Freeform optics aims to expand the toolkit of optical elements by allowing for more complex phase geometries beyond rotational symmetry. Complex, asymmetric curvatures are employed to enhance the performance of optical components while minimizing their size. Unfortunately, these high curvatures and complex forms are often difficult to manufacture with current technologies, especially at the micron scale. Metasurfaces are planar sub-wavelength structures that can control the phase, amplitude, and polarization of incident light, and can thereby mimic complex geometric curvatures on a flat, wavelength-scale thick surface. We present a methodology for designing analogues of freeform optics using a silicon nitride based metasurface platform for operation at visible wavelengths. We demonstrate a cubic phase plate with a point spread function exhibiting enhanced depth of field over 300 micron along the optical axis with potential for performing metasurface-based white light imaging, and an Alvarez lens with a tunable focal length range of over 2.5 mm corresponding to a change in optical power of ~1600 diopters with 100 micron of total mechanical displacement. The adaptation of freeform optics to a sub-wavelength metasurface platform allows for further miniaturization of optical components and offers a scalable route toward implementing near-arbitrary geometric curvatures in nanophotonics.

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Metasurface Freeform Nanophotonics

Head-mounted display (HMD) has been widely used in many fields, and most existing HMDs are complex and typically non-aesthetically pleasing. In this paper, a novel compact, lightweight and wearable off-axis HMD with freeform surface is reported. It is challenging to achieve large field of view (FOV) and maintain compact structure simultaneously for this type system. In this design, the compact off-axis HMD consists of a tilted ellipsoid combiner and a four pieces relay lenses. It offers a diagonal FOV of 30°, and an exit pupil diameter of 7 mm. No diffractive surfaces are used, thus avoiding the effect of stray light and ghost image in previous designs. The x-y polynomial freeform surface is adopted in the relay lens for improving the image quality and minimizing the structure size. Analytical expressions to determine the initial structure of HMD has been given, while structure constrains, optimization strategy and tolerance analysis are also described in details. The optical system is easy to manufacture by ordinary method which is beneficial for mass production. Further, a prototype of this compact HMD is successfully implemented with good imaging performance. The compact structure of HMD makes it well suited for integrating a normal glass, significantly advancing the application of HMD in people’s daily life.

Design and fabrication of a compact off-axis see-through head-mounted display using a freeform surface.

Freeform optics aims to expand the toolkit of optical elements by allowing for more complex phase geometries beyond rotational symmetry. Complex, asymmetric curvatures are employed to enhance the performance of optical components while minimizing their weight and size. Unfortunately, these asymmetric forms are often difficult to manufacture at the nanoscale with current technologies. Metasurfaces are planar sub-wavelength structures that can control the phase, amplitude, and polarization of incident light, and can thereby mimic complex geometric curvatures on a flat, wavelength-scale thick surface. We present a methodology for designing analogues of freeform optics using a low contrast dielectric metasurface platform for operation at visible wavelengths. We demonstrate a cubic phase plate with a point spread function exhibiting enhanced depth of field over 300 {\mu}m along the optical axis with potential for performing metasurface-based white light imaging, and an Alvarez lens with a tunable focal length range of over 2.5 mm with 100 {\mu}m of total mechanical displacement. The adaptation of freeform optics to a sub-wavelength metasurface platform allows for the ultimate miniaturization of optical components and offers a scalable route toward implementing near-arbitrary geometric curvatures in nanophotonics.

Freeform surfaces on optical components have become an important design tool for optical designers. Non-rotationally symmetric optical surfaces have made solving complex optical problems easier. The manufacturing and testing of these surfaces has been the technical hurdle in freeform optic’s wide-spread use. Computer Numerically Controlled (CNC) optics manufacturing technology has made the fabrication of optical components more deterministic and streamlined for traditional optics and aspheres. Optimax has developed a robust freeform optical fabrication CNC process that includes generation, high speed VIBE polishing, sub-aperture figure correction, surface smoothing and testing of freeform surfaces. Metrology of freeform surface is currently achieved with coordinate measurement machines (CMM) for lower resolution and interferometry with computer generated holograms (CGH) for high resolution irregularity measurements.

Fabrication of freeform optics

We review the design and assessment techniques that underlie a number of successfully deployed space and airborne imaging spectrometers that have been demonstrated to achieve demanding specifications in terms of throughput and response uniformity. The principles are illustrated with telescope designs as well as spectrometer examples from the Offner and Dyson families. We also show how the design space can be extended with the use of freeform surfaces and provide additional design examples with grating as well as prism dispersive elements.

https://www.spiedigitallibrary.org/journals/optical-engineering/volume-57/issue-4/040901/Review-of-high-fidelity-imaging-spectrometer-design-for-remote-sensing/10.1117/1.OE.57.4.040901.pdf

Review of high fidelity imaging spectrometer design for remote sensing

In this work, we present a multifield direct design method for ultrashort throw ratio projection optics. The multifield design method allows us to directly calculate two freeform mirror profiles, which are fitted by odd polynomials and imported into an optical design program as an excellent starting point. Afterward, these two mirrors are represented by XY polynomial freeform surfaces for further optimization. The final configuration consists of an off-the-shelf projection lens and two XY polynomial freeform mirrors to greatly shorten the regular projection distance from 2 m to 48 cm for a 78.3 inch diagonal screen. The values of the modulation transfer function for the optimized freeform mirror system are improved to over 0.6 at 0.5 lp/mm, in comparison with its rotationally symmetric counterpart’s 0.43, and the final distortion is less than 1.5%, showing a very good and well-tailored imaging performance over the entire field of view.

