Hard X Ray Holographic Diffraction Imaging

Abstract

We determine the absolute electron density of a lithographically grown nanostructure with 25 nm resolution by combining hard x-ray Fourier transform holography with iterative phase retrieval methods. While holography immediately reveals an unambiguous image of the object, we deploy in addition iterative phase retrieval algorithms for pushing the resolution close to the diffraction limit. The use of hard (8 keV) x rays eliminates practically all constraints on sample environment and enables a destruction-free investigation of relatively thick or buried samples, making holographic diffraction imaging a very attractive tool for materials science. We note that the technique is ideally suited for subpicosecond imaging that will become possible with the emerging hard x-ray free-electron lasers.

Three-Dimensional X-Ray Fourier Transform Holography: The Bragg Case

“…Several successful demonstrations of x ray FTH have been reported on the imaging of nanostructures [11,12], including the use of a uniformly redundant array as a reference [13]. However, the forward scattering geometry practically restricts the reconstructions to 2D approaches, while in most cases the 3D information is necessary to obtain a complete picture.…”

Spatial coherence measurement and partially coherent diffractive imaging using self-referencing holography

“…In contrast, in holography, a beam splitter is used in the light path, so that the reference is also spatially partially coherent and therefore, it is impossible to retrieve the MCF of the incident beam or reconstruct the transmission function from the interference pattern. Our method also shows that FT holography [21][22][23] and Zernike phase-shifting holography [27] are in principle able to deal with spatial partially coherence effect. Traditionally, it was believed that interferometry, holography and iterative diffractive imaging techniques all require coherent illumination to retrieve a complex-valued transmission function of the object because the randomly fast varying phase of the partially coherent fields was expected to destroy the phase information carried by the intensity measurements.…”

“…Finally, if the two interference terms do not overlap with the quadratic term as shown in Fig. 2(c), we only need to measure I(k) [21][22][23].…”

“…Meanwhile, to our knowledge, none of the non-iterative algorithms, e.g. [21][22][23], have been adapted to utilize partially coherent beams, despite the benefit of instant and unambiguous reconstruction of the object.…”

Lensless X-ray imaging in reflection geometry

“…2 Lensless x-ray imaging techniques such as coherent diffraction imaging (CDI) 1-8 and ptychography [9][10][11] , and Fourier transform holography (FTH) [12][13][14][15][16][17] can provide time-resolved, diffraction-limited images. Nearly all examples of these techniques have been focused on transmission geometry, restricting the samples and reciprocal spaces which can be investigated.…”