Previously reported crystalline structures obtained by an iterative phase retrieval reconstruction of their diffraction patterns seem to be free from displaying any irregularities or defects in the lattice, which appears to be unrealistic. We demonstrate here that the structure of a nanocrystal including its atomic defects can unambiguously be recovered from its diffraction pattern alone by applying a direct phase retrieval procedure not relying on prior information of the object shape. Individual point defects in the atomic lattice are clearly apparent. Conventional phase retrieval routines assume isotropic scattering. We show that when dealing with electrons, the quantitatively correct transmission function of the sample cannot be retrieved due to anisotropic, strong forward scattering specific to electrons. We summarize the conditions for this phase retrieval method and show that the diffraction pattern can be extrapolated beyond the original record to even reveal formerly not visible Bragg peaks. Such extrapolated wave field pattern leads to enhanced spatial resolution in the reconstruction.

1.
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.
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.
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
, and
J. C. H.
Spence
,
Nature
470
(
7332
),
73
(
2011
).
2.
J. W.
Miao
,
P.
Charalambous
,
J.
Kirz
, and
D.
Sayre
,
Nature
400
(
6742
),
342
(
1999
).
3.
J. M.
Zuo
,
I.
Vartanyants
,
M.
Gao
,
R.
Zhang
, and
L. A.
Nagahara
,
Science
300
(
5624
),
1419
(
2003
).
4.
W. J.
Huang
,
J. M.
Zuo
,
B.
Jiang
,
K. W.
Kwon
, and
M.
Shim
,
Nature Phys.
5
(
2
),
129
(
2009
).
5.
O.
Kamimura
,
T.
Dobashi
,
K.
Kawahara
,
T.
Abe
, and
K.
Gohara
,
Ultramicroscopy
110
(
2
),
130
(
2010
).
6.
L.
De Caro
,
E.
Carlino
,
G.
Caputo
,
P. D.
Cozzoli
, and
C.
Giannini
,
Nat. Nanotechnol.
5
(
5
),
360
(
2010
).
7.
J.-N.
Longchamp
,
T.
Latychevskaia
,
C.
Escher
, and
H.-W.
Fink
,
Phys. Rev. Lett.
110
(
25
),
255501
(
2013
).
8.
M. v.
Laue
,
Ann. Phys.
418
(
1
),
55
(
1936
).
9.
J. C. H.
Spence
,
R. A.
Kirian
,
X. Y.
Wang
,
U.
Weierstall
,
K. E.
Schmidt
,
T.
White
,
A.
Barty
,
H. N.
Chapman
,
S.
Marchesini
, and
J.
Holton
,
Opt. Express
19
(
4
),
2866
(
2011
).
10.
L. D.
Landau
and
E. M.
Lifshitz
,
Quantum Mechanics: Non-Relativistic Theory (Course of Theoretical Physics)
, 3rd ed. (
Pergamon Press
,
Oxford
,
1977
).
11.
NIST
,
NIST Electron Elastic-Scattering Cross-Section Database
,
2000
.
12.
M. A.
Van Hove
, The Barbieri/Van Hove phase shift calculation package "phshift2007" available at http://www.icts.hkbu.edu.hk/surfstructinfo/SurfStrucInfo_files/leed/leedpack.html.
13.
J. C.
Meyer
,
A. K.
Geim
,
M. I.
Katsnelson
,
K. S.
Novoselov
,
D.
Obergfell
,
S.
Roth
,
C.
Girit
, and
A.
Zettl
,
Solid State Commun.
143
(
1–2
),
101
(
2007
).
14.
R.
Zan
,
Q. M.
Ramasse
,
R.
Jalil
, and
U.
Bangert
, in
Advances in Graphene Science
, edited by
M.
Aliofkhazraei
(
InTech
,
2013
).
15.
I. K.
Robinson
,
I. A.
Vartanyants
,
G. J.
Williams
,
M. A.
Pfeifer
, and
J. A.
Pitney
,
Phys. Rev. Lett.
87
(
19
),
195505
(
2001
).
16.
G. J.
Williams
,
M. A.
Pfeifer
,
I. A.
Vartanyants
, and
I. K.
Robinson
,
Phys. Rev. Lett.
90
(
17
),
175501
(
2003
).
17.
I.
Robinson
and
R.
Harder
,
Nat. Mater.
8
(
4
),
291
(
2009
).
18.
R.
Harder
,
M.
Liang
,
Y.
Sun
,
Y.
Xia
, and
I. K.
Robinson
,
New J. Phys.
12
,
035019
(
2010
).
19.
M. C.
Newton
,
S. J.
Leake
,
R.
Harder
, and
I. K.
Robinson
,
Nat. Mater.
9
(
2
),
120
(
2010
).
20.
J. R.
Fienup
,
Appl. Opt.
21
(
15
),
2758
(
1982
).
21.
T.
Latychevskaia
and
H.-W.
Fink
,
Phys. Rev. Lett.
98
(
23
),
233901
(
2007
).
22.
R.
Neutze
,
R.
Wouts
,
D.
van der Spoel
,
E.
Weckert
, and
J.
Hajdu
,
Nature
406
(
6797
),
752
(
2000
).
23.
R. W.
Gerchberg
,
Opt. Acta
21
(
9
),
709
(
1974
).
24.
A.
Papoulis
,
IEEE Trans. Circuits Syst.
22
(
9
),
735
(
1975
).
25.
T.
Latychevskaia
and
H.-W.
Fink
,
Appl. Phys. Lett.
103
(
20
),
204105
(
2013
).
26.
T.
Latychevskaia
and
H.-W.
Fink
,
Opt. Express
21
(
6
),
7726
(
2013
).
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