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Multifield direct design method for ultrashort throw ratio projection optics with two tailored mirrors

Most existing techniques that are typically used by specialists to image the cornea are based on point, slit, or annular scanning due to a narrow field of view. The difficulty in achieving a larger field of view comes from the convex shape of the human eyeball. Field curvature for a refractive imaging system with positive power is typically negative and thus a concave image surface. In order to view the full cornea and sclera with snapshot imaging, we calculate qualified two- and three-mirror solutions from Seidel aberration theory. A three-mirror solution is further optimized as a high-resolution off-axis imaging system using freeform surfaces, which can obtain a full-field tailored image shell without scanning. The lateral resolution on the cornea is about 10 μm with good modulation transfer function (MTF) and spot performance. To ease the assembly, a monolithic design is achieved with slightly lower resolution, leading to a potential mass production solution.

Freeform optical design for a nonscanning corneal imaging system with a convexly curved image.

In this work, a multifields optical design method aiming to calculate two high-order aspheric lens pro- files with an embedded entrance pupil is proposed. This direct design algorithm is capable of partially coupling more than three ray bundles that enter the same pupil with only two surfaces. Both infinite and finite conjugate objectives can be designed with this approach. Additional constraints such as surface continuity and smooth- ness are taken into account to calculate smooth and accurate surface contours described by point clouds. The calculated points are then fitted with rotationally symmetric functions commonly used in optical design tools. A presented subaperture sampling strategy that introduces a weighting function for different fields allows for a very well-balanced imaging performance over a wide field of view (FOV). As an example, a � 45 deg f ∕7.5 wide- angle objective is designed and analyzed to demonstrate the potential of this design method. It provides an excellent starting point for further optimization of the surfaces' coefficients and initial design parameters, result- ing in a very good and well-balanced imaging performance over the entire FOV. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original

https://www.spiedigitallibrary.org/journals/Optical-Engineering/volume-54/issue-1/015102/Direct-design-approach-to-calculate-a-two-surface-lens-with/10.1117/1.OE.54.1.015102.pdf

Direct design approach to calculate a two-surface lens with an entrance pupil for application in wide field-of-view imaging

Recently, freeform optics has been widely used due to its unprecedented compactness and high performance, especially in the reflective designs for broad-wavelength imaging applications. Here, we present a generalized differentiable ray tracing approach suitable for most optical surfaces. The established automated freeform design framework simultaneously calculates multi-surface coefficients with merely the system geometry known, very fast for generating abundant feasible starting points. In addition, we provide a “double-pass surface” strategy with desired overlap (not mutually centered) that enables a component reduction for very compact yet high-performing designs. The effectiveness of the method is firstly demonstrated by designing a wide field-of-view, fast f-number, four-mirror freeform telescope. Another example shows a two-freeform, three-mirror, four-reflection design with high compactness and cost-friendly considerations with a double-pass spherical mirror. The present work provides a robust design scheme for reflective freeform imaging systems in general, and it unlocks a series of new ‘double-pass surface’ designs for very compact, high-performing freeform imaging systems.

Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation.

Depth mapping from binocular endoscopy images plays an important role in stereoscopic surgical treatment. Owing to the development of deep convolutional neural networks (CNNs), binocular depth estimation models have achieved many exciting results in the fields of autonomous driving and machine vision. However, the application of these methods to endoscopic imaging is greatly limited by the fact that binocular endoscopic images not only are rare, but also have unsatisfying features such as no texture, no ground truth, bad contrast, and high gloss. Aiming at solving the above-mentioned problems, we have built a precise gastrointestinal environment by the open-source software blender to simulate abundant binocular endoscopy data and proposed a 23-layer deep CNNs method to generate real-time stereo depth mapping. An efficient scale-invariant loss function is introduced in this paper to accommodate the characteristics of endoscope images, which improves the accuracy of achieved depth mapping results. Regarding the considerable training data for typical CNNs, our method requires only a few images ($960\times 720$ resolution) at 45 frames per second on an NVIDIA GTX 1080 GPU module, then the depth mapping information is generated in real-time with satisfactory accuracy. The effectiveness of the developed method is validated by comparing with state-of-the-art methods on processing the same datasets, demonstrating a faster and more accurate performance than other model frames.

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Yunfeng Nie

Papers

Multifield direct design method for ultrashort throw ratio projection optics with two tailored mirrors

Freeform optical design for a nonscanning corneal imaging system with a convexly curved image.

Direct design approach to calculate a two-surface lens with an entrance pupil for application in wide field-of-view imaging

Automated freeform imaging system design with generalized ray tracing and simultaneous multi-surface analytic calculation.

Deep Convolutional Network for Stereo Depth Mapping in Binocular Endoscopy