Developing optical systems, particularly those consisting of spherical lenses, is relevant for various applications such as lithographic scanners and metrology equipment. The design process of an optical system typically involves the optimization of specific objectives to ensure the best performance. As a common example of such an objective, we consider the problem of determining the lens curvatures that result in a sufficiently small root mean square (RMS) spot size. Optimization algorithms are commonly employed to solve this problem by heuristically eliminating sub-optimal optical designs. This class of algorithms includes the damped least squares (DLS) widely applied in commercial software and advanced methods like Saddle Point Construction. However, within a restricted computational budget, these optimizers are limited in exploring potentially promising novel solutions since they heavily rely on the initial specific designs that must conform to complex or unknown requirements. In this work, we address the considered problem with a modified Hill-Valley Evolutionary Algorithm (HillVallEA), which proved itself as one of the best state-of-the-art metaheuristics for multimodal black-box optimization. We demonstrate that our algorithm locates a diverse set of high-quality optical designs with four lenses in a single run even when initialized with random starting curvatures. This is the first result in this domain when an optimization algorithm that does not take specific optical properties into account can still generate relevant and high-performing optical systems. Furthermore, we show the benefits of the proposed methodology for the diversity of the obtained set of solutions, while maintaining a solution of the same quality as the one found by the most prominent algorithm in the domain. We provide analyses of the obtained solutions according to: 1) tolerance to the alignment of lenses, 2) susceptibility to small variations of lens curvatures.
The demand for accurate and sub-nanometer precise overlay measurements in semiconductor industry increases with the shrinking feature sizes in integrated circuits. Overlay, the lateral displacement between two layers allows monitoring the chip fabrication process and is part of an import feedback step. In our approach, a digital holographic microscope measures the complex field of the overlay target using simple optics and an additional reference beam. The measured complex valued field allows us to apply computational algorithms to correct for field-position dependent lens aberrations in a computational efficient manner. We present experimental results that show the capability of our computational aberration correction in the visible and near infrared wavelength regimes.
Optical systems in lithography machines play a significant role in their performance and, therefore, need to be optimized for specific applications. Artificial Intelligence (AI) and, in particular, metaheuristics are utilized in optimization algorithms for finding a diverse set of feasible and high-performing designs. The diversity requirement of the produced solutions is enforced to allow taking into account additional constraints that are difficult to formalize. In this work, we analyse the space of solutions previously produced by a niching evolutionary algorithm for the Cooke Triplet optical system and propose an approximation of the manifold where all high-performing designs exist. First, we show the existence of high-performing optical designs that are structurally different from the 21 previously known theoretical solutions. In order to do this, we develop a general computationally efficient methodology to create a partition of known high-quality points and their (accidentally found) improvements to their corresponding attraction basins, in the case when neither the exact number of landscape attractors nor their locations are known. We construct a manifold estimation which contains high-performing solutions by fitting a Gaussian Process-based classifier which predicts if an arbitrary design is close to high-performing. The proposed approach shows that AI-assisted optimization is beneficial, and it can be used to extend the capabilities of lithographic scanners and metrology equipment. Furthermore, it opens the possibility of studying other industrial applications.
We applied an extended version of the Niching-CMA-ES heuristic to search for local minima of the Cooke triplet, a renowned photographic lens design, of which 21 local minima were already known. The considered problem is defined by 6 input (decision) variables, namely the curvatures of the three lenses present in the Cooke triplet, and is driven by a single objective function, that is the RMS spot size. The applied approach found: (i) 19 out of the 21 known minima in a single run; (ii) 540 new local minima with objective values lower/equal to those of the known 21 minima; (iii) a large number of infeasible designs.
Sub-micron diffraction gratings have been used for two LED illumination applications. One is to create a transparent see through luminaire which can be used to illuminate and read a paper document or e-book. A second is a light sensor that can be used in a feedback loop to control a multicolor LED lamp. Optical design and experimental proof-of-principle are presented.
Angular color variation in white, phosphor-converted LEDs causes undesirable yellow rings in the beams of spotlights. We developed an inverse method to design TIR collimators that remove the angular color variation for point light sources and significantly reduce color variation for extended light sources, without the need for facets, holographic foils or scattering surfaces. We performed several numerical simulations to evaluate the performance of this point source method for extended light sources.
KEYWORDS: Ray tracing, Collimators, Monte Carlo methods, Reflectors, Light sources, Optical design, Optical spheres, Fluctuations and noise, Lens design, Light sources and illumination
In the last years it has been shown that efficient collimator systems for point sources can be designed with the
flux tube method in combination with an optimiser. In this paper it will be shown that this method can be
extended to extended light sources. Various collimator designs for different types of sources will be discussed
that transform the illuminance into imposed distribution.
Beam-shaping optics are used in various optical fields to change the luminous intensity distribution. In this paper a flexible method is presented to design beam-shaping optics with aspherical surfaces transforming the intensity profile of the light beam into any desired profile. The method is applied to a collimator lens that transforms a beam from a Lambertian emitter to a uniform light distribution.
A simple, diffraction limited, optical design for a Holographic Data Storage System with a high numerical aperture and
large field is presented. A system analysis is performed and the design is compared with different current and future
formats for optical data storage.
The design, manufacturing and application of variable liquid lenses are discussed. The interface between the two immiscible liquids that forms the lens can be altered with a voltage. Results are presented of applying this lens in miniature autofocus and zoom cameras, in optical recording and in illumination systems.
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