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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. 

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. 

A novel Vision ray metrology technique is reported that estimates the geometric wavefront of a measurement sample using the sample-induced deflection in the vision rays. Vision ray techniques are known in the vision community to provide image formation models even when conventional camera calibration techniques fail. This work extends the use of vision rays to the area of optical metrology. In contrast to phase measuring deflectometry, this work relies on differential measurements, and hence, the absolute position and orientation between target and camera do not need to be known. This optical configuration significantly reduces the complexity of the reconstruction algorithms. The proposed vision ray metrology system does not require mathematical optimization algorithms for calibration and reconstruction – the vision rays are obtained using a simple 3D fitting of a line. 

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. 

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. 

Abstract Dynamic illumination can improve functionality for multiple application areas, including lighting, AR/VR, automotive, medicine, and security. Some applications require a uniform illumination pattern of continuously variable divergence or size for improved functionality. Such dynamic functionality has previously been achieved, for example, by longitudinally moving a source relative to a curved reflector, which can result poor uniformity, or through zoom configurations in which the longitudinal distances between lenses in the system are dynamically adjusted. Advances in high precision manufacturing methods such as diamond machining have facilitated the practical implementation of freeform optical components, enabling new design approaches and concepts for illumination systems. In this paper, we explore the use of arrays of transmissive pairs of freeform surfaces to enable efficient and uniform dynamic illumination in a compact package. This work builds on the Alvarez lens concept, in which a pair of transmissive XY-polynomial freeform surfaces generates variable optical power through lateral relative shifts. Design approaches and simulation results are presented.