Ptychographical Iterative Engine Algorithm Research Articles

Stochastic minibatch approach to the ptychographic iterative engine.

The ptychographic iterative engine (PIE) is a widely used algorithm that enables phase retrieval at nanometer-scale resolution over a wide range of imaging experiment configurations. By analyzing diffraction intensities from multiple scanning locations where a probing wavefield interacts with a sample, the algorithm solves a difficult optimization problem with constraints derived from the experimental geometry as well as sample properties. The effectiveness at which this optimization problem is solved is highly dependent on the ordering in which we use the measured diffraction intensities in the algorithm, and random ordering is widely used due to the limited ability to escape from stagnation in poor-quality local solutions. In this study, we introduce an extension to the PIE algorithm that uses ideas popularized in recent machine learning training methods, in this case minibatch stochastic gradient descent. Our results demonstrate that these new techniques significantly improve the convergence properties of the PIE numerical optimization problem.

Ptychographic iterative engine with the incoherent illumination

Ptychographic iterative engine (PIE) is an ideal phase microscopic method for imaging with short wavelength including X-ray and electron beam. The traditional PIE algorithm requires a purely coherent illumination. Since the coherencies of X-ray and electron beam are always much lower than coherency of the laser, it is greatly important to develop new algorithm for enhancing the capability of PIE in handling the incoherence of the illumination. A method, named polyCDI (coherent diffraction imaging), which can generate clear reconstruction with the illumination of partial coherency, was proposed recently, however due to the use of tiny pinhole in the data acquisition the view field of the reconstructed image is limited. The polyPIE algorithm, which combines the principles of polyCDI with PIE, can realize the imaging of large object with partially coherent illumination. In this paper, an improved polyPIE algorithm is developed to realize the high-resolution phase imaging under incoherent illumination by bringing the shape of the illuminating pinhole and the spectral distribution of the light source into the iterative computation. The image of the object and the illuminating probe are reconstructed for each spectral component, and the shape of the pinhole forming the illumination is used as the same spatial constraint for all the reconstructed probes on the pinhole plane. With this method a very high convergence speed and reconstruction accuracy as well as a wide view field can be achieved. This method can find many applications in the imaging with X-ray and electron beam, which are of low coherence in most of cases. The influence of the spectral width on reconstruction accuracy is also analyzed by imaging the object with illuminations of different spectral widths. It is found that the improved polyPIE algorithm can accurately reconstruct the phase and modulus images of the object when the width of the incoherent illuminating source is smaller than 10% of the central wavelength, otherwise, the convergence speed and reconstruction accuracy will become remarkably lower. By bringing the shape of the pinhole into the iterative computation, the relevance of the reconstructed illuminating probes of different spectral components is used and accordingly the reconstruction speed can be obviously accelerated. The feasibility of this suggested method is verified by a series of numerical simulations.

Single shot ptychographical iterative engine based on multi-beam illumination

An optical alignment and a corresponding reconstruction algorithm are proposed to realize a single shot Ptychographical Iterative Engine (PIE). Multiple light beams generated by a cross grating are used to illuminate the specimen, and the resulting diffraction patterns formed on the detector plane by each beam are recorded simultaneously. The modulus and phase images are properly reconstructed with standard PIE algorithm. The proposed single shot method omits the needs for a mechanical x-y scanning of standard PIE algorithm and hence dramatically reduces the data acquisition time.

Influence of central beamstop on ptychographic coherent diffractive imaging

A beamstop is commonly used in coherent diffractive imaging (CDI) experiments to collect more high-angle diffraction signals. But it causes the low-frequency signals missed, which can make CDI reconstruction unstable or even fail. In this work, a systematic simulation investigation of the effects of the missing low-frequency signals on the quality of reconstructed images of ptychographic CDI (PCDI) is performed using the ptychographic iterative engine algorithm. We found that the robustness of PCDI to the beamstop is much higher than that of the plane-wave CDI, and a smaller incident probe or a larger probe overlap ratio ( 70%) can further decrease the negative influence of missing low-freqency signals on the reconstruction image. The probe scanning position error will be the main degrading factor of PCDI instead of the beamstop in the higher overlap cases, and needs to be corrected in experiments by using high precision motors or adopting the position refinement algorithms. Our results provide quantitative guidelines for the usage of beamstops in ptychographic CDI experiments.

Research on the key parameters of illuminating beam for imaging via ptychography in visible light band

Some key parameters of illuminating beam and the influence on imaging quality are investigated via ptychography in visible light band. The influences of overlap ratio, size and shape of illuminating beam on imaging quality and their relationship are studied using ptychographical iterative engine algorithm. The simulation results show that the overlap ratio of illuminating beam is a main factor influencing imaging quality. Shape of illuminating beam mainly influences the convergence of ptychography. And the size of illuminating beam less influences directly the imaging quality and convergence. Therefore, the simulation results play an important theoretic guiding role in optimizing the beam parameters in visible light, the X-ray and electronic band and other bands.

A general phase retrieval algorithm based on a ptychographical iterative engine for coherent diffractive imaging

Coherent diffractive imaging (CDI) is a lensless imaging technique and can achieve a resolution beyond the Rayleigh or Abbe limit. The ptychographical iterative engine (PIE) is a CDI phase retrieval algorithm that uses multiple diffraction patterns obtained through the scan of a localized illumination on the specimen, which has been demonstrated successfully at optical and X-ray wavelengths. In this paper, a general PIE algorithm (gPIE) is presented and demonstrated with an He—Ne laser light diffraction dataset. This algorithm not only permits the removal of the accurate model of the illumination function in PIE, but also provides improved convergence speed and retrieval quality.

A Lens Assisted Phase Microscope Based on Ptychography

Based on the recently developed ptychographical iterative engine (PIE), we suggest a lens assisted microscopy to realize quantitative phase imaging without using interferometry. The sample is imaged with a lens system; a pinhole on the image plane scans the image at a proper step interval; the diffraction pattern is recorded simultaneously by a CCD at Fresnel area. With a slightly changed PIE algorithm, the phase image of the sample can be accurately reconstructed from the recorded diffraction pattern. The main advantage of this suggested method lies in its capability to retrieve the phase information from the recorded intensity directly, and thus it has more flexibility over conventional interferometric techniques. The feasibility of the suggested method is verified by reconstructing the modulus and phase image of a biological sample from a set of 10 by 10 diffraction patterns, and the result matches the analysis well.