PHYSICAL REVIEW A 89, 053415 (2014) Progress toward time-resolved molecular imaging: A theoretical study of optimal parameters in static photoelectron holography S. X.-L. Sun, 1 A. P. Kaduwela, 2, 3 A. X. Gray, 1, 4, 5 and C. S. Fadley 1, 4 1 Department of Physics, University of California Davis, Davis, California 95616, USA 2 Air Resources Board, California Environmental Protection Agency, Sacramento, California 95814, USA 3 Department of Land, Air, and Water Resources, University of California Davis, Davis, California 95616, USA 4 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA 5 Stanford Institute for Materials and Energy Science, Stanford University and SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94029, USA (Received 2 August 2013; revised manuscript received 8 March 2014; published 15 May 2014) The availability of short-pulse free-electron lasers has led to the idea of using photoelectron holography as a method of directly imaging molecular dissociations or reactions in real time, as, e.g., in a recent theoretical study by Krasniqi et al., [F. Krasniqi, B. Najjari, L. Str¨ uder, D. Rolles, A. Voitkiv, and J. Ullrich, Phys. Rev. A 81, 033411 (2010)]. In this paper, we extend this earlier work and in particular look at two critical questions concerning the optimum type of data required for such holographic imaging: the choice of photoelectron kinetic energy (e.g., ∼300 eV versus ∼1700 eV as in the prior study), and the use of a single energy or multiple energies. After verifying that our calculations fully duplicate those in this prior paper, we show that using lower energies is preferable to using higher energies for image quality, a conclusion consistent with prior photoelectron holography studies at surfaces, and that multiple lower energies in which the hologram effectively spans a volume in kspace yields the best quality images that should be useful for such “molecular movies.” Although the amount of data required for such multi-energy holography is roughly an order of magnitude higher than that for single energy, the reduction of artifacts and the improved quality of the images suggest this as the optimum ultimate future strategy for such dynamic imaging. DOI: 10.1103/PhysRevA.89.053415 PACS number(s): 61.05.js, 78.47.jh I. INTRODUCTION Photoelectron holography (PH) was originally developed in the surface science community for studying near-surface atomic structure. It was first realized by Sz ¨ oke [1] that a core- level photoelectron diffraction (PD) pattern could be consid- ered to be a hologram which could be mathematically inverted to produce an image of the atoms around the emitter. Shortly thereafter, Barton [2] extended this idea into a more powerful multi-energy formulation that reduced image distortions and artifacts, including twin images. There have by now been a number of papers discussing the unique merits and limitations of PH compared to other atomic structure methods, including various refinements in the imaging algorithms to further im- prove structural accuracy [3–11]. As one indicator of activity, the Web of Science presently lists 150 papers involving the topic “photoelectron holography,” with interest at the present growing again after an initial burst of activity in the 1990s. Early on, it was also realized that PD effects are present in the angular distributions in core-level photoemission from free molecules [12,13], and that the multiple-scattering theoretical methodologies developed for studies of surface species could be used with small modifications to describe such data [14]. Most recently, with the development of several free-electron laser facilities in the world with unprecedented brightness and pulse widths in the femtosecond regime [15–17], it has been pointed out by Krasniqi et al. [18] that PH has the potential for producing real-time “movies” of atomic motion in molecular dissociations and reactions, e.g., as initiated by some sort of pump pulse. These authors have also presented theoretical calculations of single-energy PD patterns and atomic images for a test-case molecule (chlorobenzene) as excited by a hard x ray so as to produce photoelectrons at ∼1700 eV in a feasible experimental geometry and with two different radiation polarizations. The basic idea of photoelectron holography is illustrated in Fig. 1. The unscattered component of an outgoing core- photoelectron wave is considered the reference wave in a standard holographic description and the scattered components the object waves in the same sense. The measured PD pattern is then the hologram, and is usually normalized by somehow dividing out the intensity profile of the reference wave in the absence of scattering. The strong forward scattering effects that arise for photoelectrons in the keV range is known to produce image distortions in PH images that can be difficult to correct, and this has led to a proposal to suppress emission in the forward direction by going to a geometry in which the differential photoelectric cross sections are small or zero along the direction pointing toward a given strong scatterer [19]. One can thus speak of a “nodal” plane in the cross section, and for example, this is the plane of directions perpendicular to the light polarization for emission from an s subshell. In this paper, we extend the prior work by Krasniqi et al. [18] so as to explore improving the quality of the reconstructed image of the molecular structure in two ways: by exploring the choice of outgoing photoelectron kinetic energy or energies and by asking whether single or multiple photoelectron kinetic energies should be employed to optimize the image quality. It is important to note, however, that going to lower-energy photoelectrons to reduce the degree of forward scattering and enhance the degree of back scattering, and using multiple energies to reduce twin images and reduce image artifacts, 1050-2947/2014/89(5)/053415(8) 053415-1 ©2014 American Physical Society