Abstract
A semiclassical theory of incoherent diffractive imaging is given, based on the Hanbury Brown and Twiss effect when used to image inner-shell x-ray fluorescence from heavy atoms excited by the femtosecond pulses of an x-ray laser. Interference between emission from different atoms is expected when the pulse duration is shorter than the fluorescent lifetime. Simulations for atoms at the vertices of an icosahedral virus capsid are given, and reconstructions are presented based on phasing of the pair correlation function between photons emitted independently from many different atoms at two different detector pixels. The dependence of the pair-correlation function on the fluorescence lifetime relative to the pulse duration of the x-ray free-electron laser (XFEL) is computed, and a simple expression is obtained for the contrast of incoherent diffractive imaging speckles as a function of the XFEL's flux and lifetime. This indicates that compact XFELs, with reduced flux but sub-femtosecond pulses, should be ideally suited to atomic-resolution three-dimensional mapping of heavy atoms in materials science, chemistry, and biology.
Highlights
As a result of their war-time experience with radar and the early development of radio astronomy, Hanbury Brown and Twiss (HBT) established that there exists a correlation in the intensity fluctuations of radiation from a partially coherent source, detected at two different places
Sured requires a solution to the phase problem to obtain the complex degree of coherence. This method of imaging an incoherent object has been analyzed and demonstrated by several groups to provide super-resolution, in some cases using triple correlations to solve the phase problem [4,5,6]. It has recently been proposed [7] that this method might be applied to the inner-shell characteristic emission from atoms in a sample excited by an x-ray free-electron laser (XFEL)
The key relationship is that even a reduction of many orders of magnitude in pulse intensity over that available at current XFELs has very little adverse impact on the visibility so long as the pulse duration is of the order of the coherence time or briefer (V is of the order of unity or less)
Summary
As a result of their war-time experience with radar and the early development of radio astronomy, Hanbury Brown and Twiss (HBT) established (amongst much controversy) that there exists a correlation in the intensity fluctuations of radiation from a partially coherent source, detected at two different places. Sured requires a solution to the phase problem to obtain the complex degree of coherence This method of imaging an incoherent (self-luminous) object has been analyzed and demonstrated by several groups to provide super-resolution, in some cases using triple correlations to solve the phase problem [4,5,6]. It has recently been proposed [7] that this method (known as incoherent diffractive imaging or IDI) might be applied to the inner-shell characteristic emission from atoms in a sample excited by an x-ray free-electron laser (XFEL). Our calculations are done in Heaviside-Lorentz units
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