Neutron imaging with bent perfect crystals. I. Imaging conditions

Abstract

Neutron imaging with bent crystals is considered in the linear approximation of neutron optics. A matrix formalism analogous to that of conventional lens optics is developed. Various imaging conditions are discussed in relation to the crystal deformation type and to possible applications in neutron scattering. All focusing conditions known previously are included as particular cases. Arrangements combining high resolution in imaging with high resolution in scattering are examined. The concept of Bragg mirrors as devices for non-dispersive imaging is introduced. The most powerful application appears to be that of Bragg mirrors combined with the time-of-¯ight method. Imaging with a thick packet of silicon wafers at the spatial resolution of a single thin wafer is demonstrated.

Neutron Guinier camera

“…2,13,14 Neutron imaging can be done with bent perfect crystals only. Mosaic crystals spread the beam on Bragg reflectionby 2 cm for every meter of distance with highly oriented PG.…”

“…The images from all wafers can be superposed exactly by exploiting the strong correlation between angular and spatial variables of neutrons Bragg-reflected by bent crystals. 15,2 To image an object with Bragg reflection by a bent crystal one must satisfy the lens relation f 0 /L 0 +f 1 /L 1 =1 where L 0 and L 1 are the distances to object and to image, and f ! 0 and f 1 are the focal lengths of the bent crystal.…”

“…The elements of D have been calculated for elastically bent bulk plates and for packets of wafers. 13,2 The act of detection being sensitive to neutron position but not to direction or wavelength, it is the relation defining the neutron coordinate at image y 1 =d 11 y ! +d 12 γ 0 +d 13 ∆k/k which is of interest.…”

<title>Neutron imaging with Bragg mirrors</title>

“…In a terminology borrowed from conventional optics this is the case of dispersive imaging. 9,10 The object point is imaged into a line along which some physical quantity varies (wavevector, wavevector transfer, energy transfer, etc). The distribution of that physical quantity is converted into a spatial distribution.…”

“…8 Theoretical examination of neutron imaging by Bragg reflection from bent crystals was undertaken recently. 9,10 A result that came as a surprise was that thick multi-wafer packets can provide sharp imaging even if the incident beam has a broad distribution of wavelengths. The image blurring is canceled when two conditions of non-dispersive imaging are met (nondispersive = independent of wavelength).…”