Error analysis of ellipsoidal mirrors for soft X-ray focusing by wave-optical simulation

The ellipsoidal mirror is an ideal soft X-ray focusing optic that enables achromatic and highly efficient focusing to a nanometer spot size; however, a high-quality surface is necessary for ideal focusing. Knowledge of the required figure accuracy is important for fabrication. In this paper, we analyze the effects of figure errors on the focusing performance through wave-optical calculations based on the Fresnel?Kirchhoff diffraction theory, assuming coherent soft X-rays. Figure errors are classified into three types from the viewpoint of manufacturing. The effect of the alignment error is also investigated. The analytical results quantitatively indicate criteria regarding figure accuracy, which are expected to be essential for the development of high-performance ellipsoidal soft X-ray focusing mirrors.

[1]  T. Ishikawa,et al.  Development of mirror manipulator for hard-x-ray nanofocusing at sub-50-nm level , 2006 .

[2]  T. Ishikawa,et al.  Wave-optical evaluation of interference fringes and wavefront phase in a hard-x-ray beam totally reflected by mirror optics. , 2005, Applied optics.

[3]  Hidekazu Mimura,et al.  Highly accurate differential deposition for X‐ray reflective optics , 2008 .

[4]  Hidekazu Mimura,et al.  Effect of focusing flow on stationary spot machining properties in elastic emission machining , 2013, Nanoscale Research Letters.

[5]  E. Takahashi,et al.  Low-divergence coherent soft x-ray source at 13 nm by high-order harmonics , 2004 .

[6]  D. Ratner,et al.  First lasing and operation of an ångstrom-wavelength free-electron laser , 2010 .

[7]  T. Ishikawa,et al.  A compact X-ray free-electron laser emitting in the sub-ångström region , 2012, Nature Photonics.

[8]  W. Chao,et al.  Real space soft x-ray imaging at 10 nm spatial resolution. , 2012, Optics express.

[9]  A. Moewes,et al.  A scanning soft x-ray microscope with an ellipsoidal focusing mirror. , 1992, Journal of X-ray science and technology.

[10]  S. Aoki,et al.  Laboratory-Scale Soft X-ray Imaging Microtomography Using Wolter Mirror Optics , 2008 .

[11]  Kazuto Yamauchi,et al.  Simulation study of four-mirror alignment of advanced Kirkpatrick−Baez optics , 2010 .

[12]  O. Mitomi,et al.  Influence of fabrication errors on wölter mirror imaging performance. , 1998, Applied optics.

[13]  Axel Schindler,et al.  Precision optical asphere fabrication by plasma jet chemical etching (PJCE) and ion beam figuring , 2001, Optics + Photonics.

[14]  J. Kirz,et al.  Biological imaging by soft x-ray diffraction microscopy , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Tatsuo Harada,et al.  Fabrication of Wolter‐type x‐ray focusing mirror using epoxy resin , 1994 .

[16]  Takahiro Saitou,et al.  Development of surface profile measurement method for ellipsoidal x-ray mirrors using phase retrieval , 2012, Other Conferences.

[17]  Yoshiharu Namba,et al.  Figure tolerance of a Wolter type I mirror for a soft-x-ray microscope. , 2007, Applied optics.

[18]  Y. Namba,et al.  Fabrication of a soft x-ray microscope mirror using an epoxy replication method , 2008 .

[19]  E. Weckert,et al.  Solution of the phase problem for coherent scattering from a disordered system of identical particles , 2012, 1210.3519.

[20]  Lahsen Assoufid,et al.  Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors. , 2007, Applied optics.