Phase (onde) | EPFL Graph Search

En physique, la d'une fonction périodique est l'argument de cette fonction, noté souvent \Phi. Elle est définie modulo la période, c'est-à-dire à un nombre entier de périodes près. Par exemple, la hauteur d'un pendule oscillant est une fonction sinusoïdale de la forme f(t) = A \sin(\omega t + \alpha). La phase \Phi vérifie alors \Phi (t)= \omega t + \alpha à 2 \pi près, avec \omega la pulsation et \alpha la phase initiale. Présentation La phase est une grandeur sans dimension. Cependant, dans le cas d'un signal sinusoïdal, on attribue l'unité radian ou degré à la phase. En effet, on peut ramener le phénomène périodique à une rotation fictive sur le cercle unité et interpréter dans ce cas la phase en tant qu'angle. Par abus, on attribue parfois une dimension de longueur ou de temps à la phase, ce qui en pratique ne change rien. Cela peut néanmoins engendrer des incohérences d'inho

Extension of the fringe projection method to large objects for shape and deformation measurement

Anne-Isabelle Desmangles

There is a real need for methods to allow the measurement of the form and deformation of large objects. For example, for maintenance and production costs as well as for security. Even though there are many methods of measuring the form and deformation of small objects (up to 1 m2), currently none of them are able to quickly measure larger objects (i.e. at a large number of points at the same time). Among the existing techniques, the fringe projection seem to us one of the most adequate to deal with these kinds of problems. In its classical form, this technique is very simple, since it consists of projecting equispaced rectilinear fringes on an object from one direction and of observing the scene from another with a CCD camera. The displacement of the fringes distorted by the object contains the desired shape information. The phase shifting and phase unwrapping procedures allow automatic, rapid acquisition of an optical print (called a "phase map") of the object. In the case of small objects (the classical approach), the extraction of the shape information from this optical print is quite simple. A phase map of the object as well as a phase map of a reference surface plane is acquired. Then, basically, the desired shape information is obtained by subtracting these two maps from each other. For larger objects, this approach is not possible anymore. On the one hand, such a reference surface does not exist. On the other hand, in order to measure the whole surface at once, it must be fully illuminated. This suggests the use of interferometrically generated fringes, in divergent beams, which implies that the fringes are no longer rectilinear and equispaced. For these reasons the classical approach is no longer valid. It is therefore necessary to find another method to be able to extract the object shape information from the optical print. In the frame of this work, three methods have been conceived and developed in order to extract the shape information of large objects from their optical print. The first two methods proposed here are dedicated to quasi-planar objects that are parallel to the imaging plane of the camera. These assumptions allow the simplification of the equations describing the system to "mimic" the classical approach, where the desired shape information is proportional to the difference between the measured and reference phase maps. The next step is to determine the parameters of the projection head. The first method is based on two coupled interferometers (of the Mach-Zehnder and Young's type), and the other uses least squares calculations with a small number of calibration points, aiming at minimizing the difference between the theoretical and measured phase at more than four calibration points. Finally, the desired reference phase map is artificially generated. These two techniques are simple but their application is limited only to planar object parallel to the imaging plane of the camera. In the last technique, which is based on a new approach, the system is described by the interferometric equation and the central perspective equations. Solving them simultaneously allows the determination of the coordinates (x,y,z) of all measured points from the optical print. This approach is general and offers the advantage of allowing the measurement of the shape and deformation of large objects. In addition, it also makes the system more flexible. In this report, these different techniques are presented and their feasibility is shown; examples of measurements give a first evaluation of their precision, and assess the new possibilities offered in terms of object shape and configuration of the measurement system, as well as their limitations. Finally, the three methods are compared one to another and advice for their optimization is proposed.

EPFL2003

Amplitude and phase reconstruction for Low-Energy Electron Holography of individual proteins

Hannah Julia Ochner

Single-molecule imaging methods are of importance in structural biology, and specifically in the imaging of proteins, since they can elucidate conformational variability and structural changes that might be lost in imaging methods relying on averaging processes. Low-energy electron holography (LEEH) is a promising technique for imaging individual proteins with negligible radiation damage, which can be combined with a sample preparation process by native electrospray ion beam deposition (native ES-IBD) ensuring the creation of chemically pure samples suitable for holographic imaging.The central step in the analysis of data measured by LEEH is the numerical reconstruction of the object from the experimentally acquired holograms.Full information about the imaged object consists of both amplitude and phase information imprinted on the scattered wave during the interaction of the electron beam with the molecule and encoded in the hologram created by the interference of the scattered wave and the transmitted incident wave. A propagation-based algorithm with the goal of reconstructing the wave field in the plane of the object is presented and applied to holograms of individual proteins prepared by ES-IBD and measured with a low-energy electron holography microscope. The information retrieved from the reconstruction of the amplitude distribution in the object plane is discussed by analysing holograms of antibodies, demonstrating that the inherent conformational variability of these molecules can be mapped by LEEH. The influence of the sample preparation process on the surface conformations is tracked by tuning the landing energy of the proteins during deposition.To complement the amplitude data, an iterative phase retrieval algorithm is implemented to reconstruct the phase distribution in the object plane along with the amplitude distribution. The algorithm's performance and robustness is thoroughly evaluated and simulations regarding multiple scattering effects and element-dependent variations in scattering strength are carried out to provide a reference for the interpretation of phase data retrieved from experimentally acquired holograms. The iterative phase retrieval algorithm is then applied to protein data, indicating that both molecular density and charges can be related to features in the phase reconstructions, while the presence of metals does not correlate with specific phase signals at the current resolution obtainable from the experimental data.Since proteins are inherently three-dimensional, approaches towards three-dimensional reconstruction schemes are discussed, which will be the focus of future work.

EPFL2022