Imaging of Objects by Coherent Diffraction of X-Ray FEL Pulses

  • Richard A.  Kirian
  • Henry N.  Chapman
Living reference work entry

Later version available View entry history


X-ray free-electron lasers produce pulses of coherent X-rays that are up to nine orders of magnitude higher in peak brightness than the brightest synchrotron sources. These pulses vaporize any object placed in the focused beam, yet are brief enough to diffract from the object before significant radiation damage occurs. This process of “diffraction before destruction” overcomes previous exposure and dose limitations when imaging biological structures, which allow atomic-resolution structures to be determined from macromolecules without the need for large, strongly diffracting crystals that are difficult or impossible to grow. The extreme pulse intensity has allowed protein crystal sizes to be shrunk down to dimensions of hundreds of nanometers, expanding the range of structures that can be studied, potentially increasing the rate at which new structures can be determined, and allowing the tracking of conformational dynamics down to femtosecond timescales. Efforts are ongoing to reduce this all the way to the single molecule, opening up possibilities for robust phasing procedures to acquire model-free structures directly from the measurements. The new science of coherent diffractive imaging would be well understood by the Braggs and Laue but makes use of recent theoretical insights, modern computational capabilities, and the laser-like X-ray sources of the twenty-first century.


X-ray diffraction, X-ray free-electron laser, Diffractive imaging, Iterative phase retrieval, X-ray microscopy 

Glossary of Abbreviations


Atomic force microscope


Coherent diffractive imaging


Cryogenic electron microscopy


Coherent X-ray Imaging Database


Difference map (algorithm)


Drop on demand


Expansion-maximization-compression (algorithm)


Error reduction (algorithm)


Extreme ultraviolet


Free-electron laser in Hamburg


Generative topographic mapping (algorithm)


Gas-dynamic virtual nozzle


High harmonic generation


Hybrid input-output (algorithm)


Highly viscous extrusion nozzle


Linac Coherent Light Source


Light-emitting diode


Phase-retrieval transfer function


Relaxed alternating averaged reflections (algorithm)


Root mean square


Self-amplification of spontaneous emission


Serial femtosecond crystallography


Wigner distribution function


An integrated toolkit for X-ray and atomic physics (computer program)


