Open Access
Add to BibSonomyAbstract
We propose an ellipsoidal neutron focusing mirror using a metal substrate made with electroless nickel-phosphorus (NiP) plated material for the first time. Electroless NiP has great advantages for realizing an ellipsoidal neutron mirror because of its amorphous structure, good machinability and relatively large critical angle of total reflection for neutrons. We manufactured the mirror by combining ultrahigh precision cutting and fine polishing to generate high form accuracy and low surface roughness. The form accuracy of the mirror was estimated to be 5.3 μm P-V and 0.8 μm P-V for the minor-axis and major-axis direction respectively, while the surface roughness was reduced to 0.2 nm rms. The effect of form error on focusing spot size was evaluated by using a laser beam and the focusing performance of the mirror was verified by neutron experiments.
© 2014 Optical Society of America
1. Introduction
The neutron is a very powerful probe in material science, life science and industrial applications owing to its unique advantages such as deep penetration into materials, sensitivity to light elements and capability for measuring magnetic properties. Although large-scale neutron source facilities based on nuclear reactors or large proton accelerator facilities such as SNS in the U.S.A., ISIS in the UK, and JRR-3 in Japan have been constructed, the demands of neutron beams in various research fields are still increasing. In fact, more neutron sources are under construction, such as ESS in Europe and CSNS in China. Furthermore, small scale neutron sources using compact accelerators such as LENS at Indiana University, CPHS at Tsinghua University and RANS at RIKEN are also active [1]. However, even at the large-scale facilities, the intensity and brilliance of the neutron beam is quite weak compared with X-rays from synchrotron radiation. Therefore, high performance neutron focusing devices are very important for increasing the utility of neutron beam facilities [2, 3].
Most of the current neutron instruments adopt a slit-system to obtain a small spot for analysis. However, in these instruments, neutron flux is sacrificed so that beam intensity becomes low. By applying neutron focusing optics, beam intensity can be significantly improved at sampling positions, which will result in a better analysis with high precision in a shorter time. There are two kinds of neutron focusing optical devices based on refraction and reflection. Neutron refractive material lenses have chromatic aberration and there is considerable absorption by the lens material [4, 5]. Magnetic lenses can solve the problem of chromatic aberration; however, the acceptable neutron wavelength is long and the practical applications are still limited so far [6–8]. Reflective optics, which are free of chromatic aberrations, require little maintenance, and offer a relatively compact focusing system, have received more attention [9]. Recently, some types of reflective optics have been developed such as Kirkpatrick-Baez (KB) mirror, lobster eye optics and Wolter mirror [10–12]. However, the numerical aperture (NA) of KB mirror is small although it can be fabricated in a high form accuracy. In contrast, Wolter mirror has a high NA but the form accuracy is not high.
To solve the problem, we propose a new kind of neutron focusing mirror which has an ellipsoidal surface. It has a larger NA with high form accuracy. Furthermore, it is possible to fabricate large scale focusing mirror even with supermirror coating. Some techniques are reported for fabricating neutron focusing mirrors. For instance, Nagano et al. developed a one-dimensional (1D) neutron focusing mirror made of glass material finished by a numerical controlled local wet etching (NC-LWE) process with low pressure polishing [13, 14]. Ice et al. fabricated Kirkpatrick–Baez microfocusing optics by using bending techniques [15, 16]. Although the NC-LWE process and bending technique are excellent for fabricating an aspheric surface with very high form accuracy, they are still limited to 1D surfaces. It is well known that glass material requires a grinding process to fabricate the shape due to its brittle nature, but it is very difficult to grind a 2D glass mirror into a concave shape with a steep angle. In order to obtain high form accuracy, we use a metal substrate made with electroless nickel-phosphorus (NiP) plating. Electroless NiP is a good candidate for making optical devices because of its amorphous structure, good machinability and hardness. By combining diamond cutting and a subsequent fine polishing process, high form accuracy of micrometer order, and low surface roughness of sub-nanometer order can be generated [17–19]. The manufacturing method is suitable for fabricating neutron focusing mirrors as the required form accuracy of neutron focusing mirrors is not so high as mirrors for X-rays from synchrotron radiation or free electron lasers which require form accuracy of nanometer order because a neutron source has a relatively large volume. Also, the value of surface roughness is acceptable for a neutron supermirror coating. Moreover, NiP has a relatively larger critical angle of total reflection for neutrons than most other metals, and cold neutrons can be effectively reflected even without a supermirror coating [20, 21]. Compared with mirrors made of glass substrate, it is easier to fabricate and the manufacturing time can be greatly reduced. Because of the good mechanical handling property of electroless NiP owing to its ductile nature, it is possible for a large ellipsoidal mirror to be made with multiple segments of electroless NiP substrates for ease of machining and supermirror coating. Furthermore, glass material is not suitable for a high neutron irradiation field. In contrast, NiP can be used in a high irradiation field owing to its small neutron absorption and activation cross-sections, short decay life time, low cost, etc. Thus, an NiP mirror can be placed anywhere, even in a high irradiation field.
