An autofocusing algorithm for ptychography is proposed. The method optimizes a sharpness metric that would be observed in a differential interference microscope and is valid for both amplitude and phase modulating specimens. We experimentally demonstrate that the algorithm, based on the extended ptychographic iterative engine (ePIE), calibrates the sample–detector distance with an accuracy within the depth of field of the ptychographic microscope. We show that the method can be used to determine slice separation in multislice ptychography, provided there are isolated regions on each slice of the specimen that do not axially overlap.

Diffractive optics can be used to accurately control optical wavefronts, even in situations where refractive components such as lenses are not available. For instance, conventional Fresnel zone plates (ZPs) enable focusing of monochromatic radiation. However, they lead to strong chromatic aberrations in multicolor operation. In this work, we propose the concept of spatial entropy minimization as a computational design principle for both mono- and polychromatic focusing optics. We show that spatial entropy minimization yields conventional ZPs for monochromatic radiation. For polychromatic radiation, we observe a previously unexplored class of diffractive optical elements, allowing for balanced spectral efficiency. We apply the proposed approach to the design of a binary ZP, tailored to multispectral focusing of extreme ultraviolet (EUV) radiation from a high-harmonic tabletop source. The polychromatic focusing properties of these ZPs are experimentally confirmed using ptychography. This work provides a new route towards polychromatic wavefront engineering at EUV and soft-x-ray wavelengths.

Conventional (CP) and Fourier (FP) ptychography have emerged as versatile quantitative phase imaging techniques. While the main application cases for each technique are different, namely lens-less short wavelength imaging for CP and lens-based visible light imaging for FP, both methods share a common algorithmic ground. CP and FP have in part independently evolved to include experimentally robust forward models and inversion techniques. This separation has resulted in a plethora of algorithmic extensions, some of which have not crossed the boundary from one modality to the other. Here, we present an open source, cross-platform software, called PtyLab, enabling both CP and FP data analysis in a unified framework. With this framework, we aim to facilitate and accelerate cross-pollination between the two techniques. Moreover, the availability in Matlab, Python, and Julia will set a low barrier to enter each field.

Coherent multi-spectral extreme ultraviolet beams have great potential for providing high spatial and temporal resolution for microscopy and spectroscopy applications. But due to the limitations of short-wavelength optics and the broad bandwidth, it remains a challenge to perform quantitative, high-resolution beam characterization. Here we present a wavefront sensing solution based on multiplexed ptychography, with which we show spectrally resolved, high-resolution beam reconstructions. Furthermore, using these high-fidelity quantitative wavefront measurements, we investigate aberration transfer mechanisms in the high-harmonic-generation process, where we present and explain harmonic-order-dependent astigmatism inheritance from the fundamental wavefront. This ptychographic wavefront sensing concept thus enables detailed studies of the high-harmonic-generation process, such as spatiotemporal effects in attosecond pulse formation.

We report on an approach for quantitative characterization of laser beam quality, wavefronts, and lens aberrations using ptychography with a near-infrared supercontinuum laser. Ptychography is shown to offer a powerful alternative for both beam propagation ratio M² and wavefront measurements compared with existing techniques. In addition, ptychography is used to recover the transmission function of a microlens array for aberration analysis. The results demonstrate ptychography’s flexibility in wavefront metrology and optical shop testing.

Reflection ptychography is a lensfree microscopy technique particularly promising in regions of the electromagnetic spectrum where imaging optics are inefficient or not available. This is the case in tabletop extreme ultraviolet microscopy and grazing incidence small angle x ray scattering experiments. Combining such experimental configurations with ptychography requires accurate knowledge of the relative tilt between the sample and the detector in non-coplanar scattering geometries. Here, we describe an algorithm for tilt estimation in reflection ptychography. The method is verified experimentally, enabling sample tilt determination within a fraction of a degree. Furthermore, the angle-estimation uncertainty and reconstruction quality are studied for both smooth and highly structured beams.