discontinuities with unknown shapes. The problem seems formidable because one cannot even imagine how to sample the prior space: is each specific slab continuous or broken into different portions having their own interfaces? No continuous set of parameters seems to describe all the possible interfaces that we could consider. To circumvent these questions, we propose to train a Generative Adversarial neural Network (GAN) to generate models from a geologically plausible prior distribution obtained from geodynamic simulations. In a Bayesian framework, a Markov chain Monte Carlo algorithm is used to sample the low-dimensional model space depicting the ensemble of potential geological models. This enables the integration of intricate a priori information, parametrized within a low-dimensional model space conducive to efficient sampling. The application of this approach is demonstrated in the context of a downscaling problem, where the objective is to infer small-scale geological structures from a smooth seismic tomographic image.
Tight relationships exist in the local universe between the central stellar properties of galaxies and the mass of their supermassive black hole. These suggest galaxies and black holes co-evolve, with the main regulation mechanism being energetic feedback from accretion onto the black hole during its quasar phase. A crucial question is how the relationship between black holes and galaxies evolves with time; a key epoch to probe this relationship is at the peaks of star formation and black hole growth 8-12 billion years ago (redshifts 1-3). Here we report a dynamical measurement of the mass of the black hole in a luminous quasar at a redshift of 2, with a look back time of 11 billion years, by spatially resolving the broad line region. We detect a 40 micro-arcsecond (0.31 pc) spatial offset between the red and blue photocenters of the H$\alpha$ line that traces the velocity gradient of a rotating broad line region. The flux and differential phase spectra are well reproduced by a thick, moderately inclined disk of gas clouds within the sphere of influence of a central black hole with a mass of 3.2x10$^{8}$ solar masses. Molecular gas data reveal a dynamical mass for the host galaxy of 6x10$^{11}$ solar masses, which indicates an under-massive black hole accreting at a super-Eddington rate. This suggests a host galaxy that grew faster than the supermassive black hole, indicating a delay between galaxy and black hole formation for some systems.