In this paper, we propose an ellipsoidal neutron focusing mirror and we explain the mirror design, manufacturing, surface measurement as well as the focusing performance evaluation in the following sections.
2. Design and manufacturing
2.1 Mirror design
We design the mirror in a partially spheroidal surface as shown in Fig. 1. The surface can be expressed as:
where L, W, a, b, denotes the length, width, and half lengths of the major and minor axes of the mirror, respectively.The critical angle of total reflection for neutrons is given by
where λ is the wavelength of neutrons, N is the atomic density and bcoh is the mean coherent scattering length in a material [20]. The critical angle is proportional to the wavelength, and for NiP (P 11%), it is 0.9゜per nanometer.Based on the consideration of the critical angle of the incident beam, a, which represents the size of the focusing system, was set to 1250 mm. In order to reflect cold neutrons, b was set to 7 mm. Through calculation, it was found that when L equals 100 mm, cold neutrons with wavelength from 0.36 nm could be effectively reflected by the mirror. W was set to 7 mm so the mirror has a steep angle of ± 30゜in minor-axis direction.
2.2 Ultrahigh precision cutting
Due to the small incident angle, the mirror has a long-narrow and concave shape which becomes difficult to machine. As a solution to this problem, we propose a new manufacturing process by combining ultrahigh precision cutting (UPC) and fine polishing to rapidly fabricate the mirror with high form accuracy and low surface roughness. Prior to UPC, an aluminum plate (A5052) with a length of 100 mm, width of 30 mm and depth of 9 mm is processed by fast milling and precision cutting to generate an ellipsoidal shape. Then a layer of nickel-phosphorus alloy of 100 μm thickness is deposited on the aluminum plate by electroless NiP plating.
By considering the shape of the mirror, an arc envelope shaper cutting method is proposed, as shown in Fig. 2(a). It is more feasible than diamond turning because diamond turning is limited to axis-symmetric surfaces such as spherical or aspherical surfaces, although it has much higher machining efficiency. In this method, a round-nosed cutting tool is adopted which can significantly increase the cutting range of the tool and effectively reduce tool wear. The machining path of the diamond tool is calculated by following the surface of the mirror. The experiment is conducted in an ultraprecision machine with a positioning resolution of 10 nm. A single crystal diamond with a nose radius of 2.0 mm is used. The detailed experiment conditions are summarized in Table 1.With this setup, the form accuracy of the mirror of micrometer order can be generated.
Fig. 2 Schematic illustration of the manufacturing process. (a) Arc envelope shaper cutting. (b) Fine polishing.
Table 1. Experimental Conditions of UPC
2.3 Fine polishing
By UPC, a high form accuracy can be obtained, but the obtained surface roughness is still not sufficient to reflect neutron beams with low diffuse scattering. Generally, for that purpose, sub-nanometer surface roughness is required [14]. Thus, super-smooth surface must be achieved by the subsequent polishing process. However, polishing of a concave, free form surface like an ellipsoid, especially with a steep angle, is quite difficult. Therefore, to obtain sub-nm roughness without losing the profile accuracy acquired by UPC on an ellipsoidal surface was a challenge of this research.
