A theory of random-matrix bases is presented, including expressions for orthogonality, completeness and the random-matrix synthesis of arbitrary matrices. This is applied to ghost imaging as the realization of a random-basis reconstruction, including an expression for the resulting signal-to-noise ratio. Analysis of conventional direct imaging and ghost imaging leads to a criterion which, when satisfied, implies reduced dose for computational ghost imaging. We also propose an experiment for x-ray phase contrast computational ghost imaging, which enables differential phase contrast to be achieved in an x-ray ghost imaging context. We give a numerically robust solution to the associated inverse problem of decoding differential phase contrast x-ray ghost images, to yield a quantitative map of the projected thickness of the sample.
Multiple exposures, of a single illuminated non-configurable mask that is transversely displaced to a number of specified positions, can be used to create any desired distribution of radiant exposure. An experimental proof-of-concept is given for this idea, employing hard X rays. The method is termed "ghost projection", since it may be viewed as a reversed form of classical ghost imaging. The written pattern is arbitrary, up to a tunable constant offset, together with a limiting spatial resolution that is governed by the finest features present in the illuminated mask. The method, which is immune to both proximity-correction and aspect-ratio issues, can be used to make a universal lithographic mask in the hard-X-ray regime. Ghost projection may also be used as a dynamicallyconfigurable beam-shaping element, namely the hard-X-ray equivalent of a spatial light modulator. The idea may be applied to other forms of radiation and matter waves, such as gamma rays, neutrons, electrons, muons, and atomic beams.1 These potential applications are examined in more detail in the Discussion (Section IV).
The penetrating power of x rays underpins important applications such as medical radiography. However, this same attribute makes it challenging to achieve flexible on-demand patterning of x-ray beams. One possible path to this goal is “ghost projection,” a method that may be viewed as a reversed form of classical ghost imaging. This technique employs multiple exposures of a single illuminated non-configurable mask that is transversely displaced to a number of specified positions to create any desired pattern. An experimental proof of concept is given for this idea, using hard x rays. The written pattern is arbitrary, up to a tunable constant offset, and its spatial resolution is limited by both (i) the finest features present in the illuminated mask and (ii) inaccuracies in mask positioning and mask exposure time. In principle, the method could be used to make a universal lithographic mask in the hard-x-ray regime. Ghost projection might also be used as a dynamically configurable beam-shaping element, namely, the hard-x-ray equivalent of a spatial light modulator. The underpinning principle can also be applied to gamma rays, neutrons, electrons, muons, and atomic beams. Our flexible approach to beam shaping gives a potentially useful means to manipulate such fields.
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