The Ptychographical Iterative Engine (PIE) algorithm is a recently developed novel method of Coherent Diffractive Imaging (CDI) that uses multiple overlapping diffraction patterns to reconstruct an image. This method has successfully produced high quality reconstructions at both optical and X-ray wavelengths but the need for accurate knowledge of the probe positions is currently a limiting factor in the production of high resolution reconstructions at electron wavelengths. This paper examines the shape of the search landscape for producing optimal image reconstructions in the specific case of electron microscopy and then shows how evolutionary search methods can be used to reliably determine experimental parameters in the electron microscopy case (such as the spherical aberration in the probe and the probe positions).

1.
R.
Erni
,
M. D.
Rossell
,
C.
Kisielowski
, and
U.
Dahmen
,
Phys. Rev. Lett.
102
,
096101
, (
2009
).
2.
S.
Marchesini
,
Rev. Sci. Instrum.
78
,
011301
(
2007
).
3.
W.
Hoppe
,
Acta Crystallograph. Sec. A
25
,
495
(
1969
).
4.
W.
Hoppe
and
G.
Strube
,
Acta Crystallograph. Sec. A
25
,
502
(
1969
).
5.
W.
Hoppe
,
Acta Crystallograph. Sec. A
25
,
508
(
1969
).
6.
W.
Hoppe
,
Ultramicroscopy
10
,
187
(
1982
).
7.
J. M.
Rodenburg
,
Adv. Imag. Electron Phys.
150
,
87
(
2008
).
8.
J. M.
Rodenburg
and
R. H. T.
Bates
,
Philos. Trans. R. Soc. A
339
,
521
(
1992
).
9.
B. C.
Mccallum
and
J. M.
Rodenburg
,
Ultramicroscopy
45
,
371
(
1992
).
10.
H. M. L.
Faulkner
and
J. M.
Rodenburg
,
Phys. Rev. Lett.
93
(
2004
).
11.
M.
Guizar-Sicairos
and
J. R.
Fienup
,
Opt. Express
16
,
7264
(
2008
).
12.
P.
Thibault
,
M.
Dierolf
,
O.
Bunk
,
A.
Menzel
, and
F.
Pfeiffer
,
Ultramicroscopy
109
,
338
(
2009
).
13.
J. M.
Rodenburg
,
A. C.
Hurst
,
A. G.
Cullis
,
B. R.
Dobson
,
F.
Pfeiffer
,
O.
Bunk
,
C.
David
,
K.
Jefimovs
, and
I.
Johnson
,
Phys. Rev. Lett.
98
,
034801
, (
2007
).
14.
P.
Thibault
,
M.
Dierolf
,
A.
Menzel
,
O.
Bunk
,
C.
David
, and
F.
Pfeiffer
,
Science
321
,
379
(
2008
).
15.
A. M.
Maiden
and
J. M.
Rodenburg
,
Ultramicroscopy
109
,
1256
(
2009
).
16.
J. M.
Rodenburg
and
H. M. L.
Faulkner
,
Appl. Phys. Lett.
85
,
4795
(
2004
).
17.
A.
Schropp
,
P.
Boye
,
J. M.
Feldkamp
,
R.
Hoppe
,
J.
Patommel
,
D.
Samberg
,
S.
Stephan
,
K.
Giewekemeyer
,
R. N.
Wilke
,
T.
Salditt
,
J.
Gulden
,
A. P.
Mancuso
,
I. A.
Vartanyants
,
E.
Weckert
,
S.
Schder
,
M.
Burghammer
, and
C. G.
Schroer
,
Appl. Phys. Lett.
96
,
091102
(
2010
).
18.
G. R.
Brady
,
M.
Guizar-Sicairos
, and
J. R.
Fienup
,
Opt. Express
17
,
624
(
2009
).
19.
M.
Guizar-Sicairos
and
J. R.
Fienup
,
Opt. Express
17
,
2670
(
2009
).
20.
F.
Hue
,
J. M.
Rodenburg
,
A. M.
Maiden
,
F.
Sweeney
, and
P. A.
Midgley
,
Phys. Rev. B
82
(
2010
).
21.
R. W.
Gerchberg
and
W. O.
Saxton
,
Optik
35
,
237
(
1972
).
22.
E. J.
Kirkland
,
Advanced Computing in Electron Microscopy
(
Plenum Press
,
New York
,
1998
).
23.
H. M. L.
Faulkner
and
J. M.
Rodenburg
,
Ultramicroscopy
103
,
153
(
2005
).
24.
D. E.
Goldberg
,
Genetic Algorithms in Search, Optimization and Machine Learning
(
Addison-Wesley
,
Reading, MA
,
1989
).
25.
D. B.
Fogel
and
A.
Ghoziel
,
IEEE Trans. Evolution. Comput.
1
,
159
(
1997
).
26.
Z.
Michalewicz
and
D. B.
Fogel
,
How to Solve It: Modern Heuristics
(
Springer
,
Berlin
,
2000
).
27.
J. E.
Baker
, in
Proceedings of the Second International Conference on Genetic Algorithms
, edited by
J. J.
Grefenstette
(
Lawrence Erlbaum Associates
,
New Jersey
,
1987
) pp.
14
21
.
28.
P. J. B.
Hancock
, in
Evolutionary Computing - AISB Workshop, Lecture Notes in Computer Science
, Vol.
865
, edited by
T. C.
Fogarty
(
Springer-Verlag
,
Berlin
,
1994
) pp.
80
94
.
29.
K.
Deb
,
Multi-Objective Optimization Using Evolutionary Algorithms
(
John Wiley and Sons
,
New York
,
2001
).
30.
K.
Deb
and
M.
Goyal
,
Comput. Sci. Inf.
26
,
30
(
1996
).
You do not currently have access to this content.