Wavelength-multiplexed multi-mode EUV reflection ptychography based on automatic differentiation.

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.

Nanoscale Rheology: Dynamic Mechanical Analysis over a Broad and Continuous Frequency Range Using Photothermal Actuation Atomic Force Microscopy.

Polymeric materials are widely used in industries ranging from automotive to biomedical. Their mechanical properties play a crucial role in their application and function and arise from the nanoscale structures and interactions of their constitutive polymer molecules. Polymeric materials behave viscoelastically, i.e., their mechanical responses depend on the time scale of the measurements; quantifying these time-dependent rheological properties at the nanoscale is relevant to develop, for example, accurate models and simulations of those materials, which are needed for advanced industrial applications. In this paper, an atomic force microscopy (AFM) method based on the photothermal actuation of an AFM cantilever is developed to quantify the nanoscale loss tangent, storage modulus, and loss modulus of polymeric materials. The method is then validated on styrene-butadiene rubber (SBR), demonstrating the method's ability to quantify nanoscale viscoelasticity over a continuous frequency range up to 5 orders of magnitude (0.2-20,200 Hz). Furthermore, this method is combined with AFM viscoelastic mapping obtained with amplitude modulation-frequency modulation (AM-FM) AFM, enabling the extension of viscoelastic quantification over an even broader frequency range and demonstrating that the novel technique synergizes with preexisting AFM techniques for quantitative measurement of viscoelastic properties. The method presented here introduces a way to characterize the viscoelasticity of polymeric materials and soft and biological matter in general at the nanoscale for any application.

Noise-robust latent vector reconstruction in ptychography using deep generative models.

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.

Maximum-likelihood estimation in ptychography in the presence of Poisson-Gaussian noise statistics: publisher's note.

This publisher's note contains a correction to Opt. Lett.48, 6027 (2023)10.1364/OL.502344.

Maximum-likelihood estimation in ptychography in the presence of Poisson-Gaussian noise statistics.

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.

Cell wall fucosylation in Arabidopsis influences control of leaf water loss and alters stomatal development and mechanical properties.

The Arabidopsis sensitive-to-freezing8 (sfr8) mutant exhibits reduced cell wall (CW) fucose levels and compromised freezing tolerance. To examine whether CW fucosylation also affects the response to desiccation, we tested the effect of leaf excision in sfr8 and the allelic mutant mur1-1. Leaf water loss was strikingly higher than in the wild type in these, but not other, fucosylation mutants. We hypothesized that reduced fucosylation in guard cell (GC) walls might limit stomatal closure through altering mechanical properties. Multifrequency atomic force microscopy (AFM) measurements revealed a reduced elastic modulus (E'), representing reduced stiffness, in sfr8 GC walls. Interestingly, however, we discovered a compensatory mechanism whereby a concomitant reduction in the storage modulus (E'') maintained a wild-type viscoelastic time response (tau) in sfr8. Stomata in intact leaf discs of sfr8 responded normally to a closure stimulus, abscisic acid, suggesting that the time response may relate more to closure properties than stiffness does. sfr8 stomatal pore complexes were larger than those of the wild type, and GCs lacked a fully developed cuticular ledge, both potential contributors to the greater leaf water loss in sfr8. We present data that indicate that fucosylation-dependent dimerization of the CW pectic domain rhamnogalacturonan-II may be essential for normal cuticular ledge development and leaf water retention.

Optimizing illumination for precise multi-parameter estimations in coherent diffractive imaging.

Coherent diffractive imaging (CDI) is widely used to characterize structured samples from measurements of diffracting intensity patterns. We introduce a numerical framework to quantify the precision that can be achieved when estimating any given set of parameters characterizing the sample from measured data. The approach, based on the calculation of the Fisher information matrix, provides a clear benchmark to assess the performance of CDI methods. Moreover, by optimizing the Fisher information metric using deep learning optimization libraries, we demonstrate how to identify the optimal illumination scheme that minimizes the estimation error under specified experimental constraints. This work paves the way for an efficient characterization of structured samples at the sub-wavelength scale.