To solve this problem, as shown in Fig. 2(b), a fine polishing method involving use of a spherical polishing tool with loose abrasives supply is adopted. As the mirror has a long-narrow and concave shape which is quite similar to a cylinder and the difference between them is only of micrometer order, to properly contact the surface of the mirror and remove cutting scratches uniformly with high material removal efficiency, a spherical polishing tool with a diameter equaling the length of the short axis of the mirror is developed. In order to obtain a super-smooth surface, the experiment is conducted under a low polishing load with a soft polishing pad and nanometer size abrasives. The experiment conditions are shown in Table 2. During the polishing process, the polishing tool rotates perpendicular to the cutting marks with an inclination angle of 45゜, while scanning along the major-axis direction.
Table 2. Experimental Conditions of Fine Polishing
3. Surface measurement
Figure 3 shows the fabricated mirror which is reflecting a RIKEN logo. The profile of the mirror after fine polishing is measured by a non-contact laser probe instrument (Mitaka Koki NH-3N) and the form errors are shown in Fig. 4. The result indicates that the cross-sectional error of the major-axis direction is 0.8 μm while that of the short axis direction, which is mainly affected by the profile error of the diamond cutting tool, is 5.3 μm. These form errors can be used to calculate slope errors which determine the size of the focusing spot. The surface roughness is evaluated by a white light interferometer (ZYGO New View 7200) and the results are shown in Fig. 5. The surface roughness of the aluminum substrate processed by fast milling and precision cutting reaches about 10 nm rms. However, after electroless NiP plating, it worsens to 20 nm rms. By applying UPC, it is significantly improved to 3 nm rms. Furthermore, through subsequent fine polishing, the cutting marks are removed and the surface roughness is finally reduced to 0.2 nm rms.
Fig. 4 Measurement result of form errors. (a) Cross-sectional error of minor-axis. (b) Cross-sectional error of major-axis.
Fig. 5 Surface roughness of the mirror after each process. (a) Aluminum substrate after precision cutting. (b) After electroless nickel plating. (c) After UPC. (d) After fine polishing.
4. Focusing performance evaluation
4.1 Focusing test by laser beam
Due to the fact that experiment time when using a neutron beam is limited because there are few neutron sources, prior to the neutron focusing experiment, we used a laser beam to test the effect of form errors of the mirror on focusing spot size so as to indirectly evaluate whether or not a neutron beam can be properly focused by the mirror.
The experimental layout is shown in Fig. 6. An He-Ne laser (632.8nm) source of 15 mW is adopted. The laser beam is processed by a spatial filter consisting of an objective lens (10X) and an aperture (15 μm in diameter), and is then focused by the mirror. The aperture position of the spatial filter is aligned to one of the focal points of the ellipsoidal mirror (f ≈1250 mm). At another focal point, a CCD camera without a lens is placed to measure the focused spot size. Due to the effect of diffraction, the focused spot will have a certain diameter δ based on the Rayleigh Criterion, which can be estimated by using the equation
where k is the coefficient depending on the effective aperture shape of the focusing optics, λ is the wavelength of laser beam and d is the diameter of pinhole. For this mirror, as the effective aperture has a shape that is quite similar to a rectangle, k equals 1. The numerical apertures (NA) in the horizontal direction and the vertical direction can be geometrically calculated based on the incident angles of laser beams reflected by the mirror. Then by following the sinc function of the diffraction shape owing to the rectangular aperture, the theoretical size of the focusing spot at full width at half maximum (FWHM) are obtained. Figure 7 shows the focused spot captured by the CCD camera. Since the mirror has a U-shaped aperture in which the vertical size is quite narrow, the focusing spot is elongated to vertical direction. Table 3 summarizes the theoretical estimation and measurement results of the spot size at FWHM. It is found that the experiment results almost coincide with the theoretical estimation, which demonstrates that the laser beam is focused by the mirror to almost the diffraction limits, although there is about 10% difference in the horizontal direction, which is probably due to the larger form error in the minor-axis direction. For neutrons, as the wavelength is much shorter than that of a laser, the effect of diffraction on focal spot size is negligible, so the mirror is appropriate for focusing neutron beams.