X-ray free-electron laser


  1. B. Abbey, K.A. Nugent, G.J. Williams, J.N. Clark, A.G. Peele, M.A. Pfeifer, M. de Jonge, I. McNulty, Keyhole coherent diffractive imaging. Nat. Phys. 4, 394–398 (2008)CrossRefGoogle Scholar
  2. E. Allaria, C. Callegari, D. Cocco, W.M. Fawley, M. Kiskinova, C. Masciovecchio, F. Parmigiani, The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications. New J. Phys. 12, 075002 (2010)ADSCrossRefGoogle Scholar
  3. M. Altarelli, R. Brinkmann, M. Chergui, W. Decking, B. Dobson, S. Düsterer, G. Grübel, W. Graeff, H. Graafsma, J. Hajdu, J. Marangos, J. Pflüger, H. Redlin, D. Riley, I. Robinson, J. Rossbach, A. Schwarz, K. Tiedtke, T. Tschentscher, I. Vartaniants, H. Wabnitz, H. Weise, R. Wichmann, K. Witte, A. Wolf, M. Wulff, M. Yurkov, The European X-ray free-electron laser technical design report. DESY XFEL Project Group, European XFEL Project Team, Deutsches Elektronen-Synchrotron (2007)Google Scholar
  4. S. Aoki, S. Kikuta, X-ray holographic microscopy. Jpn. J. Appl. Phys. 13, 1385–1392 (1974)ADSCrossRefGoogle Scholar
  5. A. Aquila, M.S. Hunter, R.B. Doak, R.A. Kirian, P. Fromme, T.A. White, J. Andreasson, D. Arnlund, S. Bajt, T.R.M. Barends, M. Barthelmess, M.J. Bogan, C. Bostedt, H.e. Bottin, J.D. Bozek, C. Caleman, N. Coppola, J. Davidsson, D.P. DePonte, V. Elser, S.W. Epp, B. Erk, H. Fleckenstein, L. Foucar, M. Frank, R. Fromme, H. Graafsma, I. Grotjohann, L. Gumprecht, J. Hajdu, C.Y. Hampton, A. Hartmann, R. Hartmann, S. Hau-Riege, G.u.n. Hauser, H. Hirsemann, P. Holl, J.M. Holton, A.e.H.o. mke, L. Johansson, N. Kimmel, S. Kassemeyer, F. Krasniqi, K.-U. Kühnel, M. Liang, L. Lomb, E. Malmerberg, S. Marchesini, A.V. Martin, F.R.N.C. Maia, M. Messerschmidt, K. Nass, C. Reich, R. Neutze, D. Rolles, B. Rudek, A. Rudenko, I. Schlichting, C. Schmidt, K.E. Schmidt, J. Schulz, M.M. Seibert, R.L. Shoeman, R. Sierra, H. Soltau, D. Starodub, F. Stellato, S. Stern, L. Strüder, N. Timneanu, J. Ullrich, X. Wang, G.J. Williams, G. Weidenspointner, U. Weierstall, C. Wunderer, A. Barty, J.C.H. Spence, H.N. Chapman, Time-resolved protein nanocrystallography using an X-ray free-electron laser. Opt. Express 20, 2706–2716 (2012)Google Scholar
  6. V. Ayvazyan, N. Baboi, J. Bahr, V. Balandin, B. Beutner, A. Brandt, I. Bohnet, A. Bolzmann, R. Brinkmann, O.I. Brovko, J.P. Carneiro, S. Casalbuoni, M. Castellano, P. Castro, L. Catani, E. Chiadroni, S. Choroba, A. Cianchi, H. Delsim-Hashemi, G. Di Pirro, M. Dohlus, S. Düsterer, H.T. Edwards, B. Faatz, A.A. Fateev, J. Feldhaus, K. Flottmann, J. Frisch, L. Frohlich, T. Garvey, U. Gensch, N. Golubeva, H.J. Grabosch, B. Grigoryan, O. Grimm, U. Hahn, J.H. Han, M.V. Hartrott, K. Honkavaara, M. Huning, R. Ischebeck, E. Jaeschke, M. Jablonka, R. Kammering, V. Katalev, B. Keitel, S. Khodyachykh, Y. Kim, V. Kocharyan, M. Korfer, M. Kollewe, D. Kostin, D. Kramer, M. Krassilnikov, G. Kube, L. Lilje, T. Limberg, D. Lipka, F. Lohl, M. Luong, C. Magne, J. Menzel, P. Michelato, V. Miltchev, M. Minty, W.D. Moller, L. Monaco, W. Muller, M. Nagl, O. Napoly, P. Nicolosi, D. Nolle, T. Nunez, A. Oppelt, C. Pagani, R. Paparella, B. Petersen, B. Petrosyan, J. Pflüger, P. Piot, E. Plonjes, L. Poletto, D. Proch, D. Pugachov, K. Rehlich, D. Richter, S. Riemann, M. Ross, J. Rossbach, M. Sachwitz, E.L. Saldin, W. Sandner, H. Schlarb, B. Schmidt, M. Schmitz, P. Schmuser, J.R. Schneider, E.A. Schneidmiller, H.J. Schreiber, S. Schreiber, A.V. Shabunov, D. Sertore, S. Setzer, S. Simrock, E. Sombrowski, L. Staykov, B. Steffen, F. Stephan, F. Stulle, K.P. Sytchev, H. Thom, K. Tiedtke, M. Tischer, R. Treusch, D. Trines, I. Tsakov, A. Vardanyan, R. Wanzenberg, T. Weiland, H. Weise, M. Wendt, I. Will, A. Winter, K. Wittenburg, M.V. Yurkov, I. Zagorodnov, P. Zambolin, K. Zapfe, First operation of a free-electron laser generating GW power radiation at 32 nm wavelength. Euro. Phys. J. D 37, 297–303 (2006)ADSCrossRefGoogle Scholar
  7. R. Barakat, G. Newsam, Necessary conditions for a unique solution to two-dimensional phase recovery. J. Math. Phys. 25, 3190 (1984)MathSciNetADSCrossRefGoogle Scholar
  8. A. Barty, S. Boutet, M.J. Bogan, S. Hau-Riege, S. Marchesini, K. Sokolowski-Tinten, N. Stojanovic, R. Tobey, H. Ehrke, A. Cavalleri, S. Dusterer, M. Frank, S. Bajt, B.W. Woods, M.M. Seibert, J. Hajdu, R. Treusch, H.N. Chapman, Ultrafast single-shot diffraction imaging of nanoscale dynamics. Nat. Photon. 2, 415419 (2008)CrossRefGoogle Scholar
  9. A. Barty, C. Caleman, A. Aquila, N. Timneanu, L. Lomb, T.A. White, J. Andreasson, D. Arnlund, S. Bajt, T.R.M. Barends, M. Barthelmess, M.J. Bogan, C. Bostedt, J.D. Bozek, R. Coffee, N. Coppola, J. Davidsson, D.P. DePonte, R.B. Doak, T. Ekeberg, V. Elser, S.W. Epp, B. Erk, H. Fleckenstein, L. Foucar, P. Fromme, H. Graafsma, L. Gumprecht, J. Hajdu, C.Y. Hampton, R. Hartmann, A. Hartmann, G. Hauser, H. Hirsemann, P. Holl, M.S. Hunter, L. Johansson, S. Kassemeyer, N. Kimmel, R.A. Kirian, M. Liang, F.R.N.C. Maia, E. Malmerberg, S. Marchesini, A.V. Martin, K. Nass, R. Neutze, C. Reich, D. Rolles, B. Rudek, A. Rudenko, H. Scott, I. Schlichting, J. Schulz, M.M. Seibert, R.L. Shoeman, R.G. Sierra, H. Soltau, J.C.H. Spence, F. Stellato, S. Stern, L. Strueder, J. Ullrich, X. Wang, G. Weidenspointner, U. Weierstall, C.B. Wunderer, H.N. Chapman, Self-terminating diffraction gates femtosecond X-ray nanocrystallography measurements. Nat. Photon. 6, 35–40 (2012)ADSCrossRefGoogle Scholar
  10. R.H.T. Bates, Fourier phase problems are uniquely solvable in more than one dimension. 1. Underlying theory. Optik 61, 247–262 (1982)Google Scholar
  11. H.H. Bauschke, P.L. Combettes, D.R. Luke, Hybrid projection-reflection method for phase retrieval. J. Opt. Soc. Am. A 20, 1025–1034 (2003)ADSCrossRefGoogle Scholar
  12. M. Bergh, G. Huldt, N. Timneanu, F.R.N.C. Maia, J. Hajdu, Feasibility of imaging living cells at subnanometer resolutions by ultrafast X-ray diffraction. Q. Rev. Biophys. 41, 181–204 (2008)CrossRefGoogle Scholar
  13. M.J. Bogan, W.H. Benner, S. Boutet, U. Rohner, M. Frank, A. Barty, M.M. Seibert, F. Maia, S. Marchesini, S. Bajt, B. Woods, V. Riot, S.P. Hau-Riege, M. Svenda, E. Marklund, E. Spiller, J. Hajdu, H.N. Chapman, Single particle X-ray diffractive imaging. Nano. Lett. 8, 310–316 (2008)ADSCrossRefGoogle Scholar
  14. S. Boutet, L. Lomb, G.J. Williams, T.R.M. Barends, A. Aquila, R.B. Doak, U. Weierstall, D.P. DePonte, J. Steinbrener, R.L. Shoeman, M. Messerschmidt, A. Barty, T.A. White, S. Kassemeyer, R.A. Kirian, M.M. Seibert, P.A. Montanez, C. Kenney, R. Herbst, P. Hart, J. Pines, G. Haller, S.M. Gruner, H.T. Philipp, M.W. Tate, M. Hromalik, L.J. Koerner, N. van Bakel, J. Morse, W. Ghonsalves, D. Arnlund, M.J. Bogan, C. Caleman, R. Fromme, C.Y. Hampton, M.S. Hunter, L.C. Johansson, G. Katona, C. Kupitz, M. Liang, A.V. Martin, K. Nass, L. Redecke, F. Stellato, N. Timneanu, D. Wang, N.A. Zatsepin, D. Schafer, J. Defever, R. Neutze, P. Fromme, J.C.H. Spence, H.N. Chapman, I. Schlichting, High-resolution protein structure determination by serial femtosecond crystallography. Science 337, 362–364 (2012)ADSCrossRefGoogle Scholar
