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Extended depth of focus for Transmission X-ray Microscope
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The Fresnel zone plate based Transmission X-ray Microscope (TXM) has been well recognized as one of the most powerful tools for non-invasive investigation of the inner structure of thick samples, with spatial resolution down to 15-30nm, covering a wide energy range from the “water window” to around 25keV. Many studies about the methodology and applications are based on TXM system, including biological study of cells. While higher spatial resolutions are attained, the Depth-Of-Focus (DOF) of the objective zone plate decreases. The typical DOF of a water window soft x-ray TXM is below 10μm for 60nm resolution and decreases to about 1μm for 20nm resolution, while a typical eukaryotic cell is always about 10um to 100um. A small DOF limits the reconstruction volume in 3D tomographic imaging and larger samples cannot be imaged by 3D tomography. The DOF limitation becomes more significant for continued improvement in spatial resolution.

Liu, from Stanford Synchrotron Radiation Lightsource, and his cooperators developed a Fast Discrete Wavelet Transform based algorithm for extending the DOF by analyzing the image stack taken in a sample scan along the optical train. With the extended depth of focus, it is possible to obtain 3D structural information over a large volume. The feasibility of the method is confirmed with experimental data collected using a Cu anode source based hard X-ray TXM system at beamline 4W1A at the Beijing Synchrotron Radiation Facility (BSRF).

They carried the experiment on the lab source Cu rotating anode, using a test sample composed of double layer of 75μm-thick polyimide membranes with micro-sized Au particles on both sides, which is significantly thicker than the DOF of the TXM system. Transmission X-ray images were collected at a series of Z positions by scanning the sample along the optical axis with 15μm step size of a range of about 650 um, beginning from the position completely off-focus, stepping through the in-focus positions of the Au particles on both sides of the membrane, ending in a position off-focus again. The Fig.1 (a) shows the three main steps of the algorithm, with a magnified view of the composite fully-in-focus image shown in Fig.1 (b). The two Au particles marked with arrows are on the same side of the membrane, while the two on their left are on the other side.

Fig.1. Data processing algorithm of a Fast Discrete Wavelet Transform to extend DOF by analyzing the image stack collected in a sample Z scan along the optical train is illustrated in panel (a). Panel (b) is a magnified view of the composite fully-in-focus image.

The successful reconstruction of experiment data indicates large potential to image 3D structure of biological or material samples with a large volume at high resolution using the TXM system if combined with mosaic scanning and rotating the sample.

The exposure time for each image was 180 seconds with 2×2 pixel binning in the experiment. The total exposure time would be shorter using a synchrotron X-ray source. However, off-focal Fresnel fringes would be significantly enhanced due to the spatial coherence intrinsic to a synchrotron source. That will complicate the focus-stacking procedure. An X-ray diffuser could install in the system to reduce the spatial coherence to overcome that problem.


Yijin Liu*, Junyue Wang, Youli Hong, Zhili Wang, Kai Zhang, Phillip A. Williams, Peiping Zhu, Joy C. Andrews, Piero Pianetta, Ziyu Wu,Extended depth of focus for Transmission X-ray Microscope,Opt Lett. 37(17):3708-10, 2012.

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