Table 3. Comparison of Theoretical Value and Experiment Results
4.2 Neutron focusing experiment
The neutron focusing performance of the mirror was evaluated using CN3 beam line at Kyoto University Research Reactor (KUR-CN3). A supermirror guide tube is installed in KUR-CN3 to supply neutron beams from a cold neutron source (CNS). The characteristic wavelength of KUR-CN3 guide tube is 0.24 nm [22]. However, the CNS has already been shut down so it is possible to use neutron beams in which the effective wavelength is from 0.15 to 0.5 nm approximately.
Figure 8(a) and Fig. 8(b) show the schematic experiment layout and an illustration of the ray-tracing of neutron beams based on geometrical optics, respectively. The incident angle of the neutrons to the focusing mirror was 5.6 mrad so that neutrons with a wavelength from 0.36 nm, which were mentioned in Section 2.1, will be focused by the mirror. Thus, we did not use a chopper system to measure the time-of-flight (TOF) spectrometry of the neutrons due to the poor beam intensity and limited beam time in this experiment. A two-dimensional (2D) position sensitive detector with a spatial resolution of 0.1 mm is used to collect experiment data [23].
Fig. 8 Schematic illustration of neutron focusing experiment at KUR-CN3. (a) Experiment layout. (b) Illustration of ray-tracing of neutron beams based on geometrical optics.
We prepared a Cadmium (Cd) pinhole (Fig. 9(a)) with an aperture size of 1 mm in diameter to choose incident beams from the CNS, and a Cd U-shape slit (Fig. 9(b)) to remove unnecessary neutron beams affecting the focusing. However, we cannot remove neutrons entering the U-shape slit in which wavelength is shorter than 0.36 nm as most of them will be transmitted through, be scattered or be absorbed by the mirror. The size of the U-shape slit is decided by the shape of the mirror and the aperture size of the pinhole. Both the pinhole and the U-shape slit were fabricated in a high form accuracy of 10 μm.
Figure 10(a) shows the 2D image of the direct beam without the focusing mirror at the mirror center to detector distance (MDD) of 1250 mm (focal position). The image has a blurred U-shape. This is due to the non-uniform distribution of beam intensity and an alignment error of the relative position between the mirror and the pinhole. By setting the focusing mirror, cold neutrons, in which the wavelength is longer than 0.36 nm, are reflected. We measured 2D images from the MDD of 250 mm, 650 mm to 1250 mm, respectively. From Fig. 10(b), 10(c) and 10(d), it can be seen that the 2D image changes as a function of MDD and we have succeeded in observing a clear circle image at the MDD of 1250mm, as shown in Fig. 10(d). In addition, the blurred images in Fig. 10(b) and 10(c) demonstrate that the neutrons with wavelength less than 0.36 nm are transmitted through the mirror.
Fig. 10 2D images of beam shapes as a function of MDD. (a) Direct beam. (b) MDD of 250 mm. (c) MDD of 625 mm. (d) MDD of 1250 mm.
Figure 11(a) and 11(b) show the sum of the cross-sectional profiles in the vertical and horizontal directions, respectively. We mention that the profiles of B, C, D only contained long wavelength neutrons reflected by the mirror, and neutrons transmitted through the mirror were excluded. In the horizontal direction, the beam spread at FWHM reduced gradually from 3.1 mm to 1.1 mm, indicating the focusing, while the peak intensity increased significantly from B to D. In the vertical direction, neutron beams were focused to 1.0 mm at D with respect to 2.0 mm at A. Due to the small glancing angle, the short length of the mirror and the relatively large aperture size of the pinhole in this configuration, the beam spread increased from 0.7 mm at B to 1.0 mm at D. The values show a good agreement with the results calculated by geometrical optics. As shown in Fig. 8(b), the theoretical lengths at A, B, C, D named as LA, LB, LC, LD are 2.28 mm, 0.65 mm, 0.78 mm, 1.00 mm, respectively. As a result, a circular focusing spot, of which the size is almost equivalent to that of the pinhole, was achieved. Figure 12 shows a 3D view of the focused neutron beam where no significant diffuse scattering can be found.
Fig. 11 Beam profiles (A: Direct beam B: MDD of 250 mm C: MDD of 625 mm D: MDD of 1250 mm). (a) In the horizontal direction. (b) In the vertical direction.
