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We present a parameter retrieval method which combines ptychography and additional prior knowledge about the object. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of retangule with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cram{e}r Rao Lower Bound in both two applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and the correlation of particles in Application 1. For Application 2 the correlation of parameters of the rectangule is discussed.
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Incoherent Fourier ptychography (IFP) is a newly developed super-resolution method, where accurate knowledge of translation positions is essential for image reconstruction.To release this limitation, we propose a preprocessing algorithm capable of extracting translation positions of the structure light directly from raw images of IFP, termed translation position extracting (TPE). TPE mainly involves two steps. First, the speckle parts mixed in the acquired intensities, in which the illumination motion is encoded, are isolated by intensity averaging and division. Then the cross-correlations of the speckle dataset are computed to determine the shift positions. TPE-IFP improves the previous IFP by removal of the requirement for prior knowledge of translation positions. Its effectiveness is demonstrated by obtaining high-quality super-resolution images in absence of location information in both simulations and experiments. By further relaxing the practical conditions, the proposed TPE may accelerate the applications of IFP. What is more, as a preprocessing approach, TPE might also contribute to the estimation of pattern positions for the similar speckle-based imaging.
The pressing need for the detailed wavefront properties of ultra-bright and ultra-short pulses produced by free-electron lasers (FELs) has spurred the development of several complementary characterization approaches. Here we present a method based on ptychography that can retrieve full high-resolution complex-valued wave functions of individual pulses. Our technique is demonstrated within experimental conditions suited for diffraction experiments in their native imaging state. This lensless technique, applicable to many other short-pulse instruments, can achieve diffraction-limited resolution.
While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize the field. The need for a reference severely restricts the utility of holography. Phase retrieval, in contrast, is theoretically consistent with sensors that directly measure coherent or partially coherent fields with no prior assumptions. Unfortunately, phase retrieval has not yet been successfully implemented for large-scale fields. Here we show that both holography and phase retrieval are capable of quantum-limited coherent signal estimation and we describe phase retrieval strategies that approach the quantum limit for >1 megapixel fields. These strategies rely on group testing using networks of interferometers, such as might be constructed using emerging integrated photonic, plasmonic and/or metamaterial devices. Phase-sensitive sensor planes using such devices could eliminate the need both for lenses and reference signals, creating a path to large aperture diffraction limited laser imaging.
Intensity interferometry (II) exploits the second-order correlation to acquire the spatial frequency information of an object, which has been used to observe distant stars since 1950s. However, due to unreliability of employed imaging reconstruction algorithms, II can only image simple and sparse objects such as double stars. We here develop a method that overcomes this unreliability problem and enables imaging complex objects by combing II and a ptychography iterative algorithm. Different from previous ptychography iterative-type algorithms that work only for diffractive objects using coherence light sources, our method obtains the objects spatial spectrum from the second-order correlation of intensity fluctuation by using an incoherent source, which therefore largely simplifies the imaging process. Furthermore, by introducing loose supports in the ptychography algorithm, a high-quality image can be recovered without knowing the precise size and position of the scanning illumination, which is a strong requirement for traditional ptychography iterative algorithm.
The success of ptychographic imaging experiments strongly depends on achieving high signal-to-noise ratio. This is particularly important in nanoscale imaging experiments when diffraction signals are very weak and the experiments are accompanied by significant parasitic scattering (background), outliers or correlated noise sources. It is also critical when rare events such as cosmic rays, or bad frames caused by electronic glitches or shutter timing malfunction take place. In this paper, we propose a novel iterative algorithm with rigorous analysis that exploits the direct forward model for parasitic noise and sample smoothness to achieve a thorough characterization and removal of structured and random noise. We present a formal description of the proposed algorithm and prove its convergence under mild conditions. Numerical experiments from simulations and real data (both soft and hard X-ray beamlines) demonstrate that the proposed algorithms produce better results when compared to state-of-the-art methods.
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