Lensless imaging using broadband X-ray sources

Abstract

High-resolution X-ray imaging techniques using optical elements such as zone plates are widely used for viewing the internal structure of samples in exquisite detail. The resolution attainable is ultimately limited by the manufacturing tolerances for the optics. Combining ideas from crystallography and holography, this limit may be surpassed by the method of coherent diffractive imaging (CDI) 1 . Although CDI shows particular promise in applications involving X-ray free-electron lasers 2 , it is also emerging as an important new technique for imaging at third-generation synchrotrons. The limited coherent output of these sources, however, is a significant barrier to obtaining shorter exposure times. A fundamental assumption of coherent diffractive imaging is that the incident light is well-approximated by a single optical frequency. In this Letter, we demonstrate the first experimental realization of ‘polyCDI’, using a broadband source to achieve a factor of 60 reduction in the exposure time over quasi-monochromatic coherent diffractive imaging. Over the past decade, the extension of crystallographic techniques to the high-resolution imaging of non-crystalline objects 3 has proved enormously successful in a wide variety of applications 4 . Iterative retrieval of the phase of the far-field diffraction pattern permits reconstruction of the diffracting object with a spatial resolution that is limited, in principle, only by the wavelength of the incident illumination. In crystallography, the periodic arrangement of atoms amplifies the signal diffracted from the unit cell, making detection of the Bragg peaks straightforward. A main goal for coherent diffractive imaging (CDI) is to develop it into a form of highspatial-resolution microscopy that can be routinely applied using synchrotron sources. In this endeavour it must compete with the very successful results obtained using zone-plate-based full-field transmission X-ray microscopy 5 . A fundamental issue for both forms of imaging is that higher spatial resolution requires that the sample be illuminated with a greater number of photons per resolution element, scaling approximately as the fourth power of the desired spatial resolution 6 . Although it has been asserted that CDI is able to achieve equivalent resolution to zone plate microscopy, but with fewer photons 7 , the two techniques are limited to precisely the same degree by the spectral bandwidth (longitudinal coherence length) of the incident light. Significant increases in the spatial resolution require brighter sources, much longer exposure times or the capacity to increase the acceptable limits on the bandwidth. A pathway to achromatic zone plates has been proposed 8 that