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The diffraction pattern of a single non-periodic compact object, such as amolecule, is continuous and is proportional to the square modulus of theFourier transform of that object. When arrayed in a crystal, the coherent sumof the continuous diffracted wave-fields from all objects gives rise to strongBragg peaks that modulate the single-object transform. Wilson statisticsdescribe the distribution of continuous diffraction intensities to the sameextent that they apply to Bragg diffraction. The continuous diffractionobtained from translationally-disordered molecular crystals consists of theincoherent sum of the wave-fields from the individual rigid units (such asmolecules) in the crystal, which is proportional to the incoherent sum of thediffraction from the rigid units in each of their crystallographicorientations. This sum over orientations modifies the statistics in a similarway that crystal twinning modifies the distribution of Bragg intensities. Thesestatistics are applied to determine parameters of continuous diffraction suchas its scaling, the beam coherence, and the number of independent wave-fieldsor object orientations contributing. Continuous diffraction is generally muchweaker than Bragg diffraction and may be accompanied by a background that farexceeds the strength of the signal. Instead of just relying upon the smallestmeasured intensities to guide the subtraction of the background it is shown howall measured values can be utilised to estimate the background, noise, andsignal, by employing a modified "noisy Wilson" distribution that explicitlyincludes the background. Parameters relating to the background and signalquantities can be estimated from the moments of the measured intensities. Theanalysis method is demonstrated on previously-published continuous diffractiondata measured from imperfect crystals of photosystem II.

Continuous Diffraction of Molecules and Disordered Molecular Crystals