  15. W. Brehm, K. Diederichs, Breaking the indexing ambiguity in serial crystallography. Acta Crystallogr. D 70, 101–109 (2014)CrossRefGoogle Scholar
  16. A.T. Brunger, Free R value: a novel statistical quantity for assessing the accuracy of crystal structures. Nature 355, 472–475 (1992)ADSCrossRefGoogle Scholar
  17. C. Caleman, N. Timneanu, A.V. Martin, H.O. Jönsson, A. Aquila, A. Barty, H.A. Scott, T.A. White, H.N. Chapman, Ultrafast self-gating Bragg diffraction of exploding nanocrystals in an X-ray laser. Opt. Express 23, 1213–1219 (2015)ADSCrossRefGoogle Scholar
  18. H.N. Chapman, Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution. Ultramicroscopy 66, 153–172 (1996)CrossRefGoogle Scholar
  19. H.N. Chapman, K.A. Nugent, Coherent lensless X-ray imaging. Nat. Photon. 4, 833–839 (2010)ADSCrossRefGoogle Scholar
  20. H.N. Chapman, A. Barty, M.J. Bogan, S. Boutet, M. Frank, S.P. Hau-Riege, S. Marchesini, B.W. Woods, S. Bajt, H. Benner, R.A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J.R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D.A. Shapiro, K.O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M.M. Seibert, F.R.N.C. Maia, R.W. Lee, A. Szoke, N. Timneanu, J. Hajdu, Femtosecond diffractive imaging with a soft-X-ray free-electron laser. Nat. Phys. 2, 839–843 (2006a)CrossRefGoogle Scholar
  21. H.N. Chapman, A. Barty, S. Marchesini, A. Noy, S.P. Hau-Riege, C. Cui, M.R. Howells, R. Rosen, H. He, J.C.H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, D. Shapiro, High-resolution ab initio three-dimensional x-ray diffraction microscopy. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 23, 1179–1200 (2006b)ADSCrossRefGoogle Scholar
  22. H.N. Chapman, P. Fromme, A. Barty, T.A. White, R.A. Kirian, A. Aquila, M.S. Hunter, J. Schulz, D.P. Deponte, U. Weierstall, R.B. Doak, F.R.N.C. Maia, A.V. Martin, I. Schlichting, L. Lomb, N. Coppola, R.L. Shoeman, S.W. Epp, R. Hartmann, D. Rolles, A. Rudenko, L. Foucar, N. Kimmel, G. Weidenspointner, P. Holl, M.N. Liang, M. Barthelmess, C. Caleman, S. Boutet, M.J. Bogan, J. Krzywinski, C. Bostedt, S. Bajt, L. Gumprecht, B. Rudek, B. Erk, C. Schmidt, A. Homke, C. Reich, D. Pietschner, L. Struder, G. Hauser, H. Gorke, J. Ullrich, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K.U. Kuhnel, M. Messerschmidt, J.D. Bozek, S.P. Hau-Riege, M. Frank, C.Y. Hampton, R.G. Sierra, D. Starodub, G.J. Williams, J. Hajdu, N. Timneanu, M.M. Seibert, J. Andreasson, A. Rocker, O. Jonsson, M. Svenda, S. Stern, K. Nass, R. Andritschke, C.D. Schroter, F. Krasniqi, M. Bott, K.E. Schmidt, X.Y. Wang, I. Grotjohann, J.M. Holton, T.R.M. Barends, R. Neutze, S. Marchesini, R. Fromme, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover, I. Andersson, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, J.C.H. Spence, Femtosecond X-ray protein nanocrystallography. Nature 470, 73–77 (2011)ADSCrossRefGoogle Scholar
  23. H.N. Chapman, C. Caleman, N. Timneanu, Diffraction before destruction. Philos. Trans. R. Soc. B 369, 20130313 (2014)CrossRefGoogle Scholar
  24. B. Chen, B. Abbey, R. Dilanian, E. Balaur, G. Van Riessen, M. Junker, C.Q. Tran, M.W.M. Jones, A.G. Peele, I. McNulty, D.J. Vine, C.T. Putkunz, H.M. Quiney, K.A. Nugent, Diffraction imaging: the limits of partial coherence. Phys. Rev. B 86, 235401 (2012)ADSCrossRefGoogle Scholar
  25. J.N. Clark, A.G. Peele, Simultaneous sample and spatial coherence characterisation using diffractive imaging. Appl. Phys. Lett. 99, 154103 (2011)ADSCrossRefGoogle Scholar
  26. J.N. Clark, C.T. Putkunz, E.K. Curwood, D.J. Vine, R. Scholten, I. McNulty, K.A. Nugent, A.G. Peele, Dynamic sample imaging in coherent diffractive imaging. Opt. Lett. 36, 1954–1956 (2011)ADSCrossRefGoogle Scholar
  27. J.N. Clark, L. Beitra, G. Xiong, A. Higginbotham, D.M. Fritz, H.T. Lemke, D. Zhu, M. Chollet, G.J. Williams, M. Messerschmidt, B. Abbey, R.J. Harder, A.M. Korsunsky, J.S. Wark, I.K. Robinson, Ultrafast three-dimensional imaging of lattice dynamics in individual gold nanocrystals. Science 341, 56–59 (2013)ADSCrossRefGoogle Scholar
  28. J.M. Cowley, Diffraction Physics, 2nd rev. edn. (North-Holland, Amsterdam, 1981)Google Scholar
  29. R. Crowther, D. DeRosier, A. Klug, The reconstruction of a three-dimensional structure from its projections and its applications to electron microscopy. Proc. R. Soc. Lond. 317, 319–340 (1970)ADSCrossRefGoogle Scholar
  30. D.P. Deponte, U. Weierstall, K. Schmidt, J. Warner, D. Starodub, J.C.H. Spence, R.B. Doak, Gas dynamic virtual nozzle for generation of microscopic droplet streams. J. Phys. D Appl. Phys. 41, 195505 (2008)ADSCrossRefGoogle Scholar
  31. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F.-J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. HUANG, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H.-D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, J. Galayda, First lasing and operation of an angstrom-wavelength free-electron laser. Nat. Photon. 4, 641–647 (2010)ADSCrossRefGoogle Scholar
  32. T. Ekeberg, M. Svenda, C. Abergel, F.R.N.C. Maia, V. Seltzer, J.-M. Claverie, M. Hantke, O. Jönsson, C. Nettelblad, G. van der Schot, M. Liang, D.P. DePonte, A. Barty, M.M. Seibert, B. Iwan, I. Andersson, N.D. Loh, A.V. Martin, H. Chapman, C. Bostedt, J.D. Bozek, K.R. Ferguson, J. Krzywinski, S.W. Epp, D. Rolles, A. Rudenko, R. Hartmann, N. Kimmel, J. Hajdu, Three-dimensional reconstruction of the giant mimivirus particle with an X-ray free-electron laser. Phys. Rev. Lett. 114, 098102 (2015)ADSCrossRefGoogle Scholar
  33. V. Elser, Phase retrieval by iterated projections. J. Opt. Soc. Am. A 20, 40–55 (2003).ADSCrossRefGoogle Scholar
  34. V. Elser, Strategies for processing diffraction data from randomly oriented particles. Ultramicroscopy 111, 788–792 (2011a)CrossRefGoogle Scholar
  35. V. Elser, Three-dimensional structure from intensity correlations. New J. Phys. 13, 123014 (2011b)ADSCrossRefGoogle Scholar
  36. V. Elser, Direct phasing of nanocrystal diffraction. Acta Crystallogr. A 69, 559–569 (2013)CrossRefGoogle Scholar
  37. V. Elser, R.P. Millane, Reconstruction of an object from its symmetry-averaged diffraction pattern. Acta Crystallogr. Sect. A 64, 273–279 (2008)ADSCrossRefGoogle Scholar
  38. B. Erk, R. Boll, S. Trippel, D. Anielski, L. Foucar, B. Rudek, S.W. Epp, R. Coffee, S. Carron, S. Schorb, K.R. Ferguson, M. Swiggers, J.D. Bozek, M. Simon, T. Marchenko, J. Kupper, I. Schlichting, J. Ullrich, C. Bostedt, D. Rolles, A. Rudenko, Imaging charge transfer in iodomethane upon x-ray photoabsorption. Science 345, 288–291 (2014)ADSCrossRefGoogle Scholar
  39. J.R. Fienup, Reconstruction of an object from the modulus of its Fourier transform. Opt. Lett. 3, 27–29 (1978)ADSCrossRefGoogle Scholar
  40. J.R. Fienup, T.R. Crimmins, W. Holsztynski, Reconstruction of the support of an object from the support of its autocorrelation. J. Opt. Soc. Am. 72, 610–624 (1982). doi:10.1364/JOSA.72.000610MathSciNetADSCrossRefGoogle Scholar
  41. L.B. Fletcher, H.J. Lee, T. Döppner, E. Galtier, B. Nagler, P. Heimann, C. Fortmann, S. LePape, T. Ma, M. Millot, A. Pak, D. Turnbull, D.A. Chapman, D.O. Gericke, J. Vorberger, T. White, G. Gregori, M. Wei, B. Barbrel, R.W. Falcone, C.C. Kao, H. Nuhn, J. Welch, U. Zastrau, P. Neumayer, J.B. Hastings, S.H. Glenzer, Ultrabright x-ray laser scattering for dynamic warm dense matter physics. Nat. Photonics 9, 274–279 (2015)ADSGoogle Scholar
