**2.1 Nano-accuracy requirement of synchrotron optics**

Hard X-rays produced by synchrotron radiation (SR) sources are important tools for chemical, elemental, and structural analyses of matter at the nano- and atomic scale and for elucidating the molecular processes involved in biological functions at the cellular level. Scientists anticipate having one-nanometer probe spots for such research. Recently, construction started on ultra-bright SR sources with nano-focusing spots at the National Synchrotron Light Source II (NSLS II), Brookhaven National Laboratory (BNL) in the United States and at the Taiwan Photon Source (TPS) of the NSSRC. The NSLS II will allow researchers to create high-contrast X-ray images of matter at this resolution. To focus the bright, hard X-rays of a SR beam into a 1nm spot, beam lines must incorporate a series of precise optical elements. One of the most promising approaches to do so is the application of total reflection mirrors with their exceptional characteristics of broadband focusing, achromaticity, and high efficiency. Osaka University has focused hard x-rays to a spot size of approximately 7 nm using Kirkpatrick–Baez mirrors (K-B mirror) (Yamauchi et al., 2011). However, the mirror figure employed to focus a SR beam to a nanometer spot while preserving coherence requires nano-radian (nrad) accuracy. According to simple geometricoptics calculations, if the error in surface slope is 100 nrad, the beam will exhibit a lateral displacement of 4 nm at a 20mm focal distance; hence, it will greatly enlarge the 1nm spot.

Synchrotron radiation optics, operating at extreme grazing incidence angles on the order of a few milliradians, utilize surfaces consisting of planes, spheres, and aspheres including cylinders, toroids, paraboliods, and ellipsoids, up to 1.5 meters long. These lengthy cylinderlike aspheric surfaces normally have a long tangential radius of curvature, in the range from one hundred meters to several kilometers, with a sagittal radius of curvature that can be as short as a few centimeters. These surfaces are extremely difficult to measure with a traditional null interferometer, even with special computer-generated hologram (CGH) null lenses, or with an SSI. The new beam lines at the NSLS II will require many optical surfaces with 100 nrad slope error.

Fig. 1 is an example of SR optics, a K-B mirror set used for focusing X-ray beam to a nanometer spot. Two nano-accuracy elliptical cylinder mirrors are used to focus a beam to a single point in horizontal and vertical direction individually.

Fig. 1. K-B elliptical mirrors for nanometer spot focusing

Control of surface slope error is especially important in the fabrication of far off-axis aspheres used in grazing incidence x-ray applications. Incoherent x-rays act much like bullets in reflecting off of aspheric surfaces. Slight deviations in surface slope, on the order of fractions of a micro-radian, are sufficient to reduce the quality of the focal spot in long synchrotron beam lines. The stringent requirements for these precision optical components have stimulated research into new measurement methods for spheres and aspheres, and new sophisticated optical measurement instruments are rapidly evolving. A specially designed nano-accuracy profiler for synchrotron optics is urgently needed. It should be also able to measure mid-spatial frequencies and be able to test strongly curved surfaces.

Since the early 1980s, when the first and second-generation synchrotron light sources came on-line, the requirement for RMS slope error tolerance of SR optics has dropped from 5 μrad to 100 nrad as the desired focal spot size at the beam line end-station has gone from 10µm to 1 nm (Table 1). These continual machine improvements have driven the development of the metrology instrumentation from the micro-accuracy level to the nano-accuracy level.


Table 1. The requirements of slope error and spot size
