Computational optical sensing and imaging: introduction to the feature issue.

This joint feature issue of Optics Express and Applied Optics showcases technical innovations by participants of the 2023 topical meeting on Computational Optical Sensing and Imaging and the computational imaging community. The articles included in the feature issue highlight advances in imaging science that emphasize synergistic activities in optics, signal processing and machine learning. The issue features 26 contributed articles that cover multiple themes including non line-of-sight imaging, imaging through scattering media, compressed sensing, lensless imaging, ptychography, computational microscopy, spectroscopy and optical metrology.

Broadband ptychography using curved wavefront illumination.

We examine the interplay between spectral bandwidth and illumination curvature in ptychography. By tailoring the divergence of the illumination, broader spectral bandwidths can be tolerated without requiring algorithmic modifications to the forward model. In particular, a strong wavefront curvature transitions a far-field diffraction geometry to an effectively near-field one, which is less affected by temporal coherence effects. The relaxed temporal coherence requirements allow for leveraging wider spectral bandwidths and larger illumination spots. Our findings open up new avenues towards utilizing pink and broadband beams for increased flux and throughput at both synchrotron facilities and lab-scale beamlines.

PtyLab.m/py/jl: a cross-platform, open-source inverse modeling toolbox for conventional and Fourier ptychography.

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.

Addressing phase-curvature in Fourier ptychography.

In Fourier ptychography, multiple low resolution images are captured and subsequently combined computationally into a high-resolution, large-field of view micrograph. A theoretical image-formation model based on the assumption of plane-wave illumination from various directions is commonly used, to stitch together the captured information into a high synthetic aperture. The underlying far-field (Fraunhofer) diffraction assumption connects the source, sample, and pupil planes by Fourier transforms. While computationally simple, this assumption neglects phase-curvature due to non-planar illumination from point sources as well as phase-curvature from finite-conjugate microscopes (e.g., using a single-lens for image-formation). We describe a simple, efficient, and accurate extension of Fourier ptychography by embedding the effect of phase-curvature into the underlying forward model. With the improved forward model proposed here, quantitative phase reconstruction is possible even for wide fields-of-views and without the need of image segmentation. Lastly, the proposed method is computationally efficient, requiring only two multiplications: prior and following the reconstruction.

Material-specific high-resolution table-top extreme ultraviolet microscopy.

Microscopy with extreme ultraviolet (EUV) radiation holds promise for high-resolution imaging with excellent material contrast, due to the short wavelength and numerous element-specific absorption edges available in this spectral range. At the same time, EUV radiation has significantly larger penetration depths than electrons. It thus enables a nano-scale view into complex three-dimensional structures that are important for material science, semiconductor metrology, and next-generation nano-devices. Here, we present high-resolution and material-specific microscopy at 13.5 nm wavelength. We combine a highly stable, high photon-flux, table-top EUV source with an interferometrically stabilized ptychography setup. By utilizing structured EUV illumination, we overcome the limitations of conventional EUV focusing optics and demonstrate high-resolution microscopy at a half-pitch lateral resolution of 16 nm. Moreover, we propose mixed-state orthogonal probe relaxation ptychography, enabling robust phase-contrast imaging over wide fields of view and long acquisition times. In this way, the complex transmission of an integrated circuit is precisely reconstructed, allowing for the classification of the material composition of mesoscopic semiconductor systems.

aPIE: an angle calibration algorithm for reflection ptychography.

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.

Advances in laboratory-scale ptychography using high harmonic sources [Invited].

Extreme ultraviolet microscopy and wavefront sensing are key elements for next-generation ultrafast applications, such as chemically-resolved imaging, focal spot diagnostics in pump-and-probe experiments, and actinic metrology for the state-of-the-art lithography node at 13.5 nm wavelength. Ptychography offers a robust solution to the aforementioned challenges. Originally adapted by the electron and synchrotron communities, advances in the stability and brightness of high-harmonic tabletop sources have enabled the transfer of ptychography to the laboratory. This review covers the state of the art in tabletop ptychography with high harmonic generation sources. We consider hardware options such as illumination optics and detector concepts as well as algorithmic aspects in the analysis of multispectral ptychography data. Finally, we review technological application cases such as multispectral wavefront sensing, attosecond pulse characterization, and depth-resolved imaging.

