J. M. Rodenburg

An improved ptychographical phase retrieval algorithm for diffractive imaging

The ptychographical iterative engine (or PIE) is a recently developed phase retrieval algorithm that employs a series of diffraction patterns recorded as a known illumination function is translated to a set of overlapping positions relative to a target sample. The technique has been demonstrated successfully at optical and X-ray wavelengths and has been shown to be robust to detector noise and to converge considerably faster than support-based phase retrieval methods. In this paper, the PIE is extended so that the requirement for an accurate model of the illumination function is removed.

A phase retrieval algorithm for shifting illumination

We propose a method of iterative phase retrieval that uses measured intensities in the diffraction plane to solve the phase problem in a way that bypasses the problem of lens aberration, leading to greatly improved spatial resolution. This method is stable, easy to implement experimentally, and can be used to view a large area of the specimen when that is desired.

Ptychography and Related Diffractive Imaging Methods

Publisher Summary Ptychography is a nonholographic solution of the phase problem. It is a method for calculating the phase relationships among different parts of a scattered wave disturbance in a situation where only the magnitude (intensity or flux) of the wave can be physically measured. Its usefulness lies in its ability (like holography) to obtain images without the use of lenses, and hence to lead to resolution improvements and access to properties of the scattering medium that cannot be easily obtained from conventional imaging methods. The chapter discusses ptychography in the context of other phase-retrieval methods in both historical and conceptual terms. In an original and oblique approach to the phase problem, it was Hoppe who proposed the first version of the particular solution to the phase problem. The word “ptychography” was introduced to suggest a solution to the phase problem using the convolution theorem, or rather the “folding” of diffraction orders into one another via the convolution of the Fourier transform of a localized aperture or illumination function in the object plane. Apart from computers, the two most important experimental issues that affect ptychography, relate to the degree of coherence in the illuminating beam and the detector efficiency and dynamic range.

Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging

Diffractive imaging, in which image-forming optics are replaced by an inverse computation using scattered intensity data, could, in principle, realize wavelength-scale resolution in a transmission electron microscope. However, to date all implementations of this approach have suffered from various experimental restrictions. Here we demonstrate a form of diffractive imaging that unshackles the image formation process from the constraints of electron optics, improving resolution over that of the lens used by a factor of five and showing for the first time that it is possible to recover the complex exit wave (in modulus and phase) at atomic resolution, over an unlimited field of view, using low-energy (30 keV) electrons. Our method, called electron ptychography, has no fundamental experimental boundaries: further development of this proof-of-principle could revolutionize sub-atomic scale transmission imaging.

Translation position determination in ptychographic coherent diffraction imaging

Accurate knowledge of translation positions is essential in ptychography to achieve a good image quality and the diffraction limited resolution. We propose a method to retrieve and correct position errors during the image reconstruction iterations. Sub-pixel position accuracy after refinement is shown to be achievable within several tens of iterations. Simulation and experimental results for both optical and X-ray wavelengths are given. The method improves both the quality of the retrieved object image and relaxes the position accuracy requirement while acquiring the diffraction patterns.

Superresolution imaging via ptychography

Coherent diffractive imaging of objects is made considerably more practicable by using ptychography, where a set of diffraction patterns replaces a single measurement and introduces a high degree of redundancy into the recorded data. Here we demonstrate that this redundancy allows diffraction patterns to be extrapolated beyond the aperture of the recording device, leading to superresolved images, improving the limit on the finest feature separation by more than a factor of 3.

Optical ptychography: a practical implementation with useful resolution

Quantitative phase microscopy offers a range of benefits over conventional phase-contrast techniques. For example, changes in refractive index and specimen thickness can be extrapolated and images can be refocused subsequent to their recording. In this Letter, we detail a lensless, quantitative phase microscope with a wide field of view and a useful resolution. The microscope uses the recently reported coherent diffractive imaging technique of ptychography to generate images from recorded diffraction patterns.

Ptychographic transmission microscopy in three dimensions using a multi-slice approach

Generally, methods of three-dimensional imaging such as confocal microscopy and computed tomography rely on two essentials: multiple measurements (at a range of focus positions or rotations) and a weakly scattering specimen (to avoid distortion of the focal spot in the confocal microscope or to satisfy the projection approximation in tomography). Here we show that an alternative form of multi-measurement imaging, ptychography, can be extended to three dimensions and can successfully recover images in the presence of multiple scattering and when the projection approximation is not applicable. We demonstrate our technique experimentally using visible light, where it has applications in imaging thick samples such as biological tissues; however the results also have important implications for x ray and electron imaging.

Soft X-ray spectromicroscopy using ptychography with randomly phased illumination

Ptychography is a form of scanning diffractive imaging that can successfully retrieve the modulus and phase of both the sample transmission function and the illuminating probe. An experimental difficulty commonly encountered in diffractive imaging is the large dynamic range of the diffraction data. Here we report a novel ptychographic experiment using a randomly phased X-ray probe to considerably reduce the dynamic range of the recorded diffraction patterns. Images can be reconstructed reliably and robustly from this setup, even when scatter from the specimen is weak. A series of ptychographic reconstructions at X-ray energies around the L absorption edge of iron demonstrates the advantages of this method for soft X-ray spectromicroscopy, which can readily provide chemical sensitivity without the need for optical refocusing. In particular, the phase signal is in perfect registration with the modulus signal and provides complementary information that can be more sensitive to changes in the local chemical environment.

Information multiplexing in ptychography

We show for the first time that ptychography (a form of lensless diffractive imaging) can recover the spectral response of an object through simultaneous reconstruction of multiple images that represent the objects response to a particular mode present in the illumination. We solve the phase problem for each mode independently, even though the intensity arriving at every detector pixel is an incoherent superposition of several uncorrelated diffracted waves. Until recently, the addition of incoherent modes has been seen as a nuisance in diffractive imaging: here we show that not only can the difficulties they pose be removed, but that they can also be used to discover much more information about the object. If the illumination function is also mode-specific, we show that we can also solve simultaneously for a multiplicity of such illumination modes. The work opens exciting possibilities for information multiplexing in ptychography over all visible, X-ray and electron wavelengths.