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.
Ptychography as a means of lensless imaging is used in wafer metrology applications using Extreme Ultraviolet (EUV) light, where use of high quality optics is out-of-scope. To obtain sufficient diffraction intensity, reflection geometries with shallow (ca. 20 degrees) grazing incidence angles are used, which require re-sampling the diffraction data in a process called tilted plane correction (TPC). The tilt angle used for TPC is conventionally obtained through either experimentally tricky calibration, manual estimation based on diffraction pattern symmetry, although computational approaches are emerging. In this work we offer an improved numerical optimization approach as an alternative to TPC, where we use the flexibility offered by our Automatic Differentiation (AD)-based ptychography approach to include the data resampling into the forward model to learn the tilt angle. We demonstrate convergence of the approach across a range of incidence angles on simulated and experimental data obtained on an EUV beamline with either a high-harmonic generation (HHG)-based or a visible light source.
We introduce a novel method for maximum-likelihood estimation in ptychography to address the challenge posed by mixed Poisson-Gaussian noise statistics. By integrating a loss function that accounts for both noise sources in computational image retrieval, our approach significantly improves image reconstruction quality under low signal-to-noise ratio conditions. Experimental and numerical data confirm the advantage of our method over traditional approaches that consider only Poissonian noise. This advancement promises enhanced performance in computational imaging applications, particularly in situations where accurate noise modeling is crucial.
We propose and experimentally demonstrate a noniterative diffractive imaging method for reconstructing the complex-valued transmission function of an object illuminated by spatially partially coherent light from the far-field diffraction pattern. Our method is based on a pinhole array mask, which is specially designed such that the correlation function in the mask plane can be obtained directly by inverse Fourier transforming the diffraction pattern. Compared to the traditional iterative diffractive imaging methods using spatially partially coherent illumination, our method is noniterative and robust to the degradation of the spatial coherence of the illumination. In addition to diffractive imaging, the proposed method can also be applied to spatial coherence property characterization, e.g., free-space optical communication and optical coherence singularity measurement.
Liquid lenses are used to correct for low order wavefront aberrations. Electrowetting liquid lenses can nowadays control defocus and astigmatism effectively, so they start being used for ophthalmology applications. To increase the performance and applicability, we introduce a new driving mechanism to create, detect and correct higher order aberrations using standing waves on the liquid interface.
The speed of a liquid lens is in general limited, because the liquid surface cannot follow fast voltage changes, while providing a spherical surface. Surface waves are created instead and with them undesired aberrations. We try to control those surface waves to turn them into an effective wavefront shaping tool.
We introduce a model, which treats the liquid lens as a circular vibrating membrane with adjusted boundary conditions. Similar to tunable acoustic gradient (TAG) lenses, the nature of the surface modes are predicted to be Bessel functions. Since Bessel functions are a full set of orthogonal basis functions any surface can be created as a linear combination of different Bessel functions.
The model was investigated experimentally in two setups. First the point spread functions were studied and compared to a simulation of the intensity distribution created by Fresnel propagated Bessel surfaces. Second the wavefronts were measured directly using a spatial light modulator. The surface resonance frequencies confirm the predictions made by the model as well as the wavefront measurements. By superposition of known surface modes, it is possible to create new surface shapes, which can be used to simulate and measure the human eye.
The application of Moiré effect for testing of a lithographic projection lens is reported. The arrangement presented allows measuring magnification, distortion, field curvature and telecentricity of the lens and can be used for its fine tuning. The method is based on two matched two-dimensional gratings, positioned in mutually conjugated planes; one of them can be translated. Visual interpretation of Moiré fringe pattern allows quick diagnostics of position errors exceeding critical dimension, whereas lateral scanning is applied for measuring of smaller magnitude errors. Field curvature and telecentricity are measured by 3D scanning. Presented results are in a good agreement with those obtained elsewhere.
The present research is part of an effort to develop tools that make the lens design process more systematic. In typical optical design tasks, the presence of many local minima in the optical merit function landscape makes design non-trivial. With the method of Saddle Point Construction (SPC) which was developed recently ([F. Bociort and M. van Turnhout, Opt. Engineering 48, 063001 (2009)]) new local minima are obtained efficiently from known ones by adding and removing lenses in a systematic way. To illustrate how SPC and special properties of the lens design landscape can be used, we will present the step-by-step design of a wide-angle pinhole lens and the automatic design of a 9-lens system which, after further development with traditional techniques, is capable of good performance. We also give an example that shows how to visualize the saddle point that can be constructed at any surface of any design of an imaging system that is a local minimum.
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