5. Concluding remarks
In this paper, an ellipsoidal neutron focusing mirror made with electroless NiP was successfully fabricated using UPC and fine polishing, and through a neutron focusing experiment, a focused neutron beam in a circular spot of 1 mm, is put into practice with the mirror. Based on the results obtained from this research, some conclusions can be drawn, as follows:
- Electroless NiP is suitable as a metal substrate for fabrication of neutron focusing mirrors and to focus cold neutrons.
- The manufacturing process, combining UPC and fine polishing, allows the mirror to be fabricated with high form accuracy and low surface roughness. In arc envelope shaper cutting, the accuracy of the mirror in minor-axis direction will be affected by the profile error of the cutting tool, but through compensating the profile error of cutting tool in the machining program, the accuracy of the mirror could be improved.
- A focusing test with a laser beam can be used to evaluate the effect of the form error of the mirror on the focusing spot size. It is an easy-to-access, alternative method for predicting the focusing spot size as the experimental time using a neutron beam is limited.
- The fabricated mirror is proved to properly focus neutron beams.
It is feasible for this technique to fabricate a partial large-scale Wolter mirror with supermirror coating through precise alignment of multi-segment asymmetric focusing mirrors.
Acknowledgments
The authors would like to express their grateful thanks to Advanced Manufacturing Support Team, RIKEN Center for Advanced Photonics, RIKEN for the precision machining of the pinhole and slit used in the neutron focusing experiments. This work was supported by Photon and Quantum Basic Research Coordinated Development Program from the Ministry of Education, Culture, Sports, Science and Technology, Japan. The neutron experiment was supported by the inter-university program for common use of Kyoto University Research Reactor Institute.
References and links
1. Union for Compact Accelerator-driven Neutron Sources (UCANS), http://150.241.211.12:8080/UCANS.
2. A. Erko, M. Idir, Th. Krist, and A. G. Michette, eds., Modern Developments in X-Ray and Neutron Optics (Springer Series in optical science, 2008).
3. M. Utsuro and V. K. Ignatovich, Handbook of Neutron Optics (Wiley-VCH Verlag GmbH & Co. KGaA, 2010).
4. H. Frielinghaus, V. Pipich, A. Radulescu, M. Heiderich, R. Hanslik, K. Dahlhoff, H. Iwase, S. Koizumi, and D. Schwahn, “Aspherical refractive lenses for small-angle neutron scattering,” J. Appl. Cryst. 42(4), 681–690 (2009). [CrossRef]
5. H. Iwase, H. Endo, M. Katagiri, and M. Shibayama, “Modernization of the small-angle neutron scattering spectrometer SANS-U by upgrade to a focusing SANS spectrometer,” J. Appl. Cryst. 44(3), 558–568 (2011). [CrossRef]
6. T. Oku, T. Shinohara, J. Suzuki, R. Pynn, and H. M. Shimizu, “Pulsed neutron beam control using a magnetic multiplet lens,” Nucl. Instr. and Meth. A 600(1), 100–102 (2009). [CrossRef]
7. T. Shinohara, S. Takata, J. Suzuki, T. Oku, K. Suzuya, K. Aizawa, M. Arai, T. Otomo, and M. Sugiyama, “Design and performance analyses of the new time-of-flight smaller-angle neutron scattering instrument at J-PARC,” Nucl. Instr. and Meth. A 600(1), 111–113 (2009). [CrossRef]
8. T. Oku, T. Shinohara, T. Kikuchi, Y. Oba, H. Iwase, S. Koizumi, J. Suzuki, and H. M. Shimizu, “Application of a neutron-polarizing device based on a quadrupole magnet to a focusing SANS instrument with a magnetic neutron lens,” Meas. Sci. Technol. 19(3), 034011 (2008). [CrossRef]
