Magnetic Speckle Imaging

Lensless imaging is on the forefront of technical developments in synchrotron related studies. As the term suggests, there is no optical system for imaging. Instead, a simple aperture is used for limiting the illuminated area to the coherence length of the beam (the light is usually in the longer wavelengths as the lateral coherence length increases as a power of the wavelength). When the illumination can be approximated by a plane wave, a detector placed in the far-field measures a sort of "structure factor", which is proportional to the square of the fourier amplitudes of the charge (or magnetization) distribution within the area of interest. The crucial step to obtain the real space image from this far-field pattern is to retrieve the missing phases. The problem of phase retrieval is common to all diffraction based structural studies (such as in x-ray crystallography). Therefore, a lot of effort is devoted to fourier inversion from incomplete data sets.

Figure 1: Shown in the middle panel is the simulated speckle pattern at the Fe L edge for a GdFe2 film with a magnetization distribution displayed on the left. On the rightmost panel, the result of the magnetic reconstruction from the simulated data reproduces well all the features of the original image.

Clearly one has to make up for the loss of the complex phases by additional information. This information can be provided by the dimensions of the scattering region, or the energy dependence of the scattering factors, or by a holographic method in which the interference with a known object is utilized. In addition there are entropic methods (most commonly applied to astrophysical data) where one looks for the most plausible solution that gives rise to the observed data set. Among the most prominent techniques, there are the iterative ones using real and fourier space constraints (dimensions in real space, symmetry in the reciprocal space) along with back and forth fourier transforms in order to converge to a unique solution.

Figure 2: Sketch of the instrument. Note that the photodiode before the CCD detector is used as a diagnostic, and is removed during actual data acquisition. The beamstop is to protect the detector from direct x-ray beam. The pinhole is the actual beam defining aperture (about 10 micron diameter), and the zone plate is used only for direct imaging. The corner is a technical necessity in order to block out the diffraction from the pinhole aperture (i.e. the airy pattern from the circular pinhole).

Starting from a different perspective, we have developed a non-iterative reconstruction method specifically for magnetic imaging, using the different polarization dependence of the charge and magnetic scattering processes [1]. Our simple idea is based on the fact that the relative phases of the magnetic and charge distributions are coded in the interference between the two types of scattering, and can be extracted by a polarization (or energy) analysis of the intensity distributions. Consequently one can reconstruct the magnetization image with the knowledge of the interfering charge distribution. We have also built an instrument capable of performing speckle measurements and real space imaging on the same region of the sample through a setup featuring interchangable pinhole and zone plate elements [2].

Figure 3: Magnetic speckles measured at the Advanced Photon Source ID-4C beamline. The left panel shows the magnetic contribution to the diffraction pattern of a Co/Pt multilayer sample illuminated with circularly polarized x-rays at the Co L3 edge (778 eV). The right panel is a real-space reconstruction of the out-of-plane magnetic domains [3].

Indeed this field is still in its infancy, yet there is a considerable amount of interest coming from various fields such as magnetic studies (with the advantage that one can apply magnetic fields in photon-in photon-out experiments) or the biophysics community (with the motivation of imaging single cells and large molecules). This provides the motivation to work towards matching the technical developments on the imaging side to those of the sources (for example higher coherency and photons per pulse of the free electron lasers).

[1] T. O. Menteş, C. Sanchez-Hanke, C. C. Kao, "Reconstruction of magnetization density in two-dimensional samples from soft X-ray speckle patterns using the multiple-wavelength anomalous diffraction method", J. Synch. Rad. 9 (2002) 90.

[2] T. Beetz, M. R. Howells, C. Jacobsen, C. C. Kao, J. Kirz, E. Lima, T. O. Menteş, H. Miao, C. Sanchez-Hanke, D. Sayre, D. Shapiro, "Apparatus for X-ray diffraction microscopy and tomography of cryo specimens", Nucl. Inst. Meth. in Phys. Res. A 545 (2005) 459.

[3] T. O. Menteş, "Imaging Magnetic Thin Films Using Resonant X-ray Scattering", Ph.D Thesis, SUNY at Stony Brook, November 2003.