Symmetric Optical Surfaces Research Articles

RBF Interpolation Algorithm for FTS Tool Path Generation

Freeform optics are defined as nonrotational symmetric optical surfaces in the manufacturing industry. Freeform optics are extensively applied to many areas in order to improve system performance. Fast tool servo (FTS) assisting single-point diamond turning technology has high application prospects in freeform optics machining. This paper discusses the interpolation algorithm for tool path generation of FTS through the application of a radial basis function (RBF) algorithm. For this purpose, a positive definite RBF with compact support was employed as the interpolant. The existence is mathematically proven. Numerical simulations were performed to compare the performances of the RBF algorithm and commonly used algorithms for satisfying the requirements of existence, smoothness, and accuracy. Machining experiments were also conducted to validate the applicability of the algorithm. The simulation results showed that the RBF interpolation algorithm outperformed other algorithms in terms of smoothness. The RBF algorithm also provided the highest interpolation accuracy. Furthermore, the RBF interpolation algorithm exhibited the highest accuracy for error distribution, with large errors distributed mainly in transition areas. The machining results were also in general agreement with the simulation results although obvious practical errors were observed. Overall, RBF interpolation can provide higher accuracy and better smoothness in the tool path generation of FTS.

Continuous measurement of optical surfaces using a line-scan interferometer with sinusoidal path length modulation.

We present a fast approach to the continuous measurement of rotational symmetric optical surfaces. This approach is based on a line scanning interferometer with sinusoidal modulation of the optical path length. The specimen is positioned with respect to the sensor and both are moved during measurement by use of a five axes system comprising a high precision rotational table. The calibration of both the line sensor as well as the scanning and positioning system is discussed. As proof of principle of the measurement and stitching concept results of a scan of a rotational symmetric sinusoidal structure and a spherical lens with a moderate slope are shown.

Precision asphere polishing with MRF technology and Subaperture Stitching Interferometry

The paper presents results of aspheric lens manufacturing in Infrared Technology and Thermovision Section in Military University of Technology. Briefly MRF and SSI technologies utilized in the process are described and a case study of three aspherization processes follows. First two elements are silicon lenses designed for a mid-wave infrared (MWIR) lens. The third one is a parabolic mirror substrate. Technical aspects and requirements of each case are discussed. Full Text: PDF References Forbes, G. W., "Shape spcecification for axially symmetric optical surfaces", Optics Express, Vol. 15, Issue 8, pp. 5218-5226 (2007) CrossRef

Design, tolerance, and fabrication of an optical see-through head-mounted display with free-form surface elements

Free-form surfaces (FFSs) provide more freedom to design an optical system with fewer elements and hence to reduce the size and weight of the overall system than rotationally symmetric optical surfaces. In this paper, an optical see-through (OST), head-mounted display (HMD) consisting of a free-form, wedge-shaped prism and a free-form lens is designed and fabricated through the injection molding method. The free-form prism for the projection system is designed with a field-of-view (FOV) of 36°; the free-form lens is cemented to the prism for the see-through system to achieve a FOV of 50°. The free-form prism and lens are expanded at the edge area during the design stage in order to reduce the effects of surface deformation in the working area in molding fabrication process and to improve ergonomic fit with the head of a user. The tolerance analyzes considering the mold design for the free-form optical systems are carried out using the Monte Carlo method. The FFS optical elements are successfully fabricated and the system performance is carefully examined. The results indicate that the performance of the OST-HMD is sufficient for both entertainment and scientific applications.

Recent Advances in Ultraprecision Diamond Turning of Non-Rotationally Symmetric Optical Surfaces

Firstly, the superior performance and industrial application prospects of non-rotationally symmetric (NRS) optical surfaces are detailed. Secondly, those high precision machining processes to generate NRS optical surfaces are overviewed, it’s been stressed that fast tool servo (FTS) based diamond turning has been the most promising, cost-effective, and high precision machining process to generate NRS surfaces. Finally, the recent research progress in FTS based diamond turning of NRS optical surfaces is remarked, both the tool trajectory generation and the FTS actuation techniques are discussed, the limitations of the existing researches are disclosed, and then the academic and technological researches to be urgently carried out are suggested.

Real-ray-based method for locating individual surface aberration field centers in imaging optical systems without rotational symmetry

It has been found that the field dependence of the aberrations of misaligned optical systems made of otherwise rotationally symmetric optical surfaces are often multinodal, including low-order astigmatism and distortion and higher-order coma, astigmatism, oblique spherical, elliptical coma (trifoil), and distortion. The exact location of the nodes in the image is a weighted sum of individual surface contributions. The location of the center of rotational symmetry for the field dependence for all aberrations contributed by a particular rotationally symmetric surface is along the line that connects the center of curvature of the surface with the center of the pupil. Previously, a paraxial ray-trace method was developed to locate the aberration field center for a series of rotationally symmetric surfaces with small tilt and decenter perturbations. The method is based on rotating the coordinate system into the local coordinate system of the surface and then advancing using the conventional paraxial ray-trace equations. This method, developed by Buchroeder [Ph.D. dissertation (University of Arizona, 1976)], heavily constrains how tilts and decenters were implemented in the optical system model, which prevented integration of these equations into an optical design environment. In this paper, a method for locating the aberration field centers using real-ray-trace data that is entirely model independent and, significantly, that is not restricted to small tilts and decenters, is presented. With this new insight, it is now possible to extend any optical design and analysis environment to include multinodal aberration analysis.

Aspheric optics, theoretical considerations

AbstractSpherical aberration is the largest higher‐order aberration in the human eye and it is the only aberration with a nonzero population average. Furthermore, in contrast to other aberrations such as, e. g., coma, spherical aberration can be corrected by rotationally symmetric optical surfaces, so called aspheric optics. These facts form the basis for an increasing number of both IOL’s and contact lenses which manipulate the spherical aberration in the eye. This talk will give a background on spherical aberration and state of the art aberration measurements in the human eye. Different aspects of ocular spherical aberration will be reviewed and the implications and possible visual benefits of correcting, or even inducing, spherical aberration will be discussed.

Shape specification for axially symmetric optical surfaces

Advances in fabrication and testing are allowing aspheric optics to have greater impact through their increased prevalence and complexity. The most widely used characterization of surface shape is numerically deficient, however. Furthermore, with regard to tolerancing and to constraints for manufacturability, this representation is poorly suited for design purposes. Effective alternatives are therefore presented for working with rotationally symmetric surfaces that are either (i) strongly aspheric or (ii) constrained in terms of the slope in the departure from a best-fit sphere.