  42. S. Flewett, H.M. Quiney, C.Q. Tran, K.A. Nugent, Extracting coherent modes from partially coherent wavefields. Opt. Lett. 34, 2198–2200 (2009)ADSCrossRefGoogle Scholar
  43. M. Frank, D.B. Carlson, M.S. Hunter, G.J. Williams, M. Messerschmidt, N.A. Zatsepin, A. Barty, W.H. Benner, K. Chu, A.T. Graf, S.P. Hau-Riege, R.A. Kirian, C. Padeste, T. Pardini, B. Pedrini, B. Segelke, M.M. Seibert, J.C.H. Spence, C.J. Tsai, S.M. Lane, X.D. Li, G. Schertler, S. Boutet, M. Coleman, J.E. Evans, Femtosecond X-ray diffraction from two-dimensional protein crystals. IUCrJ 1, 95–100 (2014)CrossRefGoogle Scholar
  44. R. Fung, V. Shneerson, D.K. Saldin, A. Ourmazd, Structure from fleeting illumination of faint spinning objects in flight. Nat. Phys. 5, 64–67 (2009)CrossRefGoogle Scholar
  45. R.W. Gerchberg, W.O. Saxton, Practical algorithm for determination of phase from image and diffraction plane pictures. Optik 35, 237 (1972)Google Scholar
  46. D. Giannakis, P. Schwander, A. Ourmazd, The symmetries of image formation by scattering. I. Theoretical framework. Opt. Express 20, 12799–12826 (2012)CrossRefGoogle Scholar
  47. L.F. Gomez, K.R. Ferguson, J.P. Cryan, C. Bacellar, R.M.P. Tanyag, C. Jones, S. Schorb, D. Anielski, A. Belkacem, C. Bernando, R. Boll, J. Bozek, S. Carron, G. Chen, T. Delmas, L. Englert, S.W. Epp, B. Erk, L. Foucar, R. Hartmann, A. Hexemer, M. Huth, J. Kwok, S.R. Leone, J.H.S. Ma, F.R.N.C. Maia, E. Malmerberg, S. Marchesini, D.M. Neumark, B. Poon, J. Prell, D. Rolles, B. Rudek, A. Rudenko, M. Seifrid, K.R. Siefermann, F.P. Sturm, M. Swiggers, J. Ullrich, F. Weise, P. Zwart, C. Bostedt, O. Gessner, A.F. Vilesov, Shapes and vorticities of superfluid helium nanodroplets. Science 345, 906–909 (2014)ADSCrossRefGoogle Scholar
  48. A. Guinier, X-Ray Diffraction in Crystals, Imperfect Crystals, and Amorphous Bodies (Dover, New York, 1994)Google Scholar
  49. J. Gulden, O.M. Yefanov, A.P. Mancuso, R. Dronyak, A. Singer, V. Bernátová, A. Burkhardt, O. Polozhentsev, A. Soldatov, M. Sprung, I.A. Vartanyants, Three-dimensional structure of a single colloidal crystal grain studied by coherent x-ray diffraction. Opt. Express 20, 4039–4049 (2012)ADSCrossRefGoogle Scholar
  50. C. Gutt, P. Wochner, B. Fischer, H. Conrad, M. Castro-Colin, S. Lee, F. Lehmk uhler, I. Steinke, M. Sprung, W. Roseker, D. Zhu, H. Lemke, S. Bogle, P.H. Fuoss, G.B. Stephenson, M. Cammarata, D.M. Fritz, A. Robert, G. Grubel, Single shot spatial and temporal coherence properties of the SLAC linac coherent light source in the hard X-ray regime. Phys. Rev. Lett. 108, 024801 (2012)Google Scholar
  51. M.F. Hantke, D. Hasse, F.R.N.C. Maia, T. Ekeberg, K. John, M. Svenda, N.D. Loh, A.V. Martin, N. Timneanu, D.S.D. Larsson, G. van der Schot, G.H. Carlsson, M. Ingelman, J. Andreasson, D. Westphal, M. Liang, F. Stellato, D.P. DePonte, R. Hartmann, N. Kimmel, R.A. Kirian, M.M. Seibert, K. Mühlig, S. Schorb, K. Ferguson, C. Bostedt, S. Carron, J.D. Bozek, D. Rolles, A. Rudenko, S. Epp, H.N. Chapman, A. Barty, J. Hajdu, I. Andersson, High-throughput imaging of heterogeneous cell organelles with an X-ray laser. Nat. Photon. 8, 943–949 (2014)ADSCrossRefGoogle Scholar
  52. A.R. Hare, G.R. Morrison, Near-field soft X-ray diffraction modelled by the multislice method. J. Mod. Opt. 41, 31–48 (1994)ADSCrossRefGoogle Scholar
  53. N. Hartmann, W. Helml, A. Galler, M.R. Bionta, J. Grunert, S.L. Molodtsov, K.R. Ferguson, S. Schorb, M.L. Swiggers, S. Carron, C. Bostedt, J.C. Castagna, J. Bozek, J.M. Glownia, D.J. Kane, A.R. Fry, W.E. White, C.P. Hauri, T. Feurer, R.N. Coffee, Sub-femtosecond precision measurement ofrelative X-ray arrival time for free-electron lasers. Nat. Photon. 8, 706–709 (2014)ADSCrossRefGoogle Scholar
  54. P.W. Hawkes, J.C.H. Spence (eds.), Science of Microscopy (Springer, New York, 2005)Google Scholar
  55. H. He, W.P. Su, Direct phasing of protein crystals with high solvent content. Acta Crystallogr. 71, 92–98 (2015)Google Scholar
  56. R. Hegerl, W. Hoppe, Dynamische Theorie der Kristallstrukturanalyse durch Elektronenbeugung im inhomogen Primarstrahlwellenfeld. Ber. Bunsenges. Physik. Chemie 74, 1148–1154 (1970)CrossRefGoogle Scholar
  57. R. Henderson, The potential and limitations of neutrons, electrons and x-rays for atomic-resolution microscopy of unstained biological molecules. Q. Rev. Biophys. 28, 171–193 (1995)CrossRefGoogle Scholar
  58. B.L. Henke, E.M. Gullikson, J.C. Davis, X-ray interactions – photoabsorption, scattering, transmission and reflection at E = 50–30,000 eV, Z = 1–92. Atom. Data Nucl. Data Tab. 55, 349–349 (1993)CrossRefGoogle Scholar
  59. B. Henrich, J. Becker, R. Dinapoli, P. Goettlicher, H. Graafsma, H. Hirsemann, R. Klanner, H. Krueger, R. Mazzocco, A. Mozzanica, H. Perrey, G. Potdevin, B. Schmitt, X. Shi, A.K. Srivastava, U. Trunk, C. Youngman, The adaptive gain integrating pixel detector AGIPD a detector for the European XFEL. Nucl. Instrum. Methods Phys. Res. Sect. A Accel. Spectrom. Detect. Assoc. Equip. 633, S11–S14 (2011)ADSCrossRefGoogle Scholar
  60. S. Herrmann, S.x.E.b. Boutet, B. Duda, D. Fritz, G. Haller, P. Hart, R. Herbst, C. Kenney, H. Lemke, M. Messerschmidt, J. Pines, A. Robert, M. Sikorski, G. Williams, CSPAD-140k: a versatile detector for LCLS experiments. Nucl. Instrum. Methods Phys. Res. A 718, 550–553 (2013)Google Scholar
  61. K. Hirata, K. Shinzawa-Itoh, N. Yano, S. Takemura, K. Kato, M. Hatanaka, K. Muramoto, T. Kawahara, T. Tsukihara, E. Yamashita, K. Tono, G. Ueno, T. Hikima, H. Murakami, Y. Inubushi, M. Yabashi, T. Ishikawa, M. Yamamoto, T. Ogura, H. Sugimoto, J.-R. Shen, S. Yoshikawa, H. Ago, Determination of damage-free crystal structure of an x-ray-sensitive protein using an XFEL. Nat. Methods 11, 734–736 (2014)CrossRefGoogle Scholar
  62. J.X. Ho, J.R. Ruble, T.R. McInnis, D.C. Carter, H. Huang, W.M. Gibson, Convergent-beam method in macromolecular crystallography. Acta Crystallogr. D 58, 2087–2095 (2002)CrossRefGoogle Scholar
  63. A. Hosseinizadeh, P. Schwander, A. Dashti, R. Fung, R.M. D’Souza, A. Ourmazd, High-resolution structure of viruses from random diffraction snapshots. Philos. Trans. R. Soc. B 369, 20130326 (2014)CrossRefGoogle Scholar
  64. M.R. Howells, T. Beetz, H.N. Chapman, C. Cui, J.M. Holton, C.J. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D.A. Shapiro, J.C.H. Spence, D. Starodub, An assessment of the resolution limitation due to radiation-damage in X-ray diffraction microscopy. J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009)CrossRefGoogle Scholar
  65. X. Huang, M. Wojcik, N. Burdet, I. Peterson, G.R. Morrison, D.J. Vine, D. Legnini, R. Harder, Y.S. Chu, I.K. Robinson, Quantitative X-ray wavefront measurements of Fresnel zone plate and K-B mirrors using phase retrieval. Opt. Express 20, 24038–24048 (2012)ADSCrossRefGoogle Scholar
  66. J.H. Hubbell, W.J. Veigele, E.A. Briggs, R.T. Brown, D.T. Cromer, R.J. Howerton, Atomic form factors, incoherent scattering functions, and photon scattering cross sections. J. Phys. Chem. Ref. Data 4, 471–538 (1975)ADSCrossRefGoogle Scholar
