Textbook for hard X-ray focusing with Kirkpatrick-Baez optics
S. Matsuyama and H. Yumoto
Oct. 21. 2009

1. Background
Currently, grand-scale synchrotron radiation facilities, where high-quality X-ray
sources are available in wide energy ranges from the soft- to hard- X-ray regions, havesigniﬁcantly advanced the performance characteristics of analytical technologies using
the ﬂuorescence, absorption and diﬀraction eﬀects of X-rays in various materials. The
application of X-ray microscopy with these exceptional X-ray characteristics has
expanded in the ﬁelds of material, medical and biological sciences, due to the fact that
this method is capable of nondestructive analysis of material characteristics for avariety of diﬀerent samples including cells and proteins. Since focused X-ray beams are
required to transmit spatially distributed information, X-ray focusing technologies are
considered to be critical to the advancement of X-ray microscopy, with various methods
based on diﬀraction (e.g. Fresnel zone plate) refraction (e.g. Compound reflective lenses)
and total reﬂection (e.g. Kirkpatrick-Baez mirrors) being developed.

2. Kirkpatrick-Baez (KB) optics
In 1948, Kirkpatrick and Baez proposed an X-ray focusing optical system consisting of
two total reﬂection elliptical mirrors, which aligned perpendicularly (Fig. 1). Thisfocusing optical system is considered promising due to its potential to remarkably
improve the performance characteristics of X-ray microscopy by enabling more eﬃcientcollecting of X-rays than in other methods. A further advantage is that the method
maintains the focusing state with the same optical arrangement even if the wavelengthof the X-rays is shifted. However, to realize X-ray beams with an ideal focal size, higheﬃciency and absence of background noise around a main peak, it is necessary toprepare elliptical mirrors having a very high degree of ﬁgure accuracy (approximately 2nm peak-to-valley figure accuracy) and surface smoothness (approximately 0.2 nmRMS) over an entire reﬂective area, and position two mirrors accurately. Currently,
such nearly perfect mirrors (so-called Osaka Mirror) are commercially available fromJTEC (http://j-tec.co.jp/english/focusing/index.html).

x2 y21a 2 b2yb-aa0x-bL
f

Figure 1 Kirkpatrick-Baez optics. It consists of two elliptical mirrors aligned perpendicularly to eachother. X-rays from a light source placed at one focus are reflected on the mirror surface and always
reach the second focus.

3. Fabrication process of X-ray mirrors

Work

Atom on powder
particle

Atom to be
removed fromwork surface

Figure 2 Elastic emission machining (EEM). EEM is an ultraprecise machining method that utilizes
the chemical reaction between the surfaces of the workpiece and fine powder particles. Topmost atoms
on the workpiece will preferentially adhere to and move onto the surface of the powder particle.
Eventually, atomically smooth surfaces can be obtained.

Typical fabrication process (for Osaka Mirror) is described below (for more detail, see
Ref. 1 and 2). First, a substrate (e.g. synthetic silica, silicon or BK7) are roughly figured
with proper polishing methods (e.g. optical pitch polishing) until the obtained surface
has figure errors of 1.0-0.5 m. Then the mirror is figured by EEM process (Fig. 2) tohave a figure error of 2 nm peak-to-valley and an RMS surface roughness of 0.2 nm over

an area of 64 × 48 m2. For almost all mirrors, the figure accuracy is accurate enough.
The figured mirror is coated with a thin chrome binder layer and a platinum (Rhodiumor other heavy metals) layer using a coating system.

Figure 3 Typical figure error of an Osaka Mirror. Figure accuracy of 2 nm peak-to-valley can be easily
obtained with our fabrication method.

4. Tolerance limits of mirror alignments
Tolerance limits of a typical KB optics (for more detail, see Ref. 3 and 4) are shown in
Fig. 4. The most sensitive positioning is the alignment of the glancing angle. Finetuning with an accuracy of 1 rad level is required to obtain a sharp beam. On the other
hand, in-plane rotation is not so sensitive. Adjustments for the in-plane rotation easily
can proceed without special instruments.

Figure 4 Tolerance limits of mirror alignments. The vertical axis means geometrical beam size
calculated by ray-tracing simulator. The horizontal lines indicate the diffraction limits defined as thedistance between the first minima.

5. Alignment procedure
To realize X-ray beams with an ideal focal size and high eﬃciency, it is important toalign two mirrors properly. A typical alignment of KB optics proceeds in the following
order (see the other sheet distributed in the BL practice). For the alignments, a mirror
manipulator, which was specially developed, is used (Fig. 5). The most important points
are the adjustments for perpendicularity and for glancing angles. The adjustment forthe perpendicularity can easily proceed using two autocollimators and a pentaprism.
The final fine adjustment proceeds repeating measurement of beam size with a wire
scanning method and adjustments for the glancing angles and the focal lengths.

Auto collimator
Tilt stage

Flexure hinge
Flexure hinge

Mirror 1

Mirror 2
X-ray

Penta prism

Linear actuator
X-Y stage

(a)

(b)

AutoAuto-collimator
Tilt stage

Laser beam
Mirror1

Mirror2
X-ray

Rotation axis
Penta prism
Micrometer headMonitor(c)Figure 5 (a) Mirror manipulator equipped with (b) glancing angle adjustment systems and (c) aperpendicularity adjustment systemReferences
1.

Kazuto Yamauchi, Kazuya Yamamura, Hidekazu Mimura, Yasuhisa Sano, Akira Saito, Alexei
Souvorov, Makina Yabashi, Kenji Tamasaku, Tetsuya Ishikawa, and Yuzo Mori: Nearly
diffraction-limited line focusing of a hard-X-ray beam with an elliptically figured mirror, J.
Synchrotron rad., 9, pp. 313-316 (2002).

2.

K. Yamauchi, H. Mimura, K. Inagaki, and Y. Mori, Figuring with subnanometer-level accuracy bynumerically controlled elastic emission machining, Rev. Sci. Instrum., 73, (2002), pp. 4028-4033.

3.

S. Matsuyama, H. Mimura, H. Yumoto, K. Yamamura, Y. Sano, K. Endo, Y. Mori, M. Yabashi, K.
Tamasaku, Y. Nishino, T. Ishikawa and K. Yamauchi, Diffraction-limited two-dimensional
hard-X-rays focusing in 100nm level using K-B mirror arrangement, Revew of Scientific
Instrument. 76, 083114 (2005).

4.

Satoshi Matsuyama, Hidekazu Mimura, Hirokatsu Yumoto, Hideyuki Hara, Kazuya Yamamura,Yasuhisa Sano, Katsuyoshi Endo, Yuzo Mori, Makina Yabashi, Yoshinori Nishino, KenjiTamasaku, Tetsuya Ishikawa, Kazuto Yamauchi, Development of mirror manipulator for hard
X-ray nanofocusing at sub-50 nm level, Review of Scientfic Instruments, 77, 093107 (2006).