Ptychographic optical coherence tomography.

Ptychography is a robust computational imaging technique that can reconstruct complex light fields beyond conventional hardware limits. However, for many wide-field computational imaging techniques, including ptychography, depth sectioning remains a challenge. Here we demonstrate a high-resolution three-dimensional (3D) computational imaging approach, which combines ptychography with spectral-domain imaging, inspired by optical coherence tomography (OCT). This results in a flexible imaging system with the main advantages of OCT, such as depth-sectioning without sample rotation, decoupling of transverse and axial resolution, and a high axial resolution only determined by the source bandwidth. The interferometric reference needed in OCT is replaced by computational methods, simplifying hardware requirements. As ptychography is capable of deconvolving the illumination contributions in the observed signal, speckle-free images are obtained. We demonstrate the capabilities of ptychographic optical coherence tomography (POCT) by imaging an axially discrete lithographic structure and an axially continuous mouse brain sample.

Fourier ptychography: current applications and future promises.

Traditional imaging systems exhibit a well-known trade-off between the resolution and the field of view of their captured images. Typical cameras and microscopes can either "zoom in" and image at high-resolution, or they can "zoom out" to see a larger area at lower resolution, but can rarely achieve both effects simultaneously. In this review, we present details about a relatively new procedure termed Fourier ptychography (FP), which addresses the above trade-off to produce gigapixel-scale images without requiring any moving parts. To accomplish this, FP captures multiple low-resolution, large field-of-view images and computationally combines them in the Fourier domain into a high-resolution, large field-of-view result. Here, we present details about the various implementations of FP and highlight its demonstrated advantages to date, such as aberration recovery, phase imaging, and 3D tomographic reconstruction, to name a few. After providing some basics about FP, we list important details for successful experimental implementation, discuss its relationship with other computational imaging techniques, and point to the latest advances in the field while highlighting persisting challenges.

zPIE: an autofocusing algorithm for ptychography.

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.

Measuring laser beam quality, wavefronts, and lens aberrations using ptychography.

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.

Generation and characterization of focused helical x-ray beams.

The phenomenon of orbital angular momentum (OAM) affects a variety of important applications in visible optics, including optical tweezers, free-space communication, and 3D localization for fluorescence imaging. The lack of suitable wavefront shaping optics such as spatial light modulators has inhibited the ability to impart OAM on x-ray and electron radiation in a controlled way. Here, we report the experimental observation of helical soft x-ray beams generated by holographically designed diffractive optical elements. We demonstrate that these beams rotate as a function of propagation distance and measure their vorticity and coherent mode structure using ptychography. Our results establish an approach for controlling and shaping of complex focused beams for short wavelength scanning microscopy and OAM-driven applications.

Quantitative ptychographic bio-imaging in the water window.

Coherent X-ray ptychography is a tool for highly dose efficient lensless nano-imaging of biological samples. We have used partially coherent soft X-ray synchrotron radiation to obtain a quantitative image of a laterally extended, dried, and unstained fibroblast cell by ptychography. We used data with and without a beam stop that allowed us to measure coherent diffraction with a high-dynamic range of 1.7·106. As a quantitative result, we obtained the refractive index values for two regions of the cell with respect to a reference area. Due to the photon energy in the water window we obtained an extremely high contrast of 53% at 71 nm half-period resolution. The dose applied in our experiment was 9.5·104 Gy and is well below the radiation damage threshold. The concept for dynamic range improvement for low dynamic range detectors with a beam stop opens the path for high resolution nano-imaging of a variety of samples including cryo-preserved, hydrated and unstained biological cells.