  67. G. Huldt, A. Szoke, J. Hajdu, Diffraction imaging of single particles and biomolecules. J. Struct. Biol. 144, 219–227 (2003)CrossRefGoogle Scholar
  68. T. Ishikawa, H. Aoyagi, T. Asaka, Y. Asano, N. Azumi, T. Bizen, H. Ego, K. Fukami, T. Fukui, Y. Furukawa, S. Goto, H. Hanaki, T. Hara, T. Hasegawa, T. Hatsui, A. Higashiya, T. Hirono, N. Hosoda, M. Ishii, T. Inagaki, Y. Inubushi, T. Itoga, Y. Joti, M. Kago, T. Kameshima, H. Kimura, Y. Kirihara, A. Kiyomichi, T. Kobayashi, C. Kondo, T. Kudo, H. Maesaka, X.M. Maréchal, T. Masuda, S. Matsubara, T. Matsumoto, T. Matsushita, S. Matsui, M. Nagasono, N. Nariyama, H. Ohashi, T. Ohata, T. Ohshima, S. Ono, Y. Otake, C. Saji, T. Sakurai, T. Sato, K. Sawada, T. Seike, K. Shirasawa, T. Sugimoto, S. Suzuki, S. Takahashi, H. Takebe, K. Takeshita, K. Tamasaku, H. Tanaka, R. Tanaka, T. Tanaka, T. Togashi, K. Togawa, A. Tokuhisa, H. Tomizawa, K. Tono, S. Wu, M. Yabashi, M. Yamaga, A. Yamashita, K. Yanagida, C. Zhang, T. Shintake, H. Kitamura, N. Kumagai, A compact X-ray free-electron laser emitting in the sub-angstrom region. Nat. Photon. 6, 540–544 (2012)ADSCrossRefGoogle Scholar
  69. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999)zbMATHGoogle Scholar
  70. W. Kabsch, Processing of X-ray snapshots from crystals in random orientations. Acta Crystallogr. D 70, 2204-2216 (2014)CrossRefGoogle Scholar
  71. Z. Kam, Determination of macromolecular structure in solution by spatial correlation of scattering fluctuations. Macromolecules 10, 927–934 (1977)ADSCrossRefGoogle Scholar
  72. S. Kassemeyer, A. Jafarpour, L. Lomb, J. Steinbrener, A.V. Martin, I. Schlichting, Optimal mapping of X-ray laser diffraction patterns into three dimensions using routing algorithms. Phys. Rev. E 88, 042710 (2013)ADSCrossRefGoogle Scholar
  73. C.M. Kewish, P. Thibault, O. Bunk, F. Pfeiffer, The potential for two-dimensional crystallography of membrane proteins at future X-ray free-electron laser sources. New J. Phys. 12, 035005 (2010)ADSCrossRefGoogle Scholar
  74. R.A. Kirian, Structure determination through correlated fluctuations in x-ray scattering. J. Phys. B 45, 223001 (2012)ADSCrossRefGoogle Scholar
  75. R.A. Kirian, X.Y. Wang, U. Weierstall, K.E. Schmidt, J.C.H. Spence, M. Hunter, P. Fromme, T. White, H.N. Chapman, J. Holton, Femtosecond protein nanocrystallography-data analysis methods. Opt. Express 18, 5713–5723 (2010)ADSCrossRefGoogle Scholar
  76. R.A. Kirian, K.E. Schmidt, X. Wang, R.B. Doak, J.C.H. Spence, Signal, noise, and resolution in correlated fluctuations from snapshot small-angle X-ray scattering. Phys. Rev. E 84, 011921 (2011)ADSCrossRefGoogle Scholar
  77. R.A. Kirian, R.J. Bean, K.R. Beyerlein, O.M. Yefanov, T.A. White, A. Barty, H.N. Chapman, Phasing coherently illuminated nanocrystals bounded by partial unit cells. Philos. Trans. R. Soc. B 369, 20130331 (2014)CrossRefGoogle Scholar
  78. R.A. Kirian, R.J. Bean, K.R. Beyerlein, M. Barthelmess, C.H. Yoon, F. Wang, F. Capotondi, E. Pedersoli, A. Barty, H.N. Chapman, direct phasing of finite crystals illuminated with a free-electron laser. Phys. Rev. X 5, 011015–011012 (2015)Google Scholar
  79. J. Kirz, C. Jacobsen, M. Howells, Soft X-ray microscopes and their biological applications. Q. Rev. Biophys. 28, 33–130 (1995)CrossRefGoogle Scholar
  80. A.M. Kondratenko, E.L. Saldin, Generating of coherent radiation by a relativistic electron beam in an undulator. Part. Accel. 10, 207–216 (1980)Google Scholar
  81. C. Kupitz, S. Basu, I. Grotjohann, R. Fromme, N.A. Zatsepin, K.N. Rendek, M.S. Hunter, R.L. Shoeman, T.A. White, D. Wang, D. James, J.-H. Yang, D.E. Cobb, B. Reeder, R.G. Sierra, H. Liu, A. Barty, A.L. Aquila, D. Deponte, R.A. Kirian, S. Bari, J.J. Bergkamp, K.R. Beyerlein, M.J. Bogan, C. Caleman, T.-C. Chao, C.E. Conrad, K.M. Davis, H. Fleckenstein, L. Galli, S.P. Hau-Riege, S. Kassemeyer, H. Laksmono, M. Liang, L. Lomb, S. Marchesini, A.V. Martin, M. Messerschmidt, D. Milathianaki, K. Nass, A. Ros, S. Roy-Chowdhury, K. Schmidt, M. Seibert, J. Steinbrener, F. Stellato, L. Yan, C. Yoon, T.A. Moore, A.L. Moore, Y. Pushkar, G.J. Williams, S. Boutet, R.B. Doak, U. Weierstall, M. Frank, H.N. Chapman, J.C.H. Spence, P. Fromme, Serial time-resolved crystallography of photosystem II using a femtosecond X-ray laser. Nature 513, 261–265 (2014)ADSCrossRefGoogle Scholar
  82. J. Küpper, S. Stern, L. Holmegaard, F. Filsinger, A. Rouzée, A. Rudenko, P. Johnsson, A.V. Martin, M. Adolph, A. Aquila, S. Bajt, A. Barty, C. Bostedt, J. Bozek, C. Caleman, R. Coffee, N. Coppola, T. Delmas, S. Epp, B. Erk, L. Foucar, T. Gorkhover, L. Gumprecht, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, N. Kimmel, F. Krasniqi, K.-U. Kühnel, J. Maurer, M. Messerschmidt, R. Moshammer, C. Reich, B. Rudek, R. Santra, I. Schlichting, C. Schmidt, S. Schorb, J. Schulz, H. Soltau, J.C.H. Spence, D. Starodub, L. Struder, J. Thøgersen, M.J.J. Vrakking, G. Weidenspointner, T.A. White, C. Wunderer, G. Meijer, J. Ullrich, H. Stapelfeldt, D. Rolles, H.N. Chapman, X-ray diffraction from isolated and strongly aligned gas-phase molecules with a free-electron laser. Phys. Rev. Lett. 112, 083002 (2014)ADSCrossRefGoogle Scholar
  83. R.P. Kurta, R. Dronyak, M. Altarelli, E. Weckert, I.A. Vartanyants, Solution of the phase problem for coherent scattering from a disordered system of identical particles. New J. Phys. 15, 013059 (2013)ADSCrossRefGoogle Scholar
  84. F. Lehmkühler, C. Gutt, B. Fischer, M.A. Schroer, M. Sikorski, S. Song, W. Roseker, J. Glownia, M. Chollet, S. Nelson, K. Tono, T. Katayama, M. Yabashi, T. Ishikawa, A. Robert, G. Grübel, Single shot coherence properties of the free-electron laser SACLA in the hard X-ray regime. Sci. Rep. 4, 5234 (2014)ADSGoogle Scholar
  85. W. Leitenberger, R. Hartmann, U. Pietsch, R. Andritschke, I. Starke, L. Str∖”uder, Application of a pnCCD in X-ray diffraction: a three-dimensional X-ray detector. J. Synchr. Rad. 15, 449–457 (2008)Google Scholar
  86. P. Li, T.B. Edo, J.M. Rodenburg, Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design. Ultramicroscopy 147, 106–113 (2014)CrossRefGoogle Scholar
  87. H. Liu, J.C.H. Spence, The indexing ambiguity in serial femtosecond crystallography (SFX) resolved using an expectation maximization algorithm. IUCrJ 1, 393–401 (2014)CrossRefGoogle Scholar
  88. P. Liu, P.J. Ziemann, D.B. Kittelson, P.H. McMurry, Generating particle beams of controlled dimensions and divergence: I. Theory of particle motion in aerodynamic lenses and nozzle expansions. Aerosol Sci. Tech. 22, 293–313 (1995)Google Scholar
  89. Z.-C. Liu, R. Xu, Y.-H. Dong, Phase retrieval in protein crystallography. Acta Crystallogr. A 68, 256–265 (2012)CrossRefGoogle Scholar
  90. H. Liu, B.K. Poon, D.K. Saldin, J.C.H. Spence, P.H. Zwart, Three-dimensional single-particle imaging using angular correlations from X-ray laser data. Acta Crystallogr. A 69, 365–373 (2013)MathSciNetCrossRefGoogle Scholar
  91. N.T.D. Loh, V. Elser, Reconstruction algorithm for single-particle diffraction imaging experiments. Phys. Rev. E 80, 026705 (2009)ADSCrossRefGoogle Scholar
