For a solar adaptive optics system equipped with a Shack-Hartmann wavefront sensor, the local wavefront slopes are measured from the displacements of the images produced by the sub-pupils of the sensor with respect to a given reference image. Measuring these displacements is challenging because of the very low contrast (at most a few percent) of the structures at the Sun surface. Additional difficulties arise from the fact that these structures evolve in time and are slightly distorted in each sub-image. In this contribution, we describe a novel approach to process the images of a solar wavefront sensor which jointly estimates the wavefront slopes, their noise covariance matrix, and the reference image. Spatio-temporal constraints are imposed on the reference image to regularize the problem and stabilize the global tip-tilt. Automatically tuned correction factors are introduced to account for the scintillation and the local distortions. Our method yields a sufficient statistic which enables an optimal wavefront reconstruction. We propose an alternating strategy to quickly solve the joint estimation problem. Special attention has been paid to make the numerical algorithm usable in real-time. Our method is implemented in the adaptive optics system of the THEMIS solar telescope equipped with a 10 × 10 Shack-Hartmann wavefront sensor delivering 400 × 400 pixel images at 1kHz. On a single CPU core, the Julia version of our algorithm provides the measurements with 90μs of latency after the image acquisition and takes an additional 200µs to update the reference image.
Many blind deconvolution algorithms have been proposed for image deblurring when the instrumental point spread function (PSF) is unknown. Blind deconvolution can be stated as an inverse problem whose unknowns are the object of interest and the PSF. In that case, the direct model is bilinear and has an intrinsic scaling degeneracy: scaling one of the components can be compensated by inversely scaling the other one. Provided that homogeneous regularization functions are chosen for the object and for the PSF, the scaling degeneracy of the direct model can be exploited to reduce the number of hyper-parameters in the problem. Using this property, we propose an instance of a blind deconvolution algorithm that amounts to alternately estimating and scaling the two components of the bilinear model. Our algorithm is insensitive to the scaling of the initial estimate of the component (PSF or object) used to start the iterations. We show that this yields much faster convergence and, in practice, reduces the odds of being trapped in a bad local minimum. These features make our algorithm suitable for being embedded into a simple procedure to automatically tune the remaining hyper-parameter(s) and obtain a fully unsupervised method. We also propose a homogeneous version of an edge-preserving regularization to be used by our algorithm. Using Stein's Unbiased Risk Estimator (SURE) as a criterion to automatically tune the hyper-parameter(s), we assess the advantages of our algorithm for empirical astronomical images compared to other methods.
The FRiM fractal operator belongs to a family of operators, called ASAP, defined by an ordered selection of nearest neighbors. This generalization provides means to improve upon the good properties of FRiM. We propose a fast algorithm to build an ASAP operator mimicking the fractal structure of FRiM for pupils of any size and geometry and to learn the sparse coefficients from empirical data. We empirically show the good approximation by ASAP of correlated statistics and the benefits of ASAP for solving phase restoration problems.
To better understand the phenomena which take place during the formation and evolution of substellar objects, it is necessary to have access to their spectra. For that purpose, the SPHERE-IRDIS long-slit spectroscopy mode, allied with extreme adaptive optics and coronagraphy, has been designed to spectrally characterize substellar objects in the near-infrared (J, H and K bands). Residual aberrations are however responsible for stellar leaks in the form of dispersed speckles that are much brighter than the spectrum of the faint companion. Post-processing methods are thus required to extract the companion spectrum. Most existing methods consist in first subtracting the stellar contribution from the data and then measuring the companion spectrum in the residuals. We are developing a novel approach, named EXOSPEC and based on the inverse problems framework, which jointly estimates the two contributions; that of the star and that of the companion. Exospec exploits the differences of behavior of their spatio-spectral distributions in the data in order to disentangle them. The parameters of the instrumental model, which is a critical part of the approach, are refined by means of self-calibration directly from the science data. Other parameters of the problem are automatically tuned, leading to a fully unsupervised method. Compared to current methods, EXOSPEC is able to extract companion spectra with less contamination by the stellar leaks and succeeds in harder cases (e.g., closer to the mask). The benefits of our approach is demonstrated on real datasets.
