A Study On Soft X-ray Ptychography

Coherent diffractive imaging(CDI)is a promising form of X-ray microscopy that does not rely on image-forming(focusing)optical elements such as lenses.Instead,it theoretically relies on the Fourier relationship between the coherent wave exiting the sample and its far-field diffracted wave.The intensity(modulus square)distribution of the far-field diffracted wave is recorded by a detector and a subsequent phase retrieval iterative calculation is applied to retrieve the phase information of the wave-field and reconstruct an image of the sample.Without the limitations such as a finite numerical aperture and imperfect manufacturing that imposed by the image-forming optical elements,the spatial resolution of CDI is in principle only limited by the X-ray wavelength.Since CDI can be performed on non-crystalline samples and can deliver high resolution images,it has been widely used in biological,environmental,and material sciences with synchrotron radiation,X-ray free electron lasers,and high-harmonic generation and table-top X-ray lasers.However,the conventional CDI method only uses one single diffraction pattern for phase retrieval and it requires an isolated sample with lateral size much smaller than that of the illumination spot.In addition,the conventional CDI method suffers problems such as slow convergence,stagnation and the non-unique solutions that often happens in the iterative phase retrieval algorithms.It requires relatively high skill in acquiring experimental data and reconstructing the sample image.As a variant of CDI methods,ptychography can overcome these shortcomings.In ptychography,the sample is scanned across by a localized coherent X-ray beam(often referred as a “probe”).The illuminated areas by the probe at adjacent scan positions are physically overlapped.As a consequence,each given sample area contributes to a series of recorded diffraction patterns,providing a significant amount of data redundancy in the dataset.Due to the consistencies between the measured diffraction patterns from neighboring regions and the redundancy in the recorded dataset,it is possible to: retrieve both the sample complex transmission function and the probe wave-field simultaneously;recover experimental uncertainties such as probe position errors;obtain super-resolved sample images by extrapolating the diffraction patterns beyond the aperture of the detector;reconstruct stationary mixed states in the probe radiation,in the sample(including quantum mixtures or fast stationary stochastic processes)and in the detector plane;reconstruct three-dimensional objects without rotating the specimen;and realize information multiplexing.Based on the advantages mentioned above and the most advanced research direction in ptychography,we focus on the partial coherent and mixed-states soft X-ray ptychography method.The main contributions in this dissertation are summarized as follows:1.Build the experimental platform and perform ptychography experiments.This work was carried out at the scanning transmission X-ray microscopy(STXM)endstation of the soft X-ray Spectromicroscopy Beamline(BL08U1-A)at the Shanghai Synchrotron Radiation Facility(SSRF)and at the STXM endstation of the soft X-ray Spectromicroscopy Beamline(SM 10ID-1)at the Canadian Light Source(CLS).At present,using high-performance GPU workstations,real-time reconstruction has been realized in both beamlines.2.Using the experimental platforms,a large number of experiments have been carried out at BL08U1-A and SM beamline.Different kinds of samples have been imaged including: test patterns,Pt-Co alloy nanoparticles,and breast cancer cells at BL08U1-A;test patterns,Au nanoparticles,polystyrene photonic crystals,and magnetosome chains at SM.High quality reconstructed images were obtained in all experiments.The ptychography method will be open to the users soon at both beamlines.3.The differences between the in-focus mode and the de-focus mode in ptychography were investigated.The results indicate that the in-focus mode can provide higher quality images than the de-focus mode,but it highly dependent on the accuracy of the scanning positions,while de-focus mode can tolerate larger scanning error.Also,the de-focus mode can significantly shorten the time needed for imaging a large sample area.4.The effects of residual noise on the quality of reconstructed images are systematically investigated.Several methods for noise removal methods are provided.The validity of these methods are verified by numerical simulations and experimental results.The results indicate that: the localized high intensity noise mainly affects the high spatial frequency information in the reconstructed images(i.e.fine structures),while a weak global uniform noise can strongly affects the images quality even at a very low spatial frequency;the positive effect of noise removal using the provided methods usually exceeds the negative effect of the accompanied loss of high spatial frequency signals in ptychography;removing the background noise improves the consistencies between diffraction patterns which in turn can recover part of the lost high frequency signals in the iterative reconstruction calculations.Therefore,one should remove the discernible noises from the diffraction patterns as much as possible,which would help to improve the reconstruction image quality significantly.5.The last part of this dissertation aims to improve the reconstructed image quality using mixed states decomposition iterative phase retrieval algorithms to eliminate the negative influences of various types of decoherence effects.Two mixed state decomposition algorithms,the multi-mode extended ptychographic iterative engine(Mm-e PIE)algorithm and the sub-pixel up-sampling extended ptychographic iterative engine(Us-e PIE)algorithm are used to reconstruct the sample function and the probe function(s)simultaneously.The results show that the decomposition effect of state mixture from different sources is embodied in both the reconstructed sample function and probe function(s).These two mixed-state decomposition phase retrieval algorithms can both improve the quality of the reconstructed image significantly.Moreover,the multi-mode algorithm performs better than the up-sampling algorithm in removing the decoherence effects in probe radiation.In addition,we give an example where the probe size is too large,resulting in a significant degradation in reconstruction quality.In this case,the Us-e PIE algorithm significantly improves the image quality.