Holography

Summary

Holography is a technique that enables a wavefront to be recorded and later re-constructed. Holography is best known as a method of generating real , but it also has a wide range of other applications. In principle, it is possible to make a hologram for any type of wave. A hologram is made by superimposing a second wavefront (normally called the reference beam) on the wavefront of interest, thereby generating an interference pattern which is recorded on a physical medium. When only the second wavefront illuminates the interference pattern, it is diffracted to recreate the original wavefront. Holograms can also be computer-generated by modelling the two wavefronts and adding them together digitally. The resulting digital image is then printed onto a suitable mask or film and illuminated by a suitable source to reconstruct the wavefront of interest. Overview and history The Hungarian-British physicist Dennis Gabor (in Hungarian: Gábor Dénes) was awarded the Nobel Prize i

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https://en.wikipedia.org/wiki/Holography

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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

Numerical reconstruction of digital holograms

Etienne Cuche

This thesis presents a new method for the numerical reconstruction of digital holograms recorded in the off-axis configuration using a CCD camera. The propagation of the reconstructed wave front, from the hologram plane to an observation plane, is achieved by a calculation of scalar diffraction in the Fresnel approximation. An image representing the distribution of intensity at the surface of the object can be obtained by calculating the intensity of the reconstructed wave front. The focusing of this image is performed digitally by adjusting a parameter which defines the distance between the hologram and the observation plane. A second image representing the phase distribution at the surface of the object can be obtained from the same hologram by calculating the argument of the reconstructed wave front. We show here that for getting a phase distribution that represents only the contribution of the object wave, the hologram or the reconstructed wave front must be multiplied by a computed replica of the complex conjugate of the wave used as reference during the recording. For a plane reference wave, the reconstruction of the phase distribution requires a precise adjustment of two digital parameters defining its propagation direction. An application to surface profilometry has demonstrated the quantitative nature of the obtained phase distribution which gives access to the topography of the object. A vertical resolution of λ/100 has been estimated on the basis of a preliminary study. The introduction of a microscope objective along the optical path of the object wave enhances the transverse resolution of the method. In this case, the wave front deformation produced by the microscope objective can be digitally compensated. Under the assumption of a paraboloidal deformation, we show that the wave front curvature can be numerically corrected by multiplication with an array of complex numbers computed using the complex conjugate of the analytical expression describing the defocusing aberration. A preliminary study indicates that the transverse resolution of the method approaches that of classical optical microscopy (diffraction limit). The application of a digital technique of spatial filtering allows for the elimination of the zero order of diffraction and of the twin image. This operation enhances the signal to background ratio. We show also that the influence of diffraction effects associated to the numerical reconstruction method can be reduced by apodization of the hologram aperture. This operation is performed digitally by means of a procedure which defines the transmission of the hologram aperture using a cubic spline interpolation.

EPFL2000

Compact lensless digital holography

Manon Rostykus

Microscopy is of high interest for biology since it allows imaging features that are too small to be seen with naked eyes. However, cells are mostly transparent to visible and infrared light which makes it difficult to see with a traditional microscope. To do so, phase imaging was invented by F. Zernike, who received the Nobel prize in 1953 for this invention. It provides intensity contrast to visualize transparent samples such as those found in biology without any staining. Among the different implementations of phase imaging, digital holographic microscopy (DHM) is a well-known phase method which provides a quantitative value of the phase generated by the sample under test. Implementations of DHMs without the help of any lens element (so called lensless) offer the added advantage to provide large field of views (severalmm2 compared to several hundred ¹m2) and more compact setups than traditional DHMs which have high quality microscope objectives. The lateral resolution is limited by the pixel size of the camera. However, several techniques have been developed to obtain subpixel resolution with lensless setups, hence giving a resolution smaller than the pixel size. In this thesis, two lensless transmission DHMs are presented using a side illumination technique in order to further reduce the device size and keep a visual access to the sample. The first one operates in an in-line configuration: the most compact but using time-consuming image post-processing. The second one is also lensless and uses an off-axis configuration allowing quasi-real time imaging but less compact. Their practical use is described and images of transparent (phase only) samples are shown. Super-resolution (subpixel) using several subpixel shifted holograms was then investigated for the in-line configuration and demonstrated on absorptive samples. Since those microscopes are compact and made out of off-the-shelf low priced elements, they could be broadly spread in schools for educational purposes. They could also be implemented in cells incubators, allowing visualization inside processes at low cost and multiplication of the number of measurements made at the same time.

EPFL2018