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Local wet etching technique was proposed to fabricate high-performance aspherical mirrors. In this process, only the limited area facing to the small nozzle is removed by etching on objective surface. The desired objective shape is deterministically fabricated by performing the numerically controlled scanning of the nozzle head. Using the technique, a plano-elliptical mirror to focus the neutron beam was successfully fabricated with the figure accuracy of less than 0.5μm and the focusing gain of 6. The strong and thin focused neutron beam is expected to be a useful tool for the analyses of various material properties.
©2009 Optical Society of America
1. Introduction
Highly reliable analyses of various physical and chemical properties using focused X-ray and/or neutron beams are undoubtedly key techniques to develop an innovative functional material in recent leading-edge science and technology fields. An X-ray microdiffraction technique has an ability to determine three-dimensional structure based on elastic and plastic strain tensor distributions in a specimen. A neutron diffraction and scattering technique which provide additional beneficial information of the specimen because neutrons are sensitive to magnetism, can scatter strongly even from the materials of low atomic number and can penetrate deeply into specimens through environmental chambers [1]. To improve the resolution and efficiency of these analytical techniques, the focusing mirrors with higher figure accuracy, those can realize smaller focal spot size, are required. In case of the total reflection mirror of X-ray, the figure accuracy at nanometric level is crucial specification for the focusing to diffraction-limit. As for the neutron focusing, the multilayer-deposited mirrors with larger size and larger critical angle are essential to collect neutrons, because almost of neutron sources are inherently very weak. Furthermore, the surface roughness of atomic level is required in both of the X-ray and neutron mirrors to reduce scattering loss.
Various fabrication techniques are reported so far for these untraprecision mirrors. An aspherical X-ray mirror for the space telescope are fabricated by single-point-diamond-turning in combination with a precision polishing [2], a CVD-SiC mirror for synchrotron radiation by ultraprecision grinding [3] and a paraboric mirror for microfocusing of hard X-ray by bent-polishing [4], respectively. However, in conventional machining process, the figure accuracy of mirror strongly depends on stiffness of the machining equipment. It is also affected by external disturbances in the relative displacement between workpiece and tool due to vibration and thermal deformation, because the surfaces of these mirrors are created by a contact-removal mechanism. Therefore, it is very difficult to fabricate the optical component with the figure accuracy of nanometric level and also high reproducibility. To overcome these problems, high-stiffness of the machining equipment and the highly-precise temperature control facilities are required. However, those machines and utilities are very expensive.
On the contrary, an ultraprecision elliptical mirror to focus hard X-ray beam is fabricated by applying the plasma chemical vaporization machining (PCVM) in combination with elastic emission machining (EEM) [5]. Both techniques have an ability to figure an aspherical optical component with the accuracy of nanometric level [6]. However, the material removal rate and surface roughness are affected by the heat flow from plasma in the PCVM process [7] and the removal rate is low in the EEM process. As a solution of these problems, a numerically controlled local wet etching (NC-LWE) process was proposed by the authors [8-10]. In this process, the etchant is supplied through a small nozzle and is forcedly sucked after etching with its volatile component using a vacuum pump as shown in Fig. 1. Only the limited area facing to the nozzle is removed by etching on objective surface without surface roughening due to adsorption of the volatile component of the etchant. A free surface can be figured by scanning the nozzle. A distinctive future of the NC-LWE is insensitive process to the external disturbances, such as the vibration or the thermal deformation, owing to its non-contact chemical removal process. Therefore, although the initial cost of the figuring process is very low, the highly-stable and highly-reproducible figuring can be achieved more easily comparing with conventional machining processes.
2. Experimental set-up and procedure
Figure 1 shows a schematic diagram of the NC-LWE system. This system is constructed from a work holder, an XYZ-axes driven by AC-servo motors, an etchant nozzle head and an etchant circulation system with a constant temperature unit. All components are installed in the enclosure made of poly(vinyl chloride) to protect a operator from unanticipated leak of the toxic etchant. The nozzle head made of poly(tetrafluoroethylene) or poly(vinyl chloride) is constructed from the etchant supply part and the suction part, which are arranged coaxially, and the removal area is limited to inside of the suction slit. The etchant solution does not remain on the surface of the workpiece after the nozzle has passed over it, because the amount of supplied etchant and that of the etchant removed by suction are properly balanced. Therefore, it is not necessary to stop the etching reaction by rinsing with water in the LWE process. The etchant solution is circulated through a heat exchanger using a magnetic pump during the figuring operation, so that the temperature of the etchant is kept constant within the fluctuation of ±0.2°C. Therefore, the etching rate is also kept constant within the fluctuation of ±1%.
