Physica B 406 (2011) 2415–2418

Contents lists available at ScienceDirect

Physica B

0921-45

doi:10.1

n Corr

Berlin, G

E-m

journal homepage: www.elsevier.com/locate/physb

Polarized neutron imaging: A spin-echo approach

M. Strobl a,b,n, C. Pappas c, A. Hilger b, S. Wellert d, N. Kardjilov b, S.O. Seidel b, I. Manke b

a University of Heidelberg, Im Neuenheimer Feld 253, 69120 Heidelberg, Germanyb Helmholtz Centre Berlin, Hahn-Meitner Platz 1, 14109 Berlin, Germanyc Technical University Delft, Reactor Institute Delft, Mekelweg 15, 2629 JB Delft, Netherlandsd Technical University Berlin, Institut fur Chemie, Straße des 17, Juni 124, 10623 Berlin, Germany

a r t i c l e i n f o

Available online 17 October 2010

Keywords:

Neutron imaging

Polarized neutrons

Imaging magnetic fields

Neutron spin-echo

26/$ - see front matter & 2010 Elsevier B.V. A

016/j.physb.2010.10.029

esponding author at: Helmholtz Centre Berlin,

ermany. Tel.: +49 30 80622490; fax: +49 30

ail address: strobl@helmholtz-berlin.de (M. St

a b s t r a c t

Polarized neutron imaging has recently been introduced as an efficient method to three-dimensionally

visualize and measure magnetic fields even in the bulk of massive objects. Here we introduce a spin-echo

approach for polarized neutron imaging, which has the potential to overcome some drawbacks of the first

attempts, namely to deal with strong fields, arbitrary field directions and quantification. Furthermore our

novel approach increases the efficiency of quantitative studies due to relaxed monochromatisation

requirements for spin-echo neutron imaging and with respect to additional information available in the

recorded images, which allows for straightforward quantification in many cases.

& 2010 Elsevier B.V. All rights reserved.

1. Introduction

The earliest attempts of imaging with polarized neutrons [1–3]were carried out using sophisticated techniques like the use ofcrystal interferometers, which imply low flux densities, limitedspatial resolution, small beam cross sections, etc. and hence limitedpractical applications. The simplification of just adding neutronpolarizers, analysers and manipulation capabilities to existingdedicated imaging instruments had a major impact [4]. Indeedthis step came when monochromatic beams achieved acceptancefor neutron imaging for several applications, in spite of reduced fluxdensities due to monochromatisation [5,6]. While the spatiallyresolved depolarisation of a polychromatic beam yields highlyrelevant information as it allows e.g. for two-dimensional Curietemperature mapping and subsequent three-dimensional studiesof concentration gradients of certain elements in supposedlyhomogeneous crystals [7], polarized monochromatic neutronsallow for keeping track of the polarization (vector), which in tradefor intensity provides additional quantitative information about aprobed magnetic field or structure. In contrast to polychromaticstudies [7] the technique of polarized neutron imaging as intro-duced by Kardjilov et al. [4] produced images I(x,z) dependent onthe final spin phase with spatial resolution. This is not clear fromother interpretations [8]. In the case of a magnetic field orientedperpendicular to the incoming spin the image I(x,z) is given by

Iðx,zÞ ¼ Iaðx,zÞ1

2ð1þcosjðx,zÞÞ

ll rights reserved.

Hahn-Meitner Platz 1, 14109

80623094.

robl).

with the attenuated intensity Ia dependent on the attenuationcoefficient S along the beam direction y:

Iaðx,zÞ ¼ I0ðx,zÞe�RSðx,y,zÞdy

and the spin rotation anglej with respect to a magnetic field B of asample is

jðx,zÞ ¼glm

2p_

ZBðx,y,zÞdy

where g is the gyromagnetic ratio, m the mass and l the wavelengthof the neutrons. The attenuation can be measured either when thefield is switched off, or if this is not possible, by taking another imageI� with the spin flipped byp before analysis. In that case Ia¼(I+ + I�)and the image can be normalized to extract the spin dependent part.

However, in order to quantify the traversed field integral, whichis also a precondition for quantitative tomographic measurements,in general, (i.e. without a priori knowledge), several wavelengthshave to be used [9]. A single measurement results in an uncertaintywith respect to the periodicity expressed by I(j)¼ I(7j7n2p).A scan through a certain wavelength band, requiring severalmeasurements (approximately 5 is a reasonable number) atdifferent subsequent wavelengths (Fig. 1a), allows quantificationdue to the fact that if j(l1)¼j(l2)�2p, the field integral givesZ

Bdy¼2ph

gmðl2�l1Þ

Such an approach is – as proposed in Ref. [10] – most efficientlyapplied at a pulsed neutron source where a corresponding series ofimages is taken without further effort by time resolution. Thismethod is more efficient than an another approach most noticeablycalled spin phase imaging [8]. Here about twenty images arerecorded in an empty plus a sample measurement at a single