Mapping cellular nanoscale viscoelasticity and relaxation times relevant to growth of living Arabidopsis thaliana plants using multifrequency AFM.

The shapes of living organisms are formed and maintained by precise control in time and space of growth, which is achieved by dynamically fine-tuning the mechanical (viscous and elastic) properties of their hierarchically built structures from the nanometer up. Most organisms on Earth including plants grow by yield (under pressure) of cell walls (bio-polymeric matrices equivalent to extracellular matrix in animal tissues) whose underlying nanoscale viscoelastic properties remain unknown. Multifrequency atomic force microscopy (AFM) techniques exist that are able to map properties to a small subgroup of linear viscoelastic materials (those obeying the Kelvin-Voigt model), but are not applicable to growing materials, and hence are of limited interest to most biological situations. Here, we extend existing dynamic AFM methods to image linear viscoelastic behaviour in general, and relaxation times of cells of multicellular organisms in vivo with nanoscale resolution (~80 nm pixel size in this study), featuring a simple method to test the validity of the mechanical model used to interpret the data. We use this technique to image cells at the surface of living Arabidopsis thaliana hypocotyls to obtain topographical maps of storage E' = 120-200 MPa and loss E″ = 46-111 MPa moduli as well as relaxation times τ = 2.2-2.7 µs of their cell walls. Our results demonstrate that (taken together with previous studies) cell walls, despite their complex molecular composition, display a striking continuity of simple, linear, viscoelastic behaviour across scales-following almost perfectly the standard linear solid model-with characteristic nanometer scale patterns of relaxation times, elasticity and viscosity, whose values correlate linearly with the speed of macroscopic growth. We show that the time-scales probed by dynamic AFM experiments (microseconds) are key to understand macroscopic scale dynamics (e.g. growth) as predicted by physics of polymer dynamics.

AFM nanoindentation reveals decrease of elastic modulus of lipid bilayers near freezing point of water.

Cell lipid membranes are the primary site of irreversible injury during freezing/thawing and cryopreservation of cells, but the underlying causes remain unknown. Here, we probe the effect of cooling from 20 °C to 0 °C on the structure and mechanical properties of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) bilayers using atomic force microscopy (AFM) imaging and AFM-based nanoindentation in a liquid environment. The Young's modulus of elasticity (E) at each temperature for DPPC was obtained at different ionic strengths. Both at 20 mM and 150 mM NaCl, E of DPPC bilayers increases exponentially -as expected-as the temperature is lowered between 20 °C and 5 °C, but at 0 °C E drops from the values measured at 5 °C. Our results support the hypothesis that mechanical weakening of the bilayer at 0 °C  is produced by  structural changes at the lipid-fluid interface.

Atomic force microscopy-indentation demonstrates that alginate beads are mechanically stable under cell culture conditions.

Alginate microbeads are extensively used in tissue engineering as microcarriers and cell encapsulation vessels. In this study, we used atomic force microscopy (AFM) based indentation using 20 µm colloidal probes to assess the local reduced elastic modulus (E * ) using a novel method to detect the contact point based on the principle of virtual work, to measure microbead mechanical stability under cell culture conditions for 2 weeks. The bead diameter and swelling were assessed in parallel. Alginate beads swelled up to 150% of their original diameter following addition of cell culture media. The diameter eventually stabilized from day 2 onwards. This behaviour was mirrored in E * where a significant decrease was observed at the start of the culture period before stabilization was observed at ~ 2.1 kPa. Furthermore, the mechanical properties of freeze dried alginate beads after re-swelling them in culture media were measured. These beads displayed vastly different structural and mechanical properties compared those that did not go through the freeze drying process, with around 125% swelling and a significantly higher E * at values over 3 kPa.