We recently proposed REXPACO, an algorithm for imaging circumstellar environments from high-contrast angular differential imaging (ADI) data. In the context of high-contrast imaging where the signal of interest is largely dominated by a nuisance term due to the stellar light leakages and the noise, our algorithm amounts to jointly estimating the object of interest and the statistics (mean and covariance matrix) of the nuisance component. In this contribution, we first extend the REXPACO algorithm by refining the statistical model of the nuisance component it embeds. Capitalizing on the improved robustness of this new method named robust REXPACO, we then show how it can be modified to deal with angular plus spectral differential imaging (ASDI) datasets. We apply our methods on several ADI and ASDI datasets from the IRDIS and IFS imagers of the VLT/SPHERE instrument and we show that the proposed algorithms significantly reduce the typical artifacts produced by state-of-the-art algorithms. By also taking into account the instrumental point spread function (PSF), our algorithms yield a deblurred estimate of the object of interest without the artifacts observed with other methods.
We present a new method to achieve digital autofocus in holography. This method relies on the insertion of calibrated beads into the studied sample. Reconstructing the position and the radius of the beads using Inverse Problems Approach, based on Mie Model, makes it possible to accurately locate the slide on which the sampled is placed. Numerical focusing can then be performed using the standard backpropagation method or regularized reconstruction. Because the reconstruction plane can be chosen objectively with respect to the position of the slide, this numerical autofocus is reproducible whatever is the type of the observed biological sample.
In this paper, we propose to present the general ingredients involved in an inverse problems methodology dedicated to the reconstruction of in-line holograms, and compare it with the classical Gercherg-Saxton or Fienup alternating projections strategies for phase retrieval [1,2,3]. An inverse approach [4,5] consists in retrieving an optimal solution to a reconstruction/estimation problem from a dataset, knowing an approximate model of its formation process. The problem is generally formulated as an optimization problem that aims at fitting the model to the data, while favoring a priori knowledge on the targeted information using regularizations and constraints. An appropriate resolution method has to be designed, based on a convex optimization framework. We develop the end-to-end inverse problems methodology on a case-study : the reconstruction of an in-line hologram of a collection of weakly dephasing objects. This simple problem allows us to explain current physical considerations (type of objects, diffraction physics) to derive the appropriate model, and to present classical constraints and regularizations that can be used in image reconstruction. Starting from these ingredients, we introduce a simple yet efficient method to solve this inverse problem, belonging to the class of proximal gradient algorithms [6,7]. A special focus is made on the connections between the numerous alternating projections strategies derived from Fienup’s phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup’s algorithm as iterates of a proximal gradient descent for a particular cost function is given. We discuss the advantages provided by the inverse problems methodology. We illustrate both strategies on reconstructions from simulated and experimental holograms of micrometric beads. The results show that the transition from alternating projection techniques to the inverse problems formulation is straightforward and advantageous.
In in-line digital holography, the background of the recorded images is sometimes much higher than the signal of interest. It can originates, for example, from the diffraction of dusts or fringes coming from multiple reflexions in the optical components. It is often correlated, nonstationary and not constant over time. Detecting a weak signal superimposed over such a background is challenging. Detection of the pattern then requires a statistical modeling of the background. In this work, spatial correlations are locally estimated based on several background images. A fast algorithm that computes detection maps is derived. The proposed approach is evaluated on images obtained from experimental data recorded with a holographic microscope.
Digital holographic microscopy can image both absorbing and translucent objects. Due to the presence of twin-images and out-of-focus objects, the task of segmenting the objects from a back-propagated hologram is challenging. This paper investigates the use of deep neural networks to combine the real and imaginary parts of the back-propagated wave and produce a segmentation. The network, trained with pairs of back-propagated simulated holograms and ground truth segmentations, is shown to perform well even in the case of a mismatch between the defocus distance of the holograms used during the training step and the actual defocus distance of the holograms at test time.
KEYWORDS: Adaptive optics, Wavefront sensors, Linear filtering, Deformable mirrors, Wavefronts, Scintillation, Data modeling, Image resolution, Actuators, Control systems
Themis is a 90 cm solar telescope which undergoes a rejuvenation of its scientific instruments. In particular, it is about to be equipped with an adaptive optics (AO) system with a bandwidth of at least 1 kHz and featuring a 97 actuator deformable mirror and 10×10 Shack-Hartmann wavefront sensor. Nowadays, the computational power required by such a system can be provided by current multi-core CPU. We have therefore implemented from scratch the real-time control system in pure software using Julia,1 a new language for technical computations, and running on Linux OS. Our main motivation was to be able to exploit new advances in wavefront sensing and adaptive optics control.
With a computational cost comparable to state-of-the-art but sub-optimal methods used in solar AO, our wavefront sensing algorithm estimates the local slopes and their covariances following a maximum likelihood registration method.
Themis AO system has a modest size but can be used to assert the benefits of maximum a posteriori (MAP) wavefront sensing and control,2, 3 of accounting of the covariances of the measure and of the temporal correlation of the turbulent wavefront.
KEYWORDS: Exoplanets, Signal to noise ratio, Statistical analysis, Stars, Detection and tracking algorithms, Exoplanetary science, Point spread functions, Binary data, Spectrographs, Imaging systems
The search for new exoplanets by direct imaging is a very active research topic in astronomy. The detection is particularly challenging because of the very high contrast between the host star and the companions. They thus remain hidden by a nonstationary background displaying strong spatial correlations. We propose a new algorithm named PACO (for PAtch COvariances) for reduction of differential imaging datasets. Contrary to existing approaches, we model the background correlations using a local Gaussian distribution that locally captures the spatial correlations at the scale of a patch of a few tens of pixels. The decision in favor of the presence or the absence of an exoplanet in then performed by a binary hypothesis test. The method is completely parameter-free and produces both stationary and statistically grounded detection maps so that the false alarm rate, the probability of detection and the contrast can be directly assessed without post-processing and/or Monte-Carlo simulations. We describe in a forthcoming paper its detailed principle and implementation. In this paper, we recall the principle of the PACO algorithm and we give new illustrations of its benefits in terms of detection capabilities on datasets from the VLT/SPHERE-IRDIS instrument. We also apply our algorithm on multi-spectral datasets from the VLT/SPHERE-IFS spectrograph. The performance of PACO is compared to state-of-the-art algorithms such as TLOCI and KLIP-PCA.
Phase retrieval reconstruction is a central problem in digital holography, with various applications in microscopy, biomedical imaging, fluid mechanics. In an in-line configuration, the particular difficulty is the non-linear relation between the object phase and the recorded intensity of the holograms, leading to high indeterminations in the reconstructed phase. Thus, only efficient constraints and a priori information, combined with a finer model taking into account the non-linear behaviour of image formation, will allow to get a relevant and quantitative phase reconstruction. Inverse problems approaches are well suited to address these issues, only requiring a direct model of image formation and allowing the injection of priors and constraints on the objects to reconstruct, and hence offer good warranties on the optimality of the expected solution. In this context, following our previous works in digital in-line holography, we propose a regularized reconstruction method that includes several physicallygrounded constraints such as bounds on transmittance values, maximum/minimum phase, spatial smoothness or the absence of any object in parts of the field of view. To solve the non-convex and non-smooth optimization problem induced by our modeling, a variable splitting strategy is applied and the closed-form solution of the sub-problem (the so-called proximal operator) is derived. The resulting algorithm is efficient and is shown to lead to quantitative phase estimation of micrometric objects on reconstructions of in-line holograms simulated with advanced models using Mie theory. Then we discuss the quality of reconstructions from experimental inline holograms obtained from two different applications of in-line digital holography: tracking of an evaporating droplet (size~100μm) and microscopy of bacterias (size~1μm). The reconstruction algorithm and the results presented in this proceeding have been initially published in [Jolivet et al., 2018].1
Lensless color microscopy is a recent 3D quantitative imaging method allowing to retrieve physical parameters characterizing microscopic objects spread in a volume. The main advantages of this technique are related to its simplicity, compactness, low sensitivity of the setup to vibrations and the possibility to accurately characterize objects. The cost-effectiveness of the method can be further increased using low-end laser diodes as coherent sources and CMOS color sensor equipped with a Bayer filter array. However, the central wavelength delivered by this type of laser is generally known only with a limited precision and can evolve because of its dependence on temperature and power supply voltage. In addition, Bayer-type filters of conventional color sensors are not very selective, resulting in spectral mixing (crosstalk phenomenon) of signals from each color channel. Ignoring these phenomena leads to significant errors in holographic reconstructions. We have proposed a maximum likelihood estimation method to calibrate the setup (central wavelength of the laser sources and spectral mixing introduced by the Bayer filters) using spherical objects naturally present in the field of view or added (calibration objects). This calibration method provides accurate estimates of the wavelengths and of the crosstalk, with an uncertainty comparable to that of a high-resolution spectrometer. To perform the image reconstruction from color holograms following the self-calibration of the setup, we describe a regularized inversion method that includes a linear hologram formation model, sparsity constraints and an edge-preserving regularization. We show on holograms of calibrated objects that the self-calibration of the setup leads to an improvement of the reconstructions.
KEYWORDS: Sensors, Planets, Optical spheres, Gemini Planet Imager, Surface conduction electron emitter displays, Point spread functions, Data modeling, Signal detection, Fourier transforms, Signal to noise ratio
Exo-planet detection is a signal processing problem that can be addressed by several detection approaches. This paper provides a review of methods from detection theory that can be applied to detect exo-planets in coronographic images such as those provided by SPHERE and GPI. In a first part, we recall the basics of signal detection and describe how to derive a fast and robust detection criterion based on a heavy tail model that can account for outliers in the residuals. In a second part, we derive detectors that handle jointly several wavelengths and exposures and focus on an approach that prevents from interpolating the data, thereby preserving the statistics of the original data.
Most current imaging instruments have a spatially variant point spread function (PSF). An optimal exploitation of these instruments requires to account for this non-stationarity. We review existing models of spatially variant PSF with an emphasis on those which are not only accurate but also fast because getting rid of non-stationary blur can only be done by iterative methods.
A major issue in electron tomography is the misalignment of the projections contributing to the reconstruction. The current alignment techniques currently use fiducial markers such as gold particles. When the use of markers is not possible, the accurate alignment of the projections is a challenge. We describe a new method for the alignment of transmission electron microscopy (TEM) images series without the need of fiducial markers. The proposed approach is composed of two steps. The first step consists of an initial alignment process, which relies on the minimization of a cost function based on robust statistics measuring the similarity of a projection to its previous projections in the series. It reduces strong shifts resulting from the acquisition between successive projections. The second step aligns the projections finely. The issue is formalized as an inverse problem. The pre registered projections are used to initialize an iterative alignment-refinement process which alternates between (i) volume reconstructions and (ii) registrations of measured projections onto simulated projections computed from the volume reconstructed in (i). The accuracy of our method is very satisfying; we illustrate it on simulated data and real projections of different zeolite supports catalyst.
KEYWORDS: Holograms, Digital holography, Diffraction, 3D modeling, 3D image reconstruction, Sensors, Inverse problems, 3D image processing, Reconstruction algorithms, Holography
Digital holography (DH) is being increasingly used for its time-resolved three-dimensional (3-D) imaging capabilities.
A 3-D volume can be numerically reconstructed from a single 2-D hologram. Applications of DH range from
experimental mechanics, biology, and fluid dynamics. Improvement and characterization of the 3-D reconstruction
algorithms is a current issue. Over the past decade, numerous algorithms for the analysis of holograms have
been proposed. They are mostly based on a common approach to hologram processing: digital reconstruction
based on the simulation of hologram diffraction. They suffer from artifacts intrinsic to holography: twin-image
contamination of the reconstructed images, image distortions for objects located close to the hologram borders.
The analysis of the reconstructed planes is therefore limited by these defects. In contrast to this approach, the
inverse problems perspective does not transform the hologram but performs object detection and location by
matching a model of the hologram. Information is thus extracted from the hologram in an optimal way, leading
to two essential results: an improvement of the axial accuracy and the capability to extend the reconstructed
field beyond the physical limit of the sensor size (out-of-field reconstruction). These improvements come at the
cost of an increase of the computational load compared to (typically non iterative) classical approaches.
In-line digital holography conciles the applicative interest of a simple optical set-up with the speed, low cost and potential of digital reconstruction. We address the twin-image problem that arises in holography due to the lack of phase information in intensity measurements. This problem is of great importance in in-line holography where spatial elimination of the twin-image cannot be carried out as in off-axis holography. Applications in digital holography of particle fields greatly depend on its suppression to reach greater particle concentrations, keeping a sufficient signal to noise ratio in reconstructed images. We describe in this paper methods to improve numerically the reconstructed images by twin-image reduction.
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