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.

Unobscured reflective optical systems with a wide field of view (FOV) have significant application values. However, the aberration increases with the increase of the system FOV, so a wide FOV system is difficult to design. In this paper, a design method that is effective in achieving off-axis three-mirror systems with ultrawide FOV is proposed. In this method, the system FOV is expanded stepwise in the design process, and the surface optical freeform polynomial terms are extended based on the judgment of image quality and some constraint conditions, and to obtain a prospective ultrawide FOV system. A freeform off-axis three-mirror imaging system with a focal length of 1000 mm, an F-number of 10, and an ultrawide FOV of 80°×4° is designed as an example. This design result shows that the system has a high imaging quality of RMS wavefront error value of 0.040λ(λ=0.633  μm), and it demonstrates that the method is effective in achieving off-axis three-mirror systems with an ultrawide FOV.

Design of off-axis three-mirror systems with ultrawide field of view based on an expansion process of surface freeform and field of view

Aberration theory helps designers to better understand the nature of imaging systems. However, the existing aberration theory of freeform surfaces has many limitations. For example, it only works in the special case when the central area of the freeform surface is used. In addition, the light footprint is limited to a circle, which does not match the case of an elliptical footprint for general systems. In this paper, aberrations generated by freeform surface term overlay on general decentered and tilted optical surfaces are analyzed. For the case when the off-axis section of a freeform surface is used, the aberration equation for using stop and nonstop surfaces is discussed, and the aberrations generated by Zernike terms up to Z17/18 are analyzed in detail. To solve the problem of the elliptical light footprint for tilted freeform surfaces, the scaled pupil vector is used in the aberration analysis. The mechanism of aberration transformation is discovered, and the aberrations generated by different Zernike terms in this case are calculated. Finally we proposed aberration equations for freeform terms on general decentered and tilted freeform surfaces. The research result given in this paper offers an important reference for optical designers and engineers, and it is of great importance in developing analytical methods for general freeform system design, tolerance analysis, and system assembly.

Aberration analysis for freeform surface terms overlay on general decentered and tilted optical surfaces

To achieve a system combining large field of view (FOV), high image quality, high 3D detection accuracy, and high-speed tracking in a close shot, a single-layered compound eye with seven ommatidia is developed. The functional relationship among the FOV, optical axis angle, and overlapping area is established mathematically. Based on the relationship, one center ommatidium and six hexagonally arranged marginal ommatidia with large apertures are set on a spherical substrate to guarantee a large FOV and sufficient overlapping information for 3D imaging. To control the off-axis aberration of the marginal ommatidia, an optical freeform surface is applied. The algorithms of regions of interest and Kalman filter are applied to achieve high-speed capturing. Experiments show that the system can obtain a high-quality image with sufficient overlapping information for 3D tracking in shifting distance.

Bionic compound eye for 3D motion detection using an optical freeform surface

In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.

Combining freeform optics and curved detectors for wide field imaging: a polynomial approach over squared aperture.

We report on the design of an off-axis three-mirror freeform telescope with a large field of view (FOV) based on an integration mirror (IM). This design is the continuation of the authors’ previous work. Based on aberration theory, we established a suitable nonrelayed three-mirror-anastigmat initial configuration for integration mirror design. For an optical freeform surface, we analyzed the qualitative aberration correction ability of a x-y polynomial surface that can provide a simple, convenient, and user-friendly relationship between freeform surface term coefficients and aberrations and then applied the x-y polynomial surface on the tertiary mirror to improve the system optimization degrees of freedom. In an example with a focal length of 1200 mm, an F-number of 12, and a FOV of 1°×30°, the tolerance performance was analyzed, and the system presented a good imaging performance. In addition, the IM structure and opto-mechanics support structure were designed and analyzed. The confirmatory design results showed that the integration of the primary mirror and tertiary mirror can improve opto-mechanical properties judged by multiple criteria. In conclusion, the integration of the primary mirror and tertiary mirror not only offers alignment convenience as described previously but also improves system opto-mechanical properties in multiple perspectives. We believe this large linear FOV system based on IM has broad future applications in the optical remote sensing field.

Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror

Hyperspectral imaging spectrometers with a wide field of view (FoV) have significant application values. However, enhancing the FoV will increase the volume of the imaging spectrometer and reduce the imaging quality, so a wide-FoV spectrometer system is difficult to design. Based on the theory of off-axis astigmatism, we present a method that includes a "prism box," "partial anastigmatism," and a partial differential equation to solve the parameters of a freeform surface. In this method, a compact wide-FoV imaging spectrometer with a freeform surface is designed. The spectrometer is an Offner structure with two curved prisms as the dispersion elements. The primary mirror and tertiary mirror of the Offner spectrometer are an aspheric surface and a freeform surface, respectively, to correct the off-axis aberration of a wide FoV. The ratio of the slit length to the total length of the spectrometer is close to 0.4. In comparison to conventional spectrometers of the same specifications, the total length of the spectrometer is reduced by 40% and the volume by 70%. The compact imaging spectrometer has potential application in the field of space remote sensing. In addition, the design method of the spectrometer provides a reference for the design of other optical systems with freeform surfaces.

Design of a compact hyperspectral imaging spectrometer with a freeform surface based on anastigmatism

Compact hyperspectral imaging spectrometers with a wide field of view (FoV) have significant application value. However, the aberration field of such imaging spectrometers is sensitive, and varies for different wavelengths when reducing the spectrometer volume. It is difficult to explain the variation in the aberration field using traditional aberration theory. In this study, we extend the vector aberration theory (VAT) to the Offner imaging spectrometer. We deduce the expression of the aberration field decenter vector of the Offner spectrometer based on the real ray-trace method. Furthermore, we derive the expression of the third-order vector aberration of the system. Subsequently, we explain some common phenomena in the Offner imaging spectrometer. This new analysis method can provide useful guidance for designing a compact wide FoV Offner imaging spectrometer. With this new insight, we designed a compact wide FoV Offner imaging spectrometer with a freeform tertiary mirror. Compared to conventional spectrometers with the same specifications, the total length of the spectrometer decreased by 37%, and the volume by 75%. After the tolerance analysis, the freeform optics satisfied the existing machining technology. The analysis method presented in this paper furthers the designer’s understanding of the aberration field of the Offner imaging spectrometer. The method is significant in the design of a compact wide FoV Offner imaging spectrometer with freeform optics.

Analysis method of the Offner hyperspectral imaging spectrometer based on vector aberration theory.

Because of the limited space, the suture of the oral and maxillofacial surgery is a challenging task, which requires oral surgeons to master excellent techniques. This letter presents a single-arm stapling robot for oral and maxillofacial surgery using magnesium alloy staples, as well the stapling strategy of the robot, which can complete the stapling operation. The robot has six degrees of freedom to adjust position and orientation, and a novel stapler with one degree of freedom at the end of the robot. A special stapling strategy is proposed to reapproximate the wound, which is featured using the staple with two different length legs. This letter introduces the mechanism of the robot. Moreover, the kinematics control of the robot is presented. The stapling experiments have been conducted on an oral and maxillofacial model with the wounds of three different widths and different directions. The results demonstrate that the robot can staple the wounds with reasonable accuracy.

A Novel Single-Arm Stapling Robot for Oral and Maxillofacial Surgery—Design and Verification

A free-form surface prism spectrometer optical system comprises a slit, a first free-form surface prism, a second free-form surface prism, a third free-form surface prism and an image plane. The firstsurface and the second surface of the second free-form surface prism comprise a first area, a second area and a third area; the slit is opposite to the first area of the first surface of the second free-form surface prism at an interval; the first surface of the first free-form surface prism is opposite to the first area and the second area of the second surface of the second free-form surface prism at an interval, and the second surface of the first free-form surface prism can reflect light rays; the second area of the first surface of the second free-form surface prism can reflect light rays; the first surface of the third free-form surface prism is opposite to the second area and the third area of the second surface of the second free-form surface prism at an interval, and the second surface of the third free-form surface prism can reflect light rays; and the image plane is opposite to the third area of the first surface of the second free-form surface prism at an interval. Opticalelements are reduced and dispersion capability is enhanced.

Zhenhua Ji

Papers

Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror

Design of a compact hyperspectral imaging spectrometer with a freeform surface based on anastigmatism

Analysis method of the Offner hyperspectral imaging spectrometer based on vector aberration theory.

A Novel Single-Arm Stapling Robot for Oral and Maxillofacial Surgery—Design and Verification

Free-form surface prism spectrometer optical system