Possibility of single biomolecule imaging with coherent amplification of weak scattering x-ray photons

The number of photons produced by coherent x-ray scattering from a single biomolecule is very small because of its extremely small elastic-scattering cross section and low damage threshold. Even with a high x-ray flux of 3×10¹² photons per 100-nm-diameter spot and an ultrashort pulse of 10 fs driven by a future x-ray free electron laser (x-ray FEL), it has been predicted that only a few 100 photons will be produced from the scattering of a single lysozyme molecule. In observations of scattered x rays on a detector, the transfer of energy from wave to matter is accompanied by the quantization of the photon energy. Unfortunately, x rays have a high photon energy of 12 keV at wavelengths of 1 Å, which is required for atomic resolution imaging. Therefore, the number of photoionization events is small, which limits the resolution of imaging of a single biomolecule. In this paper, I propose a method: instead of directly observing the photons scattered from the sample, we amplify the scattered waves by superimposing an intense coherent reference pump wave on it and record the resulting interference pattern on a planar x-ray detector. Using a nanosized gold particle as a reference pump wave source, we can collect 10⁴–10⁵ photons in single shot imaging where the signal from a single biomolecule is amplified and recorded as two-dimensional diffraction intensity data. An iterative phase retrieval technique can be used to recover the phase information and reconstruct the image of the single biomolecule and the gold particle at the same time. In order to precisely reconstruct a faint image of the single biomolecule in Angstrom resolution, whose intensity is much lower than that of the bright gold particle, I propose a technique that combines iterative phase retrieval on the reference pump wave and the digital Fourier transform holography on the sample. By using a large number of holography data, the three-dimensional electron density map can be assembled.