High harmonic generation for coherent diffractive imaging

This dissertation presents experimental work on a high-harmonic generation source and coherent diffractive imaging. A novel and successful approach of employing harmonic emission that consists of multiple harmonic orders and its utilization for coherent diffractive imaging is presented, and associated results are discussed. This work may prove valuable particularly for time-resolved spectroscopy, sources of soft x-ray and extreme-ultraviolet radiation, and imaging based on harmonic emission. A high-harmonic generation apparatus has been built featuring a highly flexible high-harmonic interaction geometry, optical elements for tailoring of the harmonic emission and a flexible stage that serves experimental purposes, in particular for coherent diffractive imaging. Based on a semi-infinite argon or helium gas cell design, the harmonic emission can be phase-matched and tailored according to the experimental requirements for high flux and so that the spectral width of the harmonic beam is confined to only a few intense harmonic orders. This beam can be directly used for experimental purposes without any narrow-bandwidth optics in the beam path that might affect the harmonic emission in its spatial, spectral or temporal domain. Also any loss in harmonic flux due to intrinsic inefficiencies can be avoided. A technique for in-situ spectral characterization has been developed, which is based on an application of the maximum entropy method to the interference pattern from a Young double-slit pair illuminated by the harmonic emission. This approach is more flexible than and avoids serious problems associated with a different approach based on the use of a fast Fourier transform to extract the spectral information. The multiple-order high harmonic emission is utilized for coherent diffractive imaging. Due to its nature, this source provides a high degree of spatial coherence, but the temporal coherence is poor. Thus, we have developed a new algorithm for phase-retrieval that can process the diffraction pattern which is a superposition of the diffraction patterns of each individual harmonic order of the high-harmonic beam. This algorithm is a modified version of the conventional algorithm (Gerchberg-Saxton-Fienup) for coherent diffractive imaging and includes the spectrum optimization iterative procedure (gradient descent method) within the main reconstruction iterative process. Also, an application of the maximum entropy method is employed for improvement of the quality of the reconstructed image. The formalism can readily be adapted to any short-wavelength polychromatic source in which there is a high degree of spatial coherence at each sampled wavelength but poor temporal coherence across the sampled spectrum. Diffraction patterns of wide dynamic range can be acquired by means of a new design involving a beam stop and image stitching. Binary and non-binary periodic and non-periodic samples have been successfully reconstructed. It is noted that the employment of multiple-wavelength coherent diffractive imaging is a necessity when operating the high-harmonic source in the water-window (~ 4.4 to 2.3 nm). In this spectral region the spectral spacing Δ λ of adjacent harmonic orders is 0.05 nm > Δ > 0.01 nm, which may be comparable to or even smaller than the spectral resolution Δ δ of a diffraction grating that is used for selecting a single harmonic order for coherent diffractive imaging (e.g., Δ δ = 0.05 nm for the 1200 grooves/mm-grating of the monochromator Setpoint GIMS#4, spectral range from 4.4 nm to 10.6 nm). Thus, the diffracted harmonic beam may consist of several harmonic orders instead of one single harmonic order. This high-harmonic source is a potential source of extreme-ultraviolet and soft xiv ray radiation and for time-resolved spectroscopy, such as femtosecond photoelectron spectroscopy and for polychromatic diffractive imaging with high spatial resolution, where only a few harmonic orders of short wavelength or a dominant photon energy are required and any optics in the harmonic beam path, such as reflection gratings, is undesirable. The novel and flexible approach of spectral extraction based on the application of the maximum entropy method to the interference pattern of this source can be employed for efficient in-situ spectral characterization and thus allows us to effectively tailor the harmonic source for the experimental requirements. The formalism of lensless polychromatic diffractive imaging may be adapted and applied to the multimode x-ray free-electron laser sources that are under current development and thus provides a powerful tool for imaging in the extreme-ultraviolet and soft x-ray region. The current activity in the development of this novel kind of source suggests that this approach may find direct application in proposals for imaging of single molecules with atomic resolution using short pulse coherent diffractive imaging. The relaxation of the requirement that the illuminating source be strictly monochromatic in diffractive imaging may well prove to be valuable in the future design and analysis of materials and biomolecules.