Phase retrieval algorithms for lensless imaging using diffractive shearing interferometry.

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.

Extreme ultraviolet lensless imaging without object support through rotational diversity in diffractive shearing interferometry.

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.

Non-iterative method for phase retrieval and coherence characterization by focus variation using a fixed star-shaped mask.

A novel non-iterative phase retrieval method is proposed and demonstrated with a proof-of-principle experiment. The method uses a fixed specially designed mask and through-focus intensity measurements. It is demonstrated that this method is robust to spatial partial coherence in the illumination, making it suitable for coherent diffractive imaging using spatially partially coherent light, as well as for coherence characterization.

Model-independent noise-robust extension of ptychography.

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.

Non-iterative phase retrieval by phase modulation through a single parameter.

We report on a novel non-iterative phase retrieval method with which the complex-valued transmission function of an object can be retrieved with a non-iterative computation, with a limited number of intensity measurements. The measurements are taken in either real space or Fourier space, and for each measurement the phase in its dual space is modulated according to a single optical parameter. The requirement found for the phase modulation function is a general one, which therefore allows for plenty of customization in this method. It is shown that quantitative Zernike phase contrast imaging is one special case of this general method. With simulations we investigate the sampling requirements for a microscopy setup and for a Coherent Diffraction Imaging (CDI) setup.

Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm.

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.