We introduce a novel approach for ptychographic reconstruction, integrating a pre-trained autoencoder within a reconstruction framework based on automatic differentiation. This enables noise-robust imaging and insight into optimization landscapes for applications with prior object knowledge.@en

Next-generation metrology solutions in various technology areas require to image sample areas at the nanoscale. Coherent diffractive imaging based on ptychography is the route towards EUV imaging of nanostructures without lenses. A key component in a table-top EUV beamline is a high-brightness high-harmonic generation (HHG) source. Since our research is mainly directed towards wafer metrology for lithography in the semiconductor industry, we adhere to a reflection setup: the EUV light is scattered by the nanostructures at the surface of the sample, and is reflected towards a CCD camera, where a far-field diffraction pattern is recorded. A data-set comprising a multitude of these diffraction patterns is generated for partially overlapping positions of the focused probe on the sample. This provides the necessary redundancy for phase retrieval of the complex-valued field of the sample. Recent advancements in both hardware and software for computation enable the development of advanced algorithms. In particular, the benefits of automatic differentiation are exploited in order to cope with a drastic growth in model complexity. Our computational imaging algorithms realize wavelengthmultiplexed reconstruction and a modal approach for the spatial coherence of the source.@en

Computational imaging is increasingly vital for a broad spectrum of applications, ranging from biological to material sciences. This includes applications where the object is known and sufficiently sparse, allowing it to be described with a reduced number of parameters. When no explicit parameterization is available, a deep generative model can be trained to represent an object in a low-dimensional latent space. In this paper, we harness this dimensionality reduction capability of autoencoders to search for the object solution within the latent space rather than the object space. We demonstrate what we believe to be a novel approach to ptychographic image reconstruction by integrating a deep generative model obtained from a pre-trained autoencoder within an automatic differentiation ptychography (ADP) framework. This approach enables the retrieval of objects from highly ill-posed diffraction patterns, offering an effective method for noise-robust latent vector reconstruction in ptychography. Moreover, the mapping into a low-dimensional latent space allows us to visualize the optimization landscape, which provides insight into the convexity and convergence behavior of the inverse problem. With this work, we aim to facilitate new applications for sparse computational imaging such as when low radiation doses or rapid reconstructions are essential.

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Ptychographic extreme ultraviolet (EUV) diffractive imaging has emerged as a promising candidate for the next generationmetrology solutions in the semiconductor industry, as it can image wafer samples in reflection geometry at the nanoscale. This technique has surged attention recently, owing to the significant progress in high-harmonic generation (HHG) EUV sources and advancements in both hardware and software for computation. In this study, a novel algorithm is introduced and tested, which enables wavelength-multiplexed reconstruction that enhances the measurement throughput and introduces data diversity, allowing the accurate characterisation of sample structures. To tackle the inherent instabilities of the HHG source, a modal approach was adopted, which represents the cross-density function of the illumination by a series of mutually incoherent and independent spatial modes. The proposed algorithm was implemented on a mainstream machine learning platform, which leverages automatic differentiation to manage the drastic growth in model complexity and expedites the computation using GPU acceleration. By optimising over 200 million parameters, we demonstrate the algorithm's capacity to accommodate experimental uncertainties and achieve a resolution approaching the diffraction limit in reflection geometry. The reconstruction of wafer samples with 20-nm high patterned gold structures on a silicon substrate highlights our ability to handle complex physical interrelations involving a multitude of parameters. These results establish ptychography as an efficient and accurate metrology tool.@en

Optical measurements often exhibit mixed Poisson–Gaussian noise statistics, which hampers the image quality, particularly under low signal-to-noise ratio (SNR) conditions. Computational imaging falls short in such situations when solely Poissonian noise statistics are assumed. In response to this challenge, we define a loss function that explicitly incorporates this mixed noise nature. By using a maximum-likelihood estimation, we devise a practical method to account for a camera readout noise in gradient-based ptychography optimization. Our results, based on both experimental and numerical data, demonstrate that this approach outperforms the conventional one, enabling enhanced image reconstruction quality under challenging noise conditions through a straightforward methodological adjustment.

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We study femtosecond-laser-induced flows of air at a water/air interface, at micrometer length scales. To visualize the flow velocity field, we simultaneously induce two flow fronts using two adjacent laser pump spots. Where the flows meet, a stationary shockwave is produced, the length of which is a measure of the local flow velocity at a given radial position. By changing the distance between the spots using a spatial light modulator, we map out the flow velocity around the pump spots. We find gas front velocities near the speed of sound in air v_s for two laser excitation energies. We find an energy scaling that is inconsistent with the Sedov-Taylor model. Due to the flexibility offered by spatial beam shaping, our method can be applied to study subsonic laser-induced gas flow fronts in more complicated geometries.

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We study the expansion dynamics of super-heated material during ultra-fast laser ablation of water and gel, using transient-reflectivity microscopy. We find that the expansion dynamics of water and gel, as observed during the first few nanoseconds, are extremely similar over a large range of ablation energies. We measure the crater topography of the gel after irradiation with a single laser shot, using optical interferometric microscopy, and estimate the mass that is ejected during the ablation. We calculate the laser energy deposited during irradiation by simulating the precise spatial distribution of the electron plasma density and temperature. We link the amount of removed mass obtained experimentally with the simulations of the deposited laser energy.

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We demonstrate that optical transmission matrices (TMs) provide a powerful tool to extract the photonic strength of disordered complex media, independent of surface effects. We measure the TM of a strongly scattering GaP nanowire medium and compare the singular value density of the measured TM to a random-matrix-based wave transport model. By varying the transport mean free path and effective refractive index in the model, we retrieve the photonic strength. From separate numerical simulations we conclude that the photonic strength derived from TM statistics is insensitive to the surface reflection at rear surface of the sample.

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