  92. N.D. Loh, C.Y. Hampton, A.V. Martin, D. Starodub, R.G. Sierra, A. Barty, A. Aquila, J. Schulz, L. Lomb, J. Steinbrener, R.L. Shoeman, S. Kassemeyer, C. Bostedt, J. Bozek, S.W. Epp, B. Erk, R. Hartmann, D. Rolles, A. Rudenko, B. Rudek, L. Foucar, N. Kimmel, G. Weidenspointner, G. Hauser, P. Holl, E. Pedersoli, M. Liang, M.M. Hunter, L. Gumprecht, N. Coppola, C. Wunderer, H. Graafsma, F.R.N.C. Maia, T. Ekeberg, M. Hantke, H. Fleckenstein, H. Hirsemann, K. Nass, T.A. White, H.J. Tobias, G.R. Farquar, W.H. Benner, S.P. Hau-Riege, C. Reich, A. Hartmann, H. Soltau, S. Marchesini, S. Bajt, M. Barthelmess, P. Bucksbaum, K.O. Hodgson, L. Struder, J. Ullrich, M. Frank, I. Schlichting, H.N. Chapman, M.J. Bogan, Fractal morphology, imaging and mass spectrometry of single aerosol particles in flight. Nature 486, 513–517 (2012)ADSCrossRefGoogle Scholar
  93. L. Lomb, T.R.M. Barends, S. Kassemeyer, A. Aquila, S.W. Epp, B. Erk, L. Foucar, R. Hartmann, B. Rudek, D. Rolles, A. Rudenko, R.L. Shoeman, J. Andreasson, S. Bajt, M. Barthelmess, A. Barty, M.J. Bogan, C. Bostedt, J.D. Bozek, C. Caleman, R. Coffee, N. Coppola, D.P. DePonte, R.B. Doak, T. Ekeberg, H. Fleckenstein, P. Fromme, M. Gebhardt, H. Graafsma, L. Gumprecht, C.Y. Hampton, A. Hartmann, G.u. Hauser, H. Hirsemann, P. Holl, J.M. Holton, M.S. Hunter, W. Kabsch, N. Kimmel, R.A. Kirian, M. Liang, F.R.N.C. Maia, A. Meinhart, S. Marchesini, A.V. Martin, K. Nass, C. Reich, J. Schulz, M.M. Seibert, R. Sierra, H. Soltau, J.C.H. Spence, J. Steinbrener, F. Stellato, S. Stern, N. Timneanu, X. Wang, G. Weidenspointner, U. Weierstall, T.A. White, C. Wunderer, H.N. Chapman, J. Ullrich, L. Struder, I. Schlichting, Radiation damage in protein serial femtosecond crystallography using an X-ray free-electron laser. Phys. Rev. B 84, 214111 (2011)Google Scholar
  94. D.R. Luke, Relaxed averaged alternating reflections for diffraction imaging. Inv. Prob. 21, 37–50 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  95. V.Y. Lunin, A.N. Grum-Grzhimailo, E.V. Gryzlova, D.O. Sinitsyn, T.E. Petrova, N.L. Lunina, N.K. Balabaev, K.B. Tereshkina, A.S. Stepanov, Y.F. Krupyanskii, Efficient calculation of diffracted intensities in the case of nonstationary scattering by biological macromolecules under XFEL pulses. Acta Crystallogr. D 71, 293-303 (2015)CrossRefGoogle Scholar
  96. F.R. Maia, The coherent X-ray imaging data bank. Nat. Methods 9, 854–855 (2012)CrossRefGoogle Scholar
  97. F.R.N.C. Maia, T. Ekeberg, D. van der Spoel, J. Hajdu, Hawk: the image reconstruction package for coherent X-ray diffractive imaging. J. Appl. Cryst. 43, 1535–1539 (2010)CrossRefGoogle Scholar
  98. S. Marchesini, A unified evaluation of iterative projection algorithms for phase retrieval. Rev. Sci. Instrum. 78, 011301 (2007)ADSCrossRefGoogle Scholar
  99. S. Marchesini, H. He, H.N. Chapman, S.P. Hau-Riege, A. Noy, M.R. Howells, U. Weierstall, J.C.H. Spence, X-ray image reconstruction from a diffraction pattern alone. Phys. Rev. B 68, 140101 (2003)ADSCrossRefGoogle Scholar
  100. S. Marchesini, H.N. Chapman, A. Barty, C. Cui, M.R. Howells, J.C.H. Spence, U. Weierstall, A.M. Minor, Phase aberrations in diffraction microscopy. IPAP Conf. Ser. 7, 380–382 (2006)Google Scholar
  101. J. Miao, D. Sayre, On possible extensions of X-ray crystallography through diffraction-pattern oversampling. Acta Crystallogr. A 56, 596–605 (2000)CrossRefGoogle Scholar
  102. J.W. Miao, P. Charalambous, J. Kirz, D. Sayre, Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999)ADSCrossRefGoogle Scholar
  103. J. Miao, Y. Nishino, Y. Kohmura, B. Johnson, C. Song, S.H. Risbud, T. Ishikawa, Quantitative image reconstruction of GaN quantum dots from oversampled diffraction intensities alone. Phys. Rev. Lett. 95, 085503 (2005)ADSCrossRefGoogle Scholar
  104. R. Millane, Multidimensional phase problems. J. Opt. Soc. Am. A 13, 725–734 (1996)ADSCrossRefGoogle Scholar
  105. R.P. Millane, Iterative projection algorithms for solving inverse problems, in Paper Presented at the OCEANS 2003 Marine Technology and Ocean Science Conference. Proceedings, San Diego, Sept (2003)Google Scholar
  106. R.P. Millane, W.H. Hsiao, The basis of phase dominance. Opt. Lett. 34, 2607–2609 (2009)ADSCrossRefGoogle Scholar
  107. R.P. Millane, V.L. Lo, Iterative projection algorithms in protein crystallography. I. Theory. Acta Crystallogr. A 69, 517–527 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  108. A.J. Morgan, M. Prasciolu, A. Andrejczuk, J. Krzywinski, A. Meents, D. Pennicard, H. Graafsma, A. Barty, R.J. Bean, M. Barthelmess, D. Oberthuer, O. Yefanov, A. Aquila, H.N. Chapman, S. Bajt, High numerical aperture multilayer Laue lenses. Sci. Rep. 5, 09892 (2015)ADSCrossRefGoogle Scholar
  109. B. Moths, A. Ourmazd, Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison. Acta Crystallogr. A 67, 481–486 (2011)ADSCrossRefGoogle Scholar
  110. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, J. Hajdu, Potential for biomolecular imaging with femtosecond X-ray pulses. Nature 406, 752–757 (2000)ADSCrossRefGoogle Scholar
  111. K.A. Nugent, Coherent methods in the X-ray sciences. Adv. Phys. 59, 1–99 (2010)ADSCrossRefGoogle Scholar
  112. K. Nugent, A. Peele, H. Chapman, A. Mancuso, Unique phase recovery for nonperiodic objects. Phys. Rev. Lett. 91, 203902 (2003)ADSCrossRefGoogle Scholar
  113. G. Oszlanyi, A. Suto, Ab initio structure solution by charge flipping. Acta Crystallogr. A 60, 134–141 (2004)ADSCrossRefGoogle Scholar
  114. G. Oszlányi, A. Süto, The charge flipping algorithm. Acta Crystallogr. A 64, 123–134 (2008)ADSCrossRefGoogle Scholar
  115. D. Paganin, Coherent X-Ray Optics (OUP, Oxford, 2013)zbMATHGoogle Scholar
  116. K. Pande, P. Schwander, M. Schmidt, D.K. Saldin, Deducing fast electron density changes in randomly orientated uncrystallized biomolecules in a pump-probe experiment. Philos. Trans. R. Soc. B 369, 20130332 (2014)CrossRefGoogle Scholar
  117. B. Patterson, R. Abela, H. Braun, U. Flechsig, R. Ganter, Y. Kim, E. Kirk, A. Oppelt, M. Pedrozzi, S. Reiche, others, Coherent science at the SwissFEL X-ray laser. New J. Phys. 12, 035012 (2010)Google Scholar
  118. B. Pedrini, A. Menzel, M. Guizar-Sicairos, V.A. Guzenko, S. Gorelick, C. David, B.D. Patterson, R. Abela, Two-dimensional structure from random multiparticle X-ray scattering images using cross-correlations. Nat. Commun. 4, 1647 (2013)ADSCrossRefGoogle Scholar
  119. H.M. Quiney, K.A. Nugent, Biomolecular imaging and electronic damage using X-ray free-electron lasers. Nat. Phys. 7, 142–146 (2010)CrossRefGoogle Scholar
  120. J.M. Rodenburg, Ptychography and related diffractive imaging methods, in Advances in Imaging and Electron Physics, vol. 150 (Elsevier, Amsterdam, 2008), pp. 87–184Google Scholar
  121. J.M. Rodenburg, R.H.T. Bates, The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Philos. Trans. R. Soc. Lond. A 339, 521–553 (1992)ADSCrossRefGoogle Scholar
  122. J.M. Rodenburg, H.M.L. Faulkner, A phase retrieval algorithm for shifting illumination. Appl. Phys. Lett. 85, 4795–4797 (2004)ADSCrossRefGoogle Scholar
  123. B. Rupp, Biomolecular Crystallography (Garland Science/Taylor and Francis, New York, 2010)Google Scholar
