Eur. Phys. J. D 48, 459–463 (2008) DOI: 10.1140/epjd/e2008-00123-2 T HE EUROPEAN P HYSICAL JOURNAL D Optimization of the wave front of high order harmonics J. Gautier 1, a , P. Zeitoun 1 , C. Hauri 1 , A.-S. Morlens 1 , G. Rey 1 , C. Valentin 1 , E. Papalarazou 1 , J.-P. Goddet 1 , S. Sebban 1 , F. Burgy 1 , P. Merc` ere 2 , M. Idir 2 , G. Dovillaire 3 , X. Levecq 3 , S. Bucourt 3 , M. Fajardo 4 , H. Merdji 5 , and J.-P. Caumes 5 1 Laboratoire d’Optique Appliqu´ ee, ´ Ecole Nationale Sup´ erieure de Technique Avanc´ ees, ´ Ecole Polytechnique, CNRS UMR7639, Chemin de la Huni` ere, 91761 Palaiseau Cedex, France 2 Synchrotron SOLEIL, 91192 Gif-sur-Yvette Cedex, France 3 Imagine Optic, 18 rue Charles de Gaulle, 91400 Orsay, France 4 Instituto de Plasmas e Fus˜ao Nuclear, Instituto Superior T´ ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal 5 Commissariat `a l’ ´ Energie Atomique, Service des Photons, Atomes et Mol´ ecules, Bˆatiment 522, Centre d’ ´ Etude de Saclay, 91191 Gif-sur-Yvette, France Received 15 January 2008 / Received in final form 17 March 2008 Published online 18 June 2008 – c  EDP Sciences, Societ`a Italiana di Fisica, Springer-Verlag 2008 Abstract. We present a full optimization of the high harmonics wave front owing to the use of a soft X-ray Hartmann sensor. The sensor was calibrated using a high harmonic source with an accuracy of λ/50 root- mean-square (rms) with λ around 30 nm. We observed a high harmonic wave front of λ/7 rms, which is two times the diffraction-limit, astigmatism being the dominant aberration for every condition of generation. By clipping slightly the unfocused high harmonic beam, it is possible to produce a diffraction-limited beam containing approximately 90% of the incident energy. PACS. 42.15.Dp Wave fronts and ray tracing – 07.85.Fv X- and gamma-ray sources, mirrors, gratings, and detectors The High order Harmonics generated (HHG) by highly nonlinear interaction between atoms in a gas and an in- tense laser pulse provide an efficient source of soft X-ray radiation. High harmonic sources have high brightness [1], ultra-short pulse duration [2] and a high degree of spatial coherence [3]. Numerous applications have been achieved so far reaping the benefits of the unique properties of the HHG beam, such as its attosecond duration for following the ultra-fast dynamics of electrons, atoms or molecules [4] or its coherence for phase imaging, for example soft X-ray interferometry [5] or holography [6,7]. Since every phase- imaging experiment uses a reference wave, the wave front of the HHG beam must be of high optical quality, ideally diffraction-limited (DL), in order to record a distortion- free image. The wave front is defined as the surface of isophase of an electromagnetic wave. The possibility of combining the femtosecond down to attosecond pulse du- ration with the phase imaging would open up an even wider field of applications via single shot experiments [8]. Although high harmonics present excellent spatial and temporal properties, their peak flux is too low for sin- gle shot experiments. Nevertheless, this limitation can be overcome by seeding the HHG beam in a laser plasma amplifier [9] or in a free-electron laser [10] resulting in a dramatic increase of the beam intensity. In these config- a e-mail: julien.gautier@ensta.fr urations, the HHG wave front will largely determine the optical quality of the seeded soft X-ray laser achieved af- ter amplification. For seeding or for phase-imaging exper- iments, the key parameter is the energy contained in the diffraction-limited portion of the beam. The Marechal’s criterion [11] stands that a beam is diffraction-limited at a given wavelength, λ, when the aberrant wave front amplitude is lower than λ/14 root-mean-square (rms). To the authors’ knowledge, high harmonics wave front has been measured only once using a point-diffraction interferometry method [12], but without any optimization of the harmonic generation process. Furthermore, in the study reported in reference [12] the experimental error was approximately λ/15 rms, too close to the Marechal’s cri- terion for ensuring accurate measurement of the high har- monic wave front. A much higher degree of accuracy, as high as λ/120 rms at 13 nm, has since been demonstrated using soft X-ray wave front sensors based on the so-called Hartmann technique [13]. In this letter we present a full study of the high harmonic wave front for different gen- eration conditions and their optimization owing to the use of a soft X-ray Hartman wave front sensor based on the system originally developed by Merc` ere et al. [13]. In Hartmann wave-front analysis a beam passes through a hole-array and is projected onto a charge coupled de- vice (CCD) camera that detects the beamlet sampled by