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We use atomistic simulations to study mechanical properties of monolayer molybdenum disulfide MoS2. Using molecular dynamic (MD) simulations, we investigate the nano-fracture properties of monolayer MoS2 under mixed mode I and II loadings. The MD simulations are used to obtain the critical stress intensity factors of both armchair and zigzag cracks as a function of applied loading phase angle. Our atomistic simulations predict that armchair cracks are tougher than zigzag cracks, and both armchair and zigzag cracks tend to propagate along a zigzag path. Furthermore, we use density functional theory (DFT) to investigate how point defects influence the mechanical properties of nanoribbons. Our DFT simulations show that missing one S atom does not significantly affect the mechanical strength of monolayer MoS2, whereas missing one Mo atom can reduce the maximum strength of single layer MoS2 sheet by about 10%.

Dynamic illumination using tunable freeform arrays can enable spatial light distributions of variable size with high uniformity from non-uniform sources through relatively small opposing lateral shifts applied to the freeform components. We present the design, manufacturing, and characterization of a tunable LED-based illuminator using custom freeform Alvarez arrays with commercially available optics to shorten the manufacturing cycle. The optomechanical design and manufacturing of the Alvarez lens arrays and mounting parts are presented in detail. The optical performance of the system is evaluated and compared with simulation results using a custom camera-based test station. Experimental results demonstrate and confirm the dynamic illumination concept with good uniformity.

Tunable illumination with high uniformity can improve functionality for multiple application areas. In lighting applications, dynamic illumination has been achieved by applying axial movement to the source(s) or other optical elements, resulting in poor uniformity, or using a liquid lens that adds design complexity. Advances in high-precision manufacturing methods have facilitated the practical implementation of freeform optical components, enabling new design approaches for illumination systems. This paper explores the use of arrays of varifocal transmissive freeform Alvarez lenses for an LED-based illumination system. The design is initialized using paraxial geometrical optics concepts and then refined for a 1mm-by−1 mm white LED source through a multi-step optimization. Design procedures are discussed, and simulation results are presented for an example illumination system that varies from a small circular spot mode to a large square uniform flood mode through millimeter-scale lateral translation between the Alvarez lens arrays.

Shallow depth of field in imaging systems with high numerical apertures results in images with in- and out-of-focus regions. Therefore, methods to enhance the depth of field are of special interest. In point spread function engineering, a custom phase plate is designed for each system to reduce sensitivity to defocus and thereby extend depth of field. In this paper, we present a method that enables extended depth of field for a range of numerical apertures using a freeform variable logarithmic phase plate pair. We leverage a numerical design approach for the variable phase plate pair design, and explore phase plate optimization and performance by quantifying and comparing through-focus point spread function variation, and on- and off-axis performance for the designed phase plates.

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Vision ray techniques are known in the optical community to provide low-uncertainty image formation models. In this work, we extend this approach and propose a vision ray metrology system that estimates the geometric wavefront of a measurement sample using the sample-induced deflection in the vision rays. We show the feasibility of this approach using simulations and measurements of spherical and freeform optics. In contrast to the competitive technique deflectometry, this approach relies on differential measurements and, hence, requires no elaborated calibration procedure that uses sophisticated optimization algorithms to estimate geometric constraints. Applications of this work are the metrology and alignment of freeform optics.

We propose and demonstrate a general design method for refractive two-element systems enabling variable optical performance between two specified boundary conditions. Similar to the Alvarez lens, small, relative lateral shifts in opposite directions are applied to a pair of plano-freeform elements. The surface prescriptions of the boundary lenses and a maximum desired shift between freeform plates are the main design inputs. In contrast to previous approaches, this method is not limited to boundaries with similar optical functions and can enable a wide range of challenging, dynamic functions for both imaging and non-imaging applications. Background theory and design processes are presented both for cases that are conducive to analytical surface descriptions, as well as for non-analytic surfaces that must be described numerically. Multiple examples are presented to demonstrate the flexibility of the proposed method.