  124. D. Rupp, M. Adolph, L. Flückiger, T. Gorkhover, J.P. Müller, M. Müller, E. Weckert, D. Wolter, S. Schorb, R. Treusch, C. Bostedt, T. Möller, Generation and structure of extremely large clusters in pulsed jets. J. Chem. Phys. 141, 044306 (2014)ADSCrossRefGoogle Scholar
  125. D.K. Saldin, H.C. Poon, V.L. Shneerson, M. Howells, H.N. Chapman, R.A. Kirian, K.E. Schmidt, J.C.H. Spence, Beyond small-angle X-ray scattering: exploiting angular correlations. Phys. Rev. B 81, 174105 (2010)ADSCrossRefGoogle Scholar
  126. D.K. Saldin, H.C. Poon, M.J. Bogan, S. Marchesini, D.A. Shapiro, R.A. Kirian, U. Weierstall, J.C.H. Spence, New light on disordered ensembles: ab initio structure determination of one particle from scattering fluctuations of many copies. Phys. Rev. Lett. 106, 115501 (2011)ADSCrossRefGoogle Scholar
  127. N.K. Sauter, XFEL diffraction: developing processing methods to optimize data quality. J. Synchr. Rad. 22, 1–10 (2015)CrossRefGoogle Scholar
  128. D. Sayre, Some implications of a theorem due to Shannon. Acta Crystallogr. Sect. A 5, 843–843 (1952)Google Scholar
  129. D. Sayre, Prospects for long-wavelength X-ray microscopy and diffraction, in Imaging Processes and Coherence in Physics: Paper Presented at the Imaging Processes and Coherence in Physics, ed. by M. Schlenker, M. Fink, J.P. Goedgebuer, C. Malgrange, J.Ch. Vieénot, R.H. Wade. Springer Lecture Notes in Physics, vol. 112 (Springer, Berlin/Heidelberg, 1980), pp. 229–235.
  130. D. Sayre, H.N. Chapman, J. Miao, On the extendibility of X-ray crystallography to noncrystals. Acta Crystallogr. A 54, 232-239 (1998)CrossRefGoogle Scholar
  131. K.E. Schmidt, J.C.H. Spence, U. Weierstall, R. Kirian, X. Wang, D. Starodub, H.N. Chapman, M.R. Howells, R.B. Doak, Tomographic femtosecond X-ray diffractive imaging. Phys. Rev. Lett. 101(11), 115507 (2008)Google Scholar
  132. A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, H.J. Lee, B. Nagler, E.C. Galtier, B. Arnold, U. Zastrau, J.B. Hastings, D. Nilsson, F. Uhlen, U. Vogt, H.M. Hertz, C.G. Schroer, Full spatial characterization of a nanofocused X-ray free-electron laser beam by ptychographic imaging. Sci. Rep. 3, 1633 (2013)ADSCrossRefGoogle Scholar
  133. P. Schwander, R. Fung, G.N. Phillips, A. Ourmazd, Mapping the conformations of biological assemblies. New J. Phys. 12, 035007 (2010)ADSCrossRefGoogle Scholar
  134. P. Schwander, D. Giannakis, C.H. Yoon, A. Ourmazd, The symmetries of image formation by scattering. II. Applications. Opt. Express 20, 12827–12849 (2012)CrossRefGoogle Scholar
  135. M.D. Seaberg, B. Zhang, D.F. Gardner, E.R. Shanblatt, M.M. Murnane, H.C. Kapteyn, D.E. Adams, Tabletop nanometer extreme ultraviolet imaging in an extended reflection mode using coherent Fresnel ptychography. Optica 1, 39–44 (2014)CrossRefGoogle Scholar
  136. M.M. Seibert, T. Ekeberg, F.R.N.C. Maia, M. Svenda, J. Andreasson, O. Jonsson, D. Odic, B. Iwan, A. Rocker, D. Westphal, M. Hantke, D.P. Deponte, A. Barty, J. Schulz, L. Gumprecht, N. Coppola, A. Aquila, M.N. Liang, T.A. White, A. Martin, C. Caleman, S. Stern, C. Abergel, V. Seltzer, J.M. Claverie, C. Bostedt, J.D. Bozek, S. Boutet, A.A. Miahnahri, M. Messerschmidt, J. Krzywinski, G. Williams, K.O. Hodgson, M.J. Bogan, C.Y. Hampton, R.G. Sierra, D. Starodub, I. Andersson, S. Bajt, M. Barthelmess, J.C.H. Spence, P. Fromme, U. Weierstall, R. Kirian, M. Hunter, R.B. Doak, S. Marchesini, S.P. Hau-Riege, M. Frank, R.L. Shoeman, L. Lomb, S.W. Epp, R. Hartmann, D. Rolles, A. Rudenko, C. Schmidt, L. Foucar, N. Kimmel, P. Holl, B. Rudek, B. Erk, A. Homke, C. Reich, D. Pietschner, G. Weidenspointner, L. Struder, G. Hauser, H. Gorke, J. Ullrich, I. Schlichting, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K.U. Kuhnel, R. Andritschke, C.D. Schroter, F. Krasniqi, M. Bott, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, H.N. Chapman, J. Hajdu, Single mimivirus particles intercepted and imaged with an X-ray laser. Nature 470, 78–82 (2011)ADSCrossRefGoogle Scholar
  137. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A.M. Neimann, D. Sayre, Biological imaging by soft X-ray diffraction microscopy. Proc. Nat. Acad. Sci. 102, 15343–15346 (2005)ADSCrossRefGoogle Scholar
  138. V.L. Shneerson, A. Ourmazd, D.K. Saldin, Crystallography without crystals. I. The common-line method for assembling a three-dimensional diffraction volume from single-particle scattering. Acta Crystallogr. A 64, 303–315 (2008)Google Scholar
  139. R.G. Sierra, H. Laksmono, J. Kern, R. Tran, J. Hattne, R. Alonso-Mori, B. Lassalle-Kaiser, C. Glockner, J. Hellmich, D.W. Schafer, N. Echols, R.J. Gildea, R.W. Grosse-Kunstleve, J. Sellberg, T.A. McQueen, A.R. Fry, M.M. Messerschmidt, A. Miahnahri, M.M. Seibert, C.Y. Hampton, D. Starodub, N.D. Loh, D. Sokaras, T.C. Weng, P.H. Zwart, P. Glatzel, D. Milathianaki, W.E. White, P.D. Adams, G.J. Williams, S. Boutet, A. Zouni, J. Messinger, N.K. Sauter, U. Bergmann, J. Yano, V.K. Yachandra, M.J. Bogan, Nanoflow electrospinning serial femtosecond crystallography. Acta Crystallogr. D 68, 1584–1587 (2012)CrossRefGoogle Scholar
  140. J.M. Slowik, S.K. Son, G. Dixit, Z. Jurek, R. Santra, Incoherent X-ray scattering in single molecule imaging. New J. Phys. 16, 073042 (2014)ADSCrossRefGoogle Scholar
  141. J.C. Solem, G.C. Baldwin, Microholography of living organisms. Science 218, 229–235 (1982)ADSCrossRefGoogle Scholar
  142. S.-K. Son, H.N. Chapman, R. Santra, Multiwavelength anomalous diffraction at high X-ray intensity. Phys. Rev. Lett. 107, 218102 (2011)ADSCrossRefGoogle Scholar
  143. C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, J. Miao, Phase retrieval from exactly oversampled diffraction intensity through deconvolution. Phys. Rev. B 75, 012102 (2007)ADSCrossRefGoogle Scholar
  144. J.C.H. Spence, R.B. Doak, Single molecule diffraction. Phys. Rev. Lett. 92, 198102 (2004)ADSCrossRefGoogle Scholar
  145. J.C.H. Spence, U. Weierstall, M. Howells, Coherence and sampling requirements for diffractive imaging. Ultramicros 101, 149–152 (2004)CrossRefGoogle Scholar
  146. J.C.H. Spence, R.A. Kirian, X. Wang, U. Weierstall, K.E. Schmidt, T. White, A. Barty, H.N. Chapman, S. Marchesini, J. Holton, Phasing of coherent femtosecond X-ray diffraction from size-varying nanocrystals. Opt. Express 19, 2866 (2011)ADSCrossRefGoogle Scholar
  147. H. Stapelfeldt, T. Seideman, Colloquium: aligning molecules with strong laser pulses. Rep. Prog. Phys. 75, 543–557 (2003)Google Scholar
  148. D. Starodub, A. Aquila, S. Bajt, M. Barthelmess, A. Barty, C. Bostedt, J.D. Bozek, N. Coppola, R.B. Doak, S.W. Epp, B. Erk, L. Foucar, L. Gumprecht, C.Y. Hampton, A. Hartmann, R. Hartmann, P. Holl, S. Kassemeyer, N. Kimmel, H. Laksmono, M. Liang, N.D. Loh, L. Lomb, A.V. Martin, K. Nass, C. Reich, D. Rolles, B. Rudek, A. Rudenko, J. Schulz, R.L. Shoeman, R.G. Sierra, H. Soltau, J. Steinbrener, F. Stellato, S. Stern, G. Weidenspointner, M. Frank, J. Ullrich, L. Strüder, I. Schlichting, H.N. Chapman, J.C.H. Spence, M.J. Bogan, Single-particle structure determination by correlations of snapshot X-ray diffraction patterns. Nat. Commun. 3, 1276–1277 (2012)ADSCrossRefGoogle Scholar
  149. H. Stark, Image Recovery: Theory and Application (Academic, London, 1987)zbMATHGoogle Scholar
