Efficient large field of view electron phase imaging using near-field electron ptychography with a diffuser.

Most implementations of ptychography on the electron microscope operate in scanning transmission (STEM) mode, where a small focussed probe beam is rapidly scanned across the sample. In this paper we introduce a different approach based on near-field ptychography, where the focussed beam is replaced by a wide-field, structured illumination, realised through a purpose-designed etched Silicon Nitride window. We show that fields of view as large as 100 µm2 can be imaged using the new approach, and that quantitative electron phase images can be reconstructed from as few as nine near-field diffraction pattern measurements.

Diffraction-limited superresolution ptychography in the Rayleigh-Sommerfeld regime.

Superresolution in lensless near-field ptychography is demonstrated via the application of a strongly curved illumination function. The reconstruction is performed using the Rayleigh-Sommerfeld diffraction integral, which is implemented via a pixel-size adjustable angular spectrum method. In this manner, the reconstructed object details, which are not only smaller than the pixel size of the sensor but even smaller than the smallest resolvable object detail defined by the effective NA of the 2D sensor, are enabled. The expected resolution, as predicted by the angles of scatter present in the optical configuration, is experimentally validated using a US air force resolution test target. The approach discussed here is not limited to ptychography; it can be extended to other coherent diffractive imaging modalities such as object scanning holography or optical diffraction tomography, so as to enable high-resolution near-field quantitative phase imaging.

An X-ray ptycho-tomography model of `Seeing order in ``amorphous'' materials'.

The nature of the atomic structure of many non-crystalline materials remains a long-standing open question. We use X-ray scattering to model electron images of amorphous materials, where the analogue 'atoms' consist of 1 µm diameter glass beads. The beads form a substantially random close-packed structure, but are partially ordered in places. X-ray ptycho-tomography reveals the exact position of the beads in 3D and so can be used to compare the modelled electron image with full knowledge of the underlying real structure. Using this, we repeat an experiment reported by Archie Howie and colleagues in 1978 that sought to test for real structure in bright-field electron images of amorphous materials; we demonstrate the validity of the technique, at least in the case of the resolution of the microscopes available at that time and the first Born approximation. We also illustrate how extremely demanding it would have been to infer 3D structure of amorphous material from pairs of stereoscopic images obtained with the same experimental kit: an approach that Archie proposed in the 1970s. We briefly discuss the possibility of using electron ptycho-tomography to solve the amorphous structure problem.

Breaking ambiguities in mixed state ptychography.

Recent advances in ptychographic imaging have shown how the technique extends naturally to mixed state experiments, for example when the illuminating radiation is partially coherent or when the object being imaged is laterally vibrating. To date, experiments using this mixed-state form of ptychography have relied on decomposition of the illumination 'probe' into multiple modes. In this paper we demonstrate, for the first time, ptychographic imaging with the simultaneous presence of both multiple probe and multiple object states. Our results prompt a discussion of uniqueness in the reconstructed images, and we show mathematically how ambiguities can arise. This leads us to extend the reconstruction process to include additional constraints that break these ambiguities, allowing interpretation of mixed object states that are not orthogonal.

Separation of three-dimensional scattering effects in tilt-series Fourier ptychography.

We investigate a strategy for separating the influence of three-dimensional scattering effects in tilt-series reconstruction, a method for computationally increasing the resolution of a transmission microscope with an objective lens of small numerical aperture, as occurs in the transmission electron microscope (TEM). Recent work with visible light refers to the method as Fourier ptychography. To date, reconstruction methods presume that the object is thin enough so that the beam tilt induces only a shift of the diffraction pattern in the back focal plane. In fact, it is well known that the diffraction pattern changes as a function of beam tilt when the object is thick. In this paper, we use a simple visible light model to demonstrate a proof-of-principle of a new reconstruction algorithm that can cope with this difficulty and compare it with the aperture-scanning method. Although the experiment uses a model specimen with just two distinct layers separated along the optic axis, it should in principle be extendable to continuous objects.

Pixel size adjustment in coherent diffractive imaging within the Rayleigh-Sommerfeld regime.

The reconstruction of the smallest resolvable object detail in digital holography and coherent diffractive imaging when the detector is mounted close to the object of interest is restricted by the sensor's pixel size. Very high resolution information is intrinsically encoded in the data because the effective numerical aperture (NA) of the detector (its solid angular size as subtended at the object plane) is very high. The correct physical propagation model to use in the reconstruction process for this setup should be based on the Rayleigh-Sommerfeld diffraction integral, which is commonly implemented via a convolution operation. However, the convolution operation has the drawback that the pixel size of the propagation calculation is preserved between the object and the detector, and so the maximum resolution of the reconstruction is limited by the detector pixel size, not its effective NA. Here we show that this problem can be overcome via the introduction of a numerical spherical lens with adjustable magnification. This approach enables the reconstruction of object details smaller than the detector pixel size or of objects that extend beyond the size of the detector. It will have applications in all forms of near-field lensless microscopy.

Possibility of high-resolution ptychographic iterative imaging with low energy electrons: dynamical calculations.

Ptychographic iterative engine (PIE), a form of coherent diffractive imaging in which the phase of both low-angle and high-angle diffraction data is used to form an image without a lens, can in principle deliver wavelength-limited resolution. Working at low accelerating voltages (30 keV) reduces specimen knock-on damage, increases high-resolution contrast and allows a scanning electron microscope to be used as a transmission electron microscopy. However, electrons are very strongly scattered at low energy. To that end, the effect of dynamical scattering on PIE at low accelerating voltages is calculated to illustrate the possibility of generating high-resolution images with low energy electrons.

Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design.

We reconsider the closed form solution of the ptychographic phase problem called the Wigner Distribution Deconvolution Method (WDDM), which has remained discarded for twenty years. Ptychographic reconstruction is nowadays always undertaken by iterative algorithms. WDDM gives rise to a 4 dimensional data cube of all the relative phases between points in the diffraction plane. Here we demonstrate a novel method to use all this information, instead of just the small subset used in the original 'stepping out' procedure developed in the 1990s, thus greatly suppressing noise. We further develop a method for designing an improved probe (illumination function) to further decrease noise effects during the deconvolution division. Combining these two with an iterative procedure for the deconvolution, which avoids the usual difficulty of a divide by a small number, we show in model calculations that WDDM competes well with the modern conventional iterative methods like ePIE (the extended Ptychographical Iterative Engine).

Coherent x-ray imaging of collagen fibril distributions within intact tendons.

The characterization of the structure of highly hierarchical biosamples such as collagen-based tissues at the scale of tens of nanometers is essential to correlate the tissue structure with its growth processes. Coherent x-ray Bragg ptychography is an innovative imaging technique that gives high resolution images of the ordered parts of such samples. Herein, we report how we used this method to image the collagen fibrillar ultrastructure of intact rat tail tendons. The images show ordered fibrils extending over 10-20 µm in length, with a quantifiable D-banding spacing variation of 0.2%. Occasional defects in the fibrils distribution have also been observed, likely indicating fibrillar fusion events.

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 object's 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.

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.

Coherence requirement in digital holography.

In this paper the coherence requirement for different holographic setups (Fresnel hologram, Fourier hologram, and image-plane hologram) is compared. This analysis is based on the investigation of the recorded interference pattern from the superposition of reference wave and object wave in in-line and off-axis mode. The outcome of this investigation can support the choice of light source needed for certain digital holographic setups, as well as the selection of the best applicable setup to take advantage of new short coherence light sources. Moreover, as a byproduct of this investigation, the minimum required recording distance (focal length) to enable Nyquist sampling of the recorded hologram is obtained.

Noise models for low counting rate coherent diffraction imaging.

Coherent diffraction imaging (CDI) is a lens-less microscopy method that extracts the complex-valued exit field from intensity measurements alone. It is of particular importance for microscopy imaging with diffraction set-ups where high quality lenses are not available. The inversion scheme allowing the phase retrieval is based on the use of an iterative algorithm. In this work, we address the question of the choice of the iterative process in the case of data corrupted by photon or electron shot noise. Several noise models are presented and further used within two inversion strategies, the ordered subset and the scaled gradient. Based on analytical and numerical analysis together with Monte-Carlo studies, we show that any physical interpretations drawn from a CDI iterative technique require a detailed understanding of the relationship between the noise model and the used inversion method. We observe that iterative algorithms often assume implicitly a noise model. For low counting rates, each noise model behaves differently. Moreover, the used optimization strategy introduces its own artefacts. Based on this analysis, we develop a hybrid strategy which works efficiently in the absence of an informed initial guess. Our work emphasises issues which should be considered carefully when inverting experimental data.

Quantitative phase contrast optimised cancerous cell differentiation via ptychography.

This paper shows that visible-light ptychography can be used to distinguish quantitatively between healthy and tumorous unstained cells. Advantages of ptychography in comparison to conventional phase-sensitive imaging techniques are highlighted. A novel procedure to automatically refocus ptychographic reconstructions is also presented, which improves quantitative analysis.

Analysis and interpretation of the Seidel aberration coefficients in digital holography.

The most commonly used configurations in digital holography-namely Fourier holograms, Fresnel holograms, and image-plane holograms-are analyzed with respect to Seidel's wave aberration theory. This analysis is performed by taking into account the phase terms involved in the recording and reconstruction processes. The combined phase term from both processes is compared with the Gaussian-reference sphere, from which the wave aberration terms can be obtained. In conjunction with the analysis, for each of the aberration terms, conditions can be set to eliminate them. Wave aberrations are plotted to show how strongly different setups are affected.

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.

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.