Neutron tomography using a crystal monochromator W. Treimer a,b,n , S.O. Seidel a,b , O. Ebrahimi a,b a Beuth Hochschule f¨ ur Technik, University of Applied Sciences, Department of Mathematics, Physics & Chemistry, Luxemburger Str. 10, D-13353 Berlin, Germany b Helmholtz Centre for Materials and Energy, G-G1, 14109 Berlin, Germany article info Article history: Received 28 April 2010 Received in revised form 12 June 2010 Accepted 14 June 2010 Available online 30 June 2010 Keywords: Neutron tomography Energy selective tomography Crystal monochromator Spatial resolution abstract For several neutron tomography methods, the use of monochromatic radiation is important. In order to select a wavelength band from a white spectrum commonly used devices are velocity selectors, choppers and crystal monochromators. We show how a crystal monochromator changes the well- known L/D-ratio in CT instruments and how it determines the spatial resolution. We calculate the L/D-ratio as convolution integral and prove the results by the experimental determination of the modulation transfer function (MTF) of the used tomography system. & 2010 Elsevier B.V. All rights reserved. 1. Introduction and theory Several tomography methods such as energy selective tomo- graphy, Bragg edge radiography, phase contrast tomography using a grating interferometer, diffraction enhanced radiography, refraction and USANS tomography, or tomography with polarized neutrons use monochromatic radiation due to the wavelength dependency of the interaction with matter [1–10]. Use of monochromatic radiation involves the selection of radiation from a white spectrum, which is done by monochromator crystals or (especially in the case of neutrons) with chopper devices and velocity selectors, respectively. The available intensity of latter techniques is quite high, about 10–20% of the spectrum but the corresponding Dl/l is often too poor for sharp imaging contrast due to wavelength dependent smearing effects that decreases the contrast in an image and thus information of details to be extracted. The width of the wavelength band that monochromator crystals select from the spectrum depends on the mosaic spread, which is usually of the order of 0.51, corresponding to a Dl/l  1%. In the case of tomography with synchrotron radiation the high monochromaticity of radiation is yielded with an (naturally) highly collimated beam, by perfect crystal (Si) Bragg reflections and multilayers suppressing harmonics. The used Si crystals act like perfect mirrors, i.e. the reflected beam divergence is nearly the same as the incident beam due to their narrow ‘‘Darwin range’’ of some mrad. This is different for radiography and tomography instruments for neutrons and X-ray tubes. The ray geometry of both is similar to each other, they have a collimating system consisting of a (small) source (slit or hole, diameter D), a distance L to the object under investigation and a distance l d to the detector unit. Due to the size D of the micro-focus of an X-ray source (some mm) L can be kept short ( 1 m), in the case of neutron tomography D is of the order of cm and the length L about 7–18 m. In the case of tomography with monochromatic neutrons, the behavior of crystals as wavelength selecting devices is different to pin hole geometry and the L/D ratio has to be considered in conjunction with the geometry of the tomography experiment. As can be seen from Fig. 1 the beam divergence f is inversely proportionally to L/D that characterizes a tomography instrument. Assuming a pin hole having the diameter D the un-sharpness d (blur) of an image of a point is given by the product l d  f due to L/D ¼l d /d (Fig. 1). There are three conditions to decrease the blur: D and l d must be small and L must be large. Considering a standard tomography instrument D is (in the case of neutrons) usually an aperture where the whole area of D contributes to image of a point at the detector. Increasing L decreases f and the blur d and improves the sharpness of the image at the detector position. Calculating the blur b(x, y) of a point in a sample, b(x, y) is the result of the convolution of the beam divergence f with the source function S ¼S(x, Z). In the case of a neutron guide the divergence f ¼ f guide (m  0.61/nm)  l [nm]. The parameter m (m¼1, 1.2, 1.5, 2,y) defines the reflectivity range of the coating of the neutron guide normalized to the critical angle of total reflection of natural Ni. In our case m was 1.2 and l ¼0.524 nm. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods in Physics Research A 0168-9002/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2010.06.256 n Corresponding author at: Beuth Hochschule f ¨ ur Technik, University of Applied Sciences, Department of Mathematics, Physics & Chemistry, Luxemburger Str. 10, D-13353 Berlin, Germany. Tel.: + 49 30 4504 2213, + 49 30 4504 2428, + 49 30 8062 2221; fax: + 49 30 4504 2011. E-mail address: treimer@helmholtz-berlin.de (W. Treimer). Nuclear Instruments and Methods in Physics Research A 621 (2010) 502–505