  150. L. Struder, S. Eppa, D. Rolles, R. Hartmann, P. Holl, G. Lutz, H. Soltau, R. Eckart, C. Reich, K. Heinzinger, C. Thamm, A. Rudenko, F. Krasniqi, K.U. Kuhnel, C. Bauer, C.D. Schroter, R. Moshammer, S. Techert, D. Miessner, M. Porro, O. Halker, N. Meidinger, N. Kimmel, R. Andritschke, F. Schopper, G. Weidenspointner, A. Ziegler, D. Pietschner, S. Herrmann, U. Pietsch, A. Walenta, W. Leitenberger, C. Bostedt, T. Moller, D. Rupp, M. Adolph, H. Graafsma, H. Hirsemann, K. Gartner, R. Richter, L. Foucar, R.L. Shoeman, I. Schlichting, J. Ullrich, Large-format, high-speed, X-ray pnCCDs combined with electron and ion imaging spectrometers in a multipurpose chamber for experiments at 4th generation light sources. Nucl. Instrum. Methods Phys. Res. A 614, 483–496 (2010)ADSCrossRefGoogle Scholar
  151. M. Suga, F. Akita, K. Hirata, G. Ueno, H. Murakami, Y. Nakajima, T. Shimizu, K. Yamashita, M. Yamamoto, H. Ago, J.-R. Shen, Native structure of photosystem II at 1.95 Åresolution viewed by femtosecond X-ray pulses. Nature 517, 99–103 (2014)Google Scholar
  152. A. Szoke, Diffraction of partially coherent X-rays and the crystallographic phase problem. Acta Crystallogr. A 57, 586–603 (2001)CrossRefGoogle Scholar
  153. J. Tenboer, S. Basu, N. Zatsepin, K. Pande, D. Milathianaki, M. Frank, M. Hunter, S. Boutet, G.J. Williams, J.E. Koglin, D. Oberthuer, M. Heymann, C. Kupitz, C. Conrad, J. Coe, S. Roy-Chowdhury, U. Weierstall, D. James, D. Wang, T. Grant, A. Barty, O. Yefanov, J. Scales, C. Gati, C. Seuring, V. Srajer, R. Henning, P. Schwander, R. Fromme, A. Ourmazd, K. Moffat, J.J. Van Thor, J.C.H. Spence, P. Fromme, H.N. Chapman, M. Schmidt, Time-resolved serial crystallography captures high-resolution intermediates of photoactive yellow protein. Science 346, 1242–1246 (2014)ADSCrossRefGoogle Scholar
  154. M. Tegze, G. Bortel, Atomic structure of a single large biomolecule from diffraction patterns of random orientations. J. Struct. Biol. 179, 41–45 (2012)CrossRefGoogle Scholar
  155. P. Thibault, V. Elser, X-ray diffraction microscopy. Ann. Rev. Cond. Matt. Phys. 1, 237-255 (2010)ADSCrossRefGoogle Scholar
  156. P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, D. Sayre, Reconstruction of a yeast cell from X-ray diffraction data. Acta Crystallogr. A 62, 248–261 (2006)ADSCrossRefGoogle Scholar
  157. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, F. Pfeiffer, High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382 (2008)ADSCrossRefGoogle Scholar
  158. J. Vila-Comamala, A. Diaz, M. Guizar-Sicairos, A. Mantion, C.M. Kewish, A. Menzel, O. Bunk, C. David, Characterization of high-resolution diffractive X-ray optics by ptychographic coherent diffractive imaging. Opt. Express 19, 21333–21344 (2011)ADSCrossRefGoogle Scholar
  159. B.E. Warren, X-Ray Diffraction (Dover, New York, 1990)Google Scholar
  160. U. Weierstall, J.C.H. Spence, R.B. Doak, Injector for scattering measurements on fully solvated biospecies. Rev. Sci. Instrum. 83, 035108 (2012)ADSCrossRefGoogle Scholar
  161. U. Weierstall, D. James, C. Wang, T.A. White, D. Wang, W. Liu, J.C.H. Spence, R. Bruce Doak, G. Nelson, P. Fromme, R. Fromme, I. Grotjohann, C. Kupitz, N.A. Zatsepin, H. Liu, S. Basu, D. Wacker, G. Won Han, V. Katritch, S. Boutet, M. Messerschmidt, G.J. Williams, J.E. Koglin, M. Marvin Seibert, M. Klinker, C. Gati, R.L. Shoeman, A. Barty, H.N. Chapman, R.A. Kirian, K.R. Beyerlein, R.C. Stevens, D. Li, S.T.A. Shah, N. Howe, M. Caffrey, V. Cherezov, Lipidic cubic phase injector facilitates membrane protein serial femtosecond crystallography. Nat. Commun. 5, 3309 (2014)ADSCrossRefGoogle Scholar
  162. T.A. White, Post-refinement method for snapshot serial crystallography. Philos. Trans. R. Soc. B 369, 20130330 (2014)CrossRefGoogle Scholar
  163. L.W. Whitehead, G.J. Williams, H.M. Quiney, D.J. Vine, R.A. Dilanian, S. Flewett, K.A. Nugent, I. McNulty, Diffractive imaging using partially coherent X-rays. Phys. Rev. Lett. 103, 243902 (2009)ADSCrossRefGoogle Scholar
  164. G.J. Williams, H.M. Quiney, B.B. Dhal, C.Q. Tran, K.A. Nugent, A.G. Peele, D. Paterson, M.D. de Jonge, Fresnel coherent diffractive imaging. Phys. Rev. Lett. 97, 025506 (2006)ADSCrossRefGoogle Scholar
  165. S.-K. Son, R. Santra, XATOM–an integrated toolkit for x-ray and atomic physics, rev. 889 (CFEL, DESY, Hamburg, 2013)Google Scholar
  166. M. Yabashi, K. Tono, H. Mimura, S. Matsuyama, K. Yamauchi, T. Tanaka, H. Tanaka, K. Tamasaku, H. Ohashi, S. Goto, T. Ishikawa, Optics for coherent X-ray applications. J. Synchr. Rad. 21, 976–985 (2014)CrossRefGoogle Scholar
  167. O. Yefanov, C. Gati, G. Bourenkov, R.A. Kirian, T.A. White, J.C.H. Spence, H.N. Chapman, A. Barty, Mapping the continuous reciprocal space intensity distribution of X-ray serial crystallography. Philos. Trans. R. Soc. B 369, 20130333 (2014)CrossRefGoogle Scholar
  168. C.H. Yoon, P. Schwander, C. Abergel, I. Andersson, J. Andreasson, A. Aquila, S. von s a Bajt, M. Barthelmess, A. Barty, M.J. Bogan, C. Bostedt, J. Bozek, H.N. Chapman, J.-M. Claverie, N. Coppola, D.P. DePonte, T. Ekeberg, S.W. Epp, B. Erk, H. Fleckenstein, L. Foucar, H. Graafsma, L. Gumprecht, J. Hajdu, C.Y. Hampton, A. Hartmann, E. Hartmann, R. Hartmann, G. Hauser, H. Hirsemann, P. Holl, S. Kassemeyer, N. Kimmel, M. Kiskinova, M. Liang, N.-T.D. Loh, L. Lomb, F.R.N.C. Maia, A.V. Martin, K. Nass, E. Pedersoli, C. Reich, D. Rolles, B. Rudek, A. Rudenko, I. Schlichting, J. Schulz, M. Seibert, V. Seltzer, R.L. Shoeman, R.G. Sierra, H. Soltau, D. Starodub, J. Steinbrener, G. Stier, L. Strüder, M. Svenda, J. Ullrich, G. Weidenspointner, T.A. White, C. Wunderer, A. Ourmazd, Unsupervised classification of single-particle X-ray diffraction snapshots by spectral clustering. Opt. Express 19, 16542–16549 (2011)Google Scholar
  169. C.H. Yoon, M. Barthelmess, R.J. Bean, F. Capotondi, R.A. Kirian, M. Kiskinova, E. Pedersoli, L. Raimondi, F. Stellato, F.L. Wang, H.N. Chapman, Conformation sequence recovery of a non-periodic object from a diffraction-before-destruction experiment. Opt. Express 22, 8085-8093 (2014)ADSCrossRefGoogle Scholar
  170. W.-B. Yun, J. Kirz, D. Sayre, Observation of the soft X-ray diffraction pattern of a single diatom. Acta Crystallogr. A 43, 131–133 (1987)CrossRefGoogle Scholar
  171. K.Y.J. Zhang, P. Main, Histogram matching as a new density modification technique for phase refinement and extension of protein molecules. Acta Crystallogr. A 46, 41–46 (1990)CrossRefGoogle Scholar
  172. G. Zheng, R. Horstmeyer, C. Yang, Wide-field, high-resolution Fourier ptychographic microscopy. Nat. Photon. 7, 739–745 (2013)ADSCrossRefGoogle Scholar
  173. B. Ziaja, Z. Jurek, N. Medvedev, V. Saxena, S.-K. Son, R. Santra, Towards realistic simulations of macromolecules irradiated under the conditions of coherent diffraction imaging with an X-ray free-electron laser. Photonics 2, 256–269 (2015)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of PhysicsArizona State UniversityTempe,AZUSA
  2. 2.Center for Free-Electron Laser Science CFEL, Deutsches Elektronen Synchrotron DESYUniversity of HamburgHamburgGermany

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