Abstract
Full-field transmission hard X-ray microscopy (TXM) has been widely applied to study morphology and structures with high spatial precision and to dynamic processes. Zernike phase contrast (ZPC) in hard X-ray TXM is often utilized to get an in-line phase contrast enhancement for weak-absorbing materials with little contrast differences. Here, following forward image formation, we derive and simplify the contrast transfer functions (CTFs) of the Zernike phase imaging system in TXM based on a linear space-shift-invariant imaging mode under certain approximations. The CTFs in ZPC in their simplified forms show a high similarity to the one in free-space propagation X-ray imaging systems.
Highlights
X-ray microscopy (XRM) in both soft and hard X-ray regimes has been utilized to probe with higher precision into small spatial and even temporal scales [1, 2] to access the morphology of macro- and micro- 3D structures [3, 4], as well as chemical information regarding elemental distribution and concentration [5], chemical states [6], etc
Compared to soft XRM, hard XRM is more suited for investigations under more complex and flexible sample environments such as in-situ and in-vivo observation [10,11], probing non-invasively into three dimensions when combining with computed-tomography
Under the assumptions of full coherence and weak-absorbing objects, we find a high similarity between the two contrast transfer functions (CTFs)
Summary
X-ray microscopy (XRM) in both soft and hard X-ray regimes has been utilized to probe with higher precision into small spatial and even temporal scales [1, 2] to access the morphology of macro- and micro- 3D structures [3, 4], as well as chemical information regarding elemental distribution and concentration [5], chemical states [6], etc. It is shown that under the same defocus distance the oscillations of both the amplitude and phase optical transfer functions (OTF) are rapidly suppressed as the coherence is reduced It is more complicated than a simple envelope damping factor as in the temporal coherence case, but works in a similar manner in influencing the CTFs. While the damping effect on CTFs may pose a trouble for defocusing algorithms which rely on a high degree of coherence, it will have less influence on Zernike phase contrast mode when phase retrieval is not required. While the damping effect on CTFs may pose a trouble for defocusing algorithms which rely on a high degree of coherence, it will have less influence on Zernike phase contrast mode when phase retrieval is not required In this case the linearity of the exit wavefield does not need to be preserved, but it will become a linearity of the recorded image intensity instead [27]
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