Figure 2 shows a photograph of 5-axis NC-LWE machine used to fabricate an aspherical mirror. The travels of X- and Y- axes, Z-axis, A-axis and B-axis are 350 mm, 150 mm and ±25°, respectively. A rotary table the maximum rotary speed of which is 12 rpm is used as B-axis. Therefore, this machine has an ability to fabricate the any aspherical shape. The nozzle head is installed on the moving unit in XYZ-axes and A-axis facing to the work holder vertically mounted on the rotary table of B-axis.
A plano-elliptical mirror of synthesized quartz glass to focus the neutron beam was fabricated by the NC-LWE figuring process. The theoretical shape of the mirror surface was expressed by Eq. (1).
The outer size, focal length and effective aperture size of the mirror were 100 mm x 50 mm x 15 mm, 1050 mm and 90 mm x 40 mm, respectively. The initial shape of the substrate was flat plate with a flatness of 300 nm. The local removal volume on the work surface is controlled by the dwelling time of the nozzle head. The removal volume increases larger with the dwelling time increases by slower scanning speed. The volume distribution to be removed on the work surface is deterministically calculated based on the convolution method between the figures of the footprint by the nozzle and that of the objective surface profile before fabrication.
Figure 3 shows conceptual diagram of the two-stage figuring process of a plano-elliptical mirror by NC-LWE. In this process, firstly, the one-dimensional numerically controlled coarse figuring (first stage) is performed, as shown in Fig. 3(a), by using a long rectangular nozzle head because a plano-elliptical mirror has no curvature in y direction. Furthermore, the rectangular nozzle has the large volumetric removal rate because of its large contact area with objective surface. Then, the fine finishing (second stage) by a numerically controlled raster scanning is performed, as shown in Fig. 3(b), with a small circular nozzle head. The sizes of the rectangular and circular nozzle head were 51 × 12 mm2 and ϕ15 mm, respectively.
Fig. 3. Conceptual diagram of the two-stage figuring process in the NC-LWE process. (a) Coarse figuring (1st stage) and (b) Fine finishing (2nd stage).
After the raster scanning in second stage, shallow grooves like a “tool-mark” inevitably remained at the overlapping area of etching along the scanning path. The depth of residual tool-mark increases as the cumulative removal depth increases at a certain location on the objective surface. Therefore, to improve the surface waviness after second stage, it is important to reduce the depth to be removed in second stage by figuring the surface profile as close as theoretical one in first stage. In that sense, the two-stage figuring process proposed is very effective to reduce both of the processing time and the height of residual tool-mark generated by raster scanning.
The etchant used in the process was HF the concentration and temperature of which were 37 wt% and 40°C, respectively. The concentration is an azeotropic one in which an evaporation rate of a HF and a H2O are the same. Therefore, the etching rate is kept constant through all the operation time in figuring process.
3. Fabrication of mirror substrate by NC-LWE
The indicators of surface quality for the neutron mirror substrate are figure accuracy and surface roughness. The figure accuracy governs the beam size of focused neutron. The surface roughness reduces the beam intensity due to diffuse scattering of neutron.
Figure 4(a) shows the cross-sectional figure in x direction of the fabricated mirror measured by laser autofocus measuring machine (Mitaka Kohki NH-3SP, z resolution: 1nm). Figure 4(b) and 4(c) show the two-dimensional distribution of residual figure error from the theoretical figure after the first and second figuring stages, respectively.
Fig. 4. Distribution of figure error of the fabricated elliptical mirror. (a) Cross-sectional figure of the fabricated elliptical mirror. (b) Distribution of figure error after first stage. (c) Distribution of figure error after second stage.
Fig. 5. Shape of footprint in longitudinal direction formed by rectangular nozzle used in first rough figuring stage. (a) Cross-section of A-A. (b) Closeup view of B section.
Figure 5 shows the distribution of etching rate in the longitudinal direction of rectangular nozzle obtained from the footprint of the nozzle. The distribution pattern of footprint coincides with the figure error in y direction shown in Fig. 4(b). The results show that the residual figure error in y direction of the mirror is mainly reflected by the initial flatness error of the substrate and the non-uniformity of the etching rate in the rectangular nozzle head. However, as the spatial wavelength of the figure error was longer enough than the diameter of small circular nozzle. Therefore, the figure error can be corrected in the second finishing stage. In a second finishing stage, to correct the residual figure error, a raster-type numerically controlled scanning was applied with the feed pitch of 0.4 mm. The residual figure error of 2.4 μm peak-to-valley (p-v) after the first stage was improved to be 0.4 μm p-v. The processing times of the first and second figuring stage were 230 min and 88 min, respectively.