Fig. 1. Three approaches for quantitative polarized neutron images represented by schematic functions in single image points. (a) Polarized neutron imaging with wavelength

variation: different spin rotations for different wavelengths allows for quantification (compare text); (b) so called ‘‘spin phase imaging’’: measurements for several different

spin phases allow for measuring the phase with an uncertainty of 7n2p with n being a positive integer. However, further quantification needs a number of corresponding

measurements, which proves to be highly inefficient. Additionally, a simple spin turning coil fulfills the purpose for which originally a sophisticated Ramsey set-up was

introduced. (c) Spin-echo scan that provides direct quantification with relaxed monochromatisation. (Note that the number of points in the schematic curves is not

representative for real measurements—compare the corresponding section in the main text.)

Fig. 2. Schematic representation of: (a) probed field perpendicular to incident spin;

(b) field in arbitrary direction, hence final spin orientation does not allow for

statements on probed field; (c) field from case (b) superposed by strong external

field perpendicular to incident spin, consequently final spin orientation provides

(approximate) information about perpendicular component; (d) calculation includ-

ing the conditions of the measurements and depicting the results given in Ref. [8]

compared to (e) the actual field integral of the probed component. A significant

distortion of the result (which has however been completely misinterpreted in Ref.

[8]) due to insufficient external field is revealed. For example the lines of zero field

integral, which are inclined by 601, have been measured at 521.

M. Strobl et al. / Physica B 406 (2011) 2415–24182416

wavelength to determine the phase to j7n2p (Fig. 1b), while atleast two more phase scans, i.e. 20 more images, have to berecorded at other wavelengths to quantify the field integral.

However, if the fields are not aligned perpendicular to the spinorientation but are arbitrarily oriented, quantification and keepingtrack of the spin rotation are more complicated and requiree.g. polarimetric imaging approaches like those introduced inRef. [9]. An alternative option to probe only one field component

is to superpose the addressed field with a well known external fieldin the corresponding direction. The superposed field is significantlystronger than the other field components (Fig. 2a–c) and hence keepsthe precession axis close to the probed field direction (Fig. 2c). Anapplication of this method can be found in Piegsa et al. [8], eventhough the measured projection, i.e. field integral, of the correspond-ing field component has been misinterpreted as ‘‘the field lines’’ andthe distortion of the resulting image due to a too low externalfield in the vicinity of the investigated dipole has been overlooked(Fig. 2d and e). It has to be mentioned that for the investigation offield dependent magnetic structures the approach is not suitable,because the external field would significantly alter such structures,like e.g. magnetic domains. Furthermore a great number of multiplespin rotations that have to be expected when strong fields areapplied (and probed) require accurate monochromatisation in ordernot to depolarize the beam. This naturally decreases the availableflux density and increases necessary exposure times.

In order to overcome the latter drawbacks, the precessions inthe described combined external and sample fields can be com-pensated by a second, counter-oriented field. This results in a spin-echo (SE) geometry [11], which provides two major advantages.(1) The measured spatially resolved echo allows straightforwardquantification of field integrals due to the well known compensa-tion field, which produces the echo (Fig. 1c). However, this echofield should be located upstream of the sample field in order toavoid an increase in the sample–detector distance, which wouldspoil the spatial resolution (at least at constant ‘‘pinhole collima-tion’’ and hence flux densities). (2) The SE approach allows for andprofits from a relaxed wavelength resolution and hence theavailable flux density, i.e. the efficiency increases significantly.

2. Measurements

Corresponding preliminary SE imaging measurements wereperformed using the SE spectrometer SPAN at the HelmholtzCentre Berlin [12]. A wavelength of 4.5 A with a resolution ofDl/l¼15% was chosen and a pinhole with diameter D¼1 cm wasset at the end of the polarized neutron guide at the incident side ofthe instrument. The sample was placed in the second SE arm closeto the end of the precession region. A solid state polarizing bender[13] was used as a spin analyzer a few centimeters downstream ofthe sample and about the same distance in front of a state-of-the-art scintillator–CCD imaging detector [14]. The intrinsic resolutionof the detector featuring a 200 mm thick LiFZnS(Ag) scintillator and

M. Strobl et al. / Physica B 406 (2011) 2415–2418 2417

a cooled 1024�1024 pixel CCD of 13.3�13.3 mm2 in an ANDORDV434 camera system equipped with a 105 mm Nikkor lens wasapproximately 50 mm. Due to the geometry, such as sample–detector distance l¼20 cm, pinhole D and its distance from thedetector L¼5 m, the resolution was limited to d/2¼D*l/2L¼

200 mm. The SE spectrometer is indeed not optimized for polarizedneutron imaging and the intended separation of a single fieldcomponent. The precession regions are long and the magneticfields (approximately 16 mT) in the precession regions are not verystrong compared to the perpendicular components of the magneticfield of an investigated dipole. The dipole was used as a referencesample (approximately 100 mT at a pole), had the dimension50�15�5 mm3 and was aligned along the field direction of theecho field. The field of view (FOV) of the set-up was limited to15 mm width with respect to the used polarization analyzer and25.5 mm height by the detector, and did not contain the dipole

