Application of precise neutron focusing mirrors for neutron reflectometry: latest results and future prospects

A large-area focusing supermirror manufactured with ultra-precision machining has been employed at the SOFIA reflectometer at the J-PARC Materials and Life Science Experimental Facility, and a gain of approximately 100% in the neutron flux was achieved. For future upgrade, optics using the focusing mirror for multi-incident-angle neutron reflectometry are proposed, in order to reveal evolutions of interfacial structures for operando measurements with a wide reciprocal space.


Slit condition for double slit optics
presents the beam paths of neutrons with double slit optics. For a sample with a length of and an incident angle of neutrons, , the optics is required to make a beam with a size of 2 tan 2 at the sample position. Then, the divergence of the beam ∆ is defined as the angle between the two paths illuminating the edges of the sample (red and orange lines in the figure). Here, the aperture of the slits and the beam size at the sample can be written with ∆ and the distance from the crossing point of the two paths as presented in the figure. These relations provided us the aperture of the slits for given , ∆ , and as follows: where tan ≈ and tan ∆ ≈ ∆ can be applied as they are small for neutron reflectometry.
Figure S1 Beam paths of neutrons collimated by double slit optics.
Here, the product of the slit apertures is proportional to the beam flux 1 2 = − 1 2 (∆θ − 1 + 2 2 1 2 θ) 2 + ( 1 − 2 ) 2 4 1 2 ( θ) 2 , which can be maximized by choosing ∆ as ∆ = ∆ 0 = 1 + 2 2 1 2 . This condition gives a beam intensity profile with a triangle shape; when ∆ ≠ ∆ 0 , a trapezoid shape is obtained. with the same angular distribution. As the value of ′ is derived from the slit aperture and the distance from the point to the slit, the beam size at the sample can be evaluated with ′ and the distance from the point to the sample. With this relation, the aperture of the slit in the focal plane for given and is described as

Slit condition for focusing mirror optics
, that is, the magnification factor becomes Next, we consider the beam size at the other slit, as presented in Fig. S2(b). The beam size reflected from the point can be evaluated with ′. In addition, the beam divergence on the sample should be considered, in which the maximum beam divergence, ∆ 0 , is limited by the visual angle of the mirror from a point at the sample. The beam size at the slit is broadened by this effect and is converged at the sample position. Hence, the beam size at the slit can be the sum of these two terms, which is given as

Specification of 5 μm slit
A slit with an aperture of 5 μm made of Cd was placed at the sample position and scanned to measure the intensity profiles because a beam size realized by our focusing mirror was too small to perform observations with a position-sensitive detector. The blades of the slit were manufactured with trapezoidal shapes by means of ultraprecision machining (Nagase-I, NPIC-M200) as the focusing mirror. Figure S1 shows the shape of the slit blade measured by an optical interferometer (ZYGO Newview7200). The short base at the top and leg angles of the slit were approximately 0.2 mm and 1° as designed, respectively. Then, the tops of the slit blades were allowed to contact each other, and the gap of the blades was adjusted to be 5 μm by checking the gap image using an optical microscope.
Owing to the tapered shape, the transmission at the edge of the slit blade became negligible and could accept the beam divergence with 2° at maximum, which is larger than that of the focusing mirror, which is approximately 0.3°. beam size at the sample position was evaluated to be 110 μm, which was not critical but was nonnegligible to realize the smaller beam size for such slow neutrons with optics. Figure S5 Results of ray-tracing for optics of MI-NR with thermal neutrons (0.18 nm) and cold neutrons (1.76 nm) considering the effect of gravity.