Recovering magnetization distributions from their noisy diffraction data

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 82, Issue 6, 2010, Pages

  Loh, Ne Te Duane ^a,b   Eisebitt, Stefan ^c   Flewett, Samuel ^c   Elser, Veit ^a  

^a Laboratory of Atomic and Solid State Physics and Sibley School of Mechanical and Aerospace Engineering   (United States)

^b TU Berlin ^*  (United States)

^c TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFRACTION DATA; DIFFRACTIVE IMAGING; MAGNETIC DOMAIN PATTERNS; MAGNETIC DYNAMICS; MAGNETIZATION DISTRIBUTION; MISSING DATA; NOISY DATA; PHASE RETRIEVAL; RECONSTRUCTION ALGORITHMS; SCATTERING NOISE; SIMULATED EXPERIMENTS; TIME RESOLVED IMAGING; ULTRAFAST RADIATION; X-RAY DIFFRACTIVE IMAGING; X-RAY FREE ELECTRON LASERS;

DIFFRACTION; FOURIER TRANSFORMS; FREE ELECTRON LASERS; MAGNETIC DOMAINS; MAGNETIZATION; PHOTONS;

EXPERIMENTS;

EID: 78651466481     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.061128     Document Type: Article

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17. Depending on the magnetostatic and domain-wall energy, closure domains with in-plane magnetization may form where the domain walls meet the film surface. These closure domains are negligible in the very thin films which we examine in this paper.
18. There will be no interference between charge and magnetic scattering terms if the incident radiation were linearly polarized. In this case, diffraction intensities from charge and magnetic distributions are separately added, as demonstrated in Ref., and the former, ideally, can be subtracted away. Determining the static random charge scattering for subtraction is possible when the photon energy is detuned away from the core-level resonance, hence suppressing magnetic scattering. But this subtraction may be unreliable at noisy high- q signal regions where the magnetization distribution is primarily encoded. Subtraction might also be problematic in single-shot imaging, when the incident photon fluence may fluctuate between shots-guesswork is needed to match the intensities of the charge-plus-magnetic data to those of charge-only data for reliable subtraction.
19. max.
20. u is the uniaxial anisotropy constant, both of which are constants of the material being probed. One also finds that the domain width is proportional to the film thickness and inversely proportional to the applied field. As a result, a variety of contrast histograms may be observed depending on the specific material properties and geometry of the system under investigation. Here we use the magnetization constraint function shown in Fig. as a prototypical example. In a real experiment, this constraint could be determined by calculating the expected widths of the domains and their walls using magnetic domain theory presented, for example, in but properly relaxed to include intrinsic blurring in experimental diffractive imaging.
21. tot without practical significance to reconstruction success.
22. One could include the expected statistics on the charge distribution in Fig.. This will certainly make the direct-space and Fourier constraints more compatible, potentially improving the reconstruction success rate. Even having included the charge statistics it may still be fairly challenging afterwards to isolate the magnetization distribution from these reconstructions chiefly because the exact charge distribution is unknown. Smoothing operations can remove charge contrast only if it is small compared to the magnetic contrast.
23. We prefer the iterate to orbit near the Fourier constraint since it is a direct experimental measurement of a particular magnetization distribution, as opposed to the direct-space constraint which is a broader description of the ensemble of distributions.
24. The mean charge scattering amplitude f C (r) is noncritical to the reconstruction since it constitutes mainly the missing intensities in the data where the diffraction intensities from the sample's magnetization is low (see Fig.).
25. One could average the cross-correlations of the magnetic contrast with multiple references to improve the FTH reconstructions as demonstrated in Ref.. The signal-to-noise ratio of these averaged FTH reconstructions is expected to increase with the square root of the number of references. In our trials, the deviation of the FTH reconstruction Fig. falls to 0.15 when the number of references is increased from 1 to 16. Although this deviation is acceptably low, for the same performance it still requires roughly 150 times more photons than our nonholographic technique.