## 6 Conclusions  
It should be noted that the images computed from the diffraction patterns of single particles do not agree perfectly with those from two particles. This to be expected, as there will be extra interparticle interfaces in the two-particle case. It is only if the number of particles contributing to each diffraction pattern becomes large that the arguments made by [27], for suggesting that the correlations from multiple particles, approach those of a single particle, due to the fact that the phases are random, allowing interparticle inte  
Figure 8: Image reconstructed from two particles per diffraction patten.  
Figure 7: Image reconstructed from one particle per diffraction patten.  
The method of angular correlations [3; 11] is shown to be very capable of recovering accurate 3D images of any particle of azimuthal symmetry as injected into an X-ray free electron laser (XFEL), even if there are multiple particles in random orientations. We tested this by means of a simulations in the case of nanorice, one of the early particles used as a test case with an XFEL. To this end, we simulated diffraction patterns expected of random orientations of the nanorice. From this data, one is able to find quantities that enable the reconstruction of an accurate image of nanorice particles. Note that this method is also applicable for reconstruction of artificial dumbbells, as demonstrated recently in a paper by [PERSON] et al. [24].  
It should be noted that \(m=0\) is also assumed for a helical virus. The difference with that case is that the diffraction volume tends to be concentrated on \"layer planes\" implying a periodicity of the particle structure along the azimuthal axis. It is remarkable that the combination of \"layer plane\" intensities and azimuthal symmetry yield a helical structure in real space on phasing [21]. In the present case, the intensities are not concentrated on \"layer planes\" and yield a structure that is genuinely azimuthally symmetric, with no hint of helicity. Both are indications of the power of modern iterative phasing algorithms to find the correct structure from diffraction volumes.  
Our next step will be to apply this method to nanorice experimental data from an XFEL, as deposited on [28], for example.  
A problem with experimental data is that a huge number of diffraction patterns are measured, only a subset of which (\"good\" patterns) correspond to actual particle hits. In addition to all other methods that have been proposed for structure determination from XFEL diffraction patterns, one needs to filter out diffraction patterns corresponding to multiple particle hits. This is not necessary with our method. Only an elimination of patterns corresponding to no particle hits at all. Due to the huge number of diffraction patterns measured in an experiments, this needs to be done by computer. Fortunately, there has already been at least one machine learning algorithm [9] applied to discriminate between measured [9] \"good\" and \"bad\" patterns. We are collaborating with the first author of that paper [9] with an aim to apply our method to experimental data.  
**Acknowledgments:** We acknowledge a grant from the U.S. National Science Foundation to fund the bioXFEL Science and Technology Center under Grant No. STC 1231306.  
**Author Contributions:** [PERSON] developed the 2 nanorice model, applied correlation method to this model with azimuthal symmetry, generated all figures in the manuscript though rekted caculatels and corrected minor mistakes in the manuscript. [PERSON] conceived of the original theory of calculating nanorice from the angular correlations and developed the theory thereof. [PERSON] was the supervisor of the project and wrote the first draft of the manuscript.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
Figure 9: Logarithm of the intensities reconstructed from the angular correlations of two randomly spaced and oriented nanorice particles with widths of about 50 Å.