Femtosecond X-ray coherent diffraction of aligned amyloid fibrils on low background graphene

Here we present a new approach to diffraction imaging of amyloid fibrils, combining a freestanding graphene support and single nanofocused X-ray pulses of femtosecond duration from an X-ray free-electron laser. Due to the very low background scattering from the graphene support and mutual alignment of filaments, diffraction from tobacco mosaic virus (TMV) filaments and amyloid protofibrils is obtained to 2.7 A and 2.4 A resolution in single diffraction patterns, respectively. Some TMV diffraction patterns exhibit asymmetry that indicates the presence of a limited number of axial rotations in the XFEL focus. Signal-to-noise levels from individual diffraction patterns are enhanced using computational alignment and merging, giving patterns that are superior to those obtainable from synchrotron radiation sources. We anticipate that our approach will be a starting point for further investigations into unsolved structures of filaments and other weakly scattering objects.

Refinement for single-nanoparticle structure determination from low-quality single-shot coherent diffraction data

Christoph Bostedt, Christophe Nicolas

With the emergence of X-ray free-electron lasers, it is possible to investigate the structure of nanoscale samples by employing coherent diffractive imaging in the X-ray spectral regime. In this work, we developed a refinement method for structure reconstruction applicable to low-quality coherent diffraction data. The method is based on the gradient search method and considers the missing region of a diffraction pattern and the small number of detected photons. We introduced an initial estimate of the structure in the method to improve the convergence. The present method is applied to an experimental diffraction pattern of an Xe cluster obtained in an X-ray scattering experiment at the SPring-8 Angstrom Compact free-electron LAser (SACLA) facility. It is found that the electron density is successfully reconstructed from the diffraction pattern with a large missing region, with a good initial estimate of the structure. The diffraction pattern calculated from the reconstructed electron density reproduced the observed diffraction pattern well, including the characteristic intensity modulation in each ring. Our refinement method enables structure reconstruction from diffraction patterns under difficulties such as missing areas and low diffraction intensity, and it is potentially applicable to the structure determination of samples that have low scattering power.

INT UNION CRYSTALLOGRAPHY2020

Multiple scattering in wide-field optical coherence tomography

Boris Karamata

Optical Coherence Tomography (OCT), a well-established imaging method based on low-coherence interferometry, provides cross-sectional images of the internal structure of biological samples with a resolution in the micrometer range. OCT was successfully applied on various tissues such as for instance the retina, the skin or a tooth. In highly scattering tissues like the skin, probing depth is limited to approximately 2mm, mainly due to insufficient rejection of multiply scattered light. Presently, the contribution of multiple scattering in OCT is not fully understood. Therefore, there is a strong and urgent need to develop models allowing a reliable evaluation of the system's limitations as well as the improvement of the imaging capabilities. It is generally believed that a relevant model should account for loss of correlation between the reference and the sample field due to multiple scattering. We developed a new comprehensive model of OCT. Our preliminary study revealed that the reference and sample fields are actually fully correlated. This important result allowed us to model the OCT signal as a sum of stationary random phasors and treated it as a statistical signal. The mean of this signal can be calculated thanks to classical results of statistical optics and to a Monte Carlo simulation. Unlike other existing models, our model accounts for the source autocorrelation function. The model proved to be in excellent agreement with a whole range of experimental data gathered in a comprehensive study of cross-talk in wide-field OCT. Moreover, our results put in question the applicability of widely used models of OCT based on the "extended Huygens-Fresnel principle", which assume a partial correlation between interfering fields due to multiple scattering. The construction of conventional OCT images is based on lateral scanning of a beam focused within the sample. To increase image acquisition speed and eliminate the need for lateral scanning, wide-field OCT was recently developed. Our experimental and theoretical investigations of the potential and limitations of wide-field OCT revealed the crucial role played by the spatial coherence of the light source. Spatially coherent illumination generates considerable coherent optical cross-talk, which prevents shot-noise-limited detection and diffraction-limited imaging in scattering samples. The dependence on several parameters of the optical system and of the sample properties was investigated in a comprehensive study. Cross-talk increases with the wide-field diameter, numerical aperture, source coherence length, and sample optical density; and strongly depends on sample anisotropy. We showed that spatially incoherent illumination realized with a thermal light source permits cross-talk suppression in wide-field OCT, i.e. rejection of multiply scattered light to a level comparable to that of point scanning OCT. We performed a theoretical study which revealed that the power per spatial mode radiated by thermal light sources is too low to permit a high signal-to-noise ratio while maintaining a fast acquisition speed. Therefore, wide-field OCT realized with either spatially coherent or spatially incoherent illumination suffers from inherent fundamental limitation. This led us to investigate the possibility of exploiting a spatially incoherent light source brighter than a thermal light source. We came to the conclusion that such a "pseudothermal" light source can potentially lead to wide-field OCT systems devoid of cross-talk and an image acquisition speed higher than that of a point scanning OCT system. However, the attractive properties of pseudothermal light sources could be gained at the expense of the simplicity and the economical advantages offered by thermal light sources. Furthermore, fast acquisition speed also relies on a performing "smart pixel detector array". Presently, such detectors do not have sufficient sensitivity and their frequency readout is too low as shown in our feasibility study. We performed a theoretical investigation of the potential of thermal light sources in terms of axial resolution and power per mode. The former revealed that the maximum power per mode is radiated at a wavelength higher than the spectral peak of a blackbody radiator. This led to the important practical conclusion that, at 6000 K, the maximum power is collected in the therapeutic spectral window in OCT (600 - 1300 nm), while at 3000 K this peak is shifted out of the therapeutic window leading to significant power losses. More generally, our work provides a design tool for choosing the optimal thermal light source for a given therapeutic window in terms of signal-to-noise ratio. Currently available sources at 6000 K consist of high pressure gas arc lamps providing a spectrum endowed with spectral lines deleterious for OCT. By suppressing a portion of the spectrum devoid of spectral lines of a mercury arc lamp, we obtained amongst the highest axial resolution so far reported in OCT. Furthermore, the importance of the speckle statistics in OCT incited us to clarify the origin of a difference between two theoretical results reported in the literature. Indeed, two calculations of the amplitude distribution of speckles in OCT, each of them based on a different mathematical formulation, yield different results. We showed that a modification of an initial assumption in one of the formulation leads to equivalent results. In conclusion, this thesis provides a deeper understanding of the potential and limitations of widefield OCT, leading to important design rules. Moreover, it presents a new comprehensive model of OCT putting in question other widely used models.

EPFL2004

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.