We demonstrate our beamline using a table-top HHG EUV source for lensless imaging application in reflection m ode. T he s ample r eflection fu nction is reconstructed using an auto-differentiation based ptychographic algorithm built on TensorFlow platform.

We present a highly stable, easy-to-use HHG source delivering a record photon flux of >10¹¹ photons/s at 69eV-75eV, being tunable to approx. 100eV which will be used for future photon-hungry applications.

We present a parameter retrieval method which incorporates prior knowledge about the object into ptychography. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of a rectangular structure with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cramér Rao Lower Bound in both applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and analyze the correlation of particles in application 1. For application 2 the correlation of parameters of the rectangular structure is discussed.

High-harmonic generation (HHG) driven by ultrashort laser pulses is an established process for the generation of coherent extreme ultraviolet (XUV) to soft X-ray radiation, which has found widespread use in various applications [1]. In recent years photon-hungry applications such as coherent diffractive imaging [2] , [3] and applications based on statistical analysis [3] have required more powerful HHG sources, in particular, at high repetition rates. This need can be addressed by using high average power fiber lasers as the HHG drivers [4]. Here, we present a HHG-based XUV source, capable of providing a large photon flux across a wide range between 66 eV and 150 eV. It is driven by a commercial XUV beamline from Active Fiber Systems GmbH consisting of 100-W average power fiber-laser system, delivering up to 300J at <300-fs pulse duration. For HHG this system is operated at 100 W, 600 kHz. A post-compression unit is part of the device to shorten the pulses to ~35 fs, the average power remains at 63W. The turnkey source can provide unprecedented photon fluxes of >10 11 photons/s in each harmonic between 69 eV and 75 eV (HH57-HH63). All fluxes are given at the generation point, i.e. directly after the source.

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.

The imaging and inspection of extreme ultraviolet (EUV) masks is an important aspect of EUV lithography. The availability of actinic mask inspection tools able to generate highly resolved defect maps of defective EUV layouts is needed to ensure defect-free wafer prints. The technological interest towards phase-shift absorber materials for the next generation of EUV masks, and the associated need for phase metrology at the absorber level, makes phase retrieval methods a particularly interesting option for actinic inspection. In this work we use ptychography as an inspection tool for EUV masks. We show how variational and statistical methods can be employed to include a-priori information in the ptychographic inverse problem and how to cluster different update rules - stemming from the minimization of appropriate cost functionals - to optimally include prior information in ptychography under Poisson noise.

We investigate the performance of ptychography with noisy data by analyzing the Cramér-Rao lower bound. The lower bound of ptychography is derived and numerically computed for both top-hat plane wave and structured illumination. The influence of Poisson noise on the ptychography reconstruction is discussed. The computation result shows that, if the estimator is unbiased, the minimum variance for Poisson noise is mostly determined by the illumination power and the transmission function of the object. Monte Carlo analysis is conducted to validate our calculation results for different photon flux numbers. Furthermore, the performance of the maximum-likelihood method and the approach of amplitude-based cost-function minimization is studied in the Monte Carlo analysis.

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.

EUV lithography is the main candidate for patterning of future technology nodes. Its successful implementation depends on many aspects, among which the availability of actinic mask metrology tools able to inspect the patterned absorber in order to control and monitor the lithographic process. In this work, we perform a simulation study to assess the performance of coherent diffractive imaging (CDI) and related phase retrieval methods for the reconstruction of non-Trivially shaped and a-periodic nanostructures from far field intensity data.

Scatterometry is an important nonimaging and noncontact method for optical metrology. In scatterometry certain parameters of interest are determined by solving an inverse problem. This is done by minimizing a cost functional that quantifies the discrepancy among measured data and model evaluation. Solving the inverse problem is mathematically challenging owing to the instability of the inversion and to the presence of several local minima that are caused by correlation among parameters. This is a relevant issue, particularly when the inverse problem to be solved requires the retrieval of a high number of parameters. In such cases, methods to reduce the complexity of the problem are to be sought. In this work, we propose an algorithm suitable to automatically determine which subset of the parameters is mostly relevant in the model, and we apply it to the reconstruction of 2D and 3D scatterers. We compare the results with local sensitivity analysis and with the screening method proposed by Morris.

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.

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.