Fig. 3. Two raw images (shadows in the lower right corner are due to attenuation by

the sample holder) out of the SE-scan (a and b) with magnified regions of interest (c

and d). These two images are in principle enough for full quantification. The bent

orange lines indicate the spin echos found in the images, which correspond to field

integrals of 18.0 and 11.25 mT cm. For the used wavelength subsequent fringes

differ by values of about 3 mT cm. Consequently from this the whole region of

interest is quantified. The red lines correspond to line profiles, while the dots

indicate the positions of the SE-scan curves given in Fig. 4a and b. (For interpretation

of the references to colour in this figure legend, the reader is referred to the web

version of this article.)

Fig. 4. (a) SE as a function of position according to the line profiles indicated in Fig. 3c and

p-shift, i.e. a field integral difference of 1.5 mT cm. (The mean intensity has been subtracte

along the radial line indicated in Fig. 3c and d. Note that such a quantification by maxim

deviations. Due to statistics and sampling, maximum count rates might be found in the

itself but the corresponding field at one side (Fig. 3). However, themeasurements confirm in agreement with calculations that no areaaround the dipole can be found where the probed field componentis significant while other components are generally small ascompared to those of the SE precession field. Hence with the givenset-up it is impossible to probe one field component separately butall components contribute. This is indicated by a significant loss ofecho amplitude with decrease in distance to the sample. Never-theless a spin-echo scan was performed by increasing the fieldintegral in an additional coil in the first precession region in 61steps of 0.75 mT cm. For each step an image with an exposure timeof 5 min has been recorded. With increase in compensation fieldthe spin echo runs through the FOV radially from the peripherytowards the dipole position. This implies that a quantification canin principle be done for a single image already, since in the case of afield integral spatially increasing or decreasing continuously, aposition dependent echo function is measured (Fig. 4a), if at least inone point in the FOV the echo condition is fulfilled. However, it isimportant to note once more that such a quantification in the caseof an insufficient external precession field allows one to quantifyonly the field integral experienced by the beam with respect to theecho condition, but not for a defined direction. In Fig. 3 two suchimages (11.25 and 18.0 mT cm) are displayed, while the corre-sponding spatial echo functions for the diagonal line profiles in thehighlighted and enlarged areas in Fig. 3 are provided in Fig. 4d. Thepositions of the echo, i.e. the fringes with maximum modulation, ofthe two line profiles indicate the positions along the line where theprobed magnetic field integrals equal the additional field integral inthe echo fields of 11.25 and 18.0 mT cm. As a consequence thewhole corresponding circular fringes, as indicated in Fig. 3a and bcorrespond to the same field integral values. Due to the fact that thefield decreases continuously with increase in distance from thedipole and that the wavelength is well known, the field integral inthe other fringes and hence of the whole FOV (within the high-lighted areas) can be calculated and quantified easily (Fig. 4c). Inthe case of an unknown direction of the decay or an increase in thefield the second measurement would indicate that uniquely. Theincrease in width and distance of the fringes clearly indicates thatthe field decay is not linear. A plot of the field integral againstposition of the maximum (Fig. 4c) along the line profile or vice versa(Fig. 4c) suggests a quadratic decay. In Fig. 4b the (normalized)conventional SE functions are displayed for two points of theimages highlighted in Fig. 3c. Here the quantification can be donewithout spatial conditions for every image point, as demonstratedby the example of these two curves, i.e. image points.

d and (b) SE as a function of echo field integral for two image positions displaying a

d as an offset in these representations.) (c) Different straightforward quantifications

a in the raw data does not rely on a fit of the echo-signal, which explains the high

neighboring maxima of the actual maximum of the SE function.

M. Strobl et al. / Physica B 406 (2011) 2415–24182418

3. Conclusion

It was demonstrated with a preliminary and not correspondinglyoptimized set-up that a spin-echo approach in polarized neutronimaging allows for straightforward quantification with unprece-dented efficiency resulting from relaxed monochromatisation con-ditions and from the fact that in cases of continuously changing fieldseven single or twofold measurements might be sufficient. Addition-ally, how SE imaging in a more optimized set-up would allow forinvestigations of strong fields and/or arbitrary field directions byfocusing on one component at a time has been outlined.

References

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[4] N. Kardjilov, et al., Nat. Phys. 4 (2008).[5] M. Strobl, et al., J. Appl. Crystallogr. 40 (2007).[6] W. Treimer, et al., Appl. Phys. Lett. 89 (2006) 203504.[7] M. Schulz et al., J. Phys. in press.[8] F. Piegsa, et al., Phys. Rev. Lett. 102 (2009) 145501.[9] M. Strobl, et al., Physica B 404 (2009) 2611.

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