Polychromatic annular folded lenses using freeform gradient-index optics

Extended-depth-of-field imaging with an ultra-thin folded lens

Optical systems with extended depth of field (EDOF) are crucial for observation and measurement applications, where achieving compactness and a substantial depth of field (DOF) presents a considerable challenge with conventional optical elements. In this paper, we propose an innovative solution for the miniaturization of EDOF imaging systems by introducing an ultra-thin annular folded lens (AFL). To validate the practical feasibility of the theory, we design an annular four-folded lens with an effective focal length of 80.91 mm and a total thickness of only 8.50 mm. Simulation results show that the proposed folded lens has a DOF of 380.55 m. We further developed an AFL-based test system exhibiting a resolution of 0.11 mrad across a wide wavelength range of 486-656 nm. Additionally, we present experimental results from a miniature compact prototype, which further highlights the promising potential of folded lenses for long-range EDOF imaging.

Three-dimensional gradient index microlens arrays for light-field and holographic imaging and displays

The geometric, intensity, and chromatic distortions that are a result of the limitations of the material and processes used to fabricate micro-optical lens arrays (MLAs) degrade the performance of light-field systems. To address these limitations, inkjet print additive manufacturing is used to fabricate planar gradient index (GRIN) lenslet arrays, in which volumetric refractive index profiles are used to embed optical functions that would otherwise require multiple homogeneous index MLA surfaces. By tailoring the optical ink feedstock refractive index spectra, independent control over dispersion is achieved, and achromatic performance is made possible. Digital manufacturing is shown to be beneficial for optimizing individual micro-optical channels in arrays wherein the shape, size, aspect ratio, focal length, and optical axis orientation of the lenslets vary as a function of the position within the optical field. Print fabrication also allows opaque inter-lens baffling and aperture stops that reduce inter-channel cross talk, improve resolution, and enhance contrast. These benefits are demonstrated in a light-field display testbed.

Gradient-index Alvarez lenses

Gradient-index Alvarez lenses (GALs), a new, to the best of our knowledge, type of freeform optical component, are surveyed in this work for their unique properties in generating variable optical power. GALs display similar behavior to conventional surface Alvarez lenses (SALs) by means of a freeform refractive index distribution that has only recently been achievable in fabrication. A first-order framework is described for GALs including analytical expressions for their refractive index distribution and power variation. A useful feature of Alvarez lenses for introducing bias power is also detailed and is helpful for both GALs and SALs. The performance of GALs is studied, and the value of three-dimensional higher-order refractive index terms is demonstrated in an optimized design. Last, a fabricated GAL is demonstrated along with power measurements agreeing closely with the developed first-order theory.

Imaging stretching and displacement using gradient-index elements during the lens design process

In this study, we propose an approach to stretch or translate images using gradient-index (GRIN) elements with a rotationally symmetric shape in lens systems. In this method, the GRIN material, instead of optical surfaces, are utilized to enable a breaking of rotational symmetry for the two image translations. GRIN expression with anamorphic and tilting terms is introduced. A pair of GRIN elements in front of the given system alters the magnification in two orthogonal directions using the anamorphic terms in the expression, which realizes image stretching. A pair of GRIN elements with tilting terms is used after the given system tilts the optical path to achieve a transverse displacement of the image. The structure of the given system remains unchanged when these translations are performed. A design method for the GRIN elements is presented. Additionally, a design example is presented whose image is stretched by 1.33 times in one direction and displaced to one side of its axis to demonstrate the feasibility of the proposed approach. The approach in this study may enable novel imaging GRIN lens system designs with flexible image positions or special optical functions.

Achromatization of multi-material gradient-index singlets

Recent advancements in additive manufacturing have enabled new methods of fabricating gradient-index (GRIN) optics by blending multiple materials in the deposition process. A design study highlighting the advantages of multi-material GRIN optics is presented. It is shown that additional materials in the GRIN allow for higher orders of color correction. A new multi-material refractive index representation, which constrains the GRIN to real materials, is also presented.

Freeform gradient-index media: a new frontier in freeform optics

Freeform optics enable irregular system geometries and high optical performance by leveraging rotational variance. To this point, for both imaging and illumination, freeform optics has largely been synonymous with freeform surfaces. Here a new frontier in freeform optics is surveyed in the form of freeform gradient-index (F-GRIN) media. F-GRIN leverages arbitrary three-dimensional refractive index distributions to impart unique optical influence. When transversely variant, F-GRIN behaves similarly to freeform surfaces. By introducing a longitudinal refractive index variation as well, F-GRIN optical behavior deviates from that of freeform surfaces due to the effect of volume propagation. F-GRIN is a useful design tool that offers vast degrees of freedom and serves as an important complement to freeform surfaces in the design of advanced optical systems for both imaging and illumination.