Figure 6 shows the cross-sectional profile of the mirror in the feed direction (y-direction) after the second stage. The height of the residual tool-mark by the raster scanning was suppressed to be less than 20 nm. If the same mirror is fabricated by only raster scanning with the small circular nozzle, the processing time and the residual tool-mark height are estimated to be 750 min and 100 nm, respectively, based on the deconvolution simulation using the volumetric distribution to be removed, the shape of the footprint of nozzle and the scanning speed of the nozzle. Therefore, the two-stage figuring process is very effective to reduce both the processing time and the residual tool-mark height.
4. Evaluation of performance for neutron focusing mirror
As neutron can easily penetrate into usual materials, total reflection mirrors deposited with multi-layered film for neutron diffraction are used for focusing. The surface of the mirror was deposited with multi layers of Ni and Ti by ion beam sputtering. As the neutron reflectivity of Ni and Ti are high and low, respectively, the neutrons are diffracted by the laminated dual-layers of Ni/Ti following Bragg’s diffraction. The critical incident angle for neutron reflection increases as the space of dual-layers decreases. On the other hand, the parallelism of neutron flux radiated from the weak source is poor. Therefore, to increase the intensity of neutron beam, it is necessary to reflect neutrons distributed in wide range of incident angle. For that purpose, so called “supermirror” was developed [11]. On the surface of supermirror, the dual-layers of Ni/Ti are laminated with continually changing space. To reflect a neutron with large incident angle, the small space of dual-layers is required. However, as the space decreases, the effect of roughness of the reflection surface becomes more serious. The surface roughness of mirror substrate and dual-layers causes diffuse scattering of neutron, and consequently reduces the reflectivity of neutron and generate the background noise at the focal point of the focusing mirror. Therefore, the surface roughness of the mirror substrate and the interfacial roughness of the deposited layer must be improved as much as possible.
The surface of the mirror substrate fabricated by NC-LWE was deposited with multilayers of NiC and Ti by ion beam sputter deposition to produce a supermirror [12-14]. The additional carbon atoms into the nickel layer suppress the interfacial roughness by reducing the crystal grain size of the nickel layer. Furthermore, ion beam polishing, applied after the deposition of every layers, smoothen the interfacial roughness of the multi-layers. The total number and the total thickness of NiC/Ti multi-layers and the average incident angle of a neutron were 1200, 6 μm and 1.40°, respectively.
The performance of the neutron focusing mirror was evaluated at SUIREN (Apparatus for Surface and Interface Investigations with Reflection of Neutrons) of JRR-3M (Japan Research Reactor No.3 Modified of Japan Atomic Energy Agency). Figure 7 shows neutron focusing performance of the mirror. The beam size of focused neutron was measured at the focal point of the elliptical mirror by scanning the slit of 0.25 mm width using the monochromatized neutron the wavelength of which was 3.93 Å. The focusing gain of 6 in the peak intensity was achieved comparing with the case of without focusing as shown in Fig. 7. The result shows that the strong and thin neutron beam, which could not be obtained so far, can be put into practice with the mirror. The focused neutron beam is expected to be a useful tool for the analyses of various material properties by small angle scattering and that under ultra-high pressure.
5. Conclusions
A total reflection mirror to focus neutron beam was produced applying NC-LWE which is a non-contact material removal process by chemical reaction. The plano-elliptical mirror substrate of synthesized quartz glass with the effective aperture size of 90 × 40 mm2 was fabricated by two-stage NC-LWE. A large rectangular nozzle head and a small circular nozzle head were used in first rough figuring stage and the second fine finishing stage, respectively to save the processing time and to improve the surface waviness. The figure accuracy and waviness of the substrate were 0.4 μm p-v and 20 nm, respectively. The neutron focusing mirror was produced by deposition of NiC/Ti multi layers on the substrate. The neutron focusing gain of 6 was achieved by the mirror. The strong and thin focused neutron beam is expected to be a useful tool for the analyses of various material properties by small angle scattering and that under ultra-high pressure.
Acknowledgments
This work was partially supported by the Industrial Technology Research Grant Program in 2005 from the New Energy and Industrial Technology Development Organization (NEDO) of Japan and a research grant from the Machine Tool Engineering Foundation.
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