to simulate the effect or a smaller data set consisting of fewer diffraction patterns of the same signal strength. Computationally reducing the data in this way avoids confounding factors from working with different data sets collected at different times under potentially different experimental conditions.

\[sec:red\_patterns\]Reducing diffraction pattern intensity
-----------------------------------------------------------

To simulate measurement of weaker diffraction patterns we computationally reduced the number of photons in each image to produce diffraction patterns with fewer photons drawn from the same experimental data sets. Reducing the number of photons in each diffraction pattern was done by applying a Bernoulli process to each photon with a certain probability to keep or discard the photon. These selection fractions, $p$, were reduced from $2^{-1}$ to $2^{-10}$ in steps of powers of two. Due to the Poisson nature of the photon counting statistics, this simulates the effect of a factor $p$ weaker incident pulse. The effect of applying this process to a particular diffraction pattern is shown in Figure \[fig:dilution\]. The average number of photons per frame after photon dilution is shown in Table \[table:dilution\], from which it can be seen that photon counts per frame decreases from nearly 35,000 photons per frame at full strength to only 