Abstract
Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object. The uncertainty of the object support can lead to over-fitting and prevents an unambiguous metric evaluation of solutions. We propose to use a ‘free’ log-likelihood indicator, where a small percentage of points are masked from the reconstruction algorithms, as an unbiased metric to evaluate the validity of computed solutions, independent of the sample studied. We also show how a set of solutions can be analysed through an eigen-decomposition to yield a better estimate of the real object. Example analysis on experimental data is presented both for a test pattern dataset, and the diffraction pattern from a live cyanobacteria cell. The method allows the validation of reconstructions on a wide range of materials (hard condensed or biological), and should be particularly relevant for 4th generation synchrotrons and X-ray free electron lasers, where large, high-throughput datasets require a method for unsupervised data evaluation.
Highlights
Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent of the object
CDI has been successfully used on a wide range of samples, from single cells[14] to inorganic particles[15,16], with applications exploiting the temporal properties of X-ray Free Electron Lasers to viruses[17] and time-resolved strain analysis[18]
As CDI is based on the measurement of the far-field diffraction pattern of a single object, the reconstruction is only possible if the diffraction pattern is recorded at a spacing finer than the Nyquist frequency[1,3,19]
Summary
Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object. As CDI is based on the measurement of the far-field diffraction pattern of a single object, the reconstruction is only possible if the diffraction pattern is recorded at a spacing finer than the Nyquist frequency (this condition is called oversampling)[1,3,19] This is done experimentally if the sample size can be estimated, and a variety of algorithms (Error Reduction (ER), Hybrid Input-Output (HIO), Relaxed Averaged Alternating Reflectors (RAAR), Charge Flipping (CF) etc.) can be used to phase the diffraction pattern and reconstruct the object[5,20,21]. As the diffraction pattern is oversampled and the actual size and shape of the object is unknown, it is easy to create incorrect solutions which involve an object size larger than the real one (i.e. with many extra free parameters), and yield a better figure of merit by over-fitting. We show how it can be applied to evaluate the solutions and combine them to obtain the final optimal reconstruction
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