9. D. Liu, M. V. Gubarev, G. Resta, B. D. Ramsey, D. E. Moncton, and B. Khaykovich, “Axisymmetric grazing-incidence focusing optics for small-angle neutron scattering,” Nucl. Instr. and Meth. A 686, 145–150 (2012). [CrossRef]
10. R. Hudec, “Kirkpatrick-Baez (KB) and Lobster Eye (LE) Optics for Astronomical and Laboratory Applications,” X-Ray Opt. Instrum. 2010, 139148 (2010). [CrossRef]
11. G. E. Ice, C. R. Hubbard, B. C. Larson, J. W. L. Pang, J. D. Budai, S. Spooner, and S. C. Vogel, “Kirkpatrick–Baez microfocusing optics for thermal neutrons,” Nucl. Instr. and Meth. A 539, 312–320 (2005). [CrossRef]
12. D. F. R. Mildner and M. V. Gubarev, “Wolter optics for neutron focusing,” Nucl. Instr. and Meth. A 634(1), S7–S11 (2011). [CrossRef]
13. M. Nagano, F. Yamaga, N. Zettsu, D. Yamazaki, R. Maruyama, K. Soyama, and K. Yamamura, “Development of fabrication process for aspherical neutron focusing mirror using numerically controlled local wet etching with low-pressure polishing,” Nucl. Instr. and Meth. A 634(1), S112–S116 (2011). [CrossRef]
14. K. Yamamura, M. Nagano, H. Takai, N. Zettsu, D. Yamazaki, R. Maruyama, K. Soyama, and S. Shimada, “Figuring of plano-elliptical neutron focusing mirror by local wet etching,” Opt. Express 17(8), 6414–6420 (2009). [CrossRef] [PubMed]
15. G. E. Ice, C. R. Hubbard, B. C. Larson, J. W. L. Pang, J. D. Budai, S. Spooner, S. C. Vogel, R. B. Rogge, J. H. Fox, and R. L. Donaberger, “High-performance Kirkpatrick–Baez supermirrors for neutron milli- and micro-beams,” Mater. Sci. Eng. A 437(1), 120–125 (2006). [CrossRef]
16. M. R. Howells, D. Cambie, R. M. Duarte, S. Irick, A. A. MacDowell, H. A. Padmore, T. R. Renner, S. Rah, and R. Sandler, “Theory and practice of elliptically bent x-ray mirrors,” Opt. Eng. 39(10), 2748–2762 (2000). [CrossRef]
17. A. Pramanik, K. S. Neo, M. Rahman, X. P. Li, M. Sawa, and Y. Maeda, “Ultra-precision turning of electroless-nickel: Effect of phosphorus contents, depth-of-cut and rake angle,” J. Mater. Process. Technol. 208(1–3), 400–408 (2008). [CrossRef]
18. K. M. Rezaur Rahman, M. Rahman, K. S. Neo, M. Sawa, and Y. Maeda, “Microgrooving on electroless nickel plated materials using a single crystal diamond tool,” Int. J. Adv. Manuf. Technol. 27(9-10), 911–917 (2006). [CrossRef]
19. Y. Namba, T. Shimomura, A. Fushiki, A. Beaucamp, I. Inasaki, H. Kunieda, Y. Ogasaka, and K. Yamashita, “Ultra-precision polishing of electroless nickel molding dies for shorter wavelength applications,” Annals of the CIRP 57(1), 337–340 (2008). [CrossRef]
20. A. Dianoux and G. Lander, Neutron Data Booklet, (Institute Laue-Langevin, 2003).
21. S. Takeda, J. Guo, S. Morita, H. Ono, T. Oda, J. Kato, H. Sato, M. Hino, Y. Yamagata, and M. Furusaka, “Development of highly-mechanically polished metal-substrate for neutron supermirrors,” J. Phys. Conf. Ser. 528, 012011 (2014). [CrossRef]
22. M. Hino, T. Akiyoshi, M. Sugiyama, N. Achiwa, Y. Eguchi, T. Ebisawa, S. Tasaki, T. Kawai, K. Yoneda, and T. Kobayashi, “Characteristics of CN3 neutron guide tube at KUR,” Annu. Rep. Res. React. Inst. Kyoto Univ. 27, 196–204 (1994).
23. K. Hirota, T. Shinohara, K. Ikeda, K. Mishima, T. Adachi, T. Morishima, S. Satoh, T. Oku, S. Yamada, H. Sasao, J. Suzuki, and H. M. Shimizu, “Development of a neutron detector based on a position-sensitive photomultiplier,” Phys. Chem. Chem. Phys. 7(8), 1836–1838 (2005). [CrossRef] [PubMed]
