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An achromatic cold-neutron microscope with magnification 4 is demonstrated. The imageforming optics is composed of nested coaxial mirrors of full figures of revolution, so-called Wolter optics. The spatial resolution, field of view, and depth of focus are measured and found consistent with ray-tracing simulations. Methods of increasing the resolution and magnification are discussed, as well as the scientific case for the neutron microscope. In contrast to traditional pinhole-camera neutron imaging, the resolution of the microscope is determined by the mirrors rather than by the collimation of the beam, leading to possible dramatic improvements in the signal rate and resolution.Modern optical instruments for visible and synchrotron light use a variety of focusing devices, such as lenses, Fresnel zone plates and mirrors. These devices help increase the signal rate, resolution, or both. Were such powerful optical tools available for neutron scattering, they might bring significant, even transformative, improvements to rate-limited neutron methods and a) Electronic

Focusing optics based on Wolter optical geometries developed for x-ray grazing incidence beams can be designed for neutron beams. Wolter optics are formed by grazing incidence reflections from two concentric conic sections (for example, a paraboloid and a hyperboloid). This has transformed observational X-ray astronomy by increasing the sensitivity by many orders of magnitude for research in astrophysics and cosmology. To increase the collection area, many reflecting mirrors of different diameters are nested with a common focal plane. These mirrors are fabricated using nickel-electroformed replication techniques. We apply these ideas to neutron focusing using nickel mirrors. We show an initial test of a conical mirror using a beam of cold neutrons.

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