We report on a method that allows microscopic image reconstruction from extreme-ultraviolet diffraction patterns without the need for object support constraints or other prior knowledge about the object structure. This is achieved by introducing additional diversity through rotation of an object in a rotationally asymmetric probe beam, produced by the spatial interference between two phase-coherent high-harmonic beams. With this rotational diffractive shearing interferometry method, we demonstrate robust image reconstruction of microscopic objects at wavelengths around 30 nm, using images recorded at only three to five different object rotations.

Diffractive shearing interferometry (DSI) is a method that has recently been developed to perform lensless imaging using extreme ultraviolet radiation generated by high-harmonic generation. In this paper, we investigate the uniqueness of the DSI solution and the requirements for the support constraint size. We find that there can be multiple solutions to the DSI problem that consist of displaced copies of the actual object. These alternative solutions can be eliminated by enforcing a sufficiently tight support constraint, or by introducing additional synthetic constraints. We furthermore propose a new DSI algorithm inspired by the analogy with coherent diffractive imaging (CDI) algorithms: the original DSI algorithm is in a way analogous to the hybrid input-output algorithm as used in CDI, and we propose a new algorithm that is more analogous to the error reduction algorithm as used in CDI. We find that the newly proposed algorithm is suitable for final refinement of the reconstruction.

Ptychography is a form of coherent diffractive imaging; it employs far-field intensity patterns of the object to reconstruct the object. In ptychography, an important limiting factor for the reconstructed image quality is the uncertainty in the probe positions. Here, we propose a new approach which uses the hybrid input-output algorithm and cross-correlation in a way that can correct our estimates of the probe positions. The performance and limitations of the method in the presence of noise, varying overlap, and maximum recoverable error are studied using simulations. A brief comparison with other existing methods is also discussed here.

In the theory of partial coherence, coherence singularities can occur in the spectral degree of coherence (SDOC): in case the fields at two different points are completely uncorrelated, the phase of the SDOC is undefined. For a partially coherent vortex beam, the detection of coherence singularities is linked to the measurement of topological charge, whose magnitude equals the number of ring dislocations in its far field amplitude. However, the phase distribution of coherence singularities is rarely mentioned in the literature and the amplitude distribution can hardly reflect the sign of topological charge. In this letter, we present a phase-analysis method for measuring the coherence singularities by introducing a movable perturbation at a certain point in an illumination window of a finite size. Using the proposed method, we measure experimentally the coherence singularities of a partially coherent vortex beam in the focal plane. From the results, the magnitude and sign of the topological charge can be determined simultaneously from the phase distribution of the coherence singularities. Our results can find application in information transmission.

Optical angular momenta (AM) have attracted tremendous research interest in recent years. In this paper we theoretically investigate the electromagnetic field and angular momentum properties of tightly focused arbitrary cylindrical vortex vector (CVV) input beams. An absorptive particle is placed in focused CVV fields to analyze the optical torques. The spin-orbit motions of the particle can be predicted and controlled when the influences of different parameters, such as the topological charge, the polarization and the initial phases, are taken into account. These findings will be helpful in optical beam shaping, optical spin-orbit interaction and practical optical manipulation.

We propose and experimentally demonstrate a noniterative diffractive imaging method for reconstructing the complex-valued transmission function of an object illuminated by spatially partially coherent light from the far-field diffraction pattern. Our method is based on a pinhole array mask, which is specially designed such that the correlation function in the mask plane can be obtained directly by inverse Fourier transforming the diffraction pattern. Compared to the traditional iterative diffractive imaging methods using spatially partially coherent illumination, our method is noniterative and robust to the degradation of the spatial coherence of the illumination. In addition to diffractive imaging, the proposed method can also be applied to spatial coherence property characterization, e.g., free-space optical communication and optical coherence singularity measurement.

A noise-robust extension of iterative phase retrieval algorithms that does not need to assume a noise model is proposed. It works by adapting the intensity constraints using the reconstructed object. Using a proof-of-principle ptychographic experiment with visible light and a spatial light modulator to create an object, the proposed method is tested and it compares favorably to the Extended Ptychographic Iterative Engine (ePIE) with reduced step size. The method is general, so it can also be applied to other iterative reconstruction schemes such as phase retrieval using focus variation.

The complete characterization of spatial coherence is extremely di cult because the mutual coherence function (MCF) is a complex-valued function of four independent Cartesian coordinates. This di culty limits the ability to control and to optimize the spatial coherence in a broad range of key applications. Here we propose an e cient and robust scheme for measuring the complete MCF of an arbitrary partially coherent beam using self-referencing holography, which does not require any prior knowledge or making any assumptions about the MCF. We further apply our method to lensless di ractive imaging, and experimentally demonstrate the reconstruction of a phase object under spatially partially coherent illumination. This application is particularly useful for imaging at short wavelengths, where the illumination sources lack spatial coherence and no high-quality imaging optics are available.

X-rays and e-beams are used for high-resolution imaging where the requirement for highly accurate lenses is one of the limiting factors. Hence, lensless imaging is preferred. Coherent Diffractive Imaging (CDI) is a lensless imaging technique which uses intensity patterns in the far-field to obtain the complex amplitude of the object. Ptychography, an emerging area of research, belongs to the class of CDI techniques. In ptychography, the object is partially illuminated by a scanning probe and the intensity patterns in the far-field for each probe position are recorded and used to reconstruct the object. One of the important aspects to the success of this method is the overlap between the adjacent probes and the accurate knowledge of the probe positions. Recently, we proposed a new method to correct the probe positions which uses the gradient of intensity patterns in the far-field. Here, we propose another method to correct probe positions.

Ptychography, a form of Coherent Diffractive Imaging, is used with short wavelengths (e.g. X-rays, electron beams) to achieve high-resolution image reconstructions. One of the limiting factors for the reconstruction quality is the accurate knowledge of the illumination probe positions. Recently, many advances have been made to relax the requirement for the probe positions accuracy. Here, we analyse and demonstrate a straightforward approach that can be used to correct the probe positions with sub-pixel accuracy. Simulations and experimental results with visible light are presented in this work.

In this article we combine the well-known Ptychographical Iterative Engine (PIE) with the Hybrid Input-Output (HIO) algorithm. The important insight is that the HIO feedback function should be kept strictly separate from the reconstructed object, which is done by introducing a separate feedback function per probe position. We have also combined HIO with floating PIE (fPIE) and extended PIE (ePIE). Simulations indicate that the combined algorithm performs significantly better in many situations. Although we have limited our research to a combination with HIO, the same insight can be used to combine ptychographical algorithms with any phase retrieval algorithm that uses a feedback function.