We describe a method for designing freeform optics based on the aberration theory of freeform surfaces that guides the development of a taxonomy of starting-point geometries with an emphasis on manufacturability. An unconventional approach to the optimization of these starting designs wherein the rotationally invariant 3rd-order aberrations are left uncorrected prior to unobscuring the system is shown to be effective. The optimal starting-point geometry is created for an F/3, 200 mm aperture-class three-mirror imager and is fully optimized using a novel step-by-step method over a 4 × 4 degree field-of-view to exemplify the design method. We then optimize an alternative starting-point geometry that is common in the literature but was quantified here as a sub-optimal candidate for optimization with freeform surfaces. A comparison of the optimized geometries shows the performance of the optimal geometry is at least 16× better, which underscores the importance of the geometry when designing freeform optics.
We present optical designs with freeform optics in the context of hyperspectral imaging. Results show designs that are 5 × more compact in volume than similar designs using conventional spherical or aspherical surfaces. We will show how combining the concepts of spatial and spectral-band broadening, which will be introduced in this paper, led to the improvement in compactness that is uniquely enabled by freeform optics.
In the last 10 years, freeform optics has enabled compact and high-performance imaging systems. This article begins with a brief history of freeform optics, focusing on imaging systems, including marketplace emergence. The development of this technology is motivated by the clear opportunity to enable science across a wide range of applications, spanning from extreme ultraviolet lithography to space optics. Next, we define freeform optics and discuss concurrent engineering that brings together design, fabrication, testing, and assembly into one process. We then lay out the foundations of the aberration theory for freeform optics and emerging design methodologies. We describe fabrication methods, emphasizing deterministic computer numerical control grinding, polishing, and diamond machining. Next, we consider mid-spatial frequency errors that inherently result from freeform fabrication techniques. We realize that metrologies of freeform optics are simultaneously sparse in their existence but diverse in their potential. Thus, we focus on metrology techniques demonstrated for the measurement of freeform optics. We conclude this review with an outlook on the future of freeform optics.
The demand for high-resolution optical systems with a compact form factor, such as augmented reality displays, sensors, and mobile cameras, requires creating new optical component architectures. Advances in the design and fabrication of freeform optics and metasurfaces make them potential solutions to address the previous needs. Here, we introduce the concept of a metaform—an optical surface that integrates the combined benefits of a freeform optic and a metasurface into a single optical component. We experimentally realized a miniature imager using a metaform mirror. The mirror is fabricated via an enhanced electron beam lithography process on a freeform substrate. The design degrees of freedom enabled by a metaform will support a new generation of optical systems.
Studies have shown that both the act of note-taking and the use of notes for review can promote learning. Many note-taking applications have been developed for computer-based learning content. In general, they include advanced annotation functionality, and are geared toward supporting collaboration and discussion. Though these devices have been shown to change note-taking behavior, their effect on learning has not been evaluated. The goal of our research is to evaluate the effect of specific features of note-taking applications on behavior and learning, in order to develop guidelines for advanced note-taking applications that promote learning. These applications could be used as the basis for a variety of educational activities, including collaboration. In this paper, we present the results of an experiment evaluating a basic feature of note-taking technology: copy-paste. Our findings indicate that copy-paste functionality can be detrimental to learning. We describe potential implications of these results for the developers of notetaking applications.
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