Point source | EPFL Graph Search

A point source is a single identifiable localised source of something. A point source has negligible extent, distinguishing it from other source geometries. Sources are called point sources because in mathematical modeling, these sources can usually be approximated as a mathematical point to simplify analysis. The actual source need not be physically small, if its size is negligible relative to other length scales in the problem. For example, in astronomy, stars are routinely treated as point sources, even though they are in actuality much larger than the Earth. In three dimensions, the density of something leaving a point source decreases in proportion to the inverse square of the distance from the source, if the distribution is isotropic, and there is no absorption or other loss. Mathematics In mathematics, a point source is a singularity from which flux or flow is emanating. Although singularities such as this do not exist in the observable universe, mathematical poin

Localization of point sources of PCBs pollution in rivers using LDPE passive samplers, a Swiss case study

Luiz Felippe De Alencastro, Nancy El Ghorayeb, Nicolas Estoppey, Julien Omlin

Due to its situation of “Europe’s water reservoir”, Switzerland has a particular responsibility towards downstream countries. It must ensure an optimal quality of its surface waters, following thus the example of the EU members which have to reach by 2015 the good status for surface water set by the Water Frame Directive. In order to achieve that goal, there is a need to localize sources of pollution to reduce emissions to water. In this study, an investigation was conduct along the “Venoge” River to localize potential sources of PCBs pollution contaminating it. A simple, rapid and easy method using passive samplers of Low-density polyethylene (LDPE), known to adsorb PCBs, has been established. It is therefore an accessible technology and requires no power source or specialized equipment in situ. The passive samplers were placed over 2 iron bars at each measurement site. They were fully immersed during the duration of the experiment, typically 4 to 6 weeks. Once out, PCBs from the LDPE samplers were extracted using dichloromethane, purified by adsorption chromatography and analysed by gas chromatography (GC-ECD). Results show the great interest of LDPE passive samplers in the localization of sources of contamination in rivers. One industrial site, a former landfill and a wastewater treatment plant receiving waters from an industrial zone were pointed out as sources of PCBs. On-going experiments are carried out to compare LDPE with silicone in the “Venoge” River in order to determine the most appropriate polymer for point sources localization. For both polymers, the uptake kinetics of PCBs present in the river and the release kinetics of PRCs spiked on the samplers before exposure are studied.

2012

Resolution and Complex Deconvolution in Holographic Microscopy

Yann Jérôme Michel Pascal Cotte

Interest in high resolution imaging techniques has recently multiplied due to their importance in bio-medical research. Quantitative phase measurements by holographic microscopy is an extraordinary tool to gain new understanding of transparent biological samples. The extremely high demand on resolution well beyond the diffraction limit, however, sets new benchmarks for imaging techniques. Digital Holographic Microscopy is an interferometric method providing access to the complex wave front. Its capacity to image amplitude and quantitative phase simultaneously makes it an attractive research tool in many fields of biological research. It is on the verge of becoming an appealing alternative to classical fluorescence microscopy. For intensity-based microscopy, however, super-resolution methods are well established. In this thesis, approaches to unleash resolution for phase imaging techniques are explored. Based on truncated inverse filtering, a theory for deconvolution of complex fields is developed. It is a post-processing method that does not require any additional optics in the holographic microscopy setup. Gain in resolution arises by accessing the object's complex field – containing the information encoded in the phase – and deconvolving it with the characteristic coherent transfer function (CTF). By efficient harvest of a diffraction limited bandpass, complex deconvolution is demonstrated to exceed the coherent resolution limit. A novel method, called a complex point source, serves to characterize the holographic microscopy system. It consists of a coherently illuminated nano-metric hole, located on a conventional microscope slide, most common in bio-microscopy. A thin opaque film is directly evaporated on the slide and the circular sub-wavelength structures are drilled with a focused ion beam. Theoretical as well as practical work on transmission properties of apertures confirms the advantageous signal-to-noise yield of proposed method. More abstractly, the thus gained experimental amplitude point spread function is demonstrated to be suitable for experimental CTF reconstruction. Herefrom, experimental parameters are extracted and introduced into scalar and vectorial Debye theory, called synthetic CTF, adaptable to realistic imaging conditions. Also, it allows to study the role of noise in the context of complex field deconvolution. The resolution power of holographic microscopy systems is systematically examined with pairs of nano-metric apertures separated by sub-resolution pitches. Theory of information content is elaborated depending on different experimental configurations. Resolution extends beyond classical Abbe's limit by introducing spatially a varying phase into the illumination beam of a phase imaging system. In a last step, the novel deconvolution method is generalized to three-dimensional image processing of complex fields. By combining scattering theory and signal processing, the method is demonstrated to yield the reconstruction of the scattering object field under non-design microscope objective imaging conditions. The suggested technique is best suited for an implementation in high-resolution diffraction tomography based on sample and/or illumination rotation.

EPFL2012

Deconvolution of Gaussian Random Fields using the Graph Fourier Transform

Matthieu Martin Jean-André Simeoni

Real-life acquisition systems are fundamentally limited in their ability to reproduce point sources. For example, a point source object, a star say, observed with an optical telescope is blurred by the imperfect lenses composing the system. Mathematically, the point sources are convolved with a device-specific kernel. This kernel, which depends only on the characteristics of the acquisition system, can to a certain extent be designed so as to minimise the effect of the convolution. But in many applications careful design of the sensing device is not good enough, and a proper deconvolution step is needed. In this paper, we propose an efficient deconvolution algorithm for point source Gaussian random fields as sensed by phased arrays. The algorithm first obtains a continuous least-squares estimate of the random field’s second order moment. The procedure is then in two subsequent steps, decoupling sources localisation and intensity recovery. First, we sample the continuous estimate at a high enough resolution and use the covariance function to construct a weighted graph. We then define a signal on this graph by assigning to each of the sample locations in the field their corresponding intensity (variance of the field at this location). The Graph Fourier Transform (GFT) is then used in order to filter out the convolution artifacts within the estimate. Candidate locations of the sources can then be identified with local maxima of the filtered estimate. From these locations a deconvolution problem is solved by means of weighted linear regression and the intensities of the sources within the field recovered. Finally, a multi-scale approach based on the filtering of the leading eigenvalues of the covariance operator is discussed, and its benefits in terms of efficiency and accuracy are highlighted.

2016

Resolution and Complex Deconvolution in Holographic Microscopy

Yann Jérôme Michel